# Accepted Contributed Talk

Last Update : 2023/01/24 06:33

## [00001] THE BEAUTY AND THE OBSERVATION OF THE GEOMETRY OF THE SPACE EUCLIDIANAS

• Abstract : In this textual proposal and the workshops that are found in it, it promotes the construction of very novel knowledge and dynamics, which, for the present case, are mainly in the areas of mathematics and physics; they are pieces of knowledge folded into each other, and in this way they evolve to new levels of conceptual organization: they create non-linear dynamic structures, but framed in a system of multiple interconnections. Strategies in the teaching of the geometry of space are presented, with analysis and recommendations in its methodology and in some objectives in optics and topology.
Here the workshops can be carried out in the classroom or in the field, the stories are countable and at the same time uncountable, like the definition of infinity. The network of multiple senses will be discovered when the study of this material is “finished”, although of course, you can always return to it, like that taste of that homemade sweet that causes you to eat, eat without stopping and experience new playful passages. To develop the exercises contained in this production, they will have to touch paper, scissors, rulers, ties, mirrors, and even go out in search of anthills to reflect on their organization, with greater attention, the didactic proposal. Each participant will be an active agent in this teaching and learning process; in which the intention is not to memorize the concepts, but to build them by reading stories, creating topological pieces, looking in mirrors in an infinite world or being a manipulator and builder of hairstyles and hair tails.
This production offers you the opportunity to develop new skills in your logical, mathematical and physical reasoning, which are essential for the processes of academic training and the same interaction in everyday life.

Keywords: Innovation, methodologies, mathematics, didactics, construction and physics.

Each proposed activity will end up seducing the reader; in an incipiently linear reading; the notion of: numbers, infinity, image, having and not having will emerge intuitively with the text; but the reader will not be able to avoid jumping to the infinite images with mirrors and could not help but be amazed at the wonderful Möebius strip.
The proposal intends that, through readings, experiments, examples of everyday life, games and crafts, each student approaches various mathematical notions (point, geometry, relations, function, probabilities, amorphisms, reflection, knots and others) and for this employ different levels of analysis, individually or in groups.
An active intervention of the reader and the teacher is essential, and this justifies the absence of rigorous mathematical and physical conceptual explanations, since the written attempt consists of integrating knowledge from other spaces, which will be made possible by the intervention of the reader, of hence its function is a priority in this unfinished work. The systemic paradigm, in which the book and the workshops are extended as origin, allows a certain freedom of reading, so whoever wants to start with the different workshops without any restrictions.
A humanistic line runs through the writing in order to rescue values such as respect for others and nature. Likewise, the textual construction seeks to sensitize and involve the group of readers in situations that they could project in everyday life.
This writing does not pretend to be exhaustive in its content, but it is an invitation for the integrated work of the class (or the daily life of any reader) with respect to the environment, and the possible resources (sheets, stories, paintings, mirrors, hair, others) that can be used to build knowledge.
Introduction
Evaluations
The evaluations pretend that when there are students with difficulties to structure the new thinking scheme, the rest of the group offers their experience after reaching it. In the case of readers who assume a self-taught process, it will always be advisable to transmit the ideas to other people nearby to confirm the assimilation of the knowledge acquired.
The introduction to the teaching of geometry as a spatial visualization, movement of objects in the everyday, the coordinates of each of the figures within its surroundings and the relationship with the algebra as a basis in the demonstration of each one of the facts raised, with a perspective of encouragement to the reasoning of the reader and the argument that can be raised after solving the problem; the dynamic understanding and manipulation of the geometric objects that are used during this process, is a whole for the changes that there are in the programs of the teaching of mathematics and more in the subject of geometry; a teaching of problem solving based on the everyday and difficulties that each student will see reflected in each of the chapters of this text.
Illustrations
The illustrative resource has a didactic purpose, therefore, it is significant that in the reading of the proposal, the reader establishes associations with the included images, to enrich the conceptual analysis and the practical exercise. They have included: hairstyles braids, paper bands, representations of paintings, graphics, among others.
If the text promotes the use of problems in real contexts that face each person day by day, the abstract ones are considered very important within the learning process of a modern society. And more when; What is intended is the construction of skills in each person for the manipulation of mathematical and physical objects whose nature is abstract and improbable.
The strategy assumed within the proposal that is being proposed is pedagogically step by step from the concrete to the abstract, in a very comfortable way for the reader.
Drafting
This writing does not pretend to be exhaustive in its content, but it is an invitation for the integrated work of the class (or the daily life of any reader) with respect to the environment, and the possible resources (sheets, stories, paintings, mirrors, other) that can be used to build knowledge.
In the project presented to it, it assumes as its main objective the search for the strengthening of greater cognitive abilities of the reader to address the challenges of a modern society, where information, knowledge and the demand for greater abilities and mental abilities are invoked with force.
One of the points to rescue that will be faced in this project is the mathematical competence that is interpreted here as a capacity to use science to understand and act on different real contexts that we face every day, underlines a relation of this discipline with the physical, socio-cultural environments and also provides a privileged place to the approach and resolution of contextualized problems in each situation or place that the reader is.
In this vision, mathematical competence is defined by a powerful practical and analytical sense of real and complex situations.
Illusions and optical analysis
Despite the abstraction that surrounds this topic, it is possible to achieve the realization of a sequence that allows students and any reader can interpret, using concrete elements, their results about the calculation.
Problem solving as a pedagogical strategy will be emphasized in this production as a substratum of a classroom style of action and in their daily life, or in self-teaching and being a self-taught professional in several areas of knowledge. The experience in the construction game is a type of activity that is very appropriate for all types of people and that serves for the development of spatial sense, for learning mathematical contents and for solving geometric problems.
Usually the workshops begin as free play activity in which each participant makes drawings at will and qualities, indicating the importance of the symmetry of the grids and the image in different mirrors, work in corners of an enclosure or classroom, or workshops where the teacher or exhibitor is the guide of the process. Little by little it is evolving and it allows to deepen in the investigation on mathematical contents like the measurement or the symmetry.
All these processes refer to flat shapes drawn on paper to a solid form. In these activities require very little knowledge of geometry and can be solved by common sense or with a little experimentation.
Materials
To perform these experiments in the workshop you need two glass or plastic mirrors, perhaps cut out from a used recycling mirror. The dimensions are not very important. You also need to improvise some way of holding the mirrors vertically, for example as seen in the figure (each mirror attached to a wood with an elastic band).
¡In a magical, mathematical and friendly world, what would it be to say mirror, mirror … show me the infinite and beyond and I will tell you my thoughts …! Edwin Gerardo Acuña Acuña
The incredible that behind this mirror there are infinite parallel universes in which Jorge Luis Borges in his writing “I am a writer and perhaps a poet” (Borges, 1981) which indicates:
“Lately, in the world of physics, we have discovered particles that do not have the behavior of other atoms. The most risky ones affirm that a parallel universe is possible, of which we would not have knowledge, an invisible universe, similar to the one imagined by Bioy Casares in the “Celestial Plot”… “p.16
Sometimes in classrooms as it costs to transport students from that abstract world that is mathematics to a simple everyday world, one of the dilemmas is how to teach in a simple way what infinity means, or how it would be observed in the real and not in the assumption.
The games of labyrinths appear immediately if we bring two mirrors together and in between we place some object (a marble, a pencil, some dice): it will fly towards an infinite number of images! (Acuña, 2016)
In the present exercise we work with two rectangular mirrors with dimensions: 20 x 35 cm. The mirrors must be placed in lines parallel to each other to open the doors to this specular tunnel. We have to peer from the side of one of the two mirrors to confirm such a projection: we will see the image of the image, and the image of the image of the image… and so on. In this specular connection a kind of “tunnel” is constituted, formed by the successive images that go allegating (and darkening, because in each reflection a little light is lost).
In his work (Barrenechea, 1965) he gives us a vision of Jorge Luis Borges about his vision of infinity; which always seduced him in most of his works:
“I suspect that the infinite word was once an insipid equivalent of unfinished; now it is one of God’s perfections in theology and a discussion in metaphysics and an emphasis popularized in letters and a very fine conception renewed in mathematics “Russell explains the addition and multiplication and enhancement of infinite cardinal numbers and the reason for their almost terrible dynasties “and a true intuition when looking at the sky.” (P. 14)
Take your time to reflect on what is presented in that tunnel. Place yourself in different sides. Place the object in different points. Try to see how your observation varies as you change your position or that of the object. Starting from the game with the laws of reflection of light in mirrors, we will enter the world of algebra and arithmetic operations (divisibility, decomposition of a number, fractions and many more).
After this, go on to elaborate, in a group (3-4 students), the following experiment.
The argument
Experiment: “Mirrors at an angle”
Objective
To promote mathematics in reality, with ideas on didactic methodology for teaching, emphasizing on the geometry of space and topology.
Understand that: evidence, reality, necessity and curiosity are necessary situations in the teaching-learning processes of Mathematics.
Use didactic models, promoting research and the scientific method in the discovery of concepts; to facilitate that the student arrives at the mathematical knowledge with rigor, clarity, precision of results and without any mistake.
Check in the classroom the laws of light reflection and some characteristics of mirror images. To carry out a way of introducing algebra, arithmetic operations (divisibility, decomposition of a number, fractions and many more).
Achieve greater interest and participation of students in the classroom, showing specific applications regarding the subjects of infinities, multiples of a number and divisibility of a number.
It seeks to stimulate students in their communication and through this experience is trying to approach both the notion of limit and infinity.
It also tries to encourage the use of mathematical language to refer to a daily situation. (Acuña E. G., 2018)
The main thing of this type of workshops is the resolution of problems corresponds to the need to assume standards whose convention for Mathematics Education and the most important thing is to associate what has been learned as a tool to solve real situations that a person faces daily, It has also been widely proven in the international scale that seeks to lose the fear of mathematics, and change the way these processes are provided in our classrooms and learning procedures.
Dream of triumph A few days ago, a boy named Carlitos having breakfast at his house as usual, he thought and wished to have an army of a toy soldier. But he only had a little lead sailor; but this sailor was heroic and a great soldier who with the commands and strategies of his general Carlitos could do wonders. Punctuation. In one of his war games Carlitos came up with an idea, at the time he was fighting against a large army of imaginary enemies of atrocious and bloodthirsty warriors, Carlitos saw that he had everything to lose since his only sailor had to face this great test that could not go well. But he came up with a great idea to face this great emergency; placing his brave sailor on a flat base and behind a mirror book which reflected the images of his great hero. When approaching the great army of enemies Carlitos changes to the mirror book on some angles of selected references; which his strategic position of his sailor the images that were reproduced on the mirror book were infinite reinforcements that were reflected, which upon seeing them the enemies caused great fear among their ranks and began to flee from panic because they believed that they reproduced in a infinite the great hero of Carlitos; excited discovered that with strategies anyone can conquer the world if it is proposed, dreams and decisions are the main pillars of an achievement and a goal. The contextualization of what has been learned with this story and those provided by each of the topics in mathematics proposed in this text, seeks to strengthen an active student role and committed to their learning, emphasizing the identification of each process, use and design of mathematical models suitable for each educational level.
So in this workshop as we have indicated, we start with two rectangular mirrors for this workshop, which for the case of our sample, we have chosen two mirrors with dimensions: 20 x 35 cm. After this we must design some way to hold the mirrors vertically and for this it is advisable to pass adhesive tape behind the mirrors, but to maintain a separation of 1 cm between the two blocks so that the mirrors can separate and approach between Yes more easily, this to obtain data with different angles. We will start with a paper image, which contains the records for the 360º that make up a circumference; This can be done by hand or get a photocopy of this book or the Internet. Let’s place the mirrors in such a way that they form an angle; they should always keep as reference the angular blade that serves as the basis for the mirror block. If we now place an object between the mirrors (a die, a chess horse, etc.), we will see that the successive reflections show us several images of the object. And the smaller the angle between the mirrors, the greater the number of images. Try it!
It is important to bear in mind that abstract problems are crucial to bring into play different skills and processes of individuals in everyday situations and problems that they face every day. In the abstract, one trains, for example, the justification of daily challenges and demonstration of how to solve them, the use of specific mathematical language on each occasion, the rigorous abstract reasoning that is faced in each case. In the tasks of a world with greater technological challenges developed by the professional mathematical communities, most of the problems addressed are abstract, which must be transformed into a rigorous and meaningful process. Now we are going to consider that in order to carry out a more quantitative experiment, with the help of a transcarrier and a pencil, we draw angles of 90, 60, 45, 30 and 20 degrees on a sheet; now place on the sheet, our two mirrors, in such a way that they form one of these angles and we put, between these, the chosen object. We will see that the number of images reflected will be equal to 360, divided by the angle, minus 1. For example, for an angle of 60 degrees we have 360/60 – 1 = 5 and therefore, we will see 5 images. Check it out! Now it is up to you to develop an algebraic proposal of the formula for this type of operation! Angled mirrors and the multiple images they generate are the basis of the kaleidoscope, an instrument capable of generating infinite geometric images that never repeat themselves. You can complete the following chart to perform the experiment at different angles. Use the formula that you defined for this exercise.
In this chapter you should be asking what is a Möbius band and for that reason we will elaborate it. To form a Möbius band, the idea is to take the steerable ends of a flat band and twist them in order to join them, that way a non-orientable band will be produced: ¡the Möbius band!
Do you want to try?
Look for scissors and paper (bond 20), preferably without stripes or squares, and when you have mastered the technique, you can make the piece with a simple cardboard (not satin) to obtain a larger piece.
If you work with a bond sheet, cut the paper lengthwise and measure from the edge a width of 3 cm, and if you work with cardboard, you can look for a larger dimension, for example, 9 cm wide. Where you mark the width of one centimeter for the sheet or 3 cm for the cardboard, in this way you will draw three lines along the sheet of paper (with a separation of 1 cm from each other), or, three lines along the cardboard (with separation of 3 cm between them).
Cut with the scissors along the line drawn farthest from the edge of the paper or the cardboard, so you get a flat band.
Now take time to analyze the behavior of the band, join the ends, look at the structure that is formed, run your fingers on either side of the band, you will leave a point and you will reach the same point: ¿why can you to reach the same point? Does the same thing happen if instead of advancing with your fingers on this circular structure, your fingers traverse the band in plane? What differentiates each case? What should you do to pass from one side of the band to another?
After analyzing its flat paper strip, we will form the Möbius band. For this it is necessary to twist one of the ends and superimpose it on the other that will remain without bending, that is, the lines marked with a pencil will coincide. Join the ends with adhesive tape. Now it is going to arrive at the starting point, and not on the other side of the surface, that is, it is a single surface, it does not exist below or above, it is the primordial characteristic of the Möbius band. But, the analysis does not end here.
We will work with a new paper band of 3 cm, but this time draw a single line along the paper, which is the midpoint of the width, that is, the line with pencil will be located 1.5 cm from each end. Form a Möbius band and after gluing the ends with adhesive tape, cut with the scissors along the line drawn with a pencil; You have to cut all the way through, and you’ll get a band with Jordan’s ring. Analyze this band: ¿is it orientable or not ?, that is: do you have only one face or two? In short, with the medium cut, the Möbius band became another structure: Jordan’s ring.
But this is not all. If you pick up the first Möbius band and cut with the scissors along the two parallel lines drawn with a pencil, a new Möbius band and a Jordan ring band will be formed. Before cutting the structure completely, appreciate the figure and analyze the surface, pass your index finger over the surface, what do you find particular? After reflecting, make the final cut: ¡magic!
CLASS ACTIVITY
In this unit we will work:
• Presentation of a new branch of Mathematics: Topology.
• Handling of flat elemental figures.
• Mathematical vocabulary related to topology.
• Practical approach to complex topology contents: faces, edges, semigiros, cuts, orientable surfaces, continuous deformations.
• Prediction of results in topological cuts.
• Research on simple topological problems.
• Obtaining apparently impossible objects.
• Introduction to geometries other than the usual Euclidean.
• Resolution of a classic problem: the three houses and the three wells.
• Drawing of simple three-dimensional topological figures with some dexterity.
• Necessary material
• Cardboard or paper, tape, ruler, scissors, tape or glue.
• Encyclopedia to determine some terms.
• Acetates and special markers for 3-color acetate.
• Photocopy of the sheets for the students (the reader can find them at the end of this unit).
• Activities for students
• Activity nº 1 Introduction.
• Activity nº 2 Cylinders and bands.
• Activity nº 3 The crosses of Möebius.
• Activity nº 4 Houses and wells.
• Evaluation activities
• In addition to the general methods of observation present throughout the course, the following specific evaluation activities are proposed:
• Research and construction on results of cuts in the bands with different numbers of semigiros.
• Research and construction on orientation at the Möbius crossings.
• Solution and construction to the problem of the three houses and the three wells.
ACTIVITY 1. INTRODUCTION
As an introduction, the unit can be started by talking about Moebius, astronomer of the last century who gave in 1858 the first example of a unilateral surface. Together with Euler, Riemann, Jordan and Poincarè, he contributed to the creation and development of Topology.
The crosses of möebius

Cut, following the teacher’s instructions, 4 crosses of möebius. Take one of the crosses and draw on one side lines that divide each blade in half, lengthwise. Join the opposite blades forming 2 cylinders.
MÖEBIUS tape (MÖEBIUS band)
Geometric structure formed by giving half a turn to a flat rectangular ribbon and then joining the ends. A Mobius tape has only one end and one side. This remarkable property (one side) makes it extremely useful in belt driven machines because both sides of the belt are used equally to reduce wear by half.
When cutting along a line parallel to the end, only one tape is produced instead of two new tapes.
ACTIVITY 2. THE CYLINDERS AND THE BANDS
They are distributed paper or tape, and they are instructed to cut strips several centimeters wide (later they should make several cuts in half lengthwise).
We will call the surface of the strip obtained by gluing the ends of the strip without making pre-twists, while the Möbius Strip is obtained by gluing the two ends of the strip after one of them has rotated 180 degrees.
Build and paste the cylinder band:
Build and paste the Möebius band:
Build and paste two figures equal to the previous ones and draw a straight line or color with colored pencils the faces of the two surfaces have indicated the characteristics that the two molds have on:
How many faces have the cylinder: _______________________.
How many faces does the Möebius Band have: _________________.
How many different colors do you need to color the faces of a cylinder?
How many different colors do you need to color the faces of a Möbius Band?
Cutting in half. Draw on a paper tape a line that divides it along, by the half. If you form a cylinder with it and cut it down the center line, how many surfaces will you get? With how many faces and edges? Try to answer these questions before making the cuts.
Repeat the process forming a Möbius Band instead of a cylinder.
If you cut the obtained surface again, what will you get?
ACTIVITY 3. THE MÖEBIUS CROSSINGS
Cut, following the teacher’s instructions, 4 crosses of Möebius.
Take one of the crosses and draw on one side lines that divide each blade in half, lengthwise. Join the opposite blades forming 2 cylinders.
What topological characteristics does the new surface have?
¿Can you predict what you will get by cutting through the lines drawn along the entire surface?
What topological characteristics does the new surface have?
Take another one of the crosses, trace by the two sides lines that divide each blade along in half. Join two opposite blades forming one cylinder and the other two blades forming a Möbius Band.
What topological characteristics does the new surface have?
¿Can you predict what you will get by cutting through the lines drawn along the entire surface?
What have you got? Have you obtained the same as your colleagues?
Draw a straight line that goes in the middle of one of the blades and its opposite. Now draw two straight lines that divide the other two blades into three equal parts (this drawing must be done on both sides of the paper).
The following is a problem very used in the theory of graphs, computer problems and engineering. This consists of using a series of connections to bring water, gas and light to three houses, but without crossing any line or cables; neither to cross by more than one house, that is to say, it is necessary to take a line of each service to each house without crossing the lines. Try drawing it on a sheet to solve the problem. Guide yourself with the diagram.
Water, gas and light connections (left to right) to three houses (happy faces).
The previous explanations about the Möbius band will be fundamental to solve this problem. We start from the photo; then we have inserted the icons for the three services: water, gas and light, as well as the three houses.
We have already hinted at the necessary clue to solve the problem, because if you tried with a flat sheet, you will have realized that there is no way to solve the problem of connections. Now try to solve it with this particular band.
Experiment: “Virtual graphs”
Materials
Laminated paper, pencil, compass and a glass or aluminum can container
The perspective of graphs is formulated within a system of geometric representation that uses symmetry to play with the points that make up a space.
Next we will work with cylindrical anamorphosis. It is necessary that you photocopy the next photograph, or you can also design your own structure, as shown in the second photograph of the sequence.
As you can see, a type of refractory cylinder rises in front of the student’s left hand; The outer layer that covers it is made of laminated paper. What you should do is take the photocopy or the design made by yourself and place the glass or can container in the area that opens a type of circumference, precisely at the base of the design, and on this container, you will adhere the laminated paper (it will serve as a mirror).
On the paper that is on your table, you can appreciate the curved lines. Direct your gaze on the laminated paper that remains attached to the outer surface of the glass or container, how are these lines? Why does this visual transformation happen?
Another interesting case to analyze was designed by the Hungarian István Orosz, an artist of geo-metry, just as Escher was. From the piece entitled Jules Verne (1983), we turn to the cylinder with the laminated paper to find the hidden image of the following illustration.
The results
In order to verify the proposed objectives, the questionnaire was carried out with a sample of 112 participants in three international conferences and presentations that were part of this workshop; the first in the 2015 VIII Ibero-American Congress of Scientific Education and the II International Congress of Pedagogy, Didactics and ICT applied to Education (CIEDUC 2015) Bogotá – Colombia; 2014 National University of San Marcos Lima Peru and the XXVI National Congress of the Teaching of mathematics 2014 Mazatlan Sinaloa, Mexico. In which a survey of satisfaction was passed on the workshop, to then make the publication Geometry of Space. Illusions and optical analysis. .ISBN: 978-620-2-16162-6 Germany. Academic Spanish Editorial. The most representative results obtained were:

Conclusions
The objective is to present the experience of implementing new techniques in the process of teaching geometry and physics in a friendly way, for this they take as a theoretical reference the proposals that propose a series of indicators to determine the didactic tendency as the traditional, the technological, the spontaneous and the investigative. These make a difference between beliefs and conceptions in education, however the information obtained reflects this difference and that this can also be rescued through different instruments. Under the analysis of the results obtained in the processes, the conceptions of the mathematics teachers show a research tendency, although the practice contradicts it when observing a traditional and technological guideline. From where we interpret that conceptions have evolved as long as they are not found in the traditional, but thanks to various factors such as experience, refresher courses among others; these conceptions are directed towards the investigative tendency.

References
1. Acuña, E. G. (2016). Matemática y Literatura en juegos de Laberintos .ISBN: 978-9930-9473-9-5 San José: Universidad de Costa Rica.
2. Usón, J (2015) Educación Científica y Ciudadanía en el Siglo XXI. Universi-dad de Alcalá. ISBN 978-84-161333-65-9.
3. Acuña, E. G. (2018). Geometría del Espacio. Ilusiones y análisis ópticos. .ISBN: 978-620-2-16162-6 Alemania. Editorial Académica Española.
4. Acuña, E. G. (10 de 07 de 2018). http://www.cientec.or.cr. Obtenido de http://www.cientec.or.cr/matematica/2012/ponenciasVIII/Edwin-Acuna.pdf
5. Barrenechea, A. M. (1965). El Infinito en la Obra de Jorge Luis Borges. Bue-nos Aires. : Institut o de Filología.
6. Borges, J. L. (1981). La cifra. Madrid: Alianza Tres.
7. Holt, M. (1988). Matemáticas Recreativas 3. Nueva York.: Martinezz Roca. S.A.
lee, W. (17 de 05 de 2017). www.lsmespanol.org. Obtenido de https://www.iglesiaenpadrelascasas.org/camping-tren-sur-diciembre-2012/item/1183-transformacion-metamorfosis-del-griego
8. Lisi, M. A. (2012). Platón. Diálogos. Obra completa. Volumen VI. Madrid; España: Editorial Gredos.
9. Scott, J. W. (2016). El eco de la fantasía: la historia y la construcción de la identidad. Rioja: Dialnet.
10. Zenil, H. (2011). Lo que cabe en el espacio. México: CopLy-arXives.

• Author(s) :
• Edwin Gerardo Acuña Acuña (Universidad Latinoamericana de Ciencia y Tecnología)

## [00002] Propagation of Lamb wave in the plate of microstretch thermoelastic diffusion materials

• Abstract : The present study investigates the effect of three thermoelastic theories on the propagation of Lamb wave in a linearly isotropic microstretch diffusion plate subject to stress free thermally insulated/impermeable and isothermal/isoconcentrated boundary conditions. The secular equations of the Lamb wave are obtained for both symmetric and anti-symmetric modes of vibration. The phase velocities and attenuation coefficients are computed numerically for a particular model and these results are compared for the three theories: Coupled Thermoelasticity theory, Lord-Shulman theory and Green-Lindsay theory. The velocity curves and the attenuation coefficients are illustrated graphically. It is observed that there are three modes of velocity and attenuation for each symmetric and anti-symmetric vibration. We have noticed that the velocity of the corresponding Lamb wave increases from first to third mode of symmetric vibration in both thermally insulated/impermeable and isothermal/isoconcentrated plates. At short wavelength, the secular equation of symmetric mode of vibration reduces to that of Rayleigh surface wave for both the plates. Some special cases are also deduced from the present formulation.
• Author(s) :
• Sarat Singh Sanasam (Mizoram University)
• Sanjay Debnath (Mizoram University)

## [00003] Reflection of plane waves in a rotating transversely isotropic thermoelastic diffusion solid half-space from impedance boundary in a fractional-order thermo-elasticity

• Abstract : Abstract:
The governing equations of a rotating transversely isotropic thermoelastic medium with diffusion in a fractional-order derivative thermo-elasticity are formulated. Plane-wave solution method is applied to obtain the velocity equation, which indicates the existence of four quasi plane waves. Reflection of these plane waves from a stress-free thermally insulated surface with impedance boundary, where the normal and shear force tractions are varying linearly with the normal and tangential displacement components multiplied by the frequency, respectively is studied to obtain the reflection coefficients of various reflected waves. The effects of anisotropy, rotation and impedance parameter parameter are shown graphically on these coefficients.
Keywords: Anisotropy; thermo-elasticity; rotation; plane waves; reflection coefficient, Impedance boundary.

References
[1] Lord, H.W., Y. Shulman, A generalize dynamical theory of thermo-elasticity.
J. Mech. Phys. Solids 15 (1967) 299-309.
[2] Dhaliwal, R.S., H.H. Sherief, Generalized thermoelasticity for anisotropic media. Quart. Appl. Math. 33 (1980) 1-8.
[3] Schoenberg, M., D. Censor. Elastic waves in rotating media. Quart. Appl. Math. 31 (1973) 115-125.
[4] Ahmad, F., A. Khan. Thermoelastic plane waves in rotating isotropic medium. Acta Mech. 136 (1999) 243-247.
[5] Roy Chaudhuri, S.K., L. Debnath. Magneto-thermoelastic plane waves in rotating media. Int. J. Engng. Sci. 21 (1983) 155-163.
[6] Daley, P.F., F. Hron. Reflection and transmission coefficients for transversely isotropic media, Bull. Seismo. Soc. Am. 67 (1977) 661-675
[7] Crampin, S. A review of wave motion in anisotropic and cracked elastic media, Wave motion, 3 (1981) 343-391.
WAVE MO
[8] Chadwick, P. Wave propagation in transversely isotropic elastic media I. Homogeneous plane waves. Proc. R. Soc. Lond. A422 (1989) 23-66.

• Author(s) :
• Dr. Anand Kumar Yadav (Shishu Niketan Sr. Sec School Sector 22D Chandigarh, India)

## [00004] Data Mining and Analysis guide to models and algorithms in mathematics for data mining

• Abstract : The current understanding of the business, the market and the clients are not enough to face the new business challenges. There are a series of theoretical foundations in mathematical-statistical models to support commercial, financial and brand positioning decisions in the industry, as well as understand consumer behavior or propose marketing and management actions.
In the Data Mining in Business Analytics course, the student will understand how to make statistical information their first ally in managing business options, marketing and customer relations, including within this learning process the respective technological implications to optimize their work.
The main objective of this Business Analytics Data Mining book is to extract interesting and useful information from data collected from each business transaction and process. In many cases, this information is in the form of mathematical patterns that are not evident in the data and, depending on their complexity, can provide knowledge. Data mining is based on multiple techniques of computer science, statistics and artificial intelligence learning; it also has a close relationship with data warehouses and CRM.
Other important points that will be developed in this course are to study and analyze the fundamentals of data mining including: the learning of analytical statistics, the recognition of information patterns and data programming, as well as its applications to the solution of different practical problems. .
The teaching method consists of presenting the theory, discussing the algorithms and proposing to the student simple exercises that complete the learning. It must be taken into account that the exercises that require Big Data analysis have to be solved using some computer analysis environment such as R, Python, Excel and other general purpose languages ​​that allow programming, numerical calculation, symbolic calculation and making graphs. During the course it is also possible to have “software” products or “computer packages” with programmed Business Analytics data mining algorithms that only require familiarity with the graphics interface and the choice of statistical parameters to be applied in problems. Student completion of case studies, projects, and reading analysis is an important element of learning within the Business Analytics Data Mining course. In these jobs that are going to be requested during the Business Analytics data mining course, students can be asked to carry out activities that require a greater mastery of theory, such as the application of algorithms to data sets with real socioeconomic and financial information. of national and international companies, business transactions through the information provided, engineering measurements of things or texts implemented by the teacher, the modification of the methods studied to extract other useful information from the data and the development of new methods so that the company is positioned in the market.
GENERAL OBJECTIVE

• Develop the theory and practices of Data Mining in Business Analytics focused on solving problems aimed at business management, marketing, knowledge and the relationship with external customers; with which to empower the student with a general perspective of the operation, scope and limitations of the main data mining techniques and how they can be used to assist in making strategic decisions.

SPECIFIC OBJECTIVES

1. Identify the phases involved in a data mining project within an organization and industry.
2. Describe a data set selecting and generating its most relevant characteristics within the industry.
3. Apply the different techniques of data mining in classification antecedents, supervised and unsupervised.
4. Use the most appropriate classification technique to solve a specific problem within data mining.
5. Differentiate the results obtained in the resolution of the financial and brand problem of an organization.
6. Design techniques for evaluation of results, comparison of business characteristics and use of models created for the analysis of Data Mining.
7. Analyze Data Mining techniques in Business Analytics, between data mining, artificial intelligence and statistical analysis.
Introduction:
At the beginning of the project, the basic concepts of Data Mining in Business Analytics will be learned in a gradual, theoretical and very practical way, together with the algorithms most used today for information analysis and decision making. At the end of the course, each student will be able to understand the importance of managing the information provided by the industry or organization, exploring with the information in different real business databases, both national and international, to analyze and make decisions; both in the managerial field and in the field of brand positioning in the market.
This course is the first step to become a professional with the basic skills of a data analysis scientist or Data Scientist, so that you can open the door to the future.
In this first phase of the Data Mining for Business Analytics project, each student will learn the essential concepts associated with Data Mining in Business Analytics, understanding the different sources of information to be used in organizations, reviewing a pre-processing of these data, and subsequently understand and apply the different data knowledge extraction techniques in process and managerial aspects, using association rules between the data, also later decision trees with the information, regression methods (logarithmic and linear) will also be implemented. , also some data classification algorithms, evaluation of classifiers and an introduction to machine learning.
Conclusions.
In the last decade, data mining has experienced enormous growth as a result of the volumes of data processed by information systems. The successes obtained have shown the need and importance of this young and prominent field of research, however, further study is required in order to optimize the methods currently used. For example, the implementation of data mining in object-oriented and space-time databases. In its beginnings, mining focused on the generation of knowledge from thematic data. The study of spatial data had to be carried out almost manually. In many cases this consisted of observing maps, photographs and images.
New techniques allow the application of algorithms specifically designed for spatial data. This new branch of research was called spatial data mining.
An emerging technology such as Data Mining is presented as a highly applicable tool for the exploration and exploitation of information in large data warehouses, warehouses that become difficult to explore with classic Database administration tools. Data Mining uses predictive models, segmentation models, grouping and affinity models on the existing data set, which allows the efficient management and structuring of information to present visual data of great use in decision making, generation of statistical data and other useful applications in Institutions and Companies.
Bibliography
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Catalan, C. E. (02 of 01 of 2022). http://humanidades.cchs.csic.es. Obtained from Time Series: http://humanidades.cchs.csic.es/cchs/web_UAE/tutoriales/PDF/SeriesTemporales.pdf
Domínguez, Y. S. (01 of 01 of 2022). http://scielo.sld.cu. Retrieved from http://scielo.sld.cu/scielo.php?script=sci_arttext&pid=S0864-34662007000300020
Gallo AO, P.F. (2021). Data Mining and Short-Term Power Demand Forecasting in the Ecuadorian Electric System. Energy Technique., 13.
Lizarzaburu, E.R., Berggrun, L., & Quispe, J. (2012). Financial risk management. Experience in a Latin American bank. General Studies, 1-132.
M., P.M. (2016). Data mining through examples. In P.M.M., Data Mining Through Examples. 11th ed. (pp. 123-135). Alpha Omega.
Novales, A. (2016). Kalman filter: theory and applications. In A. Novales. Spain: Complutense University.
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• Author(s) :
• Edwin Gerardo Acuña Acuña (university researcher)

## [00005] ON E-STATISTICAL SUMMABILITY OF BOUNDED SEQUENCE

• Abstract : A summability method is said to be regular if it preserves the limit, i.e., it sums all convergent series to its Cauchy’s sum. In this paper, we have introduced the sequence space X(E) defined by the Euler matrix for the spaces X = l_∞, c, c_0 and l_p, (1 ≤ p < ∞). Some fundamental properties and relations related to these spaces are examined. A new regular statistical summability method (Euler statistical summability) is given. The graph for Euler and Euler statistical summability is given by using MATLAB(2018a).
• Author(s) :
• SABIHA TABASSUM (ALIGARH MUSLIM UNIVERSITY ALIGARH)

## [00006] Modified Operational Laws for Neutrosophic Numbers in Decision-Making Problems

• Abstract : This presented work results from the study of the existing basic operational laws of neutrosophic numbers (NNs) which had some shortcomings clearly stating that these are the special type of NNs and not applicable in every practical situation. To overcome this limitation the general basic operational laws of NNs are proposed in this paper and a numerical example from a real-life situation has been solved optimally to show the validity of the proposed NNs laws.
• Author(s) :
• Akanksha Singh (Chandigarh University)

## [00007] Sufficient Conditions for SDP Representability of Non-compact Convex Sets

• Abstract : The paper discusses the classical optimization problem of semidefinite representable $(SDR)$ non-compact convex sets. We introduce new notions, compactly SDR set, SDR away from 0 and SDR at infinity. We prove: the cone of feasible directions of a compactly SDR set has semidefinite representation. In addition, we characterize the polar of compactly SDR sets. It also illustrates the smallest cone containing compactly SDR set and its’ projections, which leads to new sufficient conditions for semidefinite representation.
• Author(s) :
• Anusuya Ghosh (Senior Software Engineer)
• Vishnu Narayanan (Associate professor)

## [00008] Semi Analytic Solution for Coupled (n+1)-dimensional Viscous Burgers’ Equation using Homotopy Perturbation Method

• Abstract : Semi analytic solution for coupled (n+1)-dimensional non-linear viscous Burgers’ equation has been obtained by Homotopy Perturbation Method. Potential of prescribed semi analytical technique is specifically examined for (3+1)-dimensional non-linear Burgers’ equation with very small kinematic viscosity factor has not been considered yet. Numerical experiments with illustrated absolute error and 3D graphical presentation testify the reliability of the technique. All the computational procedure has been done using MATLAB.
• Author(s) :
• Shelly Arora (Punjabi University, Patiala)
• Atul Pasrija (Punjabi University, Patiala)
• Sukhjit Singh Dhaliwal (SLIET, Longowal)

## [00009] Numerical Solution of Kuramoto–Sivashinsky Equation Using Orthogonal Collocation with Bessel Polynomials as Basis

• Abstract : Bessel polynomials has been proposed as a base function in orthogonal collocation to discretize fourth order Kuramoto-Sivashinsky equation. Convergence of numerical results have been analysed through L2 and L∞ norms to discuss the effectiveness of technique. Number of test problems have been solved and comparison of results in space as well as in time direction at different number of collocation points has been presented. The numerical values are presented graphically to confirm applicability of technique.
• Author(s) :
• Shelly Arora (Punjabi University, Patiala)
• Indu Bala (Punjabi University, Patiala)

## [00010] Convergence Analysis of Fourth Order Extended Fisher Kolmogorov Equation Using Quintic Hermite Splines

• Abstract : An improvised collocation technique has been proposed to discretize multi-parameter fourth order non-linear extended Fisher Kolmogorov equation. The spatial direction has been discretized with quintic Hermite splines whereas temporal direction has been discretized with weighted finite difference scheme. The fourth order equation in space direction has been decomposed into second order using space splitting by introducing a new variable. The space splitting has been proposed to improvise the convergence of approximate solution. The proposed equation has been analyzed on uniform grid in both space and time directions. Error bounds for general order Hermite splines are established. $epsilon$- uniform rate of convergence for the proposed scheme has also been discussed elaborately. The technique is illustrated by various numerical examples and error growth has been discussed by computing $L_2$ and $L_infty$ norms.
• Author(s) :
• Shelly Arora (Punjabi University, Patiala)
• Priyanka Bhardwaj (Punjabi University, Patiala)
• Saroj Kumar Sahani (South Asian University, New Delhi)

## [00013] Singularly perturbed problems on a graph

• Abstract : In this talk, a singularly perturbed convection diffusion problems on a graph domain will be discussed. Initially, the problem is designed on a simple graph i.e k-star graph. On the common vertex, the continuity and the Kirchhoff’s conditions will be discussed along with their complexity. The problem may be extended to a general graph with many vertices and edges. Some tests problems will be discussed based on upwind finite difference methods using piece-wise Shishkin meshes. Error estimates and the order of convergence are to be discussed.
• Author(s) :
• Vivek Kumar Aggarwal (Delhi Technological University)

## [00014] Pathway Fractional Integral Operator with Composition of Generalized function G_(ρ,η,r) [a, z]

• Abstract : The purpose of this paper is to consider the properties of generalized function G_$(ρ,η,r)$ $[a, z]$. For this purpose we obtain certain image formulas using Pathway fractional integral operators with these properties. We also mentioned some important special cases of the main results.
• Author(s) :
• Harish Nagar (Chandigarh University)
• Seema Kabra (Sangam University)

## [00015] Mehar ranking method for solving interval-valued intuitionistic fuzzy MADM problems in risk analysis

• Abstract : In this article, a new Mehar interval-valued intuitionistic fuzzy multi-attribute decision-making method method is proposed without using the concept of connection number. The suggested IVIFMADM method is applied to determine the solution for risk analysis problem in the investment sector which is more scientific and reasonable. Furthermore, the advantage of the proposed Mehar IVIFMADM method is discussed which supports that the proposed method is time-saving, reduces computational efforts, and is scientific.
• Author(s) :
• Akanksha Singh (Chandigarh University)

## [00016] Existence and Attractivity Results for Volterra Type Nonlinear Perturbed Random Integral Equations

• Abstract : In this talk, we prove an existence and locally attractivity result for Volterra type nonlinear perturbed random integral equations in separable Banach space under mixed generalised compactness, contraction and caratheodory conditions and also we will prove the existence of maximal and minimal solution Volterra type nonlinear random integral equations with some applications.
These types of Volterra type nonlinear perturbed random integral equations are used in various natural phenomena in which randomness occurs.
• Author(s) :
• SIDDHARTH GANESH SHETE (Swami Ramanand Teerth Marathwada University Nanded Maharashtra )

## [00017] Modified Operational Laws for Neutrosophic Numbers in Decision-Making Problems

• Abstract : This presented work results from the study of the existing basic operational laws of neutrosophic numbers which had some shortcomings clearly stating that these are the special type of neutrosophic numbers and not applicable in every practical situation. To overcome this limitation the general basic operational laws of neutrosophic numbers are proposed in this paper and a numerical example from a real-life situation has been solved optimally to show the validity of the proposed neutrosophic numbers laws.
• Author(s) :
• Akanksha Singh (Chandigarh University)

## [00018] Structures and evolution of bifurcation diagrams for a one-dimensional diffusive generalized logistic problem with constant yield harvesting

• Abstract : We study the diffusive generalized logistic problem with constant yield harvesting:

begin{equation*}
left {
begin{array}{ll}
u^{prime prime }(x)+lambda g(u)-mu =0, & -10$. We prove that, for any fixed$mu >0,$on the$(lambda ,left Vert uright Vert
_{infty })$-plane, the bifurcation diagram consists of a$subset $-shaped curve and then we study the structures and evolution of bifurcation diagrams for varying$mu >0.$• Author(s) : • Shin-Hwa Wang (National Tsing Hua University, TAIWAN) • Kuo-Chih Hung (National Chin-Yi University of Technology, Taiwan) • Yiu-Nam Suen (National Tsing Hua University, TAIWAN) ## [00019] A poset version of Ramanujan results on Eulerian numbers • Abstract : We explain how several results of Ramanujan follow from the formalism of order series {an algebra with a binary associative and commutative operation and a binary associative operation}. In our interpretation, Ramanujan worked with series inheriting the structure of the disjoint union of posets. We then provide new conceptual proofs of a couple of results by Ramanujan and describe a version of his results that depends on a choice of a series parallel poset. • Author(s) : • Eric Dolores Cuenca (Yonsei University) ## [00020] Image Functions Approximated by CNN • Abstract : Convolutional Neural Networks (CNN) have been widely used to image understanding. However it remains an open problem to prove the approximation of image functions via CNN. In this work, it is proved that an image function can be approximated by CNN on the basis of the axiom of choice in set theory and an uncountable number of training data from the viewpoint of image decomposition. • Author(s) : • Jian-Zhou Zhang (Sichuan University) ## [00021] Study of sonic-supersonic patch arising in axisymmetric relativistic transonic flow • Abstract : In this work, we study a sonic-supersonic patch arising in 3-D axisymmetric relativistic transonic flows. The main difficulty here is the coupling of nonhomogeneous terms due to axisymmetry and the sonic degeneracy for the relativistic flow. However, using the characteristic decompositions of angle variables, we prove the existence and regularity of solutions in partial hodograph plane first and then by using an inverse transformation, we construct a smooth solution in the physical plane. • Author(s) : • RAHUL BARTHWAL (Indian Institute of Technology Kharagpur) • RAHUL BARTHWAL (Indian Institute of Technology Kharagpur) • T Raja Sekhar (Indian Institute of Technology Kharagpur) ## [00022] Interaction between sardines, anchovies and swordfish in moroccan coasts with high and low tide • Abstract : The main objective of this work is the study of the effects of high tides and low tides on fishing effort, catches as well asprofits in a bioeconomic model of populations of Sardina pilchardus,Engraulis encrasicolus and Xiphias gladius in Moroc-can areas. To achieve this objective, we studied the stability of the equilibrium points of our biological model then we addedin our model the effect of the tides in the fishing effort which maximizes the profits of the fishermen under the constraintof the conservation of the biodiversity of these marine species using the generalized Nash equilibrium in the resolution ofthe bioeconomic model. As results, we were able to give the best fishing times according to the tides of each month of thewhole year which will allow us to achieve better yields. Hence the importance of introducing the effect of high and low tidesin bioeconomic models . • Author(s) : • Nossaiba Baba (Hassan II University of Casablanca) • Imane Agmour (Hassan II University of Casablanca) • Youssef El Foutayeni (Hassan II University of Casablanca) • Naceur Achtaich (Hassan II University of Casablanca) ## [00025] Riemann problem and limiting behaviour of a macroscopic production model • Abstract : We are concerned with a macroscopic production model which is a hyperbolic system of conservation laws with the equation of state for a Van der Waals gas. Solution to the Riemann problem for the system for all types of initial data is constructed, which contains a vacuum state for certain initial data. Delta shock wave solution and vacuum state is observed in limiting cases. • Author(s) : • Balakrishna Chhatria (Indian Institute of Technology Kharagpur) ## [00026] STRESS ANALYSIS OF AN EDGE CRACK UNDER TIME-HARMONIC WAVE DISTURBANCE • Abstract : This article determines a stress intensity factor (SIF) at the tip of an edge crack in two considered models. Problem-1 is an orthotropic strip of a finite thickness bonded by an orthotropic half-plane, and problem-2 is an orthotropic vertical semi-infinite strip. Edge cracks have been invaded perpendicularly by time-harmonic elastic waves. The system has been solved by using Fourier transform and Schmidt method to find the approximate analytical expression for the SIF. The variations of in plane normalized SIF for the different crack lengths and thickness were depicted graphically (2D) for different particular cases. • Author(s) : • Neha Trivedi (Indian Institute of Technology (BHU) Varanasi, India) • Neha Trivedi (Indian Institute of Technology (BHU) Varanasi, India) ## [00028] Riemann problem for the Chaplygin gas equations for several classes of non-constant initial data • Abstract : Using the differential constraint method, a class of exact solutions is obtained for the homogeneous quasilinear hyperbolic system of partial differential equations describing Chaplygin gas equation; these solutions exhibit linearly degenerate that leads to the formation of contact discontinuities. In fact, in this paper, we solved the gen- eralized Riemann problem through a characteristic shock(s). For several classes of non-constant and smooth initial data, the solution to the generalized Riemann problem is presented. • Author(s) : • Akshay Kumar (University of Hyderabad) • Radha R (University of Hyderabad) ## [00031] Stoneley wave in the transversely isotropic thermoelastic diffusion materials • Abstract : This paper investigate the secular equations of Stoneley wave propagating through bonded and unbonded interfaces between two dissimilar transversely isotropic thermoelastic diffusion half-spaces. These equations are solved numerically by modelling two distinct crustal rocks and the resultant phase velocities and attenuations are plotted graphically. This analysis explicates the position and permeability of fractures and also helps in the assessment of valuable materials under earth’s crust. Some particular cases are also deduced from the present formulation. • Author(s) : • Sanjay Debnath (Mizoram University) ## [00032] A geometrically preservative semi-adaptive method for the numerical solution of Kawarada equations • Abstract : This presentation concerns the numerical stability and geometric preservations of the numerical solution of Kawarada equation problems. The nonlinear partial differential equations exhibit strong quenching types of singularities that represent a number of key characteristics from industrial and multi-physical applications. A second order semi-adaptive implicit finite difference method will be constructed and investigated. We shall begin with a detailed mathematical analysis of the stability without freezing singular source terms of Kawarada equations in this talk. Preservation features of the solution vector sequences will then be studied. Realistic orders of the convergence will be given via generalized Milne’s devices. Finally, computer simulations will be carried out to demonstrate the effectiveness of the theoretical analysis and conclusions. • Author(s) : • Qin Sheng (Baylor University) ## [00034] Relative heat flux in nonlocal reaction-diffusion equations and thermoelectric efficiency • Abstract : Thermoelectric generators directly convert a temperature difference into electrical energy. To study their efficiency, we consider second-order integro-differential equations describing the steady-state temperature distribution inside thermoelectric generators when the Seebeck coefficient of the thermoelectric material is temperature-independent but the electrical resistivity and thermal conductivity are temperature-dependent. In this talk, we show that the temperature solution is unique and the relative boundary Fourier heat flux can be explicitly written. Therefore, the efficiency has an explicit formula. • Author(s) : • Jaywan Chung (Korea Electrotechnology Research Institute) • Byungki Ryu (Korea Electrotechnology Research Institute) • Hyowon Seo (Kunsan National University) ## [00035] Effects of toxicity and zooplankton selectivity under seasonal pattern of viruses on plankton dynamics • Abstract : A mathematical model for the interacting dynamics of phytoplankton-zooplankton is proposed. The phytoplankton have ability to take refuge and release toxins to avoid over predation by zooplankton. The zooplankton are provided some additional food to persist in the system. The phytoplankton are assumed to be affected directly by an external toxic substance whereas zooplankton are affected indirectly by feeding on the affected phytoplankton. We incorporate seasonal variations in the model, assuming the level of nutrients, refuge and the rate of toxins released by phytoplankton as functions of time. Our results show that when high toxicity and refuge cause extinction of zooplankton, providing additional food supports the survival of zooplankton population and controls the phytoplankton population. Prey refuge and additional food have stabilizing effects on the system; higher values of the former results in extinction of zooplankton whereas phytoplankton disappear for larger values of the latter. Seasonality in nutrients level and toxins released by phytoplankton generates higher periodic solutions while time-dependent refuge of phytoplankton causes the occurrence of a period-three solution. The possibility of finding additional food for zooplankton may push back the ecosystem to a simple stable state from a complex dynamics. • Author(s) : • Samares Pal (University of Kalyani) ## [00039] Recent developments on energy of graphs • Abstract : Let$G$be a simple graph of order$n$and with adjacency matrix$A$. If$lambda_{1},lambda_{2},dots,lambda_{n}$are the eigenvalues of$A$, Gutman defined the energy of$G$as$E(G)=sum_{i=1}^{n}|lambda_{i}|$. This definition was motivated by several earlier known results for the Huckel molecular orbital total π-electron energy and so is closely related to the concepts of theoretical chemistry. We present recent developments on graph energy. • Author(s) : • Shariefuddin Pirzada (University of Kashmir) ## [00040] Proportion of COVID-19 Pre-Symptomatic Transmission Events in South Korea • Abstract : To estimate the extent of pre-symptomatic transmission in South Korea, we used individual-level COVID-19 cases records. We inferred the probability of symptom onset per day since infection based on the density distribution of incubation period to stratify the serial interval distribution in Period 1 and Period 2, without and with expanded testing or implementation of social distancing strategies, respectively. We estimated the proportion of pre-symptomatic transmission as 43.5% and 60.0%, respectively. • Author(s) : • Youngji Song (University of Soongsil) • Eunha Shim (University of Soongsil) ## [00041] Clinical time delay distributions of COVID-19 in the South Korea • Abstract : Using the most complete nationwide COVID-19 database, we estimated the key epidemiological distributions associated with COVID-19. We determined the best model to fit the data using a Bayesian model comparison, and estimated the model parameters at the region level using a hierarchical Bayesian model with partial pooling. We found that the COVID-19 pandemic in the Republic of Korea was characterized by relatively short onset-to-diagnosis and onset-to-report intervals but by long serial intervals. • Author(s) : • Eunha Shim (Department of Mathematics, Soongsil University, Republic of Korea) • Wongyeong Choi (Department of Mathematics, Soongsil University, Republic of Korea) • Youngji Song (Department of Mathematics, Soongsil University, Republic of Korea) ## [00043] Matter-chameleon coupling in reconstructed Brans-Dicke cosmology • Abstract : In the present work, we studied the generalized Brans-Dicke (BD) model with a scalar field non-minimally coupled with the matter sector. We considered extended holographic Ricci dark energy$rho_{Lambda}=3phi (alphadot{H}+beta H^2)$in this BD cosmology framework, derived restrictions for BD parameter$omega$, and observed a stronger matter-chameleon coupling. The EoS parameter behaved like quintom. We observed an increasing potential function as matter-chameleon coupling gets stronger. Also, deceleration parameter transited from decelerated to the accelerated universe phase. • Author(s) : • Surajit Chattopadhyay (Amity University, Kolkata) ## [00044] Final size and infectious cases estimate for two-group SEIRD model • Abstract : For a two-group SEIRD model with asymmetric interaction and an approximated solution, we estimate the error of this approximation in the second group based on the error in the first one. We also study the final size of the epidemic for each group. The results are illustrated with the spread of COVID-19 pandemic in the New York County-USA for the initial stage of the contamination, and in the cities of Petrolina and Juazeiro-Brazil. • Author(s) : • Matheus Correia dos Santos (Federal University of Rio Grande do Sul – UFRGS) • Alison Marcelo Van der Laan Melo (Federal University of the São Francisco Valley – UNIVASF) ## [00045] Nonzero-sum stochastic impulse games with an application in energy markets • Abstract : We study a nonzero-sum stochastic differential game with both players adopting impulse controls, on a finite time horizon. The objective of each player is to maximize her total expected discounted profits. The resolution methodology relies on the connection between Nash equilibrium and the corresponding system of quasi-variational inequalities (QVIs in short). We prove, by means of the weak dynamic programming principle for the stochastic differential game, that the value function of each player is a constrained viscosity solution to the associated QVIs system in the class of linear growth functions. We also introduce a family of value functions converging to our value function of each player, and which is characterized as the unique constrained viscosity solutions of an approximation of our QVIs system. This convergence result is useful for numerical purpose. We apply a probabilistic numerical scheme which approximates the solution of the QVIs system to the case of the competition between two electricity retailers. We show how our model reproduces the qualitative behaviour of electricity retail competition. • Author(s) : • Mohamed Mnif (ENIT, Tunisia) • René Aid (University of Paris Dauphine) • Lamia Ben Ajmia (ENIT, Tunisia) • Mhamed Gaigi (ENIT, Tunisia) ## [00046] Global exponential synchronization of complex-valued recurrent neural networks with time-varying bounded and unbounded delay terms • Abstract : The global exponential synchronization criteria of complex-valued recurrent neural networks (CVRNNs) in presence of uncertain parameters with time-varying bounded and unbounded delay terms have been investigated. Based on Halanay inequality and matrix measure approach, the global exponential synchronization is studied. The synchronization of CVRNNs is achieved with help of Lyapunov functional, and several sufficient criteria and theorems. Finally, two numerical examples are taken to show viability and unwavering quality of our results for various cases. • Author(s) : • VIJAY KUMAR YADAV (Amity University Haryana, Gurugram, Delhi NCR India) ## [00050] Generalized Game Theoretical Model with Multiple Types of Homogeneous Players • Abstract : We introduce a decision game model with finite number of types and each type has finite number of homogeneous players. We assume that each type of player has similar characteristics and will choose only between two alternative choices or decisions). The preference for each type of players is described by a discrete utility function which gathers the influence of players in the same group and the influence of players from the other groups. We will characterize all pure ”united or separated” and mixed strategies that form Nash equilibria. The united strategies ensure that all players with same type will make same decision, while separated strategy includes at least one type of players who do not make same decision. We will determine the strategic thresholds for each type that identify the Nash regions in space. As a special case, we consider three types of homogeneous players and use geometry to construct three dimensional regions for Nash equilibria, where the horizontal axis reflects the preference for players of type one, the vertical axis reflects the preference for the players of type two, and the depth axis reflects the preferences for the players of type three, and we characterize all Nash equilibria regions. Finally, we apply our model in economics ”tourist sector” by introducing a resort model for three types of tourists distributed among two resorts and determine the competitive Nash Equilibrium prices for given preference for the three types of tourists. • Author(s) : • Abdelrahim Said Mousa (Birzeit University) ## [00051] Finite-time synchronization of multi-scroll chaotic systems with sigmoid non-linearity and uncertain terms • Abstract : Finite-time synchronization of multi-scroll chaotic systems with sigmoid non-linearity in the presence of uncertain stochastic parameters has been studied. The present chaotic system scrolls (up to five) are incorporated with the help of hyperbolic tangent functions, but in real applications, there is no limit of multi-scroll in a chaotic system. Finite-time synchronization is achieved with the help of Lyapunov stability using some lemmas and definitions. The Lyapunov exponents are also calculated for multi-scroll chaotic systems. • Author(s) : • Amit Kumar Mishra (Department of Mathematics, Shree M P Shah Arts Science College, Surendranagar, Gujarat, 363001, India) ## [00053] How predators choose their prey to maximize their utility functions by using switching prey • Abstract : In this work, we model the relationship between prey and predators by studying the interactive behavior of this prey-predator model and using the change of prey. The objective is to maximize the profit function of each predator by seeking the strategy provided by each predator to maximize its profit. To do so, we maximize this utility function being constrained by balance equations between biomass and trophic, and we show that this last problem is completely equivalent to finding the Generalized Nash Equilibrium Point. To calculate it, we use the conditions of KKT and we show that it is indeed a Problem of Linear Complementarity. • Author(s) : • Asmaa IDMBAREK (LAMS, Hassan II University of Casablanca, Casablanca, Morocco) • Yamna ACHIK (LAMS, Hassan II University of Casablanca, Casablanca, Morocco) • Hajar NAFIA (LAMS, Hassan II University of Casablanca, Casablanca, Morocco) • Imane AGMOUR (LAMS, Hassan II University of Casablanca, Casablanca, Morocco) • Youssef EL FOUTAYENi (LAMS, Hassan II University of Casablanca, Casablanca, Morocco) ## [00054] Lagrange alpha-exponential synchronization of non-identical fractional-order complex-valued neural networks • Abstract : In this article, Lagrange alpha-exponential synchronization of non-identical fractional-order complex-valued neural networks (FOCVNNs) is studied. Numerous favorable conditions for achieving Lagrange alpha-exponential synchronization and alpha-exponential convergence of the descriptive networks are constructed using additional inequalities and the Lyapunov method. Furthermore, the structure of the alpha-exponential convergence ball, in which the rate of convergence is linked with the system’s characteristics and order of differential has also been demonstrated. These findings, which do not require consideration of the existence and uniqueness of equilibrium points, help to generalize and improve previous works and may be used to mono-stable and multi-stable of the FOCVNNs. The salient feature of the article is the graphical exhibition of the effectiveness of the proposed method by using numerical simulation for synchronization of a particular case of the considered fractional order drive and response systems. • Author(s) : • Sapna Baluni (Indian Institute of Technology Varanasi (BHU), 221005, India) ## [00055] Thermocapillary dynamics of droplets and bubbles with internal thermal singularity • Abstract : In an arbitrary steady Stokes flow, we investigate the impact of an internal thermal singularity associated with the thermocapillary migration of a droplet. The type of thermal singularity and where it is located inside the drop have a significant impact on the migration velocity. This phenomenon provides a control mechanism for drop migration in the low Re and low Pe limits, which may be advantageous in various biomedical as well as industrial applications. • Author(s) : • Arindam Basak (IIT Kharagpur) ## [00056] Dead or Alive: Integrating Disease and Ecosystem Ecology Theory • Abstract : Disease-induced death is integral to the dynamics of many host populations. Dead hosts in disease models typically exit the system, disappearing into a void. This assumption lacks critical realism: empirical work demonstrates that dead hosts can alter host-pathogen dynamics and interactions through a variety of pathways. Here, we develop a carbon-based model, combining disease and ecosystem perspectives to investigate the consequences of feedbacks between living and non-living hosts. We focus on two pathways, direct transmission from diseased hosts and suppression of host growth by dead host mass. Because autotrophs are a critical link for carbon cycling, we develop parameter sets describing disease of autotrophic hosts in several aquatic and terrestrial ecosystem types. We found that when dead hosts transmit pathogens, host decomposition rate was integral to pathogen spread. Carbon fluxes and pools among live, dead, and decomposed biomass also were sensitive to pathogen-induced changes in host growth or death rates. Dynamics in aquatic systems were generally faster than in terrestrial systems, and with increasing host growth rate, disease induced shorter transient dynamics and higher infection prevalence. Thus, disease models explicitly recognizing the dynamic roles of hosts after death will provide novel insights for the ecology of infectious disease. • Author(s) : • Lale Asik (University of the Incarnate Word) • Eric Seabloom (University of Minnesota) • Angela Peace (Texas Tech University) • Rebecca Everett (Haverford College) ## [00058] Thermocapillary dynamics of viscous droplet driven by internal thermal singularity • Abstract : In a non-isothermal Poiseuille flow, we investigate the impact of an internal thermal singularity on the migration of a viscous immiscible droplet. The migration velocity strongly depends upon the type of thermal singularity and where it is located inside the droplet. In$Re to 0$and$Pe to 0$limits, this mathematical model provides a control mechanism for droplet migration, which may be useful in a variety of microfluidics as well as industrial applications. • Author(s) : • Arindam Basak (Indian Institute of Technology Kharagpur) • Rajaram Lakkaraju (Indian Institute of Technology Kharagpur) • Raja Sekhar G P (Indian Institute of Technology Kharagpur India) ## [00064] Immersed boundary simulations of fluid shear-induced deformation of a cantilever beam • Abstract : This work considered a 2D model of rectangular cantilever beam immersed in a channel filled with viscous, incompressible fluid, where one end of beam is fixed to the channel wall, bending in response to shear flow. IB method was employed to simulate fluid–structure interaction. Effect of physical parameters of the problem — stiffness , height of cantilever , flow velocity was investigated, and simulation results were qualitatively compared with respect to linear beam theory. • Author(s) : • Sudeshna Ghosh (Amity University Haryana, India) ## [00070] SDDS-SABC based Algorithm for solving non-linear optimization problems • Abstract : Optimizing complex non-linear constrained optimization problems is often a challenging task. This work proposes a new hybrid method called SDDS-SABC based on the Split-Detect-Discard-Shrink technique and Sophisticated ABC algorithm to optimize the said problems. The SDDS method is responsible for shrinking the full search region through a recursive breakdown and improves computational effort to focus on the subregion covering potential solutions for further decomposition. SABC plays a vital role in extracting the best solutions from the subregions whose values help detect the promising subregion. Both SDDS and SABC are sequentially repeated until the region reduces to a nominal width representing the optimization problem’s global/ close to global solution(s). The Ranking and selection rules have been applied to assist optimistic decision-making with an attitude to discard the subregion covering non-promising solution (s). At the same time, the subregion with a promising solution is accepted as the current shrink region for a further split. We introduce a new initialization scheme for food sources in the SABC algorithm, which excels the existing initialization process. Develop Dual-strategy Employed bee’s phase, allowing bees to split into two groups and use their respective group strategies to explore their neighbourhood while maintaining their collaborative contribution. We also introduce a new Dynamic penalty method that is free from extra parameters or factors like most existing penalty methods do to improve the optimization efficiency. To check the validity of SDDS-SABC, we have applied it to benchmark functions and engineering problems. To measure our proposed method’s statistical significance against other existing heuristic optimization methods, we carried out the non-parametric Friedman and Wilcoxon rank tests. • Author(s) : • Dhirendra Sharma (Birla Institute of Technology Mesra, Ranchi) • Darakhshan Jabeen Syeda (Birla Institute of Technology Mesra, Ranchi) ## [00071] Effects of diffusive Reynolds number on electroosmotic pulsating nanofluid flow • Abstract : The estimation of the diffusion coefficient of all ionic materials is an important domain of experimental research that has several applications including the design of electrical double-layer capacitors (EDLCS ), microfluidic devices and nanofluidic devices with nanopores, etc. The great challenging task is to transport aqueous solution in a narrow confinement microchannel with fluid suction or inject it through the permeable walls. Kong et al. (2017) experimentally observed the effects of thermal response on the ion diffusion coefficient in a Graphene nanochannel for transporting NaCl electrolyte solution. They reported that the temperature increase leads to an increase in the thermal motion of ions than the bulk motion of liquid, resulting in a stable ion diffusion coefficient. This paper intends to extend our earlier mathematical model of Mukherjee and Shit (2022) under a pulsating pressure gradient scenario thereby incorporating several new complex physiological fluid flow phenomena. We examine the pulsating electroosmotic nanofluid flow phenomena in a microchannel with porous walls. The combined effects of injected nanofluid velocity and ion diffusion coefficients on the electrical potential formation are considered. The novel boundary condition is introduced so as to examine the effects of electroosmosis and frictional forces on thermal profiles and nanoparticle volume fractions of nanofluid. Being motivated by the experimental works of Kong et al. (Phys. Chem. Chem. Phys. 19 (2017) 7678), this paper aims to extend the study of ion diffusivity in terms of diffusive Reynolds number on the nanofluid temperature in the pulsating pressure gradient setting. The semi-analytic differential transform method (DTM) is used to solve the physical equations, represented as coupled ODEs, with a special emphasis on the convergence of solutions, which is presented in terms of tables and graphs. The study shows that the nanofluid velocity, temperature and mass concentration are strongly influenced by the ion diffusion coefficient and the frequency of pulsating pressure gradient. References: 1. J. Kong, Z. Bo, H. Yang, J. Yang, X. Shuai, J. Yan, and K. Cen, “Temperature dependence of ion diffusion coefﬁcients in NaCl electrolyte conﬁned within graphene nanochannels,” Phys. Chem. Chem. Phys. 19, 7678 (2017). 2. S. Mukherjee and G. C. Shit, “Mathematical modeling of electrothermal couple stress nanoﬂuid ﬂow and entropy in a porous microchannel under injection process,” Appl. Math. Comput. 426, 127110 (2022). • Author(s) : • Gopal Chandra Shit (Department of mathematics, Jadavpur University, Kolkata, India) • Satwik Mukherjee (Jadavpur University, Kolkata) ## [00073] Scattering behavior for one dimensional wave maps into Riemannian manifolds • Abstract : In this talk, we explore the scattering behavior for wave maps from Minkowski space$mathbb{R}^{1+1}$into general Riemannian manifolds, provided the initial data are small. In particular, we show that the nonlinear scattering operator can be linearized as the corresponding linear scattering operator. The underlying physical intuition of this conclusion is that one-dimensional wave maps behave exactly in the same manner as their scattering fields detected by the far-away observers. • Author(s) : • Mengni Li (Southeast University) ## [00074] Chaos in multidimensional disordered nonlinear lattices • Abstract : We study the mechanisms of energy transport in multidimensional heterogeneous lattice models, studying in particular the case of the Klein-Gordon model of coupled anharmonic oscillators in one and two spatial dimensions. We perform an extensive numerical investigation of the dynamics of the considered model revealing (i) the effects of the type of the impurity (heterogeneity) parameter on the systems’ transport properties and classify the transport mechanisms of the nonlinear versions of the models into various dynamical regimes. (ii) that for it’s nonlineaar version, chaotic transport persists and (iii) chaotic hotspots meander in the region of energy concentration supporting the spreading mechanism of energy. • Author(s) : • Bob Senyange (Muni University) ## [00077] Machine Learning challenges to automate behavioral scales • Abstract : Psychologists often use short speech samples to classify patients according to various behavioral scales, such as depression, suicidality, and mania. We are investigating the ability of Machine Learning techniques to replicate the scores of the psychologist produced scores with the goal of tracking longitudinal behavior without the need of frequent in-person interactions. In this talk we present our results and challenges. • Author(s) : • Filippo Posta (Estrella Mountain CC) ## [00078] A higher order numerical scheme to a nonlinear McKendrick-Von Foerster equation with singular mortality • Abstract : In this paper, higher-order numerical schemes to the McKendrick-Von Foerster equation are presented when the death rate has singularity at the maximum age. The third, fourth-order schemes that are proposed are based on the characteristics, which are non-intersecting lines in this case, and are multi-step methods with appropriate corrections at each step. In fact, the convergence analysis of the schemes is discussed in detail. Moreover, numerical experiments are provided to validate the orders of convergence of the proposed third-order and fourth-order schemes. • Author(s) : • Joydev Halder (School of Mathematics and Statistics, University of Hyderabad) • Suman Kumar Tumuluri (School of Mathematics and Statistics, University of Hyderabad) ## [00079] Multi-dimensional Optimal Systems for Chaplygin Gas Cargo-LeRoux model • Abstract : The famous Cargo-LeRoux model for the isentropic Chaplygin gas is studied using classical Lie symmetry method. Optimal systems up to six-dimensions are constructed using the adjoint transformation and the invariants of the admitted Lie algebras. We obtain exact solutions to the Cargo-LeRoux model by using the one-dimensional optimal system and discussed the physical behavior of the solutions graphically. Finally, We discussed the evolutionary behavior of a discontinuity wave. • Author(s) : • Manoj Kumar Pandey (BITS Pilani K K Birla Goa Campus) • Pabitra Kumar Pradhan (BITS Pilani K K Birla Goa Campus) ## [00081] Strong stationarity for a highly nonsmooth optimization problem with control constraints • Abstract : This talk is concerned with a control constrained optimization problem governed by a nonsmooth elliptic PDE in the presence of a non-differentiable objective. In such a nonsmooth setting, the application of standard adjoint calculus is excluded. Based on the limited differentiability properties, we derive a strong stationary optimality system, i.e., an optimality system which is equivalent to a purely primal necessary optimality condition. • Author(s) : • Livia Betz (Faculty of Mathematics Würzburg) ## [00083] Modeling the dynamic of COVID-19 with different types of transmissions • Abstract : In this paper, we propose a new epidemiological mathematical model for the spread of the COVID-19 disease with a special focus on the transmissibility of individuals with severe symptoms, mild symptoms, and asymptomatic symptoms. We compute the basic reproduction number and we study the local stability of the disease-free equilibrium in terms of the basic reproduction number. Numerical simulations were employed to illustrate our results. Furthermore, we study the present model in case we took into consideration the vaccination of a portion of susceptible individuals to predict the impact of the vaccination program • Author(s) : • Mohamed AMOUCH (Chouaib doukkali, University) ## [00091] An infeasible interior-point arc-search algorithm for nonlinear constrained optimization • Abstract : Most algorithms based on interior-point methods are categorized as line search since they compute a search direction on a straight line. In this talk, we propose an interior-point method for nonlinear programming problems that computes the search direction along with an ellipsoidal arc. We discuss the convergence of the proposed method, and numerical experiments indicate it can solve the CUTEst benchmark problems in fewer iterations. A modified method can further reduce the computation time. • Author(s) : • Einosuke Iida (Tokyo Institute of Technology) • Makoto Yamashita (Tokyo Institute of Technology) • Yaguang Yang (US NRC) ## [00092] The explicit formulae for the distributions of words • Abstract : The distributions of the number of words play key roles in information theory, statistics, and DNA analysis. Bassino et al. 2010, Regnier et al. 1998, and Robin et al. 1999 showed generating functions of the distributions in rational forms. However, we can not expand rational functions except for simple cases and do not have explicit formulae for the distributions from them. We show the explicit formulae for the distributions of words for the Bernoulli models. • Author(s) : • Hayato Takahashi (Random Data Lab. Inc. ) ## [00095] Low Reynolds number hydrodynamics of a slip-stick sphere • Abstract : Low Reynolds number hydrodynamics of spherical particles with non-uniform surface roughness show potential applications in microfluidic situations like swimming micro-organisms and emulsions. In this work, we study the hydrodynamics of spherical slip-stick particle models; namely, i) axisymmetric cap/strip model and ii) non-axisymmetric patch model, suspended in an unbounded arbitrary Stokes flow whose surface is partitioned into two different slip regions. We evaluate the optimum configurations for migrational and rotational motion of the slip-stick spherical particle. • Author(s) : • Shiba Biswas (Indian Institute of Technology Kharagpur, India-721302) • Poornachandra Sekhar Burada (Indian Institute of Technology Kharagpur, India-721302) • Raja Sekhar G P (Indian Institute of Technology Kharagpur, India-721302) ## [00096] Multi-scale analysis of concentration distribution inside porous medium channel configuration • Abstract : A multiple-scale perturbation analysis is presented for the two-dimensional concentration distribution of passive contaminant released in an incompressible viscous fluid channel filled with a porous medium. The flow is driven by the combined effect of the upper plate oscillation and the periodic pressure gradient. Homogenization technique is used to find the concentration distribution up to third order. For a fixed amplitude of oscillation and pulsation, frequency of pressure pulsation has stronger effect on the dispersion. • Author(s) : • Timir Karmakar (Department of Mathematics, National Institute of Technology Meghalaya, Shillong, Meghalaya 793003) • Swarup Barik (2Department of Mathematics, SRM Institute of Science and Technology, Kattankulathur, Chennai 603203) • Raja Sekhar G P (Indian Institute of Technology Kharagpur India) ## [00097] Optimal control of pollution rate in a spatiotemporal bioeconomic model concerning phytoplankton-zooplankton • Abstract : The management of plankton production constitutes a major challenge for the development of aquaculture. To attend this objective, chlorophyll-a, a pigment present in all photosynthetic organisms, is generally and historically used as an estimator of the biomass of planktonic organisms. In this work, we use the data of chlorophyll-a and we choose two controls strategies to minimize the pollution mortality rate. By using Sea-Das software we obtain raster maps. These maps show the distribution of Chlorophyll-a in Moroccan maritime areas throughout the month of May 2019 and 2020. We notice that we choose these two maps precisely because we noticed that, during the international lockdown period (caused by Covid-19 pandemic), a significant number of marine resources have come to light. The aim purpose of this article is to proposeand analyze mathematically a bioeconomic model of plankton organism taking into account the negative effect of pollution. We seek to control the mortality pollution rate and to clarify the impact of the pollution in the reproduction of marine populations. • Author(s) : • Imane Agmour (Hassan II University) • Soukaina Benrhila (Hassan II University) ## [00098] Robust bring your own encryption algorithm using generalized heat equation associated with generalized Vigen$grave{e}$re-type table over symmetric group • Abstract : We develop a secure bring your own encryption algorithm that encrypts personal data. The proposed algorithm is based on a generalized heat equation associated with a generalized Vigen$grave{e}$re-type table over symmetric group$S_{n}$so that existing attacks will be infeasible. Encryption keys are obtained from random key sequences tested by NIST statistical test suite. The robustness of the proposed algorithm has been found by comparing it with other competing existing algorithms. • Author(s) : • Manish Kumar (BITS Pilani, Hyderabad Campus, Telangana, India) ## [00100] Pointwise Controllability of Degenerate/Singular PDEs • Abstract : This work deals with some controllability results of a one-dimensional degenerate and singular parabolic equation. We provide approximate and null controllability conditions based on the moment method by Fattorini and Russel. • Author(s) : • AMINE SBAI (Hassan 1st University) ## [00102] Existence of Sign-changing solutions to a Hamiltonian elliptic System • Abstract : We consider the Hamiltonian elliptic system begin{equation*} – Delta U + U= |V|^{p-1}V quadtext{ and } quad – Delta V + V=|U|^{q-1}U ,text{ in } mathbb{R}^N, end{equation*} where$Ngeq 4$and the non-linearities$p,q$are superlinear and satisfy sub-critical hyperbola condition. We prove the existence of nonradial sign-changing solutions. We shall work with the space of$phi$-equivariant functions where$phi:Gammato {1,-1}$and$Gammasubset O(N)$, a closed subgroup of$O(N)$. • Author(s) : • Alok Kumar Sahoo (Ph.D. student, IIT Hyderabad) • Bhakti Bhusan Manna (IIT Hyderabad) ## [00103] Two-dimensional Riemann problem for a new hyperbolic model for thin film flow of a perfectly soluble anti-surfactant solution • Abstract : This work is concerned with formulation of three-dimensional thin film model for an anti-surfactant solution and hence constructing unique global solution for a two-dimensional Riemann problem for the corresponding reduced hyperbolic form. We analyze the interactions of classical and non-classical waves in detail to construct the global solution of the corresponding 2-D Riemann problem. Further, we provide the expressions for strength, location and propagation speed of delta shock wave at each interaction point. • Author(s) : • RAJA SEKHAR TUNGALA (Department of Mathematics, Indian Institute of Technology Kharagpur) ## [00104] High order approximation of Caputo-Prabhakar derivative and its application in solving time fractional Advection-Diffusion equation • Abstract : This work aims to devise a high-order numerical scheme to approximate the CaputoPrabhakar derivative of order 0 < α < 1, using an rth degree Lagrange interpolation polynomial, where$3leq rinmathbb{Z^{+}}.$. This numerical scheme can be thought of as an extension of the presented schemes for the approximation of the Caputo-Prabhakar derivative in our previous work cite{r1}. Further, we adopt the proposed scheme to solve a time-fractional Advection-Diffusion equation with the Dirichlet boundary condition. It is shown that the method is unconditionally stable, uniquely solvable, and convergent with convergence order,$ O(tau^{r+1-alpha}, h^{2}), $where τ and h are the step sizes in the temporal and spatial directions, respectively. Without loss of generality, obtained results are supported by numerical examples for r = 4, 5. bibitem{r1} Deeksha Singh, Farheen Sultana, and Rajesh K Pandey, Approximation of Caputo Prabhakar derivative with application in solving time fractional advection-diffusion equation, International Journal for Numerical Methods in Fluids.$94(7)(2022)$, pp. 896-919. • Author(s) : • DEEKSHA SINGH (Department of Mathematical Sciences, Indian Institute of Technology, BHU, Varanasi) • Rajesh K. Pandey (Department of Mathematical Sciences, Indian Institute of Technology, BHU, Varanasi) ## [00111] A convergent numerical method for time-fractional reaction-diffusion equation • Abstract : This paper design and analyze a robust finite difference scheme for solving a time-fractional reaction-diffusion equation with smooth and non-smooth solutions. The solution of this equation exhibits a weak singularity at the initial time$mathrm{t}=0$. So we use graded temporal mesh in order to handle the singularity. We discretize the space variable using a cubic polynomial spline difference scheme. Further, the stability and convergence for both the smooth and non-smooth solutions are analyzed separately. • Author(s) : • Anshima Singh (Indian Institute of Technology (BHU) Varanasi) ## [00112] Vibration control on unplanned change in vehicle mass model • Abstract : Prolonged vibration transfer to the human body during riding affects human health. In this work, we proposed a heuristic-based chaotic artificial bee colony (ABC) optimization technique to mitigate the vibration response of running vehicle with context to the safety and comfort of passengers during a ride. We have modeled the vehicle’s six degrees of freedom dynamics as a half-car with passive suspension and passengers in a seated position. In the proposed work, two fundamental techniques are used in our analysis. Firstly, we estimate how changing the passenger mass in a vehicle affects the vibration behaviour of the entire system. This is done by simulating the dynamical model computationally and numerically over different bumpy roads. Thereby, distinguishing between the causal roles of mass, safety, and comfort, we formulate technologically constrained optimization problems and minimize the peak jerks of the vehicle and passengers. Further, implement techniques to optimize the vibration levels and design suspension parameters accordingly. The study also analyses the extreme range of vibration levels and comfort relationships for several road conditions to estimate the net effect of vehicle weight change during the ride. • Author(s) : • Darakhshan Jabeen Syeda (Birla Institute of Technology Mesra, Ranchi) ## [00115] Nanoparticle shape effect of hybrid nanofluid inside a U-shaped enclosure • Abstract : The nanoparticle shape effect on the natural convection of copper-alumina/water hybrid nanofluid inside a U-shaped enclosure is presented. The governing equations are transformed into dimensionless form. A weighted residual Galerkin triangular finite element method is used to solve the problem numerically. The isotherms and streamlines of the fluid are presented with Rayleigh numbers of$10^4$to$10^6$. The blade nanoparticle produces the highest heat transfer rate, while the sphere is the lowest. • Author(s) : • Muhammad Solleh Asmadi (University of Malaya) • Zailan Siri (University of Malaya) • Ruhaila Md Kasmani (University of Malaya) • Habibis Salleh (Universitas Islam Negeri Sultan Syarif Kasim) ## [00116] Multi-Scale Modelling of three phase lag (TPL) of lung cancer during cryosurgery • Abstract : On the basis of the study of cryosurgery with mathematical modelling we discuss about the study related to non-Fourier bio-heat transfer available numerically with various boundary conditions for frozen and non frozen region. By the CAD/ANSYS study a specific region is developed for the tumor detected area. We’ll elaborate three phase lag (TPL) bio-heat transfer model to analysis of the temperature distribution in living tissue. By this work of mathematical modelling of cryosurgery in lung cancer to elaborate the knowledge of TPL bio-heat model by using numerical methods. • Author(s) : • Sarita Singh (Doon University Dehradun Uttarakhand IndiaDoon University Dehradun Uttarakhand ) ## [00122] Exact expansion of functions using partial derivatives: sensitivity analysis • Abstract : Expansions of functions such as Taylor’ series, ANOVA and anchored decompositions are widely used for approximating and analyzing complex mathematical models. We propose a novel and exact expansion of functions using their cross-partial derivatives, the distribution functions and densities of the input variables. In uncertainty quantification and multivariate sensitivity analysis, such expansion allows for developing a dimension-free computation of sensitivity indices for dynamic models, and for proposing new lower and upper bounds of total indices. • Author(s) : • Matieyendou LAMBONI (université de Guyane) ## [00128] A Numerical Approximation for Generalized Fractional Sturm-Liouville Problem with Application • Abstract : In this paper, we present a numerical scheme for the generalized fractional Sturm-Liouville problem (GFSLP) with mixed boundary conditions. The GFSLP is defined in terms of a B-operator consisting of an integral operator with a kernel and a differential operator. One of the main features of the B-operator is that for different kernels, it leads to different Sturm-Liouville Problems (SLPs), and thus the same formulation can be used to discuss different SLPs. We prove the well-posedness of the proposed GFSLP. Further, the approximated eigenvalues of GFSLP are obtained for two different kernels namely a modified power kernel and Prabhakar kernel in the B-operator. We obtain real eigenvalues and corresponding orthogonal eigenfunctions. The theoretical and numerical convergence orders of eigenvalues and eigenvectors are also discussed. Further, the numerically obtained eigenvalues and eigenfunctions are used to construct an approximate solution of the one-dimensional fractional diffusion equation defined in a bounded domain. • Author(s) : • Eti Goel (Department of Mathematical Sciences, Indian Institute of Technology, BHU, Varanasi, Uttar Pradesh, India) • Rajesh K. Pandey (Department of Mathematical Sciences, Indian Institute of Technology, BHU, Varanasi, Uttar Pradesh, India) ## [00129] Anomalous diffusion in standard maps with extensive chaotic phase spaces • Abstract : In this work, we investigate the long-term diffusion transport and chaos properties of single and coupled standard maps (SMs). We analyze parameters that are known to produce anomalous diffusion in the phase spaces of maps, with the presence of so-called accelerator modes. We study how different ensembles affect the behavior, asymptotic diffusion rates, and time scales required for these maps. We also explore the global diffusion properties and chaotic dynamics of various coupled SM configurations. • Author(s) : • Henok Tenaw Moges (University of Cape Town) • Henok Tenaw Moges (University of Cape Town) • Charalampos Skokos (University of Cape Town) ## [00130] THE DYNAMICS OF THE MONKEYPOX VIRUS IN THE PRESENCE OF ENVIRONMENTAL TRANSMISSION • Abstract : A deterministic model for the environmental transmission dynamics of monkeypox with the presence of quarantine and vaccination is presented. The analysis of the model presented three important equilibrium states namely; monkeypox-free equilibrium (MPXV-FE), infected rodent-free endemic equilibrium (IRF-EE) and coexistence equilibrium (CO-EE). The local and global stability of the equilibrium states is established in terms of the basic reproduction number,$mathcal{R}_0.$For global stability, the Comparison theory is used for MPXV-FE while the Voltera-Lyapunov matrix theory is used for both IRF-EE and CO-EE. Sensitivity analysis is performed using the Latin Hypercube sampling method with the results showing that environmental transmission parameters are the main driver of infection in the dynamics of monkeypox infection. This is further supported by numerical simulations to show the impact of environmental transmission on monkeypox infection and also the validity of the theoretical analysis presented. Based on the results, it is recommended that health practitioners and policy-makers should constitute control strategies that will focus on reducing environmental transmission and shedding of the virus in the environment while increasing the environmental decay rate of the monkeypox virus. This will complement the quarantine and vaccination strategies in place. 34C60, 92B05, 34D23, 34D20 • Author(s) : • Chinwendu Emilian MADUBUEZE (Federal university of Agriculture Makurdi Nigeria ) ## [00132] Incompatibility-governed deformations: a new approach to Elastoplasticity • Abstract : We present theoretical as well as numerical results concerning a novel approach to model elasto-plastic phenomena in deformable solids based on a decomposition of the total deformation tensor into a compatible (i.e., a symmetric gradient) and an incompatible part at each point of the domain. The incompatible part aims to model the part of the deformation due to dislocation movement that eventually is responsible for the creation of plastic regions. This is a joint work with Samuel Amstutz (Ecole Polytechnique de Palaiseau, France). • Author(s) : • Nicolas Van Goethem (Universidade de Lisboa ) ## [00136] Variable Metric Composite Proximal Alternating Linearized Minimization for Nonconvex Nonsmooth Optimization • Abstract : In this talk I propose a proximal algorithm for minimizing an objective function of two block variables consisting of three terms: 1) a smooth function, 2) a nonsmooth function which is a composition between a strictly increasing, concave, differentiable function and a convex nonsmooth function, and 3) a smooth function which couples the two block variables. I propose a variable metric composite proximal alternating linearized minimization (CPALM) to solve this class of problems. Building on the powerful Kurdyka-L ojasiewicz property, we derive the convergence analysis and establish that each bounded sequence generated by CPALM globally converges to a critical point. We demonstrate the CPALM method on parallel magnetic resonance image reconstruction problems. The obtained numerical results show the viability and effectiveness of the proposed method. • Author(s) : • Maryam Yashtini (Georgetown University) ## [00141] Multiscale Perturbed Gradient Descent: Chaotic Regularization and Heavy-Tailed Limits • Abstract : Recent studies have shown that gradient descent (GD) can achieve improved generalization when its dynamics exhibits a chaotic behavior. However, to obtain the desired effect, the step-size should be chosen sufficiently large, a task which is problem dependent and can be difficult in practice. In this talk, we introduce multiscale perturbed GD (MPGD), a novel optimization framework where the GD recursion is augmented with chaotic perturbations that evolve via an independent dynamical system. We analyze MPGD from three different angles: (i) By building up on recent advances in rough paths theory, we show that, under appropriate assumptions, as the step-size decreases, the MPGD recursion converges weakly to a stochastic differential equation (SDE) driven by a heavy-tailed LÃ©vy-stable process. (ii) By making connections to recently developed generalization bounds for heavy-tailed processes, we derive a generalization bound for the limiting SDE and relate the worst-case generalization error over the trajectories of the process to the parameters of MPGD. (iii) We analyze the implicit regularization effect brought by the dynamical regularization and show that, in the weak perturbation regime, MPGD introduces terms that penalize the Hessian of the loss function. Empirical results are provided to demonstrate the advantages of MPGD. • Author(s) : • Soon Hoe Lim (Nordita, KTH Royal Institute of Technology and Stockholm University) ## [00144] The flux perturbed Riemann solution for isentropic Cargo-LeRoux model • Abstract : In this research, we study the pressureless Cargo-LeRoux model of conservation laws, which is modeled from the one-dimensional constant gravity Euler equations. Introducing flux perturbation of a van der Waals isentropic gas equation of state, the exact solution of Riemann problem is derived and establish the existence and uniqueness of the Riemann solution globally. Finally, the influence of van der Waals excluded volume on the physical quantities is illustrated graphically using MATLAB software. • Author(s) : • Sahadeb Kuila (DEPARTMENT OF MATHEMATICS, SRM Institute of Science and Technology, Kattankulathur, Tamil Nadu 603203) • Sumita Jana (DEPARTMENT OF MATHEMATICS, SRM Institute of Science and Technology, Kattankulathur, Tamil Nadu 603203) ## [00146] A mathematical model to the melanoma dynamics involving CAR-T cells • Abstract : Melanoma is considered one of the most aggressive types of cancer. Melanoma has been used as an experimental model in several studies aiming the development of therapies, such as immunotherapy with CAR T-cells. Our ODE model: a) captured the expansion, contraction and persistence phases of CAR-T cells; b) exhibited the suppression caused by tumor cells on CAR-T cells; c) showed that macrophages negatively impact CAR-T cell dynamics. • Author(s) : • Paulo F. A. Mancera (UNESP) • Jairo G. Silva (IFMT) • Guilherme Rodrigues (UNESP) ## [00156] Convergence of adaptive algorithms for parametric PDEs with lognormal coefficients • Abstract : Numerical methods for random parametric PDEs can greatly benefit from adaptive refinement schemes, in particular when functional approximations are computed as in stochastic Galerkin methods with residual based error estimation. In this talk we derive an adaptive refinement algorithm for an elliptic parametric PDE with unbounded lognormal diffusion coefficient steered by a reliable error estimator for both the spacial mesh and the stochastic space. Moreover, we will prove the convergence of the derived adaptive algorithm. • Author(s) : • Nando Farchmin (Physikalisch-Technische Bundesanstalt) ## [00158] Mean field portfolio games with consumption • Abstract : We establish an equivalence between the Nash equilibrium of mean field portfolio games with consumption and the solution to some BSDE. Our approach relies on martingale optimality principle and dynamic programming principle. When the market parameters are deterministic, we obtain the unique Nash equilibrium in closed form. As a byproduct, we answer the question proposed in the paper by Lacker and Soret: the strong equilibrium is unique! • Author(s) : • Guanxing Fu (The Hong Kong Polytechnic University) ## [00159] Wave interactions in drift- flux equations of two-phase flows • Abstract : In this talk, we consider the interactions of arbitrary shocks for a$3times 3$system of conservation laws governing drift-flux equations of two-phase flows with isothermal and isentropic equation of states. Here, we use the properties of Riemann solution and interaction of weak shocks for this study. Consequently, we reduce the system of equations by taking the projection of shocks in the phase plane to investigate the interactions of arbitrary shocks. • Author(s) : • Minhajul Minhajul (Department of Mathematics, Birla Institute of Technology and Science Pilani, K K Birla Goa Campus, India) • Rakib Mondal (Department of Mathematics, Birla Institute of Technology and Science Pilani, K K Birla Goa Campus, India) ## [00165] A convergent scheme for stochastic compressible Euler equations • Abstract : In this talk, we discuss a finite volume scheme for the three-dimensional barotropic compressible Euler equations driven by a multiplicative Brownian noise. We derive necessary a priori estimates for numerical approximations, and show that the Young measure generated by the numerical approximations converge to a dissipative measure-valued martingale solution to the stochastic compressible Euler system. These solutions are probabilistically weak in the sense that the driving noise and associated filtration are integral part of the solution. To the best of our knowledge, this is the first attempt to prove the convergence of numerical approximations for the underlying system. • Author(s) : • Ujjwal Koley (Associate Professor) ## [00169] Decentralized strategies for coupled shape and parameter inverse problems • Abstract : We present a novel family of algorithms framed within game theory setting and dedicated to solve ill-posed inverse problems, where unknown shapes (obstacles or inclusions) or sources are to be reconstructed as well as missing boundary conditions, for steady Stokes fluids. Some theoretical results and several numerical experiments are provided that corroborate the ability of the approch to tackle harsh problems. • Author(s) : • Abderrahmane HABBAL (University Cote d’Azur Inria CNRS) ## [00173] Symmetries and Explicit Solutions of Fractional Nonlinear Drinfeld–Sokolov–Satsuma–Hirota System • Abstract : In this work, a space-time fractional nonlinear Drinfeld–Sokolov–Satsuma–Hirota system is considered. The symmetry approach and power series expansion technique are applied to derive the explicit solutions of the system. The coupled DSSH system was seen as a special form example of Lax pairs and a special case of the four-reduced Kadomtsev–Petviashvili hierarchy in literature. The main motivation for present work is the global behaviour and various applications of fractional DSSH in applied science. The results obtained in the paper can be useful in calculating in conservation laws of the system. • Author(s) : • Komal Singla (Chandigarh University) ## [00175] pFemView: An Open-Source Visualization Library for p-FEM • Abstract : We present a new approach to visualize p-hierarchical basis finite element (p-FEM) solutions on the scientific visualization application ParaView. Since ParaView uses a linear/quadratic interpolation at specific geometric nodes, a refined visualization mesh needs to be constructed efficiently. This is accomplished via the key steps “p-hierarchical to nodal projection” and “higher-order to lower-order projection”, which have been implemented in an open-source C++ library “pFemView”. Furthermore, examples are presented to illustrate the effectiveness of this library. • Author(s) : • Janitha Gunatilake (University of Peradeniya) ## [00177] Bifurcations of Limit Cycles and Multistability in Polynomial Dynamical Systems • Abstract : We study global limit cycle bifurcations and multistability in 2D polynomial dynamical systems, namely, in: the general Liénard polynomial system, the Euler-Lagrange-Liénard mechanical system, Leslie-Gower ecological or biomedical systems, and a reduced quartic Topp system which models the dynamics of diabetes. We study also 3D polynomial dynamical systems and, in particular, complete the strange attractor bifurcation scenarios in Lorenz type systems connecting globally the homoclinic, period-doubling, Andronov-Shilnikov, and period-halving bifurcations of limit cycles. • Author(s) : • Valery A. Gaiko (United Institute of Informatics Problems, National Academy of Sciences of Belarus) ## [00180] Relationship between musical notes and socio-political events • Abstract : Historians and scientists long suspected that sounds and music impact different cultures. However, empirical data to support such claim is sparse. Previous research using Supervised Machine Learning algorithms, i.e. ANFIS (Adaptive Neuro-Fuzzy Inference System) has successfully categorised musical genre classification and predicted the outcome of the United Kingdom’s election results using popular music released in that period by feeding sound wave features to the ANFIS algorithm. This study reports similar research for the Moroccan elections using two different supervised machine learning algorithms namely, k-NN and SVM. • Author(s) : • Choi-Hong Lai (University of Greenwich) • Nakunam Kokulan (University of Greenwich) • Yahya Chahine (University of Greenwich) ## [00181] Control of the Stefan problem • Abstract : The Stefan problem is the quintessential macroscopic model of phase transitions in liquid-solid systems. We consider the one-phase Stefan problem with surface tension, set in two-dimensional strip-like geometry. We discuss the local null controllability of the system in any positive time, by means of control supported within an arbitrary open and non-empty subset. • Author(s) : • Debayan Maity (TIFR Centre for Applicable Mathematics) ## [00188] Two-Phase Modelling of Plaque Growth in Early Atherosclerosis • Abstract : We discuss the early stage of atherosclerotic plaque formation within arteries. The production of foam cells characterizes such plaque. Foam cells generate from the differentiated form of monocytes (called macrophages) owing to oxidized low-density lipoprotein (ox-LDL) cholesterol intake. Initially, plaque radius grows exponentially and later on, it stabilizes with time. Such behaviour is due to the death of foam cells owing to the toxicity of excess ox-LDL intake, although ox-LDL enhances foam cell proliferation. • Author(s) : • Abdush Salam Pramanik (Department of Mathematics, University of North Bengal) • Bibaswan Dey (Department of Mathematics, University of North Bengal) ## [00189] A New Strategy in Developing Location Model • Abstract : The location model (LM) is designed to enable classification when a dataset contains both continuous and categorical variables. Due to the issue of empty cells, a smoothed location model (smoothed LM) is introduced. However, the smoothing process caused changes in the original information of the non-empty cells. It is well known that original information is valuable and important that should be maintained. Thus, a new strategy is proposed by amalgamating maximum likelihood and smoothing estimations to construct a new LM. Consequently, maximum likelihood estimation will be used if the cell was found to be non-empty, otherwise smoothing estimation will be used instead. The analysis shows that the newly constructed LM can provide optimal classification results and demonstrates better performance compared to the old models, i.e. classical LM and smoothed LM, where the estimation used is based on the cell’s conditions. The new proposed strategy of parameter estimation could handle all situations; whether the cells are empty or not, limited sample size with many variables measured mainly the binary. • Author(s) : • Hashibah Hamid (SQS, UUM) ## [00191] Two-Phase Modelling of Subcutaneous Injection of Drugs • Abstract : Various drugs and vaccines are administered through the subcutaneous pathway. The adipose cells within the subcutaneous layer impart structural anisotropy. We address the mechanical response of the adipose tissue in terms of the computed stress fields to understand the pain a patient realizes. Tissue anisotropy instigates the interstitial fluid to generate one or more eddies. Eddies help a low viscous injected drug homogenize when the skin pinching height is high at the injection apply area. • Author(s) : • Bibaswan Dey (Department of Mathematics, University of North Bengal) • Abdush Salam Pramanik (Department of Mathematics, University of North Bengal) • Timir Karmakar (Department of Mathematics, National Institute of Technology Meghalaya, India) • Kalyan Saha (Department of Mathematics, University of North BengalDepartment of Mathematics, University of North Bengal) ## [00197] Mathematical analysis of a nonlinear SIS model with effect of migration • Abstract : We consider a nonlinear SIS epidemic model with nonlocal disease transmission rate and diffusion in space which is a system of parabolic equations. The existence and uniqueness of steady state are studied using compact and nonsupporting operators, and strongly continuous semigroup theory, respectively. Due to the nonlinearity in the disease transmission rate, proof of the uniqueness of a steady state requires a completely different approach. The linearization around the nontrivial steady state of the model requires the study of a perturbed operator. Spectral analysis is used to study the local stability and the global stability of the steady state. • Author(s) : • Soumak Nag (University of Hyderabad) • Suman Kumar Tumuluri (University of Hyderabad) ## [00199] Covering Array on Product of Hypergraphs • Abstract : Covering array ((CA)) on a hypergraph$H$is a combinatorial object, used in interaction testing of a complex system modeled as$H$. It is a matrix and the number of rows in it, called size, indicates the required number of tests. Minimizing the size of (CA) is important in industrial applications. Given$H$, determining the optimal size is NP-hard. We present a polynomial-time approximation algorithm to construct$CA$on 3-uniform hypergraphs. • Author(s) : • Yasmeen Akhtar (Birla Institute of Technology and Science, Pilani-Goa Campus) • Soumen Maity ( Indian Institute of Science Education and Research, Pune) ## [00200] Montgomery identity and Ostrowski type inequalities via Katugampola integral operator • Abstract : In this talk, we will discuss the extended version of Montgomery identity using Katugampola integral operators. Also we will establish Ostrowski type integral inequalities and fractional integral inequality for product of two functions. • Author(s) : • Henok Desalegn Desta (Addis Ababa university ) • Deepak B. Pachpatte (Dr. Babasaheb Ambedkar Marathwada University, India) • Tadesse Abdi (Addis Ababa University) • Jebessa B. Mijena ( Georgia College & State University) ## [00204] Periodicity and Symmetry on a Class of Integral Equations with Weakly Singular Kernels • Abstract : In this study, we introduce the periodic and symmetric properties of the states in a class of weakly singular integral equations. Motivation of this paper is based on the main results of previous paper: bounded forces produce bounded states in the infinite field. We furthermore observed that in finite times, steady states show. For each periodicity, two kinds of initial conditions apply: one is same as the original one, the other is the steady state from previous period. For symmetry, we apply same magnitudes of forces but opposite directions. • Author(s) : • Shihchung Chiang (Chung Hua University) ## [00205] Period doubling’ induced by optimal control in a behavioral SIR epidemic model. • Abstract : We consider a behavioral SIR epidemic model to describe the action of the public health system aimed at enhancing the social distancing during an epidemic outbreak. An optimal control problem is proposed where the control acts in a specific way on the contact rate. We show that the optimal control of social distancing is able to generate a period doubling–like phenomenon. Namely, the ‘period’ of the prevalence is double the ‘period’ of the control, and an alternation of small and large peaks of disease prevalence can be observed. • Author(s) : • Sileshi Sintayehu Sharbayta (Addis Ababa University) • Bruno Buonomo (University of Naples Federico II) • Alberto d’Onofrio (University of Trieste) • Tadesse Abdi (Addis Ababa University) ## [00206] Tensor product-type methods for solving Sylvester tensor equations • Abstract : The tensor biconjugate gradient$($TBiCG$)$method has recently been proposed for solving Sylvester tensor equations. TBiCG is based on BiCG that may exhibit irregular convergence behavior. To overcome the limitations of BiCG, product-type methods have been proposed. In this study, we propose tensor product-type methods to solve Sylvester tensor equations. Furthermore, we consider the preconditioned versions using the NKP preconditioner. Numerical experiments illustrate that the proposed methods are competitive with some existing methods. • Author(s) : • Jing Niu (Nagoya University) • Tomohiro Sogabe (Nagoya University) • Lei Du (Dalian University of Technology) • Tomoya Kemmochi (Nagoya University) • Shao-Liang Zhang (Nagoya University) ## [00208] Love wave along the interface with triangular irregularity • Abstract : Propagation of the love wave is studied along the irregular interface between the porous layer and the elastic half-space. The porous layer is assumed to be saturated by two immiscible fluids. The irregularity at the interface is considered in the form of a triangular pit embedded in the half-space. The elastic half-space is considered to be initially stressed under the effect of gravity. A complex transcendental and implicit relation between the frequency and the phase speed of the Love wave is derived in the form of a dispersion relation. A numerical study is conducted to observe the effect of material parameters and irregularity on the behavior of the Love wave. A significant impact of the triangular pit, porosity, and frequency is observed on the phase speed of the propagating Love wave and depicted graphically. • Author(s) : • Ashish Arora (I. K. Gujral Punjab Technical University) ## [00212] Optimal control for a SIR epidemic model with limited quarantine • Abstract : Social distance and total lock-downs are interventions that have been used to mitigate the spread of the COVID-19 virus. However, these measures could be harmful to societies in terms of social and economic costs. Using optimal control tools and numerical computations we investigate the optimal strategies that minimize the impact of an epidemic, by studying the conditions for an optimal control of a Susceptible-Infected-Recovered model. • Author(s) : • Rocio Celeste Balderrama (Departamento de Matematica-Universidad de Buenos Airesu) • Javier Peressutti (Universidad de Mar del Plata) • Juan Pablo Pinasco (Universidad de Buenos Aires-IMAS-CONICET) • Constanza Sanchez de la Vega (Universidad de Buenos Aires_IMAS_CONICET) • Federico Vazquez (Universidad de Buenos Aires-IC-CONICET) ## [00213] Advances in Derivative-free Methods and the DFO VU-algorithm • Abstract : The VU-algorithm is a method of minimizing convex, nonsmooth functions by splitting the space into two subspaces: the V-space, on which the objective function’s nonsmooth behavior is captured, and the orthogonal U-space, on which the function behaves smoothly. The algorithm’s convergence is accelerated, as it takes a (slow) proximal point step in the V-space, then a (fast) quasi-Newton step in the U-space, since gradients and Hessians exist there. New convergence rates and subroutines are presented. • Author(s) : • Chayne Planiden (University of Wollongong) ## [00218] Characterizations of diffusion matrices in homogenization of nondivergence-form elliptic equations • Abstract : We provide characterizations of diffusion matrices A for which the sequence of solutions$(u^{varepsilon})_{varepsilon > 0}$to$-A(x/varepsilon):D^2 u^{varepsilon} = f$in$Omega$,$u^{varepsilon} = g$on$partialOmega$, converges to the solution of the homogenized problem with$L^{infty}$-rate$mathcal{O}(varepsilon^2)$for all sufficiently regular$f,g$. Whereas such diffusion matrices can be characterized via the third-order homogenized tensor, we provide more explicit characterizations and prove an open conjecture posed by Guo and Tran. • Author(s) : • Xiaoqin Guo (University of Cincinnati) • Timo Sprekeler (National University of Singapore) • Hung Vinh Tran (University of Wisconsin Madison) ## [00219] Approximation methods for solving pursuit-evasion differential game • Abstract : In this study we present an appropriate singular, zero-sum, linear-quadratic differential game. One of the main features of this game is that the weight matrix of the minimizer’s control cost in the cost functional is singular. Due to this singularity, the game cannot be solved either by applying the Isaacs MinMax principle, or the Bellman–Isaacs equation approach. As an application, we introduced an pursuit-evasion differential game with an appropriate regularized cost functional and developed an appropriate dual representation. Developing the variational derivatives of this regularized cost functional, we apply several approximation methods and show how the numerical results coincide with the dual representation. • Author(s) : • Oleg Kelis • Oleg Kelis (The Technion—Israel Institute of Technology) ## [00224] Multi-objective multi-route STP with carbon emission and risk mitigation in Pharmaceutical Supply Chain under Pythagorean fuzzy Environment • Abstract : This research proposes multi-objective multi-route fixed-charge solid transportation problem with carbon emission and risk mitigation in Pharmaceutical Supply Chain (PSC) under trapezoidal Pythagorean fuzzy environment. A novel ranking index is proposed to convert the suggested Pythagorean fuzzy model into its deterministic version. This study develops new computational procedure to minimize the chosen factors in PSC. Thereafter the model is solved by intuitionistic fuzzy and hybrid programming. Finally, an example is included to show the effectiveness of the model. • Author(s) : • Dr. Sankar Kumar Roy (Dept. of Applied Mathematics, Vidyasagar University, Midnapur-721102, West Bengal, India) ## [00225] Multidimensional WENO-AO Reconstructions Using A Simplified Smoothness Indicator • Abstract : Finite volume, weighted essentially non-oscillatory (WENO) schemes using the simple smoothness indicator$sigma= 1/(L-1) sum_{j} (u_{j} – u_{m})^2$, are presented, where$L$is the number of mesh elements in the stencil,$u_j$is the local function average over$j$th element, and index$m$gives the target element. We develop a modification of WENO-Z weighting that gives a reliable and accurate reconstruction of adaptive order. Convergence results are proved. Numerical experimental results are also provided. • Author(s) : • Chiehsen Huang (National Sun Yat-sen University) • Todd Arbogast (University of Texas; Austin) • Chenyu Tian (University of Texas; Austin) ## [00228] Density functional theory for two dimensional homogeneous materials • Abstract : We study Density Functional Theory models for 2D materials. We first show that a homogeneous material can be seen as a limit of crystals. Next, we derive reduced models in the orthogonal direction. We show how the different terms of the energy are modified and prove some properties of the ground state. In Kohn-Sham models, we prove that the Pauli principle is replaced by a penalization term in the energy. • Author(s) : • Salma Lahbabi (UHIIC, UM6P) • David Gontier (Université Paris Dauphine) • Salma Maichine (UM6P) • Abdelqoddous Moussa (UM6P) ## [00229] Mathematical modeling of spatial distribution of COVID-19 epidemic • Abstract : This study provides a mathematical study of the Susceptible, Exposed, Infected, Recovered, and Vaccinated population model of the COVID-19 pandemic by the bias of reaction-diffusion equations. We showed the spatial distribution of the model compartments when the basic reproduction rate R0 < 1 and R0 > 1. We demonstrate the model’s effectiveness by performing numerical simulations and then investigated the impact of vaccination and the significance of spatial distribution parameters in the spread of COVID-19 epidemic. • Author(s) : • Kayode Oshinubi (Université Grenoble Alpes) • Jacques Demongeot (University of Grenoble Alpes) • Brice Kammegne (University of Dschang ) ## [00233] Revisiting Businesses Vulnerability and Classifying the Main Problems of MSMEs During the COVID-19 Pandemic • Abstract : Design/methodology/approach: This paper recalculates the MSME business vulnerability index in 503 districts and 34 provinces in Indonesia using Principal Component Analysis. Then, we conducted in-depth interviews with MSME actors in Medan, Central Java, Yogyakarta, Bali, and Manokwari West Papua and discussed how they could survive the COVID-19 pandemic and the extent of digital literacy, technology application to maximize sales and business. Purpose: We conducted the knowledge management of MSME actors for business, agriculture, and industry sectors with the in-depth interview result using text mining Latent Dirichlet Allocation Mallet to obtain information on their problems. Findings: For the sake of sustainability, the Penta-Helix collaboration is needed to get the best solution to the COVID-19 problem for the new normal and especially for Micro, Small, and Medium Enterprises’ business activities. Originality/value: From the results of a deep survey of MSMEs involved in this research, which covers three sectors, namely agriculture, trade, and processing, there are 7 (58.33%) of them experienced a decrease in income during the pandemic, 12.66% experiencing an increase in revenue, and 25% did not experience changes in income before and during the pandemic. • Author(s) : • Rezzy Eko Caraka (Badan Riset dan Inovasi Nasional) ## [00240] Phantom cosmological model with observational constraints in symmetric teleparallel gravity • Abstract : The cosmological model of the Universe has been presented in symmetric teleparallel gravity and the parameters are constrained from the cosmological datasets. The nonmetricity function considered here contains higher power of the nonmetricity. With some algebraic manipulation the Hubble parameter has been obtained in redshift. The cosmological and geometrical parameters are obtained and constrained using the recent Hubble and Pantheon + SHOES datasets. The model shows early deceleration and late time acceleration. • Author(s) : • Bivudutta Mishra (BITS-Pilani, Hyderabad Campus) ## [00241] Adaptive sparse interpolation in high dimensions and applications to surrogate modeling in chemical engineering. • Abstract : We present theoretical and practical aspects on the development of accurate surrogate models from first-principles, multiscale, PDE models for industrial chemico-physical processes. We will present many applications in Phosphate industry done in collaboration with OCP-Group in Morocco. The surrogate models are based on sparse multivariate polynomial interpolation. The goal is to reduce the computational time while preserving its physical properties such as monotonicity and positivity. • Author(s) : • saad benjelloun (UM6P) • saad benjelloun (UM6P) • Abdellah Chkifa (UM6P) ## [00250] Formation of delta shock waves and vacuum states in the vanishing pressure limit of the Riemann solution to the isentropic Euler system for logarithmic equation of state with the Coulomb-like friction term • Abstract : We investigate the limiting behavior of the Riemann solution to the isentropic Euler equations for logarithmic equation of state with the Coulomb-like friction term. The formation of vacuum state and delta shock waves are identified and analyzed when the pressure vanishes. Unlike the homogeneous case, the Riemann solution is no longer self-similar. We prove that the Riemann solution of the isentropic Euler equations for logarithmic equation of state with friction term converges to the Riemann solution of the zero-pressure gas dynamics system with a body force when the pressure vanishes. • Author(s) : • Anupam Sen (Post Doctoral Fellow at Centre for Applicable Mathematics, Tata Institute of Fundamental Research) ## [00251] Separable Variable Method and Exact Solution of Fractional Differential Equations • Abstract : We demonstrate how the method of separation of variables provides an effective tool to derive exact solution of nonlinear time fractional PDEs as well as partial differential-difference equations. More specifically, exact solutions to discrete time fractional K-dV equation, time fractional Toda – lattice equation, time fractional heat equation and nonlinear time fractional telegraph equation with variable coefficients have been derived. The question of deriving exact solution satisfying initial and boundary conditions is also addressed. • Author(s) : • Ramajayam Sahadevan (Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai-600005 ) ## [00252] Stabilization and adaptive event-triggered tracking control for non-linear systems • Abstract : An adaptive event-triggered-based output tracking problem for non-linear network control systems with malicious attacks is discussed in this work. An adaptive event-triggered mechanism is developed to reduce the number of triggering and communication burdens. Feedback control is constructed to force the output trajectories to track reference input with disturbance and malicious attacks. Tracking objective transformed into input-output finite time stabilization. Sufficient conditions are developed based on Lyapunov–Krasovskii functional and advanced integral inequalities. • Author(s) : • Vijayakumar Muthusamy (Anna University ) ## [00254] Estimation of Directional Marginal Productivity in Supply Chain Capacity Planning and Resource Allocation: A Case Study of the Power Industry • Abstract : Marginal productivity (MP) estimation is utilized to plan for maximum output levels and to allocate resources to address fluctuating demand for fuel in the power plant sector as well as adjust the power generated in the transmission and distribution lines. It also adjusts the amount of energy produced in the transmitter and distributor lines. In this paper, a data envelopment analysis (DEA) model is introduced for estimating the directional marginal productivity (DMP) of supply chain divisions. This model measures efficiency by maximizing the marginal profit for multiple outputs in predetermined directions. The purpose of this study is to establish whether adding an extra unit of input or reallocating resources can have significant effects on economic return. • Author(s) : • Mojgan pouralizadeh (Islamic Azad University, Lahijan Branch,Lahijan,Iran) ## [00261] Translational motion of a slightly deformed viscous spherical droplet in Stokes flow • Abstract : The problem of steady translational motion of a slightly deformed spherical droplet immersed in an immiscible viscous fluid is studied analytically under the consideration of vanishing Reynolds number. The flow fields in both the regions i.e. in the interior of droplet and exterior of droplet are governed by steady Stokes equations that are solved asymptotically using a method of perturbed expansions undersuitable boundary conditions. The deformation from spherical shape is characterized by a small parameter called deformation parameter, therefore, we have solved the problem up to the second order of the deformation parameter by neglecting the higher orders. The effect of deformation parameter is observed by means of force expression. The explicit expressions for the hydrodynamic drag force exerted on the droplet surface are obtained for the special cases of prolate and oblate spheroids. Our results are in good agreement with the exisitng results in literature for deformed solid sphere up to first and second order. • Author(s) : • Jai Prakash (Mahindra University, Hyderabad) • Huan J. Keh (National Taiwan University, Taipei) ## [00275] A fast data-driven method for designing compressible shock dominant flows • Abstract : We will present a new class of high-order numerical algorithms for computational fluid dynamics. Called “GP-MOOD,” the new finite volume method is based on the Gaussian Processes modeling that generalizes the Gaussian probability distribution. Solutions at shocks and discontinuities are handled by the improved Multidimensional Optimal Order Detection (MOOD) strategy, which controls numerical stability and accuracy in an “a posteriori” shock-capturing formalism. We also introduce a new data-driven “a priori” MOOD method. • Author(s) : • Dongwook Lee (University of California Santa Cruz) ## [00281] Simulation of the mechanical behaviour of steel-concrete-steel structures including concrete voids • Abstract : Numerical tools, including finite element simulations, are considered to investigate the effect of initial voids inside concrete on the mechanical behavior of steel-concrete composite structures in compression. A refined numerical strategy is first defined, including a particular care on the relations between each structural component. Due to high computational cost, progressive numerical simplifications are then discussed to conclude in the most acceptable simplified hypothesis. A parametric study is finally launched and perspectives are discussed. • Author(s) : • Ludovic JASON (Université Paris-Saclay, CEA, Service d’Études Mécaniques et Thermiques) ## [00282] Data Assimilation in Operator Algebras • Abstract : An algebraic framework for data assimilation of dynamical systems and uncertainty quantification is developed. In this framework, the Bayesian formulation of data assimilation is embedded in a non-abelian operator algebra – observables are represented by multiplication operators and probability densities by quantum states. The forecast step is represented by a quantum operation induced by the Koopman operator of the dynamical system. The analysis step is described by a quantum effect. Data-driven implementation uses kernel methods. • Author(s) : • Joanna Maja Slawinska (Dartmouth College, Department of Mathematics) ## [00284] Stability analysis of solutions of nonlinear Schrodinger equation in presence of PT-symmetric potential • Abstract : We extract exact stationary solutions of nonlinear Schrödinger equation in the presence of complex deformed supersymmetric potential (PT -symmetric Scarf potential) in terms of bright soliton and dark soliton. The corresponding spectrum of linear Schrödinger equation has been investigated and the PT broken and unbroken regions of linear Schrödinger equation have been delineated analytically. The stability of these solutions is corroborated by means of linear stability analysis and validated by direct numerical simulations. • Author(s) : • Amiya Das (University of Kalyani) ## [00290] Multiple trajectories’ learning method for time series data • Abstract : Statistical time-series techniques (ARIMA, Holt-Winters, regressions) help smoothing noise/external effects and provide short-term forecasts. These models may not assist in understanding underlying processes. Instead of a single trajectory’s approximation, we reconstruct dynamical systems. This allows treating external effects as switches between initial conditions. The dynamical systems’ reconstruction accounts to physical principles and data fitting. Examples demonstrate accurate short-term prediction and approximation of global dynamics. Qualitative analysis of the latter shows various scenarios of process development. • Author(s) : • Victoria Rayskin (Haverford) ## [00291] Graph Convergence and Iterative Algorithm for a System of Generalized Nonlinear Variational-like Inclusions • Abstract : We focus on the investigation of the problem of finding a common point lying in the solutions set of a system of generalized nonlinear variational-like inclusions and the fixed points set of a total asymptotically nonexpansive mapping. A new iterative algorithm is suggested by employing the concepts of$P$-$eta$-proximal-point mapping and graph convergence. Convergence of a sequence of above is established. We Prove the strong convergence and stability of the sequence generated by our algorithm. • Author(s) : • Suliman S Al-Homidan (King Fahd University of Petroleum and Minerals) ## [00293] Reverse supply chain design and planning in a Mean-Risk framework • Abstract : In this paper, we determine the supply chain structure together with the planning decisions that optimize simultaneously the net present value in the presence of uncertain parameters. The model considers all main supply chains operations. The novelty of this paper is the model for the design and planning of supply chains with the simultaneous consideration of the reverse logistics activities, operational risk induced by the uncertainty of products demands, and decision maker’s loss-aversion. • Author(s) : • Cristinca FULGA (The Bucharest University of Economic Studies) ## [00298] A mathematical model for new biomarkers in prostate cancer • Abstract : Prostate cancer is the fourth most diagnosed cancer subtype in the world and the most common among men. The high mortality related to the disease can be explained by the difficulty of detecting it in its early stage. The objective of this work is to build a mathematical model to assist in the characterization of a new panel of biomarkers for prostate cancer, aiming to predict the chance of an individual to develop the disease. • Author(s) : • Paulo F. A. Mancera (UNESP) • Marta H. Oliveira (UFU) • Thaise G. Araujo (UFU) • Maria E. Antunes (UNESP) ## [00300] Coupling macro-micro simulations in complex fluids • Abstract : Some of the most remarkable properties and functions served by some complex fluids originate from the interplay between external fields and microstructural dynamics. From a computational point of view this generates a set of challenges related to the need of coupling dynamics at different length and times scales, sometimes spanning several orders of magnitude. Micro-macro simulations have gained a lot of recognition within the field because these methods allow capturing full dynamics at the macroscale without losing resolution at the microscale. In this talk, we will review our efforts to couple existing macroscopic solvers for the Navier-Stokes equations with microstructural dynamics described by Langevin-type equations. In particular, we will discuss dumbbells models -under viscometric and capillary thinning flows fields- and parallel computing using GPUs. • Author(s) : • Paula A Vasquez (University of South Carolina) • Michael Cromer (RIT) ## [00301] On some modifications in the conjugate gradient method and its application in unconstrained optimization problems • Abstract : Conjugate gradient (CG) methods are preferably used to solve large-scale unconstrained optimization problems due to strong local and global convergence properties and low memory requirements. To enhanse its convergence, we introduce an improved hybrid form of the conjugate gradient method in this work. We propose a new form of CG parameter (βk), combining the Fletcher Reeves (FR) and three-term search directions. Our proposed search directions formula satisfies the sufficient descent condition independent of any line search and are bounded. For the global convergence, some proper assumptions on the objective function and its gradient have been taken into account, which fulfills the strong Wolfe-Powell line search conditions. Finally, numerical experiments have been carried out on some standard benchmark test functions and compared with other CG methods from the literature to check the validity of the proposed algorithm. Numerical results guarantee the efficiency and robustness of our proposed CG method. • Author(s) : • Sweta Kumari (Birla Institute of Technology Mesra, Ranchi) • Darakhshan Jabeen Syeda (Birla Institute of Technology Mesra, Ranchi) ## [00310] Human Activity Recognition from Inertial Motion Data • Abstract : Human activity recognition (HAR) using inertial motion streaming has gained a lot of momentum in recent years. This has been driven by smart environments and the ubiquity of inertial-motion sensors in modern commodity devices. HAR applications span all aspects of human life such as healthcare, sports, manufacturing, etc. In this talk we give a brief description of the state-of-the-art work in HAR including action recognition, biometrics analysis (gender, age,..), sensor’s location determination, gait analysis, etc. • Author(s) : • Walid Gomaa (Egypt Japan University of Science and Technology) ## [00314] The Orthogonal Spline Collocation Method for Parabolic Problems with Interfaces • Abstract : The parabolic problems with interfaces are solved using a method in which orthogonal spline collocation (OSC) is employed for the spatial discretization and the Crank–Nicolson method for the time-stepping. The derivation of the method is described in detail for the case in which cubic monomial basis functions are used in the development of the OSC discretization. The results of extensive numerical experiments involving examples from the literature are presented. • Author(s) : • Danumjaya Palla (BITS-Pilani KK Birla Goa Campus) • Santosh Kumar Bhal (Centurion University of Technology and Management) • Graeme Fairweather (Mathematical Reviews, American Mathematical Society) ## [00315] Motion Assessment in Human Action Performance • Abstract : Elderly people can be provided with safer independent living by the early detection of abnormalities in their motion actions performance. Low-cost depth sensing is one of the emerging technologies that can be used for unobtrusive and inexpensive motion abnormality detection and quality assessment. In this study, we developed and evaluated vision-based methods to detect and assess neuromusculoskeletal disorders manifested in common daily activities using three-dimensional skeletal data provided by the SDK of depth camera. • Author(s) : • Walid Gomaa (Egypt Japan University of Science and Technology) ## [00318] Efficient iterative methods for solving systems of nonlinear equations • Abstract : The aim of this talk is to discuss the iterative methods for solving system of nonlinear equations. Many problems in Science and Engineering lead to solve a system of nonlinear equations. Solving such equations with the use of analytic methods is almost impossible, so one has to rely on iterative methods. One of the basic scheme to solve such problems is the Newton-Raphson’s method. Based on Newton-Raphson’s iterative scheme many higher order and computationally efficient methods have been derived in the literature. These methods have been used to solve Hammerstein’s integral equation, boundary value problems, Burger’s equation and many more such type of equations. Moreover, these methods can solve system of equations with large number of equations. But Newton-Raphson’s method and the methods based on this have one drawback that they require the evaluation of the derivative. So, keeping this in mind many methods have derived in the literature which are derivative free and use only function evaluations. In these methods, the derivative is approximated by their divided difference approximation. The basic method in this category is the Traub-steffensen’s method. This talk will present recent work in this area and will contain the following topics: – iterative methods with derivative – iterative methods without derivative – implementation on numerical problems like integral equations, ODES and PDES – discussion on efficiency of these methods • Author(s) : • Himani Arora (Guru Nanak Dev University, Amritsar, Punjab) • Arvind Mahindru (DAV University, Jalandhar) ## [00320] Sensing the electrical world: modelling to understand aerial electroreception • Abstract : Bees and spiders (and other arthropods) can sense naturally occurring electrical fields. This recent discovery expands our view of how such organisms explore their environments, revealing previously unknown sensory capabilities. This talk consists of three topics: 1) the physical and biological feasibility of this sense, 2) how interactions between sensory hairs alter their sensitivity to different stimuli, and 3) the new sensory possibilities (e.g., object identification) and biological implications of this sense (e.g., decision-making). • Author(s) : • Ryan Palmer (University of Bristol) • Daniel Robert (University of Bristol) • Isaac Chenchiah (University of Bristol) ## [00321] Modeling of hydromagnetic unsteady flow over a upright plate using Pseudospectral method • Abstract : This study looks at the effects of a crosswise magnetic field along with thermal radiation proceeding the unsteady two-dimensional magneto hydrodynamic viscous flow, electrically insulating, and Newtonian fluid across an upright plate next to a Darcian rule. For governing equations, Pseudospectral Method is used. In this inquiry, the governing non-linear, coupled partial differential equations are decoded using Pseudospectral scheme that is reliable, effective, and has undergone substantial validation. The technique’s precision and efficacy are proven. • Author(s) : • Anju Saini (Graphic Era (Deemed to be University) Dehradun) ## [00325] Constrained Spectral Dilation of a Matrix • Abstract : Let$ A in mathbb{C}^{n times n}$and$ B in mathbb{C}^{m times m}.$Then$A$is said to be a spectral dilation of$B$and written as$ B subset A$if$ m< n$and there exist matrices$C$and$D$such that $$A= Sleft[begin{array}{c|c} B & C \ hline 0 & D end{array}right] S^{-1}$$ for some nonsingular matrix$S in mathbb{C}^{ntimes n}. $Obviously, if$A$is a spectral dilation of$B$then$A$has a partially specified eigen-structure as given by the eigen-structure of$B.$Now, given an$ntimes n$matrix$A$and an$mtimes m$matrix$B$with$m < n,$consider the constrained spectral dilation problem$($CSDP$)$$$widehat{A} = mathrm{arg}min { | X- A |_2 : X in mathbb{C}^{ntimes n}, ; B subset X }.$$ If$widehat{A}$exists then it is a spectral dilation of$B$nearest to$A$and $$mathrm{d_S}(A, B) := |widehat{A}- A|_2 = min{ |X - A|_2 : X in mathbb{C}^{ntimes n}, ; B subset X}$$ is the shortest distance from$A$to a spectral dilation of$B.$The main aim of this work is to present a concise framework for solving the constrained spectral dilation problem and undertake an in-depth analysis of various issues that influence existence of a solution. • Author(s) : • Rafikul Alam (Indian Institute of Technology Guwahati) ## [00326] Estimating the lowest-order eigenvalue in Sturm-Liouville boundary value problem • Abstract : We investigate a special case of the Sturm–Liouville boundary value problem$($BVP$)$and examine the BVP in the Schrödinger form. By considering a reciprocal quadratic form of the corresponding invariant function, we estimate the lowest-order eigenvalue without solving the eigenvalue problem but by utilizing the localized landscape and effective potential functions. Some combinations of parameter values yield poor spectrum estimates. Other combinations are satisfactorily although the values tend to overestimate results from numerical computations. • Author(s) : • Natanael Karjanto (Sungkyunkwan University) ## [00327] COBIT As An Information Governance Framework • Abstract : This contributed talk aimed to present the information governance frameworks , In order to answer to the problem of the study, first we will present the information governance definition and importance, the information governance frameworks, then we’ll show the COBIT as one of the important frameworks, its benefits and its principles, finally the study concluded that COBIT is a framework that ensure an optimum information technology. • Author(s) : • Amina Feddaoui (Chadli Bendjedid university el tarf) ## [00328] Schrödinger map and Multifractality • Abstract : In this talk, we will explore the richness of the Schrödinger map equation by discussing some recent results on its evolution in both hyperbolic and Euclidean geometrical settings. In the latter case, the equivalent form of the equation describes the motion of a vortex filament, e.g., smoke rings, tornadoes, etc. With numerical, theoretical techniques, we will show that when the filament curve initially has corners, its evolution and the trajectory of its corners exhibit multifractality. • Author(s) : • Sandeep Kumar (CUNEF University) • Luis Vega (Basque Center for Applied Mathematics) • Francisco de la Hoz (The University of the Basque Country) ## [00329] A-posteriori error estimates for parabolic optimal control problems with controls acting on lower dimensional manifolds • Abstract : In this talk, we shall present a-posteriori error estimates for the fully discrete finite element approximation to the optimal control problem governed by parabolic partial differential equations where the control is acting on lower dimensional manifolds. We use piecewise linear and continuous finite elements for the approximations of state and adjoint variables whereas piecewise constant functions are employed to approximate the control variable. Moreover, the time derivative is approximated by using the backward Euler scheme. We derive a-posteriori error estimates for the various dimensions of the manifold. Numerical results reveal the effectiveness of the error estimators. • Author(s) : • Rajen Kumar Sinha (Indian Institute of Technology Guwahati) • Ram Manohar (Indian Institute of Technology Kanpur) ## [00335] Fractional Relaxation-Oscillation and Fractional Biological Population Equations: Applications of the Elzaki Decomposition Method • Abstract : In various suitable habitat scenarios, the Elzaki decomposition method is used to handle the fractional order relaxation and damped oscillation equation along with the time-fractional spatial diffusion biological population model. According to the graphs for the found solutions, fractional relaxation is a super-slow phenomenon due to its protracted descent, and fractional damped oscillation is an intermediate process that explains damped oscillation dynamic systems generated by some attenuated oscillations. The biological population model of time-fractional spatial diffusion portrays a rapid increase in population density in an ecosystem migrating from an unfavourable zone to a good habitat. • Author(s) : • Daya Lal Suthar (Wollo University) ## [00337] Extending Matrix-less Methods for Eigenvalues and Eigenvectors • Abstract : Toeplitz and Toeplitz-like matrices arise in many fields; of special interest are the discretisations of differential equations. Matrix-less methods exploit the fact that we can view these Toeplitz(-like) matrices as part of a sequence of matrices and that the eigenvalues in the sequence behave as samplings of a function, called the symbol. We will discuss recent developments to handle the case of variable coefficient matrices, the approximation of eigenvectors, and Toeplitz(-like) matrices with non-monotone symbols. • Author(s) : • David Meadon (Uppsala University) ## [00338] Classifying datasets with imputed missing values: does imputation quality matter? • Abstract : Classifying samples in incomplete datasets is a common non-trivial task. Missing data is commonly observed in real-world datasets. Missing values are typically imputed, followed by classification of the now complete samples. Often, the focus is to optimise the downstream classification performance. In this talk, we highlight the serious consequences of using poorly imputed data, demonstrate how the common quality measures for measuring imputation quality are flawed and introduce an improved class of imputation quality measures. • Author(s) : • Michael Roberts (University of Cambridge) ## [00343] A wavelet-based methodology to compare the impact of COVID-19 pandemic versus Russia-Ukraine conflict on crude oil sector and its interconnectedness with other energy and non-energy markets • Abstract : We address the important question of whether the COVID-19 pandemic and the Russia-Ukraine conflict have the same economic impact. Our study focuses on a comparative analysis of the crude oil markets with other energy and non-energy markets in terms of market efficiency and interconnectedness during the two crises. We deploy a novel methodology that utilizes the wavelet decomposition of time series, which facilitates capturing of information in both time and frequency domain, to evaluate the market efficiency of these markets. Subsequently, the wavelet coherence, along with a vector-valued GARCH model applied to the wavelet details, helps us in quantifying the interconnectedness and spillover dynamics between different markets. Our analysis suggests that the energy sector is impacted more than the non-energy sector in times of both crises, however, the nature of the impact is different for different energy markets. Brent crude oil suffers more during the Russia-Ukraine war than during the pandemic, while natural gas suffers more during the pandemic than the war and WTI suffers equally during both crises. We also report increased interconnectedness between markets during the pandemic and the war, however, the degree of comovement varies from one time scale to another. This information would help investors to choose a safe market and plan their portfolio accordingly in a crisis period. • Author(s) : • Archi Roy (Doctoral student (Indian Institute of Science, Education and Research, Pune)) • Anchal Soni (Doctoral student (Indian Institute of Management, Banglaore)) • Soudeep Deb (Assistant professor (Indian Institute of Management, Bangalore)) ## [00344] Forced convection from an isothermal square cylinder in shear flow • Abstract : Forced convection from an uniformly heated square cylinder placed in linear shear flow of constant properties fluid is numerically investigated at Reynolds number, Re=100, shear rate, K=0.0-0.2 and Prandtl number, Pr=0.5. The two-dimensional mathematical equations of flow motion and energy are solved using a higher order compact (HOC) finite difference scheme on Cartesian grids. The effect of K is investigated on flow and thermal fields in terms of isotherm patterns, Nusselt number distributions etc. The resulting vortex shedding phenomena behind the cylinder is detected and thermal field is determined. • Author(s) : • Atendra Kumar (National Institute of Technology Srinagar, India) ## [00348] Design of control for IT2 fuzzy stochastic systems with multi disturbances • Abstract : Anti disturbance control design problem is proposed for a class of interval type-2 fuzzy stochastic systems subject to uncertainty and multiple disturbances. A fuzzy exogenous system considers a new fuzzy disturbance observer to precisely evoke the properties of interval type 2 fuzzy stochastic models with multiple disturbances. In order to ensure the stochastic stability of the closed-loop fuzzy system, a new sufficient condition is constructed using the method of linear matrix inequalities by integrating the$textit{Ito}$operator and choosing the appropriate Lyapunov-Krasovskii functional candidate dissipativity performance index. Finally, the provided theory is demonstrated with the example. • Author(s) : • Aarthi S (Research Scholar) • Marshal Anthoni S (Anna University Regional Campus Coimbatore) ## [00360] Computational Analysis of Soot Production in an Internal Combustion (IC) Engine • Abstract : A numerical technique for decreasing soot formation in emitted runoff streams is proposed. It helps remove soot particles in IC combustion engine exhaust streams continuously. The given model assists in decreasing pollutant formation, which contains selective reducing agents. It is reduced selectively in high-grade fuels such as diesel surrounding to form carbon-rich composition products. Results are obtained by implementing the Moss-Brooks model. The results of the proposed model showed good agreement with the literature data. • Author(s) : • Muhammad Ahsan (National University of Sciences & Technology, Islamabad) • Muhammad Farhan Rafique (National University of Sciences & Technology, Islamabad, Pakistan) ## [00362] Nonlinear biphasic mixture model: existence and uniqueness results • Abstract : The purpose of this study is to develop a multiphase mathematical model based on interstitial hydrodynamics and tissue deformation mechanics within an in vitro solid tumor. We use classical mixture theory to derive the balance equations for mass and momentum. The study makes a significant contribution by treating hydraulic resistivity as anisotropic and heterogeneous, which leads to strongly coupled and nonlinear PDEs. We further establish existence and uniqueness result in a weak sense. • Author(s) : • Meraj Alam (Mahindra University, Hyderabad) • Adrian Muntean (University of Karlstad) • Raja Sekhar G P (Indian Institute of Technology Kharagpur India) ## [00363] Neighborhood effects, college education, and social mobility • Abstract : This study models the impact of environmental factors on upward social mobility, where the educational environment is measured by the proportion of college-educated individuals, and social mobility is measured by a change in the proportion of people in different income classes. The dynamics of the educational environment are modeled using a modified version of the invasion/extinction ecological model of Richard Levins. The educational environment influences the educational choices of poor people, becoming effective only after a threshold point is reached. The rate of growth in influence is modeled using a monotonically increasing saturation function, which includes a delay parameter referred to as handling time, that measures the speed of influence. Our simulations indicate that poor people choose to become educated at a rate that primarily depends on the density of the local environment. • Author(s) : • Cesar Montalvo (University of Virginia) ## [00365] Advancing Computerized Tomography: Deep-Learning based Regularization in Diffuse Optical Tomography • Abstract : X-rays Computed Tomography is a main pillar of medical imaging which at present is experiencing a strong innovation phase. While new tomographic systems try to minimize X-rays exposure, non-trivial challenges exist, mainly increased noise levels and the need for dealing with low and high contrast regions. In this talk we will refer about our research on new algorithms able to efficiently deal with this trade–off, with specific reference to Diffuse Optical Tomography. • Author(s) : • Paola Causin (University of Milano ) • Andrea Aspri (University of Milano ) ## [00374] Recent numerical and theoretical advances in the study of matrix sequences • Abstract : We present recent developments in the study of the spectral behaviour of structured matrix sequences. For example, all PDE discretizations, such as FEM, FDM, and DGM, generate these types of sequences. We will mainly discuss matrix-less methods for non-Hermitian sequences, where the generating symbol does not describe the eigenvalue distribution; we can now numerically approximate, with high accuracy, the spectral symbol describing the eigenvalue distribution. Standard double precision eigenvalue solvers typically fail for these matrices. • Author(s) : • Sven-Erik Ekström (Uppsala University) ## [00375] Modelling Typhoid Fever Transmission: Optimal control and Cost-Effectiveness Analysis • Abstract : Typhoid fever has been a public health challenge globally, most especially in the developing countries where sanitation and personal hygiene are not taken serious coupled with non-availability of safe-drinking water. In this paper, a deterministic mathematical model of direct and indirect mode of transmission of Typhoid fever dynamics is formulated to investigate the influence of limited clinical efficacy of antibiotics administer to patients suffering from the disease with optimal control and cost-effectiveness analysis. Typhoid fever has been a public health challenge globally, most especially in the developing countries where sanitation and personal hygiene are not taken serious coupled with non-availability of safe-drinking water. In this paper, a deterministic mathematical model of direct and indirect mode of transmission of Typhoid fever dynamics is formulated to investigate the influence of clinical efficacy of antibiotics administer to patients suffering from the disease. The basic reproduction number is analytically computed, and existence and local stability condition of disease-free equilibrium is investigated. Subsequently, the global sensitivity analysis of the model parameters is computed. The optimal control and cost-effectiveness analysis were also computed. Our results suggest that hygiene practice and awareness campaign, and disinfection or sterilization or bacteria decay control is the most cost-effective in eliminating the disease from the population and from preventing the susceptible individuals from contracting the bacteria disease. • Author(s) : • kazeem Austin TIJANI (Federal University of Agriculture(J. S Tarka university), Makurdi) • Chinwendu Emilian MADUBUEZE (Federal university of Agriculture Makurdi Nigeria ) • Iortyer Reuben GWERYINA (Federal university of Agriculture(J.S. Tarka University), Makurdi)) ## [00376] Adaptive Optimal Market-Making Strategies with Inventory Liquidation Costs • Abstract : An optimal market-making strategy for a high-frequency market maker under a discrete-time Limit Order Book model is presented. Interestingly, the optimal market-making strategy adapts to the past arrivals of market orders, making it adapted to previous market information. Admissibility and optimality of the optimal strategy are also proved. Finally, we test our assumptions empirically and compare the optimal strategy to one used under a non-adaptive framework where only the “average” past information is considered. • Author(s) : • Jonathan Allan Chávez Casillas (University of Rhode Island) • José Enrique Figueroa López (Washington University in St. Louis) • Chuyi Yu (Washington University in St. Louis) • Yi Zhang (University of Illinois Urbana-Champaign) ## [00380] Mathematical approach for understanding the impact of rainfall on cocoa production. • Abstract : Cocoa is a delicate crop which is of great economic importance in Africa and is predominantly grown for export. However, there have been declines in production and many factors have been identified to be responsible. A significant factor is the effect of climate variation as this can result in a low farm-level yield. To understand the contribution of the variability, we construct and analyse a time-delayed model for the effect of rainfall on cocoa production. • Author(s) : • Oluwatosin Leke Babasola (University of Bath) • Oluwatosin Babasola (University of Bath ) ## [00383] A kernel-based method for Schrödinger bridges • Abstract : We report a kernel-based approach to Schrödinger’s bridge problems, where the terminal time distribution constraint is described by a kernel-based metric on the space of probability measures. The resulting problem is reduced to a weak form of Mckean-Vlasov type stochastic control problems that allows an explicit solution. • Author(s) : • Yumiharu Nakano (Tokyo Institute of Technology) ## [00386] Optimizing the Location of Exit Doors for a Safer Crowd Evacuation • Abstract : This work deals with the optimal design for the location of exit doors at meeting places to guarantee an efficient emergency evacuation in any type of events. The problem is set as an optimal control problem of nonlinear partial differential equations. We provide a full numerical algorithm for solving the problem: a finite element technique for the discretization and a gradient-free procedure for the optimization, and show several numerical results for a realistic case. • Author(s) : • Lino J. Alvarez-Vazquez (University of Vigo) • Nestor Garcia-Chan (University of Guadalajara) • Aurea Martinez (University of Vigo) • Carmen Rodriguez (University of Santiago de Compostela) • Miguel E. Vazquez-Mendez (University of Santiago de Compostela) ## [00388] Numerical solution of distributed order time-fractional diffusion equations. • Abstract : In this work, we solved distributed order time-fractional diffusion equation with the help of a wavelet approximation scheme and the Gauss quadrature rule. First, we construct wavelet-based operational matrices of distributed order fractional derivatives and integer order derivatives. After the construction of the operational matrix apply the tau method and convert the original mathematical problem into a system of linear algebraic equations and solve the equations for finding the approximate solutions. For method validation, we have provided some test examples, convergence analysis, and error estimation, and verify with the existing scheme with one of the existing schemes. • Author(s) : • Yashveer Kumar (Indian Institute of Technology(BHU), Varanasi, India.) • Vineet Kumar Singh (Department of Mathematical Sciences, Indian Institute of Technology (Banaras Hindu University), Varanasi, India.) ## [00393] Mathematical Modelling of Bilayered Cathodes for Lithium-Ion Batteries • Abstract : Bilayered cathodes are promising candidates to improve lithium-ion battery performance by optimising the electrode design. In this work, lithium iron phosphate and nickel manganese cobalt chemistries are connected in two discrete layers within a cathode and improves the C-rate performance above 2C compared to uniform cells. To inform the design process we create mathematical model to accommodate multilayers. The model is solved numerically, validated against data and explains how each layer acts. • Author(s) : • Eloise Tredenick (University of Oxford) ## [00394] Numerical methods for option pricing: need and challenges • Abstract : The stability analysis of numerical methods is often challenging. In this talk, compact schemes are considered for the variable coefficient PDEs arising in option pricing. A sufficient condition for stability of the schemes has been derived using novel difference equation based approach. The condition number of amplification matrix is also analyzed, and an estimate for the same is derived. An example is provided using MATLAB to support the assumption taken to assure stability. • Author(s) : • KULDIP SINGH PATEL (Indian Institute of Technology Patna) ## [00395] What can be the potential risk of Mpox outbreak in the endemic country?: Non-Markovian stochastic modeling study • Abstract : In 2022, the Mpox outbreak shocked the world, with a completely different pattern and scale compared to past incidences in non-endemic countries, more than 80,000 cases have been confirmed. In this talk, we present how we analyzed the risk of local spread using a non-Markovian stochastic model. Multiple factors, which are suspected to affect the early stage of the outbreak significantly, the contact tracing, self-report-related behavior of the primary case, and secondary infectees were examined. • Author(s) : • Youngsuk Ko (Department of mathematics, Konkuk university) • Victoria May Mendoza (Institute of Mathematics, University of the Philippines Diliman) • Renier Mendoza (Institute of Mathematics, University of the Philippines Diliman) • Yubin Seo (Hallym University College of Medicine) • Jacob Lee (Hallym University College of Medicine) • Eunok Jung (Department of mathematics, Konkuk University) ## [00396] A Stochastic Approach for the Computation of Large-Scale Matrix Functions • Abstract : Although many scientific problems can be described in term of functions over matrices, their high computational cost and the lack of parallel and scalable numerical tools propel scientists to seek alternative solutions. In this talk, we will introduce a Monte Carlo method that is capable of computing matrix functions for large-scale datasets and in particular present how it can be used to solve time-fractional differential equations. • Author(s) : • Nicolas Guidotti (INESC-ID, Instituto Superior Técnico, Lisboa) ## [00397] A continuum model for the bulldozing of an immersed granular material in a confined geometry • Abstract : We present a reduced-order continuum model for the bulldozing of an immersed, sedimented granular material by a rigid piston in a fluid filled gap between two parallel plates. In our model, the granular pile and the overlying fluid layer evolves as coupled thin-films. We solve our model numerically for a variety of different scenarios to develop insight into the interactions between wall friction, internal viscous-like stresses, and fluid flow both above and through the pile. • Author(s) : • Liam Morrow (University of Oxford) • Chris MacMinn (University of Oxford) ## [00398] Approximation of Abel type nonlinear fractional integral equations by the use of orthogonal polynomials • Abstract : The nonlinear fractional integral equations of the type Abel are presented in this study with general framework for determining the approximate solution. As basis functions, this method makes use of Lagrangian interpolating polynomials (LIPs) and shifting Legendre polynomials (SLPs). The original problem is converted into a system of algebraic nonlinear equations using operational matrices of SLPs and LIPs, which are first developed. We investigated at the provided techniques’ stability and convergence under several significant conditions. • Author(s) : • Aman Singh (Department of Mathematical Sciences, Indian Institute of Technology (Banaras Hindu University)) • Vineet Kumar Singh (Department of Mathematical Sciences, Indian Institute of Technology (Banaras Hindu University)) ## [00403] Exact Penalization at Stationary Points of Sparse Constrained Problem • Abstract : Nonconvex sparse optimization problems with the trimmed l1 norm or truncated nuclear norm, which is a penalty function of cardinality or rank constraint, have been actively studied. A unified framework that includes all the existing trimmed l1-penalized problems is introduced. We show that under mild conditions, any d-stationary point of the penalized problem satisfies the corresponding constraint. Our result is superior to almost all existing results, especially from the viewpoint of practice. • Author(s) : • Shotaro Yagishita (Chuo University) • Shotaro Yagishita (Chuo University) • Jun-ya Gotoh (Chuo University) ## [00408] Reducing Complexity of a Population Balance Model for Synthesis of Composite Polymer Particles • Abstract : An accurate prediction of the formation of polymer particles is vital for synthesis of high quality materials, but still not feasible due to its complexity. We present a Population Balance Equations model as a tool targeting the task. Aimed to enhance model performance, we derive a quantitative criterion for locating regions of “slow” aggregation among particles. Within such a regime, the aggregation terms can be neglected and computational efficiency improves by several orders of magnitude. • Author(s) : • Simone Rusconi (CUNEF Universidad) • Christina Schenk (IMDEA Materials Institute) • Arghir Zarnescu (Basque Center for Applied Mathematics) • Elena Akhmatskaya (Basque Center for Applied Mathematics) ## [00414] Asymptotically Modelling Plastic Deformation during Cold Rolling of Sheet Metal • Abstract : Cold rolling is a metal forming process where strip of metal passes between two rollers and comes out thinner. We present a multiple-scale asymptotic model of cold rolling. Assuming rigid perfectly-plastic material and large rolls, we explain how to rederive and go beyond existing theories. Results agree well with FE simulations, and suggest the origin of residual stress in the resulting strip. This modelling approach has potential applications in many metal forming processes. • Author(s) : • Mozhdeh Erfanian (School of Mathematics, University of Warwick) • Ed Brambley (School of Mathematics, University of Warwick) • Francis Flanagan (Department of Mathematics and Statistics, University of Limerick) • Doireann O’Kiely (Department of Mathematics and Statistics, University of Limerick) ## [00415] Finite time horizon mixed control of vibrational systems • Abstract : We consider a vibrational system control problem over a finite time horizon. The performance measure of the system is taken to be$p$-mixed$H_2$norm which generalizes the standard$H_2$norm. Our novel procedure efficiently takes into account the structure of the vibrational system. An objective function is represented in terms of integrals which are solved using adaptive quadrature rules. We illustrate our approach by numerical examples concerning an$n$-mass oscillator with one damper. • Author(s) : • Zoran Tomljanovic (University of Osijek, Department of Mathematics) • Ivica Nakic (epartment of Mathematics, University of Zagreb) • Marinela Pilj Vidakovic (University of Osijek, Department of Mathematics) ## [00422] On Some fractional integrodifferential equations using$psi$Hilfer fractional operator • Abstract : In this talk we present the study some properties of fractional integrodifferential equations. We have studied the equations using$psi$fractional derivative and$psi$Riemann-Liouville integral operator. The existence and uniqueness solution is studied. Schaefer’s fixed point theorem and Banach contraction principle is used for obtaining the results. • Author(s) : • Deepak B Pachpatte (Dr. Babasaheb Ambedkar Marathwada University) ## [00423] Understanding elastic-plastic stress distributions during cold rolling of sheet metal • Abstract : In cold rolling, a metal sheet is passed between two rotating rollers which reduce the thickness of the sheet. In this talk, we present our new elastic-plastic mathematical model for describing the stress distribution during cold rolling, which is an extension of some existing asymptotic models, where elastic effects are neglected. At leading order, our model returns the popular slab-type analysis, but at higher orders, through-thickness variations can be predicted accurately. • Author(s) : • Francis Flanagan (Department of Mathematics and Statistics, University of Limerick) • Doireann O’Kiely (Department of Mathematics and Statistics, University of Limerick) • Alison O’Connor (School of Engineering, Bernal Institute, University of Limerick) • Mozhdeh Erfanian (School of Mathematics, University of Warwick) • Ed Brambley (School of Mathematics, University of Warwick) ## [00424] A Hydrodynamic Model of Active Polar liquid crystals with Variable Polarization Magnitudes • Abstract : We present a hydrodynamic model of active polar liquid crystals with variable polarization magnitudes. We consider sheared active polar liquid crystals and study dynamics of the polar order and shear rheology of the system. Under shear, we show that shear may increase or decrease the polarization magnitudes and the polar order is either inclined to the flow at a fixed Leslie angle or rotates continuously, tracing an ellipse. We derive the apparent viscosity formula showing a regime of negative apparent viscosity for pushers. Our results echo previous results from numerical simulations and experiments. • Author(s) : • Zhenlu Cui (Fayetteville State University) ## [00427] Numerical Analysis of Finite dimensional approximations in Finite Temperature DFT • Abstract : We study the nonlinear eigenvalue problems derived from finite temperature density functional theory. We introduce the density matrix as the basic variable to describe the problem. Then with some mild assumptions, we justify the convergence of the numerical approximations and give a priori error estimate base on the tool of operator analysis. We also present some numerical experiments to support the theory. • Author(s) : • Ge Xu (Beijing Normal University) ## [00429] Mathematical Theory to Maximize Enzymatic Activity Under Thermodynamic Constraints • Abstract : Understanding the relationship between enzymatic activity is critical not only for bioengineering, but also for rationalizing enzyme optimization in nature. Here, we applied the Arrhenius and Bronsted-Evans-Polanyi equations to the Michaelis-Menten model of enzyme catalysis, and show that enzymatic activity is maximized when the binding affinity between the enzyme and the substrate (Km) is equal to the substrate concentration. • Author(s) : • Hideshi Ooka (RIKEN) • Yoko Chiba (RIKEN) • Ryuhei Nakamura (RIKEN) ## [00430] Nearest singular pencil via Riemannian optimization • Abstract : The problem of finding the nearest complex$($real$)$singular pencil can be cast as a minimization problem over the manifold$U(n) times U(n)left( O(n) times O(n) right)$via the generalized Schur form. This novel perspective yields a competitive numerical method by pairing it with an algorithm capable of doing optimization on a Riemannian manifold. • Author(s) : • Lauri Nyman (Aalto University) ## [00431] Modeling Impact of Temperature Changes on Onchocerciasis Disease with Control Strategies • Abstract : This study develops temperature autonomous and temperature non-autonomous compartmental models to examine temperature effect on Onchocerciasis transmission dynamics. We conduct analyses including computation of basic reproduction number, existence of equilibrium, stability of equilibrium states and sensitivity to detect crucial parameters of programs targeted to eradicate the disease. We formulate optimal control model to adopt the cost effectiveness and best control options and perform numerical simulations to evaluate the effect of alternative and complementary control strategies. • Author(s) : • Godwin Nwachukwu Nkem (Department of Mathematical Sciences and Computing, Walter Sisulu University, Mthatha, Eastern Cape, South Africa) ## [00433] Markov Decision Processes under Model Uncertainty • Abstract : We introduce a general framework for Markov decision problems under model uncertainty in a discrete-time infinite horizon setting. By providing a dynamic programming principle we obtain a local-to-global paradigm, namely solving a local, i.e., a one time-step robust optimization problem leads to an optimizer of the global (i.e. infinite time-steps) robust stochastic optimal control problem, as well as to a corresponding worst-case measure. Moreover, we apply this framework to portfolio optimization involving data of the S&P 500. We present two different types of ambiguity sets; one is fully data-driven given by a Wasserstein-ball around the empirical measure, the second one is described by a parametric set of multivariate normal distributions, where the corresponding uncertainty sets of the parameters are estimated from the data. It turns out that in scenarios where the market is volatile or bearish, the optimal portfolio strategies from the corresponding robust optimization problem outperforms the ones without model uncertainty, showcasing the importance of taking model uncertainty into account. • Author(s) : • Julian Sester (National University of Singapore) • Ariel Neufeld (Nanyang Technological University) • Mario Šikić (University of Zurch) ## [00434] Three pieces Riemann problem for$2$-D full Euler system in the Noble-Abel gas • Abstract : We present Riemann problem governed by$2$-D full Euler system in the Noble-Abel gas. Riemann data, consisting three constants, are distributed in three distinct regions with an assumption that two adjoining regions can be connected by only one planar elementary wave. We present criteria for existence of different configurations of elementary waves for isentropic, as well as full, Euler system. We also discuss the effect of the Noble-Abel gas and the angle of regions on elementary waves and corresponding stream curves. Note: The present article has been published on 17 May 2022 in the journal ”Mathematical Methods in the Applied Sciences”/ Volume 45, Issue 16 with DOI:10.1002/mma.8377. • Author(s) : • Harsita Srivastava (Dr. B. R. Ambedkar National Institute of Technology Jalandhar, Punjab) • M. Zafar (Dr. B. R. Ambedkar National Institute of Technology Jalandhar, Punjab) ## [00439] Successive Approximations for Fractional BVPs with Non-local Boundary Conditions • Abstract : In joint work with Dr. Kateryna Marynets, we adapt a numerical-analytic technique for constructing approximations to a system of nonlinear fractional differential equations with integral boundary conditions. The boundary conditions are parametrized, and the parameter values, which govern the solution’s behavior, are calculated numerically. The convergence of the method is improved using a dichotomy-type approach, and its applicability is extended to a wider class of problems. Our results are confirmed by a model example. • Author(s) : • Dona Pantova (TU Delft) • Kateryna Marynets (TU Delft) ## [00440] SIMULATION OF SHALLOW WATER EQUATIONS WITH DEPTH PERTURBATIONS AND WITH AND WHITHOUT THE CORIOLIS EFFECT • Abstract : Shallow water equations are a system of partial differential equations that describe the superficial layer of a fluid with hydrostatic equilibrium derived from the Navier-Stokes equations which are used to describe fluid movements based on characteristics such as density, etc. We perform simulations of the evolution of water surface with various bottom variations, with and without the Coriolis effect using finite differences to analyze and understand how these variations affect the fluid dynamics. • Author(s) : • Daniel Francisco Sanabria Bernal (Universidad Militar Nueva Granada) ## [00442] On the dynamical properties of a max-plus model identified with the Lozi map • Abstract : We focus on a max-plus discretized model that is identified with the Lozi map in this talk. The max-plus model can be derived from the generalized Sel’kov model composed of non-linear differential equations via tropical discretization and ultradiscretization. Based on the Poincare mapping method and the estimation of Lyapunov exponents, the dynamical properties of the max-plus model and its transformation from the generalized Sel’kov model are discussed. • Author(s) : • Shousuke Ohmori (Waseda University) • Yoshihiro Yamazaki (Waseda University) ## [00446] Beyond Empirical Risk Minimization: Minimax Risk Classifiers • Abstract : The empirical risk minimization (ERM) approach for supervised learning has been the workhorse of machine learning. However, ERM methods strongly rely on the specific training samples available and cannot easily address scenarios affected by distribution shifts and corrupted samples. This talk presents a learning framework based on the generalized maximum entropy principle that leads to minimax risk classifiers (MRCs). MRC learning is based on expectation estimates and does not strongly rely on specific training samples. • Author(s) : • Santiago Mazuelas (Basque Center for Applied Mathematics (BCAM)) ## [00450] SOSMAR: a Software for Modelling Oil Spills in the Sea • Abstract : We present a Compositional Eulerian model to forecast the evolution of oil spills in the sea. The model allows studying the fate of not only the oil concentration but also of each component. Therefore, the problem is formulated as a consevvation equation for each component, plus an equation to estimate the age of the oil, which allows us to assess weathering processes and the associated changes in oil properties. • Author(s) : • Benjamin Ivorra (Universidad Complutense de Madrid) • Angel M. Ramos (Universidad Complutense de Madrid) • Susana Gomez (Universidad Nacional A. de México) • Jesús Carrera (IDAEA) ## [00451] Transmission problems for composite layered elastic structures containing interfacial cracks • Abstract : We investigate mixed transmission problems of the generalized thermo-electro-magneto elasticity theory for complex elastic multi-layered structures containing interfacial cracks. We apply the potential method and the theory of pseudodifferential equations and analyze smoothness properties and asymptomatic behaviour of solutions near the edges of cracks and near the curves where different type boundary conditions collide. We describe the stress singularity exponents explicitly. • Author(s) : • David Natroshvili (Georgian Technical University) ## [00456] Network representations of attractors for surrogates generation and change detection • Abstract : Attractors arising from delay embedded time-series can characterise system dynamics. However, extracting useful representations is challenging for systems with high-dimensional or complex structure. We propose a data-driven method to represent attractors as networks, where dynamics are encoded as node transition probabilities. The usefulness of this representation is demonstrated in two tasks: (1) surrogate data generation; and (2) change point detection. These methods are applied to chaotic time-series, and experimental ECG data for heart attack detection. • Author(s) : • Eugene Tan (The University of Western Australia) • Shannon Dee Algar (The University of Western Australia) • Debora Correa (The University of Western Australia) • Thomas Stemler (The University of Western Australia) • Michael Small (The University of Western Australia) ## [00457] On limit cycles of discrete dynamical systems with positivity • Abstract : We focus on limit cycles of discretized Sel’kov model derived from continuous Sel’kov model via tropical discretization. The discretized model possesses a parameter for time step. We numerically found, by varying the parameter, that density profile of phase in the limit cycles transits between continuous and ultradiscrete, and that the ultradiscrete state corresponds to a max-plus dynamical system. In this talk, we discuss these findings from the viewpoint of nonlinear dynamical systems. • Author(s) : • Yoshihiro Yamazaki (Waseda University) • Shousuke Ohmori (Waseda University) ## [00459] Tropical linear regression and mean payoff games: or, how to measure the distance to equilibria • Abstract : We study a tropical linear regression problem consisting in finding a best approximation of a set of points by a tropical hyperplane. We establish a strong duality theorem, showing that the value of this problem coincides with the maximal radius of a Hilbert’s ball included in a tropical polyhedron. We show that this problem is polynomial-time equivalent to mean payoff games. We illustrate our results by solving an inverse problem from auction theory. • Author(s) : • Omar Saadi • Marianne Akian (INRIA and CMAP, École polytechnique) • Stéphane Gaubert (INRIA and CMAP, École polytechnique) • Yang Qi (INRIA and CMAP, École polytechnique) ## [00460] A Multigrid Method for Many-Electron Schrodinger Equations with ACE • Abstract : We parameterize the many-electron wave functions by atomic cluster expansion$($ACE$)$approach and calculate ground-state energies and electron densities of some molecule systems within the variational Monte Carlo framework. Compared with the neural-network-based representations, the novelty of our method lies in$($i$)$a convenient and accurate linear polynomial expansion;$($ii$)$a hierarchical structure that applies naturally to a multigrid variation; and$($iii$)$possibly revealing the correlation of the system by increasing the body-order. • Author(s) : • Dexuan Zhou (Beijing Normal University) ## [00461] hp/Spectral Element Methods for Elliptic Boundary Layer Problems • Abstract : Elliptic boundary layer problems arise in many applications including fluid dynamics, gas dynamics, plate and shell problems in structural mechanics, modeling of semiconductor devices and many more. We propose a least-squares hp-spectral element method for 1D elliptic boundary layer problems. The regularity estimates are stated and the main stability theorem is obtained using non-conforming spectral element functions. For the hp-version we use a 3 element mesh which allows us to resolve the boundary layers completely by placing very thin needle like elements near the boundary layer and a coarse mesh away from the layer. Numerical scheme and error estimates are obtained which are robust i.e. independent of the boundary layer parameter and decay exponentially in terms of the degree of the approximating polynomials. Numerical results confirm convergence results with various combinations of the boundary layer thickness, degrees of the approximating polynomials, and layers in the mesh. • Author(s) : • Akhlaq Husain (BML Munjal University Gurgaon) ## [00463] A kinetic model of crowd evacuation dynamics coupled with infectious disease contagion • Abstract : We propose a kinetic theory model coupling crowd evacuation and disease spreading. Movement of individuals is modeled by a description of interactions among individuals. Interactions among healthy and infectious individuals may generate disease spreading if exposure time is long enough. Immunization of the population and awareness to contagion is also considered. The model is qualitatively studied and different scenarios related to gathering formation within indoor venues under the spread of an infectious disease are explored. • Author(s) : • Juan Pablo Agnelli (CIEM CONICET & FaMAF Universidad Nacional de Córdoba) • Bruno Buffa (FaMAF Universidad Nacional de Córdoba) • Damian Alejandro Knopoff (CONICET, Argentina & Intelligent Biodata SL, Spain) • German Torres (IMIT CONICET & FaCENA UNNE) ## [00464] Predicting the role of poroelastic coatings for cell therapies via an asymptotic approach • Abstract : Cell therapies are a promising alternative for treating liver disease. Encapsulation modulates the mechanical cues inflicted on a cell, which can increase engraftment at the injury site. We model an individual, hydrogel-coated stem cell translating axially along a fluid-filled channel due to a Stokes flow, obtaining semi-analytic solutions in the limit of a stiff coating. We conduct a parametric study to predict the role of coatings and discuss implications for biological cells. • Author(s) : • Simon Mark Finney (University of Oxford) • Sarah Louise Waters (University of Oxford) • Andreas Muench (University of Oxford) • Matthew Gregory Hennessy (University of Bristol) ## [00466] One-Way propagation methods for Navier-Stokes equations • Abstract : The One-Way approach is an effective tool to compute wave propagation in a privileged direction. Towne & Colonius developed a purely numerical One-Way method based on a non-reflective boundary condition applied to hyperbolic equations and slowly varying flows. We propose a new factorization of the propagation operator for Navier-Stokes equations, which allows to sort modes according to their direction and accessing to a refraction/reflection operator. One-Way models with broader validity can then be derived. • Author(s) : • Maëlys RUELLO (ONERA The French Aerospace Lab) • Sébastien PERNET (ONERA The French Aerospace Lab) • Jean-Philippe BRAZIER (ONERA The French Aerospace Lab) ## [00469] Mathematical and Exploratory Data Analysis on Blood Transfusion Transmitted Malaria • Abstract : Malaria is a disease spread by an infected mosquito or through transfusion of plasmodium-infected blood to susceptible individuals. Many interventions have been implemented to control malaria transmission, including blood screening, Long-Lasting Insecticide Bed Nets (LLIN), treatment with an anti-malaria drug, spraying chemicals/pesticides on mosquito breeding sites, and indoor residual spray, among others. As a result, a deterministic model is developed to study the impact of various malaria control and mitigation strategies against malaria transmission. • Author(s) : • Michael Olaniyi Adeniyi (Lagos State University of Science and Technology) • Raphael Oluwaseun Aderele (Lagos State University of Science and Technology ) • Olajumoke Y Oludoun (Department of Mathematics, Bowen University, Iwo, Nigeria) • Matthew Iwada Ekum (Lagos State University of Science and Technology) • Segun Isaac Oke (Department of Mathematics, Ohio University, Athens, OH 45701-2979, USA) ## [00470] Mathematical and Exploratory Data Analysis on Blood Transfusion Transmitted Malaria • Abstract : Malaria is a disease spread by an infected mosquito or through transfusion of plasmodium-infected blood to susceptible individuals. Many interventions have been implemented to control malaria transmission, including blood screening, Long-Lasting Insecticide Bed Nets (LLIN), treatment with an anti-malaria drug, spraying chemicals/pesticides on mosquito breeding sites, and indoor residual spray, among others. As a result, a deterministic model is developed to study the impact of various malaria control and mitigation strategies against malaria transmission. • Author(s) : • Michael Olaniyi Adeniyi (Lagos State University of Science and Technology) • Raphael Oluwaseun Aderele (Lagos State University of Science and Technology ) • Olajumoke Y Oludoun (Department of Mathematics, Bowen University, Iwo, Nigeria) • Matthew Iwada Ekum (Lagos State University of Science and Technology) • Segun Isaac Oke (Department of Mathematics, Ohio University, Athens, OH 45701-2979, USA) ## [00472] Modeling with instantaneous changes by Caputo type fractional differential equations • Abstract : In this talk some nonlinear differential equations with Caputo type fractional derivatives and impulses will be presented and discussed. Instantaneous impulses as well as non-instantaneous impulses will be considered and compared. The integral presentations of the solutions will be presented. Some stability properties of the given equations will be studied. Sufficient conditions will be given. Appropriate Lyapunov like functions will be applied. Several examples will illustrate the problems. • Author(s) : • Snezhana Hristova (Plovdiv University) ## [00474] Discrete solitons of discrete Schrodinger equations with general nonlinearities • Abstract : The discrete nonlinear Schrodinger$($DNLS$)$equations are very important nonlinear lattice models in the nonlinear science, ranging from molecular biology to condensed matter physics. One central problem for the DNLS equations is the existence of discrete solitons. We will report some recent progress on the existence and multiplicity of discrete solitons for a class of DNLS equations with general nonlinearities. • Author(s) : • Genghong Lin (Guangzhou University) ## [00476] Hierarchical Sampling Techniques and Goal-Oriented Adaptive Finite Element for Elliptic PDE with Lognormal Coefficients • Abstract : We propose our Adaptive Multilevel Monte Carlo (AMLMC) method to solve an elliptic partial differential equation with lognormal random input data where the PDE model has geometry-induced singularities. This work combines (MLMC) and the dual-weighted-residual goal-oriented adaptive finite element. Specifically, for a given input coefficient realization and an accuracy level, the (AMLMC) constructs its approximate sample as the ones using the first mesh in the sequence of pre-generated, non-uniform meshes satisfying the sample-dependent bias constraint. • Author(s) : • Joakim Beck (King Abdullah University of Science and Technology) • Yang Liu (King Abdullah University of Science and Technology) • Erik von Schwerin (King Abdullah University of Science and Technology) • Raul Tempone (King Abdullah University of Science and Technology) ## [00477] Relaxation process of Cahn–Hilliard equations with dynamic boundary conditions • Abstract : This talk is concerned with a numerical analysis of the initial value problem for the Cahn–Hilliard equation with dynamic boundary conditions in one-dimensional space, using a structure preserving scheme based on the discrete variational derivative method. We discuss the relationship between the parameter related to the time evolution on the boundary and the time it takes for the numerical solution to approach a stationary solution. • Author(s) : • Keiichiro Kagawa (Waseda University) • Yoshihiro Yamazaki (Waseda University) ## [00480] Mathematics, the Mind and Alzheimer’s disease: Systematical progression on brain graphs • Abstract : Neurodegenerative diseases, Alzheimer’s disease (AD) in particular, present a clear challenge to modern medicine due to brain delicate in vivo environment and limited insight from the human whole nervous system. Mathematical network models of dementia, such as AD, offer a path forward that can be deployed using the multitude of anatomical brain-graph data from real human patients. The dynamical processes of the model support front-like propagation on networks, where an initial localized perturbation grows and systematically invades all nodes in the network. The main question is to understand its overall dynamics. For instance, if a process starts at a seed location, how long will it take to appear at other locations, and then develop through a full-scale invasion, leading to dementia for the brain? The arrival-time problem, that consists in determining the time it takes for a quantity of interest to reach a certain level at each node, greatly depends on the coupling dynamics between nodes. In this talk, I address a question to extract estimates for the dynamics motivated by the study of toxic protein propagation in neurodegenerative diseases: if a single node is seeded at a small concentration, when will other nodes reach the same initial concentration? My research demonstrates that different estimates can give their important insights to understand the dynamics and, in particular, analytical methods to estimate and compute the arrival times are extremely powerful and can capture essential features in AD. • Author(s) : • Prama Setia Putra (Mathematical Institute, University of Oxford) • Alain Goriely (Mathematical Institute, University of Oxford) ## [00481] Optimal Control Analysis of Estrogen Paradox for Breast Cancer Treatment • Abstract : Although it is well known that estrogen promotes the formation of breast cancer, it can also be used to treat the condition. The “estrogen paradox” refers to this. In addition, estrogen treatment given for a brief period of time can effectively eradicate breast cancer, however, long-term treatment can result in cancer recurrence. We suggest a unique ODE-based mathematical model that takes into account p53 and the estrogen hormone, as well as dormant and active cancer cells. Numerical analyses were used in conjunction with optimal control theory. • Author(s) : • Segun Isaac Oke (Ohio University, Athens) • Rachid Ouifki (University of Pretoria, South Africa) ## [00482] Delta Shocks and vacuum states in the Riemann solutions of Chaplygin Euler equations as pressure and magnetic field drop to zero • Abstract : The aim of the present study is to solve the Riemann problem of isentropic magnetogasdynamics equations for a more realistic version of the extended Chaplygin gas model. The analysis demonstrates that under some special circumstances, delta shock and vacuum appear in the solution, describing the phenomena of concentration and cavitation, respectively. By examining the limiting behavior, it is obtained that solutions coincide with corresponding Riemann solutions of the transport equations when both the magnetic field and pressure drop to zero. PS: This paper has been published in J. Math. Phys. 63, 121505 (2022); https://doi.org/10.1063/5.0132580 • Author(s) : • Priyanka . (Dr. B.R. Ambedkar NIT Jalandhar) • M. Zafar (Dr. B. R. Ambekdar NIT Jalandhar, Jalandhar, India) ## [00486] Singularity formation in the Keller-Segel system • Abstract : The talk will give an up-to-date result on singularity formation in the Keller-Segel system in$mathbb{R}^d$. For$d geq 2$, there exist blowup solutions that are of Type II with finite mass. Blowup rates are completely quantized. There also exist Type I blowup solutions with infinite mass for$d = 3, 4$. The constructed solution is asymptotically self-similar with a logarithmic correction to its profile which is either radial or non-radial. • Author(s) : • Van Tien Nguyen (National Taiwan University) ## [00487] A strongly nonlinear anisotropic parabolic-elliptic system: analysis and numerical simulation • Abstract : We study the existence of a capacity solution to a nonlinear coupled parabolic-elliptic system. This system is a generalization of the so-called thermistor problem which models a temperature dependent electrical resistor. In this analysis we have considered the case where$Au$is an operator of the Leray-Lions class defined in an anisotropic Sobolev space. We also show some numerical simulations of this problem and we discuss the obtained results. • Author(s) : • Francisco Ortegón Gallego (Universidad de Cádiz) • Manar Lahrache (Moulay Ismail University) • Mohamed Rhoudaf (Moulay Ismail University) • Hajar Talbi (Moulay Ismail University) ## [00489] Curvature related properties of Finsler manifolds and applications • Abstract : Finsler manifolds are important generalizations of Euclidean and Riemannian ones with applications in different domains of mathematics, physics and engineering. In the present talk we are going to present some recent results concerning Finsler connections, curvature and relation with statistical models in the real world. We suggest possible development of information geometry on Finsler manifolds that would allow a wide range of applications. • Author(s) : • Sorin Sabau (Tokai University) ## [00492] Asymptotic convergence of heterogeneous first-order aggregation models: from the sphere to the unitary group • Abstract : We provide the detailed asymptotic behavior for first-order aggregation models of heterogeneous oscillators. Due to the dissimilarity of natural frequencies, one could expect that all relative distances converge to definite positive value and furthermore that each oscillator converges to a possibly different stationary point. In order to establish the desired results, we introduce a novel method, called dimension reduction method that can be applied to a specific situation when the degree of freedom of the natural frequency is one. In this way, we would say that although a small perturbation is allowed, convergence toward an equilibrium of the gradient flow is still guaranteed. Several first-order aggregation models are provided as concrete examples by using the dimension reduction method to study the structure of the equilibrium, and numerical simulations are conducted to support theoretical results. • Author(s) : • Dohyun Kim (Sungshin Women’s University) • Dohyun Kim (Sungshin Women’s University) ## [00501] Efficient numerical method for simulation of plasma • Abstract : Understanding the dynamics of plasma is crucial in many concurrent applications. Those include astrophysics, space discovery, and designing fusion reactors. Numerical methods are a great tool for this purpose. In this talk, an efficient numerical method based on Galerkin approximations is presented. The method has high accuracy, capability of capturing shocks and turbulence, and consistency with thermodynamics. We show several interesting numerical simulations to demonstrate those properties. • Author(s) : • Tuan Anh Dao (Uppsala University) ## [00502] The Helmholtz-Hodge decomposition of polynomial vector fields • Abstract : The Helmholtz-Hodge decomposition is a fundamental tool in the study of vector fields and has many applications. In this talk, we will focus on the case of polynomial vector fields. First, we will introduce results on the general properties and methods for finding a decomposition. As an application, we will explain the relationship between the Helmholtz-Hodge decomposition and the construction of Lyapunov functions. • Author(s) : • Tomoharu Suda (Keio University) • Tomoharu Suda (Keio University) ## [00504] Solar Influence on Earth’s Seismicity and Applications in Earthquake Forecasting • Abstract : The scientific community is yet to find an effective method to forecast and avoid earthquake hazards, due to the problem complexity. After decades of debate, the Sun has again been recently brought forth as a potential precursor to earthquakes. This study aims to investigate the existence of such relationship from a dynamical systems perspective. Having confirmed the existence, we also show that Sun data can be included in forecasting models to improve forecasting accuracy. • Author(s) : • Matheus Henrique Junqueira Saldanha (University of Tsukuba) • Matheus Henrique Junqueira Saldanha (Graduate School of Science and Technology, University of Tsukuba) • Yoshito Hirata (Faculty of Engineering, Information and Systems, University of Tsukuba) ## [00510] Optimal Impact Portfolios with General Dependence and Marginals • Abstract : Impact investing typically involves ranking and selecting assets based on a non-financial impact factor, such as the environmental, social, and governance (ESG) score and the prospect of developing a disease-curing drug. We develop a framework for constructing optimal impact portfolios and quantifying their financial performances. Under general bivariate distributions of the impact factor and residual returns from a multi-factor asset-pricing model, the construction and performance of optimal impact portfolios depend critically on the dependence structure (copula) between the two, which reduces to a correlation under normality assumptions. More generally, we explicitly derive the optimal portfolio weights under any copula. In particular, we investigate two widely-used copulas—the Gaussian copula and the Archimedean copula family, and find that the optimal weights depend on the tail characteristics of the copula. In addition, when the marginal distribution of residual returns is skewed or heavy-tailed, assets with the most extreme impact factors have lower weights than non-extreme assets due to their high risk. Our framework requires the estimation of only a constant number of parameters as the number of assets grow, an advantage over traditional Markowitz portfolios. Overall, these results provide a recipe for constructing and quantifying the performance of optimal impact portfolios with arbitrary dependence structures and return distributions. • Author(s) : • Andrew W Lo (Massachusetts Institute of Technology) • Lan Wu (Peking University) • Ruixun Zhang (Peking University) • Chaoyi Zhao (Peking University) ## [00511] Metapopulation network models explain non-Poissonian statistics of intercontact times • Abstract : Intercontact times in empirical data obtained from humans and animals typically obey heavy-tailed distributions as opposed to exponential distributions that would correspond to Poisson processes. We show that this phenomenon is a mathematical property of a most basic metapopulation network model used in epidemiology and ecology modeling, in which individuals move from a patch to another according to the simple or other types of random walks. Our results hold true for any network structure. • Author(s) : • Elohim Fonseca dos Reis (State University of New York at Buffalo) • Naoki Masuda (State University of New York at Buffalo) ## [00512] Rigged Hilbert Space Formulation for Many-Body Quantum Theory • Abstract : The rigged Hilbert space that associates the distribution functions with the Hilbert space is the fundamental one of quantum mechanics to define the bra-ket vectors. Their construction has been attempted mainly for single-particle systems. We are trying to extend the rigged Hilbert space formulation to various realistic quantum systems. In this presentation, we present the result of extending this formulation to quantum many-body systems. • Author(s) : • Junichi Takahashi (Waseda University) • Shousuke Ohmori (Waseda University) ## [00513] The perfectly matched layer for elastic waves in layered media • Abstract : The perfectly matched layer (PML) is widely used to truncate domains in large-scale simulation of wave propagation in open boundaries. PML absorbs outgoing waves without reflection and significantly improves computational efficiency. However, it is very challenging to prove stability of PML models. In this talk, I present our recent contribution on the stability analysis of PML models for the elastic wave equation in layered media modeling seismic wave propagation in the Earth layers. • Author(s) : • Siyang Wang (Umeå University) ## [00514] Diffusion approximation of a Markov-modulated infinite-server queue • Abstract : In a queue, overdispersion nature of arrivals and stochastic nature of service times can be captured by incorporating modulation into the queue dynamics. We discuss stochastic approximations for an infinite-server queue, where the stochastic arrival and service rates are determined by a Markovian environment. The incorporation of modulation leads to an Ornstein-Uhlenbeck process as its diffusion approximation with the variance parameter capturing the stochastic variations of both modulating and modulated processes. • Author(s) : • Selvaraju Natarajan (Indian Institute of Technology Guwahati, India) • Ankita Sen (Indian Institute of Technology Guwahati, India) ## [00516] Parameters Estimation For Car Following Models Using Bayesian Inference • Abstract : Car following (CF) models play an important role in traffic simulation software. Estimating their parameters is necessary to enhance predictive performance and is traditionally accomplished through optimisation. In this research, we adopted Bayesian inference which is advantageous for uncertainty quantification. As the CF model depends on its parameters through solution of a delay differential equation, the likelihood is analytically intractable so we employed an adaptive Markov chain Monte Carlo algorithm to sample from the posterior. • Author(s) : • Samson Ting (The University of Western Australia) • Michael Small (The University of Western Australia) • Thomas Stemler (The University of Western Australia) • Chao Sun (The University of Western Australia) • Thomas Lymburn (The University of Western Australia) ## [00519] Non-Newtonian fluids with discontinuous-in-time stress tensor. • Abstract : We consider the system of equations describing the flow of incompressible fluids in bounded domain. Here, the Cauchy stress tensor has asymptotically$(s-1)$-growth with the parameter$s$depending on the spatial and time variable. We do not assume any smoothness of$s$with respect to time variable. Such a setting is a natural choice if the material properties are instantaneous. We establish the existence of weak solution provided that$sgefrac{3d+2}{d+2}$. • Author(s) : • Miroslav Bulicek (Charles University) • Piotr Gwiazda (Polish Academy of Sciences) • Jakub Skrzeczkowski (University of Warsaw) • Jakub Woźnicki (University of Warsaw) ## [00522] Modeling of concentration and electric field dependent susceptibilities in electrolytes • Abstract : Electrolytes are everywhere: in fundamental electrochemistry, biochemical-systems, semiconductors, and many industrial devices. Their mathematical description is mainly characterised by Poisson-Nernst-Planck-type equations and their successors. However, the dielectric susceptibility of the Poisson equation is frequently considered as a constant. In this talk we derive a thermodynamically consistent concentration and electric field dependent susceptibility. We provide insights in the resulting equation system, discuss some important theoretical aspects and show its impact on the electrochemical double layer. • Author(s) : • Manuel Landstorfer (Weierstrass Institute for Applied Analysis and Stochastics (WIAS)Weierstrass Institute for Applied Analysis and Stochastics (WIAS)) • Jürgen Fuhrmann (Weierstrass Institute for Applied Analysis and Stochastics (WIAS)Weierstrass Institute for Applied Analysis and Stochastics (WIAS)) • Rüdiger Müller (Weierstrass Institute for Applied Analysis and Stochastics (WIAS)Weierstrass Institute for Applied Analysis and Stochastics (WIAS)) ## [00527] A fast Multiplicative Update algorithm for non-negative matrix factorization • Abstract : This work proposes an efficient algorithm called fastMU (Multiplicative Updates) to deal with a Non-Negative Matrix Factorization problem, based on majorization minimization principle. We derive theoretical convergence results and show the effectiveness of our method through comparison with state-of-the-art methods on both synthetic and realistic data. Practical results show that fastMU is often several orders of magnitude faster than the regular MU proposed by Lee and Sung, and can even be competitive with state-of-the-art methods. • Author(s) : • Mai-Quyen PHAM (IMT Atlantique) • Jeremy Cohen (CREATIS, CNRS) • Thierry Chonavel (IMT Atlantique) ## [00531] Calibration of hardening parameters for the absence of hysteresis test-data • Abstract : A mathematical model is developed to estimate combined nonlinear isotropic-kinematic hardening parameters of ductile materials using Ramberg-Osgood constants for monotonic and cyclic stress-strain curves. This compact model can be performed even if the hysteresis curves test results are unavailable for the specimens subjected to high amplitude cyclic loading. The model is applied for AW6082 and HX220-BD, Finite Element simulation results are compared with test results, and very good agreements are obtained. • Author(s) : • Eray Arslan (TU Wien) • Milan Zigo (MAGNA STEYR Fahrzeugtechnik GmbH & Co KG) ## [00532] Pullback Operator Methods in Dynamical Systems: Theory and Computation • Abstract : Koopman operator methods along with the associated numerical algorithms have provided a powerful methodology for the data-driven study of nonlinear dynamical systems. In this talk, we will give a brief outline of how the Koopman group of operators can be generalized beyond function spaces to the space of sections of various vector bundles over the state space. We describe their relationship with the standard Koopman operator on functions as well as describe the new spectral invariants produced by these generalized operators. We then demonstrate how the recently developed spectral exterior calculus framework can be utilized to compute the spectral properties of the generator of the induced operator on sections of the cotangent bundle. We conclude with some applications of the algorithm to some well-known dynamical systems. • Author(s) : • Allan M. Avila (AIMdyn Inc.) ## [00540] Random product homotopies for decomposing tensors • Abstract : The rank one decomposition of the tensor is considered. The upper bound of rank is derived under which computing the decomposition is equivalent to solving a structured polynomial system that is determined by the full rank factorization of the matricization of the tensor. Under the generic uniqueness conditions, the solutions of the system are isolated and can be efficiently achieved by random product homotopies. • Author(s) : • Tsung-Lin Lee (National Sun Yat-sen University) ## [00541] Reinforcement Learning-based Data Collection and Energy Replenishment in SDIoT • Abstract : In software-defined internet of things (SDIoT) with wireless rechargeable sensor networks, a novel reinforcement learning-based method is proposed for collecting data and scheduling mobile sinks to recharge the sensor nodes. The suggested technique extends the network lifetime while ensuring the QoS of the SDIoT. Finally, the results show that the suggested approach significantly increases the energy efficiency and also increases the network’s lifetime. • Author(s) : • Vishnuvarthan Rajagopal (Research scholar, Department of Electronics and Communication Engineering, Anna University Regional Campus, Coimbatore.) • Bhanumathi V (Assistant Professor, Department of Electronics and Communication Engineering,Anna University Regional Campus, Coimbatore.) ## [00542] Approximations of quasi-linear elliptic optimal control problems under variational and virtual discretizations • Abstract : This talk will discuss virtual and variational discretizations for the numerical approximation of optimal control problems governed by the quasi-linear elliptic equation with distributed control. A conforming virtual element method is employed for the discretization of state and co-state equations that appeared in the model problem. The numerical approximation of the control variable is based on two different discretizations: variational and virtual. In the variational approach, the discrete space associated with the control is not discretized explicitly, whereas, for the virtual discretizations, the discrete spaces are taken as virtual element spaces that include linear polynomials and non-polynomials functions over the polygonal mesh, and a discretize-then-optimize approach is used for the computation of control. With the help of certain projection operators, optimal a priori error estimates are established for the control, state, and co-state variables in suitable norms. Numerical experiments are presented under general polygonal meshes to illustrate the performance of the proposed scheme and verify the theoretical convergence rate. • Author(s) : • Anil Kumar (BITS Pilani KK Birla Goa Campus, Goa (India)) • Jai Tushar (BITS Pilani KK Birla Goa Campus, Goa (India)) • Sarvesh Kumar (ndian Institute of Space Science and Technology, Thiruvananthapuram) ## [00543] Quantification of Entangled Bipartite Systems • Abstract : Gauging the distance between a mixed state and its nearest separable state is important but challenging in the quantum mechanical system. We, in this talk, propose a dynamical system approach to tackle low-rank approximation of entangled bipartite systems, which has several advantages, including 1) A gradient dynamics in the complex space can be described in a fairly concise way; 2) The global convergence from any starting point to a local solution is guaranteed; 3) The requirement that the combination coefficients of pure states must be a probability distribution can be ensured; 4) The rank can be dynamically adjusted. The theory, algorithms, and some numerical experiments will be presented in this talk. • Author(s) : • Matthew M. Lin (National Cheng Kung University) • Moody T. Chu (North Carolina State University) ## [00544] Quantification of Entangled Bipartite Systems • Abstract : Gauging the distance between a mixed state and its nearest separable state is important but challenging in the quantum mechanical system. We, in this talk, propose a dynamical system approach to tackle low-rank approximation of entangled bipartite systems, which has several advantages, including 1) A gradient dynamics in the complex space can be described in a fairly concise way; 2) The global convergence from any starting point to a local solution is guaranteed; 3) The requirement that the combination coefficients of pure states must be a probability distribution can be ensured; 4) The rank can be dynamically adjusted. The theory, algorithms, and some numerical experiments will be presented in this talk. • Author(s) : • Matthew M. Lin (National Cheng Kung University) • Moody T. Chu (North Carolina State University) ## [00546] Recent advances on the conjugate discrete-time algebraic Riccati equation. • Abstract : In this talk, we consider a class of conjugate discrete-time Riccati equations, arising originally from the linear quadratic regulation problem for discrete-time antilinear systems. A constructive proof is given for the existence of the maximal solution. Furthermore, an accelerated fixed-point iteration based on the semigroup property is developed for computing the maximal solution and the convergences is at least R-superlinear. An example is given to demonstrate the correctness of our main theorem. • Author(s) : • Chun-Yueh Chiang (Center for General Education, National Formosa University) • Hung-Yuan Fan (National Taiwan Normal University) ## [00547] Fictitious domain methods with finite elements and penalty over spread interface • Abstract : We present a spread interface approach in fictitious domain methods to decipher the elliptic PDEs depicted over curved complex domains. In this approach, we employ the$L^2$penalty for a small tubular neighborhood$Omega_{delta}$near$partialOmega$in$mathrm{R}backslashOmega$in place of the substantial penalty for the whole fictitious part$mathrm{R}backslashOmega$. We achieve strong convergence results concerning the penalty parameter$epsilon$in addition to the a priori estimates and stability analysis. We implement the linear finite elements and acquire the expected error estimates. The comprehensive numerical investigations support the mathematical findings, which also anticipate optimal convergence regardless of the convexity and shape of the domain. Keywords: Fictitious domain methods, Elliptic problems, Curved domain, Error estimates, Uniform mesh. References: 1. S. Kale, and D. Pradhan, An augmented interface approach in fictitious domain methods, Comput. Math. with Appl., Vol. 125, pp. 238-247, (2022). 2. B. Maury, Numerical Analysis of a finite element/volume penalty method, SIAM J. Numer Anal., Vol. 47(2), (2009), pp. 1126-1148. 3. N. Saito and G. Zhou, Analysis of the fictitious domain method with an$L^2$-penalty for elliptic problems, Numer. Funct. Anal. Optim., Vol. 36, (2015), pp. 501-527. 4. S. Zhang, Analysis of finite element domain embedding methods for curved domains using uniform grids, SIAM J. Numer. Anal., Vol. 46(6), (2008), pp. 2843-2866. • Author(s) : • Swapnil Kale (Defence Institute of Advanced Technology, Pune) • Debasish Pradhan (Defence Institute of Advanced Technology, Pune) ## [00549] On the penalty approach in finite difference methods • Abstract : We introduce a finite difference method with the$H^1$and$L^2$penalties to solve the elliptic PDEs over curved complicated domains. The sharp convergence of the penalized solution to the original one is provided. The accuracy in both strategies is almost analogous, provided the penalty parameter$epsilon$is$O(h^2)$in the$H^1$penalty approach and$O(h^4)$in the$L^2$penalty approach. The iterative methods developed for the proposed idea are highly efficient and furnish the theoretical outcomes. Keywords: Finite difference method, Elliptic PDEs, Penalty, Curved domain, Cartesian mesh. References: 1. S. Kale, and D. Pradhan, Error estimates of fictitious domain method with an$H^1$penalty approach for elliptic problems, Comp. Appl. Math., Vol. 41, (2022), pp. 1-21. 2.B. Maury, Numerical Analysis of a finite element/volume penalty method, SIAM J. Numer Anal., Vol. 47(2), pp. 1126-1148, (2009). 3.N. Saito and G. Zhou, Analysis of the fictitious domain method with an$L^2$-penalty for elliptic problems, Numer. Funct. Anal. Optim. Vol. 36, (2015), pp. 501-527. 4.H. Suito, and H. Kawarada, Numerical simulation of spilled oil by fictitious domain method, Japan J. Indust. Appl. Math., Vol. 21, (2004), pp. 219-236. • Author(s) : • DEBASISH PRADHAN (Defence Institute of Advanced Technology, Pune – 411025, India) • Swapnil Kale (Defence Institute of Advanced Technology, Pune) ## [00551] Network suppression of the pathogen spread within the healthcare system • Abstract : We consider an impulsive-differential-equation system, based on SIS model, to describe the spread of pathogens in healthcare systems accounting for patient mobility. We propose sufficient conditions guaranteeing network suppression of infection and an algorithm to indicate hospitals prone to high bacteria prevalence and ultimately to ensure the stability of a disease-free state. As an illustration, we present a model of hospital-acquired multidrug-resistant bacteria transmission based on hospital admission records provided by a German insurance company. • Author(s) : • Monika Joanna Piotrowska (Institute of Applied Mathematics and Mechanics, University of Warsaw) • Aleksandra Puchalska (Institute of Applied Mathematics and Mechanics, University of Warsaw) • Konrad Sakowski (Institute of Applied Mathematics and Mechanics, University of Warsaw and Institute of High Pressure Physics, Polish Academy of Sciences) ## [00557] Three dimensional laminar flow in a dividing channel • Abstract : This talk will describe a mathematical-modelling study concerned with fluid flow within a channel using asymptotic methods to study fluid behaviour on long axial length scales. Although many 3D problems can be solved through direct numerical simulations, it is generally useful to verify them with concrete analytical theory, which this study aims to do. Motivations for this research relate to providing insights into branching flows for cardiovascular vessels, industrial problems and Hele-Shaw cells. • Author(s) : • Thuy Duong Dang (University College London) • Frank Smith (University College London) • Christian Klettner (University College London) ## [00560] Semiparametric Kernel Estimation with Bayesian Bandwidths for Multivariate Nonnegative Data • Abstract : We introduce a flexible semiparametric kernel method for smoothing distributions on nonnegative supports. This multivariate estimator is guided by a given parametric part, here an uncorrelated exponential distribution estimated by maximum likelihood, and a nonparametric part which is a weight function to be smoothed through multiple gamma kernels. Also, a diagnostic model discusses the choice between the parametric, semiparametric and nonparametric approaches. Finally, practical multivariate semicontinuous datasets illustrate the usefulness of the method. • Author(s) : • Sobom Matthieu Somé (Université Thomas SANKARA) • Célestin C. Kokonendji (Université Bourgogne Franche-Comté) ## [00561] Quantum-parallel vectorized data encodings and computations on trapped-ions and transmons QPUs • Abstract : We introduce new quantum data representations derived from uniformly controlled rotation gates. QCrank encodes a sequence of real-valued data as rotations of the data qubits allowing for high storage density. QBArt directly embeds a binary representation in the computational basis and requires a lower number of quantum measurements. We demonstrate quantum algorithms for DNA pattern matching, Hamming weight calculation, complex value conjugation, and O(400) bits image retrieving executed on Quantiunuum, IBMQ, and IonQ QPUs. • Author(s) : • Jan Balewski (National Energy Research Scientific Computing Center, Lawrence Berkeley National Laboratory) • Mercy G. Amankwah (Case Western Reserve University, Cleveland) • Roel Van Beeumen (Applied Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory) • E. Wes Bethel (Computer Science Department, San Francisco State University) • Talita Perciano (Scientific Data Division, Lawrence Berkeley National Laboratory) • Daan Camps (National Energy Research Scientific Computing Center, Lawrence Berkeley National Laboratory) ## [00562] Steady-state density preserving method for second-order stochastic differential equations • Abstract : We devise a method for the long-time integration of a class of damped second-order stochastic mechanical systems. The introduced numerical scheme has the advantage of being completely explicit for general nonlinear systems while, in contrast with other commonly used integrators, it has the ability to compute the evolution of the system with high stability and precision in very large time intervals. Notably, the method has the important property of preserving, for all values of the stepsize, the steady-state probability density function of any linear system with a stationary distribution. Numerical experiments are presented to illustrate the practical performance of the introduced method. • Author(s) : • Hugo Alexander de la Cruz Cancino (School of Applied Mathematics. FGV-EMAp) • Hugo de la Cruz (School of Applied Mathematics) ## [00565] Resonance with a Delay Differential Equation • Abstract : We propose here a delay differential equation with a linear time coefficient that produces transient resonant behavior. The oscillatory transient dynamics appear and disappear as the delay is increased between zero to asymptotically large delay. Also, for an appropriately tuned value of the delay, the height of the power spectrum goes through the maximum. This resonant behavior contrasts itself against the general behaviors observed with the constant coefficient delay differential equations. • Author(s) : • Kenta Ohira (Nagoya University) • Toru Ohira (Graduate School of Mathematics, Nagoya University) ## [00566] Numerical study of Draw resonance in Fibre spinning using multi-mode constitutive model • Abstract : We study the instability called Draw resonance that occurs in the industrial process of manufacture of thin polymer fibres, called fibre spinning using a multi-mode viscoelastic constitutive equation. We do a linear stability analysis of the equations by carrying out numerical simulations for a varying number of modes in the constitutive equation. We compare our results with those got by using single-mode viscoelastic models and discuss our findings. • Author(s) : • Renu Dhadwal (Center for Mathematical Modelling, FLAME University ) ## [00567] Topology-aware algorithm for constructing cartograms from density-equalising map projections • Abstract : Cartograms are maps in which the areas of enumeration units$text{(}$e.g. administrative divisions$text{)}$are proportional to quantitative data$text{(}$e.g. population$text{)}$. Generating cartograms with density-equalising map projections guarantees that geographic neighbours remain neighbours in the cartograms if all boundaries are infinitely dense sequences of points. However, computers represent boundaries with only finitely many points, often causing invalid topologies in the cartogram. This talk shows how line densification and topology-aware simplification solve this problem. • Author(s) : • Michael T Gastner (Yale-NUS College) • Nguyen Phong Le (Yale-NUS College) • Nihal Z Miaji (Yale-NUS College) • Adi Singhania (Yale-NUS College) ## [00572] Model uncertainty for statistical arbitrage • Abstract : We consider an optimal stopping problem that addresses textit{model uncertainty}, which affects the model assumptions, e.g., the parameters embedded in the probability distribution. The result presented in this talk shows the explicit form of the boundary indicating the optimal stopping time, assuming the portfolio value as an Ornstein-Uhlenbeck process. Applying our method might make statistical arbitrage more robust because the trading code for statistical arbitrage often depends on incorrect estimation. • Author(s) : • Daisuke Yoshikawa (Kansai University) ## [00576] Modeling the Dispersion of Effluents Discharged into Tidally Coastal Waters • Abstract : Mixing and dispersion of effluents discharged under the spring neap tidal oscillations are studied analytically on a flat seabed and a uniformly sloping bed. The solutions of two-dimensional advection-diffusion equations are presented graphically to visualize and analyze the spreading of effluent plumes in coastal waters, following discharges from a single sea outfall, multiple outfalls, and multiport diffusers, to showcase the model applications of marine outfall systems for disposal from industrial plants in the far field. • Author(s) : • Anton Purnama (Sultan Qaboos University) • Ahmed Al-Kasbi (University of Technology and Applied Sciences) ## [00577] Mixed Finite Element Method for Dirichlet Boundary Optimal Control Problem • Abstract : The optimal control problems (OCPs) subjected to partial differential equations (PDEs) have numerous applications in fluid dynamics, image processing, mathematical finance etc. The objective of OCPs is to find the optimal control which minimizes or maximizes the given cost functional with certain constraints (mainly in form of PDEs) being satisfied. There are mainly two types of OCPs available in literature namely, Distributed Control Problems where the control acts on the system through an external force and Boundary Control Problems where the control acts on the system through a Dirichlet or Neumann or Robin boundary conditions. Dirichlet boundary control problems are difficult to handle due to variational difficulty. In many applications, it is important to obtain accurate approximation of the scalar variable and its gradient simultaneously. A common way to achieve this goal is to use mixed finite element methods. The main aim of my talk is to analyze the mixed finite element method for the second order Dirichlet boundary control problem in which the control is penalized in the energy space. Mixed finite element methods have the property that they maintain the discrete conservation law at the element level. For the variational formulation, the state equation is converted to the mixed system using the mixed variational scheme for second order elliptic equations and then the continuous optimality system is derived. In order to discretize the continuous optimality system, the lowest order Raviart-Thomas space is used to numerically approximate the state and co-state variables whereas the continuous piece-wise linear finite element space is used for the discretization of control. Based on this formulation, the optimal order a priori error estimates for the control in the energy norm and$L_2$-norm is derived. The reliability and the efficiency of proposed a posteriori error estimator is also discussed using the Helmholtz decomposition. Finally, several numerical experiments are presented to confirm the theoretical findings. • Author(s) : • Divay Garg (Indian Institute of Technology Delhi) • Kamana Porwal (Indian Institute of Technology Delhi) ## [00578] Secret Sharing Scheme with Perfect Concealment by Quasigroup • Abstract : A secret sharing scheme was introduced by Shamir in 1979. A quasigroup is equivalent to a Latin square. The concept of perfect concealment is called perfect security. The word ‘security’ describes a property of a phenomena, and the word ‘concealment’ describes an action which makes a phenomena. In this talk, we force an action rather than a property, and we give new construction of secret sharing scheme with perfect concealment by quasigroup. • Author(s) : • Tomoko Adachi (Shizuoka Institute of Science and Technology) • Izumi Takeuti (National Institute of Advanced Industrial Science and Technology) ## [00579] Explosion times and its bounds for a system of semilinear SPDEs • Abstract : In this paper, we obtain lower and upper bounds for the blow-up times to a system of semilinear stochastic partial differential equations. Under suitable assumptions, the bounds of the explosion times are obtained by using explicit solutions of an associated system of random PDEs and a formula due to Yor. We provide an estimate for the probability of the finite-time blow-up and the impact of the noise on the solution is investigated. • Author(s) : • Karthikeyan Shanmugasundaram (Periyar University) ## [00585] Computational and Optimization Frameworks for Tissue Vascularization in Bioprinted Grafts • Abstract : Template channels within tissue-engineered skin grafts can provide a promising tool for faster microvasculature formation and transport of nutrients to cells outside channels. Developing viable grafts requires the optimal design to support cell viability by controlled channel geometry and biomaterial properties. We discuss the recent advances in creating a robust computational framework to simulate physical and biological phenomena in graft samples. The first computational results will speak for future applications to models using laboratory data. • Author(s) : • Chris Bashur (Florida Institute of Technology) • Beste Caner (Florida Institute of Technology) • Vladislav Bukshtynov (Florida Institute of Technology) ## [00590] Feedback control of propagating bubbles: stabilization and control-based continuation • Abstract : We study the propagation of air bubbles into fluid filled Hele-Shaw channels. Feedback control is used to manipulate the system to a desired configuration and also as a tool to explore the full range of nonlinear behaviour. Control is implemented by the addition of time-dependent fluid injection along the channel. Control-based continuation allows unstable steady states to be observed and stabilised directly in our time-dependent simulations. Steady and time-dependent simulations are performed using finite elements. • Author(s) : • Joao Fontana (The University of Manchester) • Alice Thompson (The University of Manchester) ## [00599] Advances on estimation of temperature and moisture of soil using sensor networks. • Abstract : Given a sensor network set up on an agricultural field, we review methods based on PDE, regression and Principal Component Analysis algorithms to estimate the temperature and moisture of soil. With PCA it is possible to identify those sensors or groups of sensors which are influential at the time of measuring the temperature or moisture at a given point of the field. Validation results are provided based on real data from agricultural fields. • Author(s) : • Carlos Fresneda-Portillo (Universidad Loyola Andalucía (Spain)) • Carmelina Ierardi (Universidad Loyola Andalucía ) • José Ramón Salvador-Ortiz (Universidad Loyola Andalucía) • Javier Pérez (Universidad Loyola Andalucía ) • Diego Luis Orihuela (Universidad Loyola Andalucía ) ## [00601] Assessment of Mathematics in Higher Education over the COVID19 pandemic. • Abstract : A comparative analysis of various assessment methods on Higher Education Mathematics is provided. A discussion on the reliability of these methods is provided with particular emphasis on distance/online (uncontrolled) assessment methods and face to face (controlled) assessment methods. We analyse the data collected from an assessment strategy based on a set of tests before and throughout the COVID pandemic. Results show that online assessment is less reliable for those students with lower academic performance. • Author(s) : • Carlos Fresneda-Portillo (Universidad Loyola Andalucía (Spain)) • James Maunder (Oxford Brookes University) ## [00610] Input-output finite time stabilization for nonlinear networked control systems • Abstract : In this talk, we discuss the problem of input-output finite time stabilization for nonlinear networked control systems with network induced delay. The nonlinear system can be linearized by fuzzy model with weighted membership functions. Memory event-triggering mechanism incorporated to reduce frequent packets transmission. The sufficient stabilization conditions are developed in the form of linear matrix inequalities with aid of Lyapunov stability theory. Finally, numerical example is provided to demonstrate the viability of the suggested approach. • Author(s) : • Marshal Anthoni Selvaraj (Anna University Regional Campus Coimbatore) ## [00613] Phase-field systems coupled with large deformations • Abstract : Multiphase dynamical systems coupled with finite strain are used for the mathematical description of many phenomena in soft matter physics and biology, such as swelling and wetting processes of gels. We derive a thermodynamically consistent framework to couple phase fields and mechanics in a gradient flow structure allowing for various dissipation mechanisms. Combining modeling tools, rigorous analytical considerations, and the construction of numerical implementations allows us to understand practical and technical details from different perspectives. • Author(s) : • Leonie Schmeller (Weierstrass Institute) • Barbara Wagner (Weierstrass Institute) • Dirk Peschka (Weierstrass Institute) ## [00619] Optimal Transport for Positive and Unlabeled Learning • Abstract : Positive and unlabeled learning (PUL) aims to train a binary classifier based on labeled positive samples and unlabeled Samples, which is challenging due to the unavailability of negative training samples. This talk will introduce a novel optimal transport model with a regularized marginal distribution for PUL. By using the Frank-Wolfe algorithm, the proposed model can be solved properly. Extensive experiments showed that the proposed model is effective and can be used in meteorological applications. • Author(s) : • Jie ZHANG (University of Hong Kong) • Yuguang YAN (Guangdong University of Technology) • Michael Ng (University of Hong Kong) ## [00620] Development of an ion channel model-framework • Abstract : Ion channels in cell membranes are of ultimate importance in physiology. They control a large fraction of biological processes and are mainly investigated by current-voltage experiments. To support the interpretation of measured results, we develop a model-framework based on non-equilibrium thermodynamics that accounts for various important aspects, e.g., finite-volume effects and the surface charges of the channel. Julia-based numerical simulations are performed to compute current-voltage relations, with varying ion concentrations, applied voltages, and channel properties. • Author(s) : • Christine Keller (Weierstrass Institute for Applied Analysis and Stochastics (WIAS)) • Juergen Fuhrmann (Weierstrass Institute for Applied Analysis and Stochastics (WIAS)) • Manuel Landstorfer (Weierstrass Institute for Applied Analysis and Stochastics (WIAS)) • Barbara Wagner (Weierstrass Institute for Applied Analysis and Stochastics (WIAS)) ## [00629] Stability Analysis of Split Equality and Split Feasibility Problems • Abstract : In this talk, the stability of solutions to parametric split equality and split feasibility problems is addressed for the first time. Characterizations for the Lipschitz-likeness of solution maps are obtained by exploiting special structures of the problems and by using an advanced result of B.S. Mordukhovich on parametric generalized equations. Examples are presented to illustrate how the obtained results work in practice and to show that extra mild assumptions made cannot be omitted. • Author(s) : • Huong Thi Vu (Institute of Mathematics, Vietnam Academy of Science and Technology) • Hong-Kun Xu (Hangzhou Dianzi University) • Yen Dong Nguyen (Institute of Mathematics, Vietnam Academy of Science and Technology) ## [00637] Wave Scattering from Layers of Random Particulate Materials • Abstract : To characterise any material with sound waves, the wave will propagate through several layers before reaching the material. If that material is a random particulate material, then to date there is no simple model to deal with the layers. In this talk we show how extending the quasi-crystalline approximation (text{(a technique from statistical physics)}) to layers leads to clear and simple models which separate the influence of the microstructure from the material geometry. • Author(s) : • Paulo Sergio Piva (The University of Sheffield) • Kevish Napal (The University of Sheffield) • Artur Gower (The University of Sheffield) ## [00648] Bounds for effective conductivity of multimaterial composites • Abstract : The paper discusses the exact bounds for the effective properties of multimaterial composites. We refine Hashin-Shtrikman bounds in the region where the last ones are loose. We show that fields in optimal structures vary in restricted domains, modify the Translation method, and obtain new exact bounds and optimal structures. Different volume fractions of components correspond to topologically different types of optimal structures. • Author(s) : • Andrej Cherkaev (University of Utah) ## [00651] Parallel Coordinate Descent Methods for Full Configuration Interaction • Abstract : Solving the time-independent Schrödinger equation gives us full access to the chemical properties of molecules. Among all the ab-initio methods, full configuration interaction (FCI) provides the numerically exact solution under a predefined basis set. However, the FCI problem scales factorially with respect to the number of bases and electrons and suffers from the curse of dimensionality. The FCI problem could be reformulated as an unconstraint minimization problem. This work proposes a novel algorithm to address the minimization problem. The algorithm introduces an extra search dimension to enable the exact linesearch for the multi-coordinate descent method, which could be fully parallelized. Hence, the proposed algorithm benefits from both exact linesearch and parallelization. Numerically, we demonstrate the parallel efficiency of the algorithm. The algorithm achieves better energy and parallelism on systems with approximately a hundred electrons than other existing methods. • Author(s) : • Yuejia Zhang (Fudan University) • Yingzhou Li (Fudan University) ## [00655] Finite-time fault-tolerant robust control design for parabolic partial differential equations • Abstract : In this paper, a finite-time fault-tolerant robust control design for parabolic partial differential equations in the presence of uncertainties, actuator faults and external disturbances is discussed. The main aim is to design a non-fragile fault-tolerant control to ensure the robust stabilization of the considered PDEs. By employing Lyapunov method, a novel set of conditions is obtained to ensure the required result. Finally, simulations are provided to demonstrate the effectiveness of the developed control design. • Author(s) : • Sakthivel Rathinasamy (Bharathiar University) ## [00659] Understanding persisting onchocerciasis hotspots in Africa using mathematical models • Abstract : Onchocerciasis/river blindness is a vector-borne neglected tropical disease with persistent transmission hotspots despite the repeated distribution of ivermectin in endemic communities in Africa. One of the hypotheses for the persistence of transmission is due to the movement of parasites via infected humans and/or vectors between neighbouring communities. I have explored how vector movement affects transmission using spatially-structured mathematical models informed by genetic and environmental data, which might aid in making public-health decisions to eliminate onchocerciasis. • Author(s) : • Himal Shrestha (La Trobe University) • Himal Shrestha (La Trobe University) • Shannon Hedtke (La Trobe University) • Karen McCulloch (La Trobe University) • Warwick Grant (La Trobe University) • Rebecca Chisholm (La Trobe University) ## [00660] Dynamical system analysis of cosmological models in f(T,B) Gravity • Abstract : We analyze the cosmological solutions of$f(T,B)$gravity using dynamical system analysis where$T$is the torsion scalar and$B$be the boundary term scalar. In our work, we assume two specific cosmological models. For first model, we consider$ f(T,B)=f_{0}(B^{k}+T^{m})$, where$k$and$m$are constants. For second model, we consider$f(T,B)=f_{0}T B$. We generate an autonomous system of differential equations for each models by introducing new dimensionless variables. To solve this system of equations, we use dynamical system analysis. We also investigate the critical points and their natures, stability conditions and their behaviors of Universe expansion. For both models, we get four critical points. The phase plots of this system are analyzed in detail and study their geometrical interpretations also. In both model, we evaluated density parameters such as$Omega_{r}$,$Omega_{m}$,$Omega_{Lambda}$and$omega_{eff}$and deceleration parameter$(q)$and find their suitable range of the parameter$lambda$for stability. For first model, we get$omega_{eff}=-0.833,-0.166$and for second model, we get$omega_{eff}=-frac{1}{3}$. This shows that both the models are in quintessence phase. Further, we compare the values of EoS parameter and deceleration parameter with the observational values. • Author(s) : • Sanasam Surendra Singh (National Institute of Technology Manipur) • Amit Samaddar (National Institute of Technology Manipur) ## [00661] A variational methods for fractional Sturm-Liouville eigenvalue problem • Abstract : we consider a regular Fractional Sturm–Liouville Problem (FSLP) of order$ mu $($ 0
• Author(s) :
• Prashant Kumar Pandey (Vellore Institute of Technology (VIT) Bhopal University)
• Rajesh K. Pandey (Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi, Varanasi)
• Om P Agrawal (Mechanical Engineering and Energy Processes, Southern Illinois University, Carbondale, IL)

## [00663] Random Deep Splitting Algorithm for nonlinear parabolic PDEs and PIDEs

• Abstract : In this talk, we present a new deep learning based algorithm to solve high-dimensional nonlinear parabolic PDEs and PIDEs, extending the Deep Splitting algorithm developed in Beck, Becker, Cheridito, Jentzen, Neufeld in 2021.
We use random neural networks, instead of fully trained neural networks, which immensely speeds-up the algorithm. Moreover, we provide a convergence analysis of the algorithm and demonstrate its application to high-dimensional problems in finance.
• Author(s) :
• Ariel Neufeld (NTU Singapore)
• Philipp Schmocker (NTU Singapore)
• Sizhou Wu (NTU Singapore)

## [00665] Estimating pressure distribution on a surface via electrical sensing skin

• Abstract : Sensing skins allow for monitoring of a surface by electrically imaging a conductive layer on an object. One example is fracture detection of concrete elements by imaging a conductive paint layer. In this talk, we present a way to estimate pressure distribution on a surface by using sensing skin -based techniques.
• Author(s) :
• Petri Kuusela (University of Eastern Finland)
• Moe Pour-Ghaz (North Carolina State University)
• Aku Seppänen (University of Eastern Finland)

## [00668] Solution of Non-linear Problems Through Variant of Newton’s Method with Applications in Engineering

• Abstract : Various non-linear problems that formulated from sciences and engineering like Combustion problems, Chemistry of rainwater, Heat problems, etc. are difficult to solve with analytical methods. So, the approximate solution of such non-linear problems is obtained through iterative methods. Hence, we will discuss variant of Newton’s method and its validity in terms of a convergence order, minimum computation cost, time, and efficiency over existing techniques.
• Author(s) :
• Sonia Bhalla (Chandigarh University)

## [00671] A new drone swarm model for zone occupation

• Abstract : We focus on fluid modeling for decentralized fleets of autonomous drones with Newtonian models. The corresponding system of hyperbolic conservation laws is obtained through mean field limit and moments closure assumption. The objective is to reduce the complexity for swarm tasks simulations such as zone occupation. Taking advantage of the macroscopic representation of the density, we introduce a new model for this task accounting for the drones inertia, which has been neglected so far.
• Author(s) :
• Axel Maupoux (ONERA / Institut Mathématique de Toulouse)
• Guillaume Dufour (ONERA)

## [00676] Recent Advances in 2-Lagrange Multiplier Method for Multiscale PDEs

• Abstract : The heterogeneous 2LM method, introduced in Loisel et al., SIAM J. Sci. Comput., 37, 2015, is a domain decomposition method where the coarse space is built using eigenvectors associated with subdomain eigenproblems. In this talk, we provide a new a-priori estimate for the norm of the coarse problem to guarantee further that the method is robust w.r.t the changes in the contrast of the diffusion coefficient. Numerical results are provided to support the theoretical findings.
• Author(s) :
• Hieu Nguyen (Fulbright University Vietnam)
• Sébastien Loisel (Heriot-Watt University)

## [00677] Mathematical Epidemiology as a decision tool

• Abstract : Mathematics is a powerful tool for tackling real world problems; concretely, we are interested in monitoring epidemics. Some members of the MOMAT Research Group -Complutense University of Madrid- have worked in collaboration with veterinary groups, healthcare companies and public entities of the Spanish healthcare system. In this talk, we present some mathematical models developed by this research group for both animal -e.g., Classical Swine Fever, Bluetongue- and human -e.g., COVID-19, Ebola- infectious diseases.
• Author(s) :
• Miriam R. Ferrández (Instituto de Matemática Interdisciplinar)

## [00678] Monitoring distributed strains on solid surfaces by electrical impedance tomography

• Abstract : Measuring strains induced by loads on structural elements is a key component of structural health monitoring $(text{SHM})$. Current methods are mostly based on localized measurements and offer limited information on distributed strain. We present results on distributed strain monitoring based on electrical impedance tomography $(text{EIT})$ imaging of a painted, elastic surface coating. The method can extract information on the surface strain field by solving the EIT inverse problem based on measured data.
• Author(s) :
• Mikko Räsänen (University of Eastern Finland)
• Aku Seppänen (University of Eastern Finland)
• Moe Pour-Ghaz (North Carolina State University)
• Jari Kaipio (University of Eastern Finland)

## [00680] Computing p-Harmonic Descent Directions for Shape Optimization

• Abstract : Recent development in shape optimization suggests enhanced results by using a $p$-harmonic approach to determine descent directions. Therefore, we present the extension of an algorithm to solve the occurring vector-valued $p$-Laplace problem subject to a boundary force without requiring an iteration over the order $p$ and thus compute higher-order solutions efficiently. Results are verified by numerical experiments in a fluid dynamic setting.
• Author(s) :
• Henrik Wyschka (University of Hamburg)
• Martin Siebenborn (University of Hamburg)
• Winnifried Wollner (University of Hamburg)

## [00681] A revised Hughes model for pedestrian flow

• Abstract : In this talk, we analyse the modified Hughes model for pedestrian dynamics, in which individuals seek to minimize their travel time. We present the existence and uniqueness of the solution and illustrate the behavior of the model with various numerical results. This is joint work with Prof Nader Masmoudi
• Author(s) :

## [00683] Linearized Saint-Venant Equation with Lateral Inflow in a Finite Channel

• Abstract : We present a solution for linearized Saint-Venant equations with uniformly distributed lateral inflow for a finite rectangular channel. The discharge is presented as the convolution of the distributed lateral inflow and lateral channel response function. We study the behavior of lateral channel response function for different parameters. To find discharge at any location of a channel for a given channel width, the choice of reference discharge and slope of the channel play a significant role.
• Author(s) :
• Swaroop Nandan Bora (Indian Institute of Technology Guwahati)
• Shiva Kandpal (Indian Institute of Technology Guwahati)

## [00684] Aggregation of Anisotropic Inclusions on Elastic Membranes

• Abstract : Elastic interactions mediated by biological membranes are an important class of sorting mechanisms used to organise proteins in living systems and with applications for biotechnology. Proteins that bind to the membrane and generate this curvature are often anisotropic and this broken symmetry yields new phenomena in their interactions. In this talk, I will discuss the many-body structures that can emerge from these elastic, quadrupole-like interactions and explore the consequences of these aggregates.
• Author(s) :
• Matthew William Cotton (University of Oxford)
• Jon Chapman (University of Oxford)
• Alain Goriely (University of Oxford)

## [00691] GROWTH TUMOR, PROLIFERATION AND DIFFUSION IN CELL LINES OF OSTEOSARCOMA

• Abstract : Osteosarcoma is a bone cancer. According to medical studies, it has a high genetic complexity, with different mechanisms of appearance and evolution. Our goal is to describe how is the diffusive behavior of cell lines at early times, that is, times close to the instant of inoculation and when the volumes are still small compared to the largest experimental volume reached by the cell lines studied.
• Author(s) :
• María Isabel Romero Rodríguez

## [00692] Well-posedness with large data for a weighted porous medium equation

• Abstract : The large data problem for the porous medium equation is to determine the optimal class of initial data for which local well-posedness is guaranteed for the Cauchy problem. The starting point is the classical results by Widder for the heat equation $u_t=Delta u$ and later those of Benilan, Crandall, and Pierre for the porous medium equation $u_t=Delta u^m$ for $m>1$. We extend these results for weighted equations $rho(x)u_t=Delta u^m$ for $rho(x)cong|x|^{-gamma}$ for $gammain(0,2)$.
• Author(s) :
• Troy Petitt (Politecnico di Milano)
• Matteo Muratori (Politecnico di Milano)

## [00693] Enzyme: Fast and Effective Automatic Differentiation for Academia and Industry

• Abstract : Automatic differentiation (AD) is key to training neural networks, Bayesian inference, and scientific computing. Applying these techniques requires rewriting code in a machine learning framework or manually providing derivatives. We present Enzyme, an AD extension for the industry-standard LLVM/MLIR compiler. Enzyme differentiates programs in any LLVM-based language. Unlike traditional tools, Enzyme performs AD on optimized code, resulting in a 4.2x speedup on the CPU and orders of magnitude speedup on the GPU.
• Author(s) :
• William Steven Moses (MIT)
• Valentin Churavy (MIT)
• Ludger Paehler (TUM)

## [00697] A macroscopic model for collective oscillations in self-propelled particles system

• Abstract : In this project we investigate a ‘Vicsek-style’ model, where noisy self-propelled particles align orientation and angular velocity through interaction with their neighbours. This work has been inspired by the model introduced by Chen, C., Liu, S. et al. to describe the behaviour of dense colony of bacteria, which self-organize into robust collective oscillatory motion. The main focus is to investigate how individual-level behaviours influence the emergence of macroscopic patterns in complex systems.
• Author(s) :
• Carmela Moschella (University of Vienna )

## [00698] Rigidity for Sobolev inequalities and radial PDEs on Cartan-Hadamard manifolds

• Abstract : We aim at classifying all the Cartan-Hadamard manifolds supporting an optimal function for the $p$-Sobolev inequality. We prove that, under the validity of the Cartan-Hadamard conjecture, which is known to be true in dimension $nle 4$, the only such manifold is $mathbb{R}^n$, up to isometries. We also investigate radial solutions to the related $p$-Laplace Lane-Emden equation, obtaining rigidity of finite-energy solutions regardless of optimality. Furthermore, we study the asymptotic behavior of infinite-energy solutions.
• Author(s) :
• Matteo Muratori (Politecnico di Milano)
• Nicola Soave (Politecnico di Milano)

## [00700] Enhanced Numerov method for the solution of Boundary Value Problems

• Abstract : Boundary Value Methods, BVMs are methods based on the Linear Multistep Methods, LMMs. The BVMs were introduced to overcome some of the limitations of the LMMs.
In this work, a BVM based on the Numerov method is derived. This is achieved by constructing the Numerov method via interpolation and collocation process and implementing it as a BVM. Numerical tests on both linear and nonlinear Boundary Value Problems, BVPs were presented using this enhanced Numerov method.
• Author(s) :
• Grace Oluwafunke ALAO (Covenant University)

## [00706] Peak and Short-term Electricity demand using Kalman Filtered Monte-Carlo Method

• Abstract : The study seeks to predict the next day’s peak and energy demand in Ghana. Since electricity can’t be stored in large quantities for an extended period of time, hence making it relevant to predict the demand by consumers. Moreover, a peak demand forecast becomes necessary since transmission companies lose energy during peak periods. Therefore, a Kalman-filtered Monte Carlo method was implemented to forecast the peak and short-term demand.
• Author(s) :
• Frank Kofi Owusu (Kumasi Technical University)
• Nana Kena Frempong (Kwame Nkrumah University of Science and Technology)
• Peter Amoako Yirenkyi (Kwame Nkrumah University of Science and Technology)
• Isaac Adjei Mensah (Kwame Nkrumah University of Science and Technology)

## [00709] Mathematical modeling reveals P2X1 purinoceptor antagonist as a male contraceptive

• Abstract : Condoms and vasectomies are the only male contraceptive options with disruption of foreplay and reversibility issues. The vas deferens smooth muscle (VDSM) contracts for sperm transportation. The pharmacological inhibition of VDSM contraction might explore promising new contraceptives. We established a mathematical model of VDSM cell using ordinary differential equations for an insilico electrophysiological investigation. The findings from our mathematical model reveal that the P2X1-purinoceptors antagonist 2-phenyl-5,6,7,8- tetrahydroquinoxaline might be considered as a new male contraceptive.
• Author(s) :
• CHITARANJAN MAHAPATRA (Paris-Saclay Institute of Neuroscience – CNRS)
• Ashish Kumar Pradhan (Indian Institute of Sciences Bangalore)

## [00713] Mathematical Modeling of Lymphatic Filariasis-Buruli ulcer co-infection

• Abstract : A mathematical model for Lymphatic Filariasis -Buruli ulcer co-infection is explored to provide a theoretical analysis of the disease’s dynamics. The disease free equilibrium is proved to be locally asymptotically stable; the model was found to be showing transcritical and backward bifurcation, time dependent controls are incorporated to obtain necessary conditions for optimal control of the diseases. Numerical simulation results suggest best strategy in controlling the diseases is using all the controls at the same time.
• Author(s) :
• Helen Olaronke Edogbanya (Federal University Lokoja)
• Helen Olaronke Edogbanya (Federal University Lokoja)
• Zamurat Ayobami Adegboye (Institute of Mathematical and Physcical Sciences, IMSP-UAC, Dangbo)

## [00716] Resource Efficient Boolean Function Solver on Quantum Computer

• Abstract : Grover’s algorithm is the best-known quantum search algorithm for problems when classical ones cannot outperform brute-force search. We propose several novel techniques to improve efficiency in solving boolean equations under Grover’s algorithm framework. A W-cycle circuit construction strategy and a greedy compression technique are proposed for the oracle to reduce quantum resource usage. A randomized Grover’s algorithm further reduces the circuit depth. Numerical results on boolean quadratic equations demonstrate the advantage of the proposed techniques.
• Author(s) :
• Xiang Li (Fudan University)
• Hanxiang Shen (Fudan University)
• Yingzhou Li (Fudan University)
• Weiguo Gao (Fudan University)

## [00717] Approximate Secular Equations for the Cubic Regularization Subproblem

• Abstract : The cubic regularization method (CR) is a popular algorithm for unconstrained non-convex optimization. At each iteration, CR solves a cubically regularized quadratic problem, called the cubic regularization subproblem (CRS). In this paper, we propose and analyze a novel CRS solver based on an approximate secular equation, which requires only some of the Hessian eigenvalues and is therefore efficient. Numerical experiments on real data-sets show the performances of the proposed method.
• Author(s) :
• Yihang Gao (The University of Hong Kong)
• Man-Chung Yue (The University of Hong Kong)
• Michael Kwok-Po Ng (The University of Hong Kong)

## [00723] Density Maximum Effect on Natural Convection in a Porous Enclosure

• Abstract : The maximum density effect on natural convection in an enclosure filled with porous medium is numerically examined. One of the vertical walls is either fully or partially heated and various thermal boundary walls are considered for the cooling location. The nonlinear partial differential equations are solved by finite volume method together with power-law-scheme using SIMPLE algorithm. The qualitative results are expressed in the graphical form. The motivation for the study is the cooling of equipment.
• Author(s) :

## [00726] Considerations of similarity with Sato’s hyperfunction and Birkhoff-Rott equation

• Abstract : Many fluid phenomena such as vortices have singularities, and these phenomena can be mathematically described by distribution functions. However, the vortex layer has not been described by distribution functions yet.
In this study, we have compared the Sato’s hyperfunction with the Birkhoff-Rott equation, which describes the time evolution of the vortex layer, and discussed whether the Sato’s hyperfunction is useful for describing the vortex layer. Moreover, we have considered the similarity between these two equations.
• Author(s) :
• Yuya Taki (Graduate School of Science and Engineering, SOKA University)
• Yoshio Ishii (Faculty of Science and Engineering, SOKA University)

## [00729] q-LAPLACE TRANSFORMS FOR THE PRODUCT OF BASIC ANALOGUE FOR H-FUNCTIONS FOR TWO VARIABLES AND THE GENERAL CLASS OF q-POLYNOMIALS

• Abstract : The q-Laplace transforms for the product of basic analogue of H-function of two variables and the general class of q-polynomials has been evaluated in the present paper. Few cases of the main outcomes including the applications involving the basic analogues of Fox’s H-functions as well as general class of q-polynomial are also evaluated.
• Author(s) :
• Vijay Kumar Vyas (Sur University College,Oman)
• Ali A. AL-JARRAH (Sur University College,Oman)

## [00735] Turing instability of a diffusive predator-prey model with Monod-Haldane response

• Abstract : In this talk, we discuss the asymptotic behavior and Hopf bifurcation of the Monod-Haldane predator-prey model with diffusion. The stability of the positive equilibrium and the existence of Hopf bifurcation are investigated by analyzing the distribution of eigenvalues without diffusion. The diffusion-driven instability of the positive equilibrium solutions and Turing instability region regarding the parameters are established. Finally, we show the numerical simulations provided to illustrate theoretical results.
• Author(s) :
• Muniyagounder Sambath (Periyar University )

## [00738] Proper Orthogonal Decomposition methods for the Navier Stokes equations

• Abstract : In this talk we study numerical approximations to the incompressible Navier-Stokes equations by
means of proper orthogonal decomposition (POD) methods. Several questions are considered:
the influence of including snapshots that approach the velocity time derivative and the influence
of considering different discretizations for the nonlinear term in the full order model and the reduced order model. Error bounds with constants independent of the Reynolds numbers are obtained in the numerical analysis.
• Author(s) :

## [00743] Recent Advances on POD methods for the Navier-Stokes equations.

• Abstract : We present some recent advances on proper orthogonal decomposition (POD) methods for the Navier-Stokes equations. Among them, recovering the pressure in a robust manner when the snapshots are discretely divergence-free. We analyze the different sources of error and how they affect the pressure recovery. We also study how to adapt the POD method for varying values of the Reynolds number.
• Author(s) :
• Bosco García-Archilla (Universidad de Sevilla)

## [00744] On the Burgers-type equations used in soft solid acoustics

• Abstract : A strain-rate model of soft viscoelastic solid is presented. The constitutive law accounts for finite strain, incompressibility, material frame-indifference, nonlinear elasticity, and viscous dissipation. Shear waves are governed by a nonlinear viscous wave equation, of which a one-way Burgers-type approximate equation is derived. Analysis of the travelling wave solutions shows that the two equations produce distinct solutions, unless amplitudes are infinitesimal. In the inviscid case, links with simple wave theory are established.
• Author(s) :
• Harold Berjamin (School of Mathematical and Statistical Sciences, University of Galway, University Road, Galway, Republic of Ireland)

## [00748] New probabilistic algorithms for scientific supercomputing

• Abstract : Sustained strong scalability is hard to sustain beyond 10K processors due to the communication and synchronisation involved in domain decomposition for PDEs. Seeking to overcome them, Spigler and Acebrón introduced probabilistic domain decomposition, which inserts stochastic calculus in the formulation—however with slow error convergence. I will present a hybrid idea, SpAc, which retains most of the scope for embarrassing parallelism, while being orders of magnitude faster. Proof of concept supercomputing simulations will be discussed.
• Author(s) :
• Francisco Bernal (Carlos III University of Madrid)

## [00750] Bayesian inverse problems for some hyperbolic conservation laws

• Abstract : We study some inverse problems for hyperbolic conservation laws. Given observations of the entropy solution, we consider the problem of identifying the initial field or the flux function. Due to shockwaves, direct observations of the entropy solution are not “regulated” enough to fit in the Bayesian framework in Stuart (2010). To get round this, we propose a new approach by studying the trajectories for hyperbolic conservation laws and exploring their existence, uniqueness and stability.
• Author(s) :
• Duc-Lam Duong (LUT University)
• Duc-Lam Duong (LUT University)
• Masoumeh Dashti (University of Sussex)

## [00751] Crack Loading and Growth Analyses with the Virtual Element Method

• Abstract : The virtual element method is a modern discretization scheme for solving boundary value problems on polytopal meshes, sparing the explicit knowledge of element shape functions. In the context of numerical fracture mechanics, crack tip loading analyses and in particular crack growth simulations benefit from its ability of handling arbitrary complex meshes straightforwardly. This work aims to discuss challenges and opportunities of implementing concepts of fracture mechanics in the context of the virtual element method.
• Author(s) :
• Kevin Schmitz (University of Kassel)
• Andreas Ricoeur (University of Kassel)

## [00755] A variational approach for nonlinear elasticity

• Abstract : This research concerns the Weighted Energy-Dissipation approach for nonlinear elasticity. We introduce a family of $epsilon-$dependent functionals defined over entire trajectories and we prove that they admit minimisers which are solutions of the corresponding Euler-Lagrange problem. Considering the limit $epsilon rightarrow 0$ we prove that those minimisers converge to the solutions of a specific nonlinear elasticity equation. Eventually, linearized elastic energies are proven to be the $Gamma$-limits of the rescaled nonlinear energies.
• Author(s) :
• Riccardo Voso (University of Vienna)

## [00756] Using photogrammetry for the objective morphological study of early violins

• Abstract : Some early violins were reduced during their history to fit imposed morphological standards. We propose an objective photogrammetric approach to differentiate between a reduced and an unreduced instrument by examining 3D meshes, previously validated with a sub-millimetre accuracy through a comparison with CT scans. We show how quantitative and qualitative features can be automatically extracted from the meshes with geometrical, statistical and machine learning tools, allowing to successfully highlight differences between reduced and unreduced instruments.
• Author(s) :
• Philémon Beghin (UCLouvain)
• François Glineur (UCLouvain)
• Anne-Emmanuelle Ceulemans (UCLouvain)

## [00757] Effect of electrostatic forces and moments on cracked electrostrictive dielectrics

• Abstract : Going beyond the scope of solely mechanical considerations, fracture mechanics of smart dielectrics is additionally concerned with the implications of electric fields on crack tip loading. In this work, the oftentimes neglected electric body and surface forces as well as body couples stemming from the Maxwell stress tensor are studied in the context of a crack in an infinite electrostrictive dielectric by exploiting holomorphic potentials and Cauchy’s integral formulae within the framework of complex analysis.
• Author(s) :
• Lennart Behlen (University of Kassel)
• Daniel Wallenta (University of Kassel)
• Andreas Ricoeur (University of Kassel)

## [00759] CODIMENSION-ONE BIFURCATIONS OF AN SIRS-TYPE MODEL FOR COVID-19 REINFECTION CASE

• Abstract : During the omicron wave, reinfection cases with the same or different variants occur in many countries, and it is possible to get COVID-19 two or even more times. We propose a SIRS (Susceptible-Infected-Recovery-Susceptible) epidemic model for the spread of three major variants of COVID-19, i.e. Alpha, Delta, and Omicron. We detect some bifurcation points and by some numeric simulations, we generate the dynamics of the model’s behaviors for various pairs of parameter values.
• Author(s) :
• Livia Owen (Parahyangan Catholic University)

## [00762] On the dissolution of particles subject to natural convection

• Abstract : The dissolution of a solid spherical particle is a canonical problem that finds many areas of application, including the pharmaceutical industry. In this work, we provide a generalized theory that tackles the role of natural convection in the surrounding dissolving medium. We investigate its effects on hydrodynamics and how it interacts with the diffusion during dissolution to deform the particle geometry whilst altering the release profile of pharmaceutical ingredients, a key aspect in drug delivery.
• Author(s) :
• Milton Assunção (University of Limerick)
• Michael Vynnycky (University of Limerick)
• Kevin Moroney (University of Limerick)

## [00765] V-KEMS: Tackling industrial and COVID problems via virtual study groups

• Abstract : During the pandemic a group of UK mathematicians formed the Virtual Forum for Knowledge Exchange in the Mathematical Sciences (V-KEMS). This ran many online virtual study groups (VSGs), using mathematics to tackle urgent societal challenges. These varied from keeping shops, workplaces, and universities safe, to advising the transport, healthcare, and leisure industries. VSGs were so effective that they informed government policy. My talk will describe how VSGs work, and plans for their future development.
• Author(s) :
• Chris Budd (University of Bath)

## [00770] Rellich eigendecomposition of paraHermitian matrices, with applications

• Abstract : Let $H(z)$ be paraHermitian, that is, analytic and Hermitian on the unit circle $S^1$. We prove that $H(z)=U(z)D(z)U(z)^P$ where, for all $z in S^1$, $U(z)$ is unitary, $U(z)^P=U(z)^*$, and $D(z)$ is real diagonal; moreover, $U(z), D(z)$ are analytic in $w=z^{1/N}$ for some positive integer $N$, and $U(z)^P$ is the paraHermitian conjugate of $U(z)$. We discuss the implications on the svd of an $S^1$-analytic matrix and the sign characteristics of unimodular eigenvalues of $*$-palindromic matrix polynomials.
• Author(s) :
• Vanni Noferini (Aalto University)
• Giovanni Barbarino (Aalto University)

## [00771] New class of Nested Hierarchical matrices in two and three dimensions

• Abstract : I’ll discuss a new class of nested Hierarchical matrices in $2$D (HODLR2D^2) and $3$D (HODLR3D^2). Using this Hierarchical framework, one can perform a matrix-vector product that scales almost linearly; hence, large dense linear systems arising out of $N$ body problems can be solved using iterative solvers with almost linear complexity. Also, I’ll discuss its performance over other Hierarchical matrices and applications in solving integral equations.
• Author(s) :
• Ritesh Khan (Indian Institute of Technology Madras)
• Sivaram Ambikasaran (Indian Institute of Technology Madras)

## [00772] Fourth Order Fractal Quartic Spline Method for Solving Second Order Boundary Value Problem

• Abstract : This work introduces a fourth-order fractal quartic spline solution for a second-order BVP $u”=f(x,u,u’)$ with Dirichlet boundary conditions. We obtain the fractal quartic spline solution using function values and second and third-order derivative values at the knots. Using shooting method to this BVP with the fourth-order explicit Runge-Kutta method, we obtain the parameters for the fractal spline solution. Numerical illustrations are given to support the proposed theoretical results.
• Author(s) :
• ARYA KUMAR BEDABRATA CHAND (Indian Institute of Technology Madras)
• Vijay V (Indian Institute of Technology Madras)

## [00773] Machine Learning Model for Thin Metal Sheet Counting and Thickness Measurement

• Abstract : In this talk we are to discuss about counting stacked metal foils in real time. For the purpose a non-contact method based on broadband X-ray absorption spectra was employed to scan the experimental samples and artificial neural network was built to count and measure thickness of the stacked foil. Further, the attained results are compared with polynomial fitting model and linear regression in order to verify the difference in prediction accuracy of the three models.
• Author(s) :
• Elayaperumal Ayyasamy (Anna University, Chennai)

## [00775] Weak Shock diffraction in a van der Waals gas

• Abstract : The objective of this study is to analyze the diffraction of a weak shock hitting a thin semi-infinite wedge screen. The Riemann problem is formulated for two-dimensional compressible Euler system for real gas considering the van der Waals equation of state. To study the incident and diffracted shock the self-similar flow has been considered. Also, in some regions of semi-infinite wedge screen rarefaction waves are found and studied. The real gas effects have been studied.
• Author(s) :
• Gaurav Gaurav (IIT(BHU), Varanasi, India)

## [00776] Towards a modeling class for port-Hamiltonian systems with time-delay

• Abstract : The framework of port-Hamiltonian (pH) systems is a broadly applicable modeling paradigm. In this talk, we extend the scope of pH systems to time-delay systems. Our definition of a delay pH system is motivated by investigating the Kalman-Yakubovich-Popov inequality on the corresponding infinite-dimensional operator equation. Moreover, we show that delay pH systems are passive and closed under interconnection. We describe an explicit way to construct a Lyapunov-Krasovskii functional and discuss implications for delayed feedback.
• Author(s) :
• Dorothea Hinsen (TU Berlin)
• Tobias Breiten (TU Berlin)
• Benjamin Unger (University of Stuttgart)

## [00790] Machine learning methods with error analysis for optimal control problems

• Abstract : We consider optimal control with partial differential equations (()PDE()) and present a numerical method based on machine learning including control error analysis. Physics-Informed Neural Networks (()PINN()) are used with the cost and penalty terms for the PDE as loss function. The model size is iteratively increased until the a posteriori estimated control error satisfies a given accuracy. The method is illustrated with numerical examples for 1D heat transfer and 3D turbine activation.
• Author(s) :
• Georg Vossen (Kreleld University of Applied Sciences)
• Semih Sirin (Kreleld University of Applied Sciences)
• Nicolai Friedlich (Kreleld University of Applied Sciences)

## [00791] FunFact: Tensor Decomposition, Your Way

• Abstract : FunFact simplifies the design of matrix and tensor factorization algorithms. It features a powerful programming interface that augments the NumPy API with Einstein notations for writing concise tensor expressions. Given an arbitrary forward calculation scheme, the package will solve the inverse problem using stochastic gradient descent, automatic differentiation, and multi-replica vectorization. It is GPU- and parallelization-ready thanks to modern numerical linear algebra backends such as JAX/TensorFlow and PyTorch. We demonstrate a variety of use cases.
• Author(s) :
• Daan Camps (Lawrence Berkeley National Laboratory)
• Yu-Hang Tang (NVIDIA)

## [00797] Shape optimization methods and Stokes equations

• Abstract : In this work, we want to detect the shape and the location of an inclusion w via some measurement on the
boundary of the domain D. In practice, the body w is immersed in a fluid flowing in a greater domain D and
governed by the Stokes equations. We aim to study the inverse problem with Neumann and mixed boundary
conditions.
• Author(s) :
• Chahnaz Zakia TIMIMOUN (Université Oran1 Ahmed Ben Bella)

## [00798] Accelerating Low-Order Matrix-Free Finite Element Methods for Geophysics on GPU Architectures

• Abstract : Low-order matrix-free FEMs offer an alternative approach that avoids the need to construct a global stiffness matrix. In this study, we compare the performance of low-order matrix-free FEMs with a sparse-matrix approach on GPU architectures for geophysics applications. Our results show that low-order matrix-free FEMs can significantly accelerate the solution of large linear systems on GPU architectures.
• Author(s) :
• Yohann Dudouit (Lawrence Livermore National Lab)
• Randy Settgast (Lawrence Livermore National Lab)
• Nicola Castelletto (Lawrence Livermore National Lab)

## [00799] Local Exactness of de Rham Conforming Hierarchical B-spline Differential Forms

• Abstract : Conservation laws present in partial differential equations arising in fluid mechanics and electromagnetics are frequently described using the de Rham sequence of differential forms. Stability of numerical methods solving these equations requires discrete preservation of these conservation laws. This talk will present sufficient local exactness criteria for a set of smooth, high-order, isogeometric, locally-refinable spline spaces in Euclidean space of arbitrary dimension in order to enable stable high-order, geometrically-precise finite element analyses.
• Author(s) :
• Kendrick M Shepherd (Brigham Young University)
• Deepesh Toshniwal (TU Delft)

## [00805] A Topological Model of Textile Structures

• Abstract : Textiles are complex entangled structures made of threads embedded in a thickened plane. From nano to macro scale and high functionality to pure esthetic, they have been studied and fabricated for thousands of years in disciplines as diverse as materials science and art. Currently an active research topic in mathematics, we will present a topological model that aims to define, construct and classify specific textile structures from a knot theory viewpoint and highlight some applications.
• Author(s) :
• Sonia Mahmoudi (Drexel University)

## [00809] Mathematical Aspects of Metaheuristics in Medical Imaging and Pattern Recognition

• Abstract : Medical imaging and pattern recognition have very important applications in the health and other industrial sectors. In this talk, we will be focusing on the mathematical model that deals with high-order graph matching using a metaheuristic technique. This model has been tested real-life images including identifying white blood cells in human blood. The models work on the idea of artificial intelligence and have a high level of efficiency with good results. The role of AI is in terms of AI-based metaheuristics which are used as search and optimization techniques to address aforementioned problems.
• Author(s) :
• Anupam Yadav (Dr BR Ambedkar National Institute of Technology Jalandhar)

## [00817] Understanding Flood Flow Physics via Data-Informed Learning

• Abstract : Modeling the dynamics of fast-moving floods has historically been an intractable problem due to the inherent complexity and multi-scale physics of the underlying processes involved. Recent advancements in physics-constrained machine learning indicate that neural networks can be used to effectively model phenomena for which physical laws are poorly understood. By combining real data and first principles, we show that we can enhance knowledge about the underlying physics of flood phenomena via the learned constitutive laws.
• Author(s) :

## [00820] Chemotaxis system with signal-dependent motility and the singular limit problem

• Abstract : We study the reaction-diffusion model that consists of equations that govern the evolution of bio-cells in a chemotactic environment. In our modeling framework, we assume that if the chemical concentration is low, then the cells move actively, whereas if the chemical concentration is high, they become less active. As we take a limit of conversion process, we formally obtain the singular limit problem of Fokker-Planck type diffusion. The aim of this study is to prove the global well-posedness of the singular limit problem and its convergence rigorously.
• Author(s) :
• Changwook Yoon (Chungnam National University)
• Yong-Jung Kim (KAIST)

## [00821] ADAPTIVE QUADRATIC DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD FOR THE UNILATERAL CONTACT PROBLEM

• Abstract : The proposed title of my talk will be ADAPTIVE QUADRATIC DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD FOR THE UNILATERAL CONTACT PROBLEM . In the talk, I will be discussing about employing discontinuous Galerkin methods (DG) for the finite element approximation of frictionless unilateral contact problem using quadratic finite elements over simplicial triangulation. We shall analyze a posteriori error estimates in the DG norm wherein, the reliability and efficiency of the proposed a posteriori error estimators will be addressed. Further we will show that numerical results substantiate the theoretical findings,

• Author(s) :
• Kamana Porwal (IIT DELHI)

## [00822] Dynamics and Diffusion Limit of a Two-Species Chemotaxis Model

• Abstract : The traveling wave solutions to a two-species chemotaxis model with logarithmic sensitivity, which describes the initiation of angiogenesis using reinforced random walks theory and the chemotactic response of two-interacting species to a chemical stimulus are examined. The existence, asymptotic decay rates, stability, wave speed, and convergence, as the chemical diffusion coefficient goes to zero, of the traveling wave solutions are discussed.
• Author(s) :
• Annapoorani N (Bharathiar University)

## [00823] Weighted Trace-Penalty Minimization for Full Configuration Interaction

• Abstract : A novel unconstrained optimization model named weighted trace-penalty minimization (WTPM) is proposed to address the extreme eigenvalue problem arising from the Full Configuration Interaction (FCI) method. The coordinate descent method is adapted to WTPM and results in WTPM-CD method. With the sparse features of both FCI matrices and the global minimizers in mind, the reduction of computational and storage costs shows the efficiency of the algorithm.
• Author(s) :
• Weiguo Gao (Fudan University)
• Yingzhou Li (Fudan University)
• Hanxiang Shen (Fudan University)

## [00824] Asymptotics for Some Singular Limits

• Abstract : The asymptotic behavior of solutions as a small parameter tends to zero is determined
for a variety of singular-limit PDEs. In some cases even existence for a time independent of
the small parameter was not known previously. New examples for which uniform existence
does not hold are also presented.

Some of the results are joint work with Samuel Nordmann.

• Author(s) :
• Steve Schochet (Tel Aviv University)

## [00826] Saffman-Taylor fingers selection mechanism in non-newtonian fluids

• Abstract : We present an analytical approach, based on the Wentzel-Kramers-Brillouin technique, to predict the finger width of a simple fluid driving a non-Newtonian, power-law fluid. We find that in the limit of small surface tension, (nu), the relation between the dimensionless (nu), viscosity and finger width, (Lambda), has the form: (Lambda sim frac{1}{2} – mathrm{O}(nu ^ {-1/2})) for shear thinning case, and (Lambda sim frac{1}{2} + mathrm{O}(nu^{2/(4-n)})) for shear thickening case. A detailed comparison is provided.
• Author(s) :
• Diksha Bansal (IIIT Delhi)
• Dipa Ghosh (IIIT Delhi)
• Sarthok Sircar (IIIT Delhi)

## [00829] A Cartesian Grid-Based Boundary Integral Method for Moving Interface Problems

• Abstract : Moving interface problems are ubiquitous in natural sciences. Often the interface motion is coupled with PDEs in the bulk domain. This talk will present a Cartesian grid-based boundary integral method for solving moving interface problems. Layer potentials are evaluated by solving simple interface problems on a Cartesian grid to take advantage of fast solvers such as FFTs and the geometric multigrid method. Numerical simulations, including crystal growth and two-phase flows, will be reported.
• Author(s) :
• Han Zhou (Shanghai Jiao Tong University)
• Wenjun Ying (Shanghai Jiao Tong University)

## [00833] Exact controllability for imperfect interface problems

• Abstract : We study the exact internal and boundary controllability for a second order linear evolution problem defined in a two-component domain. We prescribe a homogeneous Dirichlet condition on the exterior boundary and a jump of the displacement proportional to the conormal derivatives on the interface. This last condition is the mathematical interpretation of an imperfect interface. The results are achieved via a constructive method known as Hilbert Uniqueness Method, HUM for short, introduced by J. -L. Lions. Unlike classical cases, we find lower bounds for the control times depending not only on the geometry of the domain and on the coefficient matrix of our problems but also on the coefficient of proportionality of the jump with respect to the conormal derivatives.

References
[1] S. Monsurro, A. K. Nandakumaran, C. Perugia, Exact Internal Con- trollability for a Problem with Imperfect Interface, Appl. Math. Op- tim. (2022), 1-33.
[2] S. Monsurro`, A. K. Nandakumaran, C. Perugia, A Note on the Exact Boundary Controllability for an Imperfect Transmission Problem, Ric. Mat. 40 (2021), 1-18.

• Author(s) :
• Sara Monsurrò (University of Salerno)

## [00835] A shifted LOPBiCG method for solving nonsymmetric shifted linear systems

• Abstract : Premature convergence of the seed system can lead to shifted systems being unsolved when applying shifted Krylov subspace methods to solve shifted linear systems. To avoid this, a seed-switching technique may be a method of choice; however, the conventional product-type methods cannot use this technique since it requires the collinear residuals between the seed and shifted systems. We propose a variant of the shifted BiCGStab method so that the technique can be applied.
• Author(s) :
• Ren-Jie Zhao (Nagoya University)
• Tomohiro Sogabe (Nagoya University)
• Tomoya Kemmochi (Nagoya University)
• Shao-Liang Zhang (Nagoya University)

## [00836] Reynolds-blended weights for BDDC in applications to Navier-Stokes equations

• Abstract : We solve incompressible Navier-Stokes equations by the finite element method with one step of the Balancing Domain Decomposition by Constraints (BDDC) method. This method requires a scaling operator at the interface between subdomains. We introduce a new interface scaling tailored to Navier-Stokes equations. The weights in this averaging consider a local Reynolds number. This Reynolds-blended scaling is compared with several existing approaches on 3D lid-driven cavity and backward-facing step problems.
• Author(s) :
• Martin Hanek (Czech Technical University in Prague, Institute of Mathematics of the Czech Academy of Sciences)

## [00841] Destabilization of interfacial elastic waves due to friction

• Abstract : Elasticity theory permits several interfacial wave solutions. In antiplane elasticity, the well-known Love wave occurs in bonded contact of an elastic layer on a dissimilar elastic half-space. A new interfacial elastic wave solution, namely the antiplane slip wave, which occurs in slipping contact of a layer on a half-space or on another layer will be discussed. It is shown that the interfacial elastic waves are often destabilized when frictional slipping occurs.
• Author(s) :
• Ranjith Kunnath (Mahindra University)

## [00842] Iterative projection methods for solving cone-constrained eigenvalue complementarity problems

• Abstract : Cone-constrained eigenvalue complementarity problems are associated with unstable modes and vibrations of dynamic systems in engineering. In this talk, iterative projection methods are proposed to quickly search the corresponding K-eigenvalues and K-eigenvectors. Particularly, it is also designed to find specific solutions of the considered problem. Convergence analysis is studied in detail and the sufficient conditions are given. Numerical results are shown to confirm the advantages of our algorithms.
• Author(s) :
• Nan Li (Nagoya University)
• Tomohiro Sogabe (Nagoya University)
• Jun-Feng Yin (Tongji University)
• Tomoya Kemmochi (Nagoya University)
• Shao-Liang Zhang (Nagoya University)

## [00845] Hierarchical simulation of shallow water flows using moment models

• Abstract : We introduce hierarchical moment models as a flexible way to derive model hierarchies for shallow flows. The hierarchical models are based on velocity expansion and include the standard shallow water equations but also allows for more accuracy using more equations. We exemplify 1D and 2D application cases and highlight runtime and accuracy improvements with respect to standard models. Lastly, we discuss the future extension towards adaptive self-learning models that leverage the hierarchical model structure.
• Author(s) :
• Julian Koellermeier (University of Groningen)

## [00846] ESR fractional model with non-zero uniform average blood velocity

• Abstract : This article discusses a new solution to the time-fractional ESR model, taking into account the non-zero average blood velocity. We not only obtain an analytic solution to the generalized model of Sharma et al. and da Sousa et al., but also we present some new results which establish that the developed fractional order model is better-suited one by using which predicting the ESR rate can take place more accurately.
• Author(s) :
• Abhijit Shit (Indian Institute of Technology Guwahati)
• Swaroop Nandan Bora (Indian Institute of Technology Guwahati)

## [00847] Acute Lymphoblastic Leukemia diagnosis and treatment: a mathematical analysis

• Abstract : Despite the recent medical advances, treatments are unsuccessful in 15-20% of cases in Acute Lymphoblastic Leukemia ( ALL ) patients. The main aim of our study is to analyse data from bone marrow samples and to use artificial intelligence to improve current techniques of diagnosis in ALL protocols. Using machine learning techniques, our results predict bone marrow behavior and allow us to classify patients depending on their relapse risk.
• Author(s) :
• Ana Niño-López (Department of Mathematics, Universidad de Cádiz)
• Salvador Chulián (University of Cádiz)
• Álvaro Martínez-Rubio (Department of Mathematics, Universidad de Cádiz)
• María Rosa (Department of Mathematics, Universidad de Cádiz)

## [00850] Boundary stabilization of time fractional reaction- diffusion systems with time delays

• Abstract : Paper aims is to design boundary control for the considered fractional reaction-diffusion system with delays by proving the wellposedness of kernel function using backstepping method. An invertible Volterra integral transformation is used to find an appropriate stable target system. Different from existing ones, the results are discussed using Lyapunov-Krasovskii theory and sufficient conditions are derived with the help of LMI approach. Finally, proposed conditions are numerically validated over time fractional-order reaction-diffusion cellular neural network model.
• Author(s) :
• Mathiyalagan Kalidass (Bharathiar University, Coimbatore)

## [00853] Numerical Approximation of Fractional Burgers Equation with Non-singular Time-Derivatives

• Abstract : Fractional Burgers equation (FBE) is a partial differential equation being non-linear in space. This work presents a numerical method to solve a time-FBE with second order of convergence. The fractional time-derivative is taken as non-singular derivative whose kernel contains the Mittag-Leffler function. The discretization of derivatives is done by using finite difference method and Newton iteration method. Developed numerical scheme is stable and convergent in L^∞ norm. Examples have been illustrated to validate the theory.
• Author(s) :
• Rajesh Kumar Pandey (IIT BHU, Varanasi)

## [00855] Mathematical modelling of edge wave on a functionally graded thermo-poro-elastic plate

• Abstract : An analysis of flexural edge waves propagating in a thermally affected poroelastic plate supported by a Pasternak foundation is presented. The Kirchhoff plate theory and Moore-Gibson-Thomson (MGT) thermos elasticity theory are applied to study the displacement field of the plate and temperature distribution on edge wave, respectively. There are seven different porosity models considered to compare the edge wave behavior in different porous structures. The grid dispersion is optimized by applying the FDM to the wave equation. The effects of porosity, temperature, elastic foundation, cutoff-frequency, and wave frequency are investigated numerically.
• Author(s) :
• Santanu Manna (Department of Mathematics, Indian Institute of Technology Indore, Simrol, Khandwa road, Indore-453552, M.P., India)
• Rahul Som (Department of Mathematics, Indian Institute of Technology Indore, Simrol, Khandwa road, Indore-453552, M.P., India)
• Tanisha Kumari (Department of Mathematics, Indian Institute of Technology Indore, Simrol, Khandwa road, Indore-453552, M.P., India)

## [00857] An ecological study of mathematical model on intermittent phytoplankton distribution

• Abstract : A microscale ecological study is done using the closure approach to understand the impact of productivity controlled by geographical and seasonal variations on the intermittency of phytoplankton. Parameters are estimated from the nature of productivity and spread of phytoplankton density during field observation done at four different locations of Tokyo Bay. The model validation shows that our results are in good agreement with the field observation and succeeded in explaining the intermittent phytoplankton distribution.
• Author(s) :
• Sandip Banerjee (Indian Institute of Technology Roorkee)

## [00858] An adaptive spectral method for oscillatory second-order linear ODEs with frequency-independent cost

• Abstract : I will introduce an efficient method for solving 2nd order, linear ODEs whose solution may vary between highly oscillatory and slowly changing over the solution interval. Within a marching scheme, the solution is generated either via a nonoscillatory phase function (computed by defect correction), or spectral collocation, whichever is more efficient for the current timestep. With numerical experiments I will show that our algorithm outperforms other state-of-the-art oscillatory solvers and has a frequency-independent runtime.
• Author(s) :
• Fruzsina Julia Agocs (Center for Computational Mathematics, Flatiron Institute)
• Alex Harvey Barnett (Center for Computational Mathematics, Flatiron Institute)

## [00859] A mathematical model of immunotherapy: CD19 relapses in B leukemia

• Abstract : B-cell Acute Lymphoblastic Leukemia (B-ALL) is the most common type of pediatric leukaemia. For relapsing patients, a treatment possibility is chimeric antigenic receptor (CAR)-T cells, which recognize target cells with the antigen CD19, expressed in B-ALL. We show a mathematical model based on partial differential equations and focus on how CAR-T cell therapy can lead to positive or negative CD19 relapses. The analysis presented represents real-life scenarios, where optimal treatment can be studied.
• Author(s) :
• Salvador Chulián (Department of Mathematics, University of Cádiz)
• Álvaro Martínez-Rubio (Department of Mathematics, University of Cádiz)
• Ana Niño-López (Department of Mathematics, Universidad de Cádiz)
• María Rosa (Department of Mathematics,)

## [00860] Probabilistic Domain Decomposition: Challenging Amdahl’s curse on partial differential equations.

• Abstract : Probabilistic Domain Decomposition allows solving elliptic BVPs with remarkable scalability by taking advantage of probabilistic representations of BVPs. This representation is less convenient when dealing with non linear problems or even unknown in the case of the Helmholtz equation. However, these limitations can be circumvented by introducing some iterative schemes. In this presentation we aim to provide an insight on these algorithms alongside some proof of concept results obtained in FUGAKU and CINECA.
• Author(s) :
• Jorge Morón-Vidal (University Carlos III of Madrid)

## [00861] Using elastic waves to measure mechanical stress

• Abstract : In principle, elastic waves could be used to assess the stress in a material, as the higher the stress, the faster the wave will propagate. However, the speed also depends on material parameters, which is why there are no robust (non-invasive) measurement techniques. In this talk we show how to overcome these challenges by using universal relationships between stress and wave speeds. This has led to robust measurements with either bulk waves [2] or surface waves [3].

Universal relationships in continuum mechanics are those that hold for any type of material, or constitutive choice [1]. To measure stress, it would be ideal to have a relationship between the wave speed and the stress that holds for any elastic material. However, there is only one such universal relationship: $rho v_{12}^2 – rho v_{21}^2 = sigma_{11} – sigma_{22}$, where $sigma_{ij}$ are the components of the Cauchy stress tensor, and $v_{12} (v_{21})$ is the speed of a shear wave propagating in the $x_1 (x_2)$ direction that is polarised in the $x_2 (x_1)$ direction. Inspired by this identity we propose, and experimentally validate, several new ultrasonic methods.

[1] Truesdell, Clifford, and Walter Noll. “The non-linear field theories of mechanics.” The non-linear field theories of mechanics. Springer, Berlin, Heidelberg, 1992. 1-579.
[2] Li, Guo-Yang, Artur L. Gower, and Michel Destrade. “An ultrasonic method to measure stress without calibration: The angled shear wave method.” The Journal of the Acoustical Society of America 148.6 (2020): 3963-3970.
[3] Li, Guo-Yang, et al. “Non-destructive mapping of stress and strain in soft thin films through sound waves.” Communications Physics 5.1 (2022): 1-7.

• Author(s) :
• Art Gower (University of Sheffield)
• Michel Destrade (University of Galway)
• Guo-yang Li (Harvard Medical School and Wellman Center for Photomedicine)

## [00863] Statistical Analysis of Earthquake in Nepal-Himalaya including Bengal Basin Zone

• Abstract : The statistical analysis of earthquakes in the Nepal-Himalaya and Burma plates including the Bengal Basin and Bay of Bengal Zones is investigated. There are 13352 earthquakes in the dataset with magnitudes ranging from 2 to 7.8 between January 2000 to June 2021 are collected and analyzed. The Gautenberg-Richter law is used to estimate a-values and b-values for the entire data as well as for different zones. R programming has been used for data cleaning, and data filtering as well as to carry out all the statistical analysis and visualization.
• Author(s) :
• Santanu Manna (Department of Mathematics, Indian Institute of Technology Indore, Simrol, Indore, Madhya Pradesh 453552, India)
• Harsh Joshi (University of Delhi, Hansraj College, Malka Ganj, Delhi110007, India)

## [00864] Stabilization of time-periodic flows

• Abstract : At first, I shall explain the stability and stabilizability of an ODE around a periodic trajectory. A characterization of the stability of ODEs around a periodic trajectory using the Poincare map and Floquet theory will be discussed. Then, I shall explain the extension of the idea to the parabolic type of PDEs. In particular, as an application, the stabilization of the incompressible Navier-Stokes equation around a time-periodic trajectory will be discussed.

• Author(s) :
• Debanjana Mitra (Department of Mathematics, IIT Bombay )

## [00865] A hybrid microphysical–rheological multiscale constitutive model of ferroelectrics

• Abstract : For describing mutually coupled dissipative processes in ferroelectrics, in particular ferroelectric domain switching and viscoelasticity, a hybrid micromechanical – rheological constitutive model is developed and embedded in the framework of a multiscale modeling approach. The mathematical theory is consistent against the background of rational thermodynamics and deals with two types of internal variables. The advanced modeling approach is applied to identify novel energy harvesting cycles exploiting dissipative effects, resulting in a major electric work output.
• Author(s) :
• Andreas Warkentin (University of Kassel)
• Andreas Ricoeur (University of Kassel)

## [00871] Stochastic Sampling Techniques for Muscle Recruitment Distribution with Longitudinal Prior

• Abstract : Several muscles contract and relax around joints to enable movement in humans. For each muscle, these contractions generate a wide range of muscle activation forces due to muscle redundancy. We estimate feasible muscle forces in the Bayesian framework using Markov Chain Monte Carlo methods while quantifying uncertainties in these solution samples. These solutions conform to the uncontrolled manifold theory. Furthermore, inspired by Feynman-Kac formula, we propose an approach to mimic smoothness in human movement.
• Author(s) :
• Mercy Gyamea Amankwah (Case Western Reserve University)
• Erkki Somersalo (Case Western Reserve University)
• Daniela Calvetti (Case Western Reserve University)

## [00873] Stress Intensity factor for an interface crack between two orthotropic material

• Abstract : This present article deals with the investigation of elasto-dynamic response of a finite crack under normal impact loading at the interface of two semi-infinite orthotropic strips. Laplace and Fourier Integral transforms are
employed to reduce the problem to the solution of a pair of dual integral equations. The analytical expressions of stress intensity factors of the crack at the interface problem are found.
• Author(s) :
• Anuwedita Singh (Tel Aviv University, Tel Aviv, Israel)

## [00875] Deep learning based reduced ensemble Kalman inversion for microscopic parameter estimation

• Abstract : In the scope of nonlinear multiscale problems, estimating the macroscopic distribution of the microscopic geometrical parameters given macroscopic measurements is of interest. In general, inverse estimation is challenging due to the need of derivatives of the complex forward model and the high cost of the forward solver. We introduce derivative-free ensemble Kalman inversion and deep-learning based model reduction to tackle the aforementioned challenges, and assess the performance of the proposed method on a hyper-elastic problem.
• Author(s) :
• Yankun Hong (Eindhoven University of Technology)
• Harshit Bansal (Eindhoven University of Technology)
• Karen Veroy (Eindhoven University of Technology)

## [00878] Large-amplitude problem of BGK model

• Abstract : BGK equation is a relaxation model of the Boltzmann equation for simulation of various kinetic ﬂow problems. In this work, we study asymptotic stability of the BGK model when the initial data is not necessarily close to global equilibrium pointwisely. Main diﬃculty of the BGK equation comes from the highly nonlinear structure of the relaxation operator. To overcomes this issue, we derive reﬁned control of macroscopic ﬁelds to guarantee the system enters quadratic nonlinear regime.
• Author(s) :
• Gichan Bae (Seoul National University)
• Gyounghun Ko (POSTECH)
• donghyun lee (POSTECH)
• Seokbae Yun (Sungkyunkwan University)

## [00883] Convergence of the Eberlein diagonalization method

• Abstract : The Eberlein method is a Jacobi-type process for solving the eigenvalue problem of an arbitrary matrix. In each iteration two transformations are applied on the underlying matrix, a plane rotation and a non-unitary elementary transformation. In this talk we present the method under the broad class of generalized serial pivot strategies. We provide the proof of the global convergence and give several numerical examples.
• Author(s) :
• Erna Begovic (University of Zagreb)
• Ana Perkovic (University of Zagreb)

## [00884] Time-Frequency Analysis of Functional Datasets

• Abstract : We introduce an operator valued Short-Time Fourier Transform for certain classes of operators with operator window, and show that the transform acts in an analogous way to the STFT for functions. This object reflects the time-frequency behaviour for datasets of functional data in both a intra- and inter-functional manner, showing the function-wise time-frequency distribution and cross correlation of time-frequency concentration between datapoints, hence combining desirable aspects of existing basis selection methods for functional data science.
• Author(s) :
• Monika Dörfler (University of Vienna)
• Franz Luef (Norwegian University of Science and Technology (NTNU))
• Henry McNulty (Norwegian University of Science and Technology (NTNU))
• Eirik Skrettingland (NA)

## [00885] Hybrid nanofluid of Heimenz flow over electromagnetic surface: Enhancement in thermal energy

• Abstract : Over decades, the Hiemenz ﬂow for heat transfer mechanism has gained a lot of signiﬁcant consideration from engineers and researchers owing to the optimal rates of heat transfer, pressure and mass deposition near stagnation point in high speed ﬂows. The stagnation region ﬂows, initiated by Hiemenz [1], are very frequent and extensively adopted for modeling in considerable ﬁelds, such as micro cooling systems, extrusions with a die, continuous casting, jet impingements, and-so-forth.
The novel and advanced concepts of nanofluids offer fascinating heat transfer characteristics compared to conventional heat transfer fluids. Applications of nanofluids in industries such as heat exchanging devices, cool automobile engines and welding equipment and to cool high heat-flux devices such as high power microwave tubes and high-power laser diode arrays. Hybrid nanofluids can also effectively be used for a wide variety of industries, ranging from transportation to energy production and in electronics systems like microprocessors, drug distributors to check the chemical reactions of drugs in blood, as coolants and heat exchangers for better heat transfer, as lubricators, in nuclear reactors for thermal emission and absorption, solar concentrators for absorbing much of the solar radiation, and many more.
The objective of this study to improve the heat transfer rate by solving Hiemenz ﬂow of hybrid nanoﬂuid over an electromagnetic surface.
• Author(s) :
• Islam Zari (University of Peshawar)
• Karlygash Dosmagulova (Ghent University, Belgium)
• Chinwendu Emilian MADUBUEZE (Federal university of Agriculture Makurdi Nigeria )

## [00887] Higher order Haar wavelet method for parabolic inverse problem

• Abstract : In the talk, we propose a higher order Haar wavelet method for solving parabolic inverse problem with a
control parameter. Haar wavelets are used for the spatial discretization whereas backward Euler scheme is used for
the temporal discretization. Stability results and error estimates are derived. is The proposed
method is tested on few examples and the results are compared with some existing literature.
The proposed method is performing better in terms of absolute error and maximum error.
• Author(s) :
• Gopal Priyadarshi (KIng Abdullah University of Science and Technology)

## [00892] Predicting response to pediatric leukemia with flow cytometry data

• Abstract : 15% of children with B-cell acute lymphoblastic leukemia fail to achieve response or long-term remission. With new treatments being developed to provide an alternative for this subset of patients, an improved risk classification at diagnosis can help to plan and prepare for this eventuality. Flow cytometry is currently used to characterize the leukemic clone but it has no prognosis value. In this work we use flow cytometry data at diagnosis from 250 pediatric patients from hospitals in Spain to find features associated with response by means of an array of computational methods.
• Author(s) :
• Alvaro Martínez-Rubio (University of Cadiz)
• Salvador Chulián (University of Cádiz)
• Ana Niño-López (Department of Mathematics, Universidad de Cádiz)
• Víctor Manuel Pérez-García (University of Castilla-La Mancha)
• María Rosa (University of Cadiz)

## [00894] ODE models relating irrigation to kidney bean yield

• Abstract : Chippewa Valley Bean, located in Wisconsin, USA, is the world’s largest processor of dark red kidney beans and works with farmers over several states. Current trends in farming are pressuring producers to generate higher yields with fewer resources, particularly water resources. This project describes our work creating ODE models that describe the relationship between irrigation inputs, soil parameters, and kidney bean yields that CVB can use to advise farmers for productive yet sustainable practices.
• Author(s) :
• Tyler Skorczewski (University of Wisconsin Stout)
• Keith Wojciechowski (University of Wisconsin Stout)

## [00896] Error analysis of Jacobi modified projection-type method for weakly singular Volterra–Hammerstein integral equations

• Abstract : In this paper, polynomially based projection-type and modified projection-type methods are developed for weakly
singular Volterra-Hammerstein integral equations of the second kind, using Jacobi polynomials as basis functions.
In general, this type of equations has a singular behavior at the left endpoint of the interval of integration with
exact solutions being typically nonsmooth. In the considered approach a transformation of the independent variable
is first introduced in order to find a new integral equation with a smoother solution, so that the Jacobi spectral
method can be applied conveniently to the transformed equation and a complete convergence analysis of the method
is carried. The effectiveness of the proposed approach is illustrated through different numerical tests.
• Author(s) :
• Kapil Kant (Indian Institute of Technology Kanpur)

## [00900] Controllability of fractional impulsive damped stochastic systems with distributed delays

• Abstract : This paper investigates the controllability of nonlinear fractional impulsive damped stochastic systems with distributed delays. The fractional derivatives in the considered system are assumed to have Caputo derivatives. The sufficient conditions for controllability are derived using the Banach fixed point theorem and the controllability Grammian matrix which is defined by the Mittag-Leffler matrix function. At last, an example is given to illustrate the usefulness of the main results.
• Author(s) :
• Arthi Ganesan (PSGR Krishnammal College for Women, Coimbatore)

## [00901] Effect of porous layer fitted on a floating bridge in mitigating waveload

• Abstract : Scattering of oblique water waves by a floating bridge with porous wall fitted on its vertical sides is studied. Significant changes are noticed in wave reflection due to changes in porosity. It is observed that as the porosity increases, the values of the reflection coefficient decrease. The behavior of various parameters, such as depth, porous wall width, porosity and angle of incidence, on the reflection coefficient are also carried out.
• Author(s) :
• Shilpi Jain (IIT Guwahati )
• Swaroop Nandan Bora (Indian Institute of Technology Guwahati)

## [00904] Quadrature Methods and Error Estimates for Particles in Stokes Flow

• Abstract : For axisymmetric particles in Stokes flow, boundary integral methods can be utilized for numerical evaluation of flow velocity on and outside particle surfaces. Precomputation yields a highly efficient and accurate quadrature by expansion $($QBX$)$ method for singular integrals when evaluating on-surface. For evaluation close to the particle surface $($nearly singular integrals$)$, a line interpolation method aided by quadrature error estimates is introduced and compared to QBX in terms of both accuracy and efficiency.
• Author(s) :
• Pritpal Matharu (KTH Royal Institute of Technology)
• Anna-Karin Tornberg (KTH Royal Institute of Technology)

## [00905] Robust repetitive tracking control design for Takagi-Sugeno fuzzy model based Markovian jump systems with disturbances

• Abstract : In this work, the robust repetitive tracking control design problem for Takagi-Sugeno fuzzy model based Markovian jump systems in the presence of disturbances is investigated. Specifically, a new set of adequate conditions is derived in the form of matrix inequalities with the use of Lyapunov technique to obtain the controller gain matrices. In order to verify the effectiveness and supremacy of the proposed control design, the simulation results with numerical examples are presented.

• Author(s) :
• Mohanapriya Saminathan (Karpagam Academy of Higher Education, Coimbatore, Tamil Nadu, India)

## [00909] Lipschitz stability of an inverse problem for Tumor Growth Model

• Abstract : We address an inverse problem of recovering a space-dependent semilinear coefficient in the
Cahn–Hilliard type system modeling tumor growth described by a system of partial differential equations
with Dirichlet boundary condition using boundary-type measurement. First, we establish a new
higher-order weighted Carleman estimate for the given system and then a suitable regularity of solutions
for this nonlinear system is derived. Finally, we prove Lipschitz type stability for the tumor growth model.
• Author(s) :
• Barani Balan Natesan (Central University of Tamil Nadu)

## [00910] An integral equation method for the advection-diffusion equation on time-dependent domains in the plane

• Abstract : Boundary integral methods are attractive for solving homogeneous elliptic partial differential equations on complex geometries, since they can offer accurate solutions with a computational cost that is linear or close to linear in the number of discretization points on the boundary of the domain. However, these numerical methods are not straightforward
to apply to time-dependent equations, which often arise in science and engineering. We address this problem with an integral equation-based solver for the advection-diffusion equation on moving and deforming geometries in two space dimensions. In this method, an adaptive high-order accurate time-stepping scheme based on semi-implicit spectral
deferred correction is applied. One time-step then involves solving a sequence of non-homogeneous modified Helmholtz equations, a method known as elliptic marching. Our solution methodology utilizes several recently developed methods, including special purpose quadrature, a function extension technique and a spectral Ewald method for the modified Helmholtz kernel. Special care is also taken to handle the time-dependent geometries. The numerical method is tested through several numerical examples to demonstrate robustness, flexibility and accuracy.
• Author(s) :
• Fredrik Fryklund (New York University)
• Sara Pålsson (KTH Royal Institute of Technology)
• Anna-Karin Tornberg (KTH Royal Institute of Technology)

## [00912] Simulation-based Bayesian optimization over categorical covariates

• Abstract : Optimizing black-box functions of categorical variables has important applications, including the design of biological sequences with specific properties. Bayesian optimization is widely used in this type of problem. It involves adjusting a probabilistic machine learning model of the objective and using an acquisition function to guide the optimization process. We propose a new algorithm to sequentially optimize the acquisition function inspired in simulated annealing. We address convergence issues and demonstrate its effectiveness on RNA-sequence optimization.
• Author(s) :
• Roi Naveiro (CUNEF University)

## [00914] Quantifying the Impact of Impact Investing

• Abstract : We propose a quantitative framework for assessing the financial impact of any form of impact investing, including socially responsible investing (SRI), environmental, social, and governance (ESG) objectives, and other non-financial investment criteria. We derive conditions under which impact investing detracts from, improves on, or is neutral to the performance of traditional mean-variance optimal portfolios, which depends on whether the correlations between the impact factor and unobserved excess returns are negative, positive, or zero, respectively. Using Treynor-Black portfolios to maximize the risk-adjusted returns of impact portfolios, we propose a quantitative measure for the financial reward, or cost, of impact investing compared to passive index benchmarks. We illustrate our approach with applications to biotech venture philanthropy, semiconductor R&D consortium, divesting from “sin” stocks, investing in ESG, and “meme” stock rallies such as GameStop in 2021. This work bridges academic research with the rapidly growing industry of “green” investments.
• Author(s) :
• Andrew W Lo (Massachusetts Institute of Technology)
• Ruixun Zhang (Peking University)

## [00916] Deep Learning Approach Combined with Simulation As a Service to Generate Simulation from Sketched Image

• Abstract : A Simulation environment is an integrated software combining various interactive objects into one graphical user interface. This paper presents a new approach to generate simulation software from simulation sketched image. We use deep learning method based on (CNNs) and (RNN) with feature extractors MobileNet and ResNet for recognition combined with a Simulation as a Service (SaaS) to provide services for detected objects. We evaluated our approach on “Tu-berlin” dataset, 80% of accuracy was achieved.
• Author(s) :
• Mohamed Serrhini (University Mohamed Premier Oujda Morocco)

## [00921] Inverse Coefficient Problem – Coupling Fourth and Second Order Equations

• Abstract : In this paper, the recovery of the diffusion coefficient from the final time-measured data is carried out using the quasi-solution approach. The inverse coefficient problem is formulated as a minimization problem using an objective functional. The existence of the minimizer is proved, then the necessary optimality condition is derived, and by using that condition, the stability results are proved. To illustrate the efficiency of this method, numerical results are investigated using the conjugate gradient method.
• Author(s) :
• NAVANEETHA KRISHNAN M (CENTRAL UNIVERSITY OF TAMIL NADU, THIRUVARUR – 610005)

## [00922] Matrix Factorization for Change Detection in HyperSpectral Images

• Abstract : When hyperspectral images are analyzed, a big amount of data needs to be processed and therefore, specific matrix factorization algorithms are used to express the original problem in suitable subspacesWe show some recent results derived also by using spatial and spectral functions to compute a lower rank approximation of the original matrix and to measure the reconstruction error between the input image and the approximate one, with applications to the task of change-detection.
• Author(s) :
• Antonella Falini (Università degli studi di Bari Aldo Moro)
• Francesca Mazzia (Università degli studi di Bari Aldo Moro, Italy)

## [00925] Effects of temperature-dependent parameters on the reflection of thermoelastic waves under Moore-Gibson-Thomson heat conduction

• Abstract : This work discusses reflection of thermoelastic waves under Moore-Gibson-Thomson thermoelasticity theory which is generalized form of Green-Naghdi (GN) and Lord-Shulman (LS) theories. Owing to realistic scenario, an isotropic medium with temperature-dependent elastic parameters is considered to study the plane waves. To highlight the nature of physical fields under the theory, analytical result along with graphical representation for amplitude ratio and phase velocity for various waves are illustrated. Effects of empirical-index parameter and phase-lags are emphasized.
• Author(s) :
• Manushi Gupta (JK Lakshmipat University, Jaipur)

## [00926] Recent developments on non-uniqueness for stochastic PDEs

• Abstract : We review recent developments in applications of convex integration to PDEs forced by various types of random noise. The examples of equations include the Navier-Stokes equations, Euler equations, Boussinesq system, MHD system, surface quasi-geostrophic equtaions, and power-law models. The types of noise include additive, linear multiplicative, trasport, nonlinear, space-time white noise, etc.
• Author(s) :
• Kazuo Yamazaki (Texas Tech University)

## [00927] Bone marrow stem cells and exosomes control doxorubicin-induced CRCC: A mathematical model

• Abstract : Doxorubicin (DOX), a widely used chemotherapeutic agent, can cause neurodegeneration in the brain, which leads to cancer-related cognitive changes (CRCC). In fact, CRCC is a deteriorating condition which adversely affects the day-to-day life of cancer survivors. Recent studies reported that bone marrow mesenchymal stem cells (BMSCs) and exosome may significantly affect the CRCC conditions in a combination therapy (DOX+Exosome). In this study, we investigate the interaction among intracellular signaling (NFκB-Bcl-2-BAX), DOX, exosome, and IL-6.
• Author(s) :
• hyungchul Kim (Konkuk University)
• Donggu Lee (Konkuk University)
• Haneol Cho (Konkuk university)
• Junho Lee (Konkuk University)
• Yangjin Kim (Konkuk University)

## [00928] Controllability of Fractional Evolution Systems with Impulses.

• Abstract : In this article, we establishes a set of sufficient conditions for the controllability of fractional semilinear evolution inclusions with state dependent delay and interval impulses involving the caputo derivative in Banach spaces. For our results, we used fixed point theorem for condensing maps due to Bohnenblust-Karlin and α- resolvent family . As an application, the controllability of a fractional partial differential equations is discussed and verified our main results.
• Author(s) :
• Malar Kandasamy (Bharathiar University )
• Sandeep Ganesan (Anna University)

## [00931] The vaginal microbiota and its association with Chlamydia infection

• Abstract : Chlamydia trachomatis is the most common bacterial sexually transmitted infection in the U.S. While genital chlamydia infection can beget devastating pathologies, it is unclear why some women are more likely to develop severe infections but others are asymptomatic or remain uninfected after exposure to C. trachomatics. We use mice as a model organism, seek to evaluate the potential impact of the time of day of pathogen exposure on the genital tract microbiome in chlamydia infection.
• Author(s) :
• Lihong Zhao (University of California Merced)
• Lihong Zhao (University of California Merced)

## [00933] Hankel Matrices of Finite Rank and Generalized Fibonacci Sequences

• Abstract : In this talk, we show the existence of the generalized Fibonacci sequence as a tool to study the infinite Hankel matrix of finite rank, associated to a nonzero sequence $S = {s_n}_ {ngeq 0}$ of real numbers. We make use this data to give some characterizations of the generating and representing measure for a sequence whose associated Hankel matrix is of finite rank.
• Author(s) :
• RAJAE BEN BEN TAHER (Faculty of Sciences, University Moulay Ismail- MEKNES- Morocco)
• RAJAE BEN TAHER ( University Moulay Ismail, Meknes)

## [00934] Slab LU, a sparse direct solver for heterogeneous architectures

• Abstract : This talk describes a scalable sparse direct solver for linear systems that arise from the discretization of elliptic PDEs in 2D or 3D. The scheme uses a decomposition of the domain into thin subdomains, or “slabs”. The general framework is easier to optimize for modern heterogeneous architectures than
than traditional multi-frontal schemes. Crucial to the scalability, are novel randomized algorithms that recover structure from matrix-free samples and reduce the dimensionality of large dense matrices.
• Author(s) :
• Anna Yesypenko (University of Texas at Austin)
• Per-Gunnar Martinsson (University of Texas at Austin)

## [00937] Asymptotic and numerical approaches to degeneracies in Stefan problems

• Abstract : This talk discusses how asymptotic analysis and numerics can be combined to devise computational schemes to moving boundary $($Stefan$)$ problems more accurately; in particular, this relates to degenerate situations where the solution domain is initially of zero extent, or where a domain that was initially present disappears completely. A further subtlety concerns whether a new domain starts to form instantaneously or after some delay time.
• Author(s) :
• Michael Vynnycky (University of Limerick)
• Sarah Mitchell (University of Limerick)

## [00939] Learning Dynamical Systems from Invariant Measures

• Abstract : Standard data-driven techniques for learning dynamical systems struggle when observational data has been sampled slowly and state derivatives cannot be accurately estimated. To address this challenge, we assume that the available measurements reliably describe the asymptotic statistics of the dynamical process in question, and we instead treat invariant measures as inference data. We reformulate the velocity learning as a PDE constrained optimization and present several numerical examples to demonstrate the effectiveness of the proposed approach.
• Author(s) :
• Jonah Botvinick-Greenhouse (Cornell University)
• Yunan Yang (ETH Zürich)

## [00940] Central-Upwind Schemes for Weakly Compressible Two-layer Shallow-Water Flows

• Abstract : We formulate a weakly compressible two-layer shallow water flows in channels with arbitrary cross sections which is a non-conservative systems. Using the method of generalised Rankine-Hugoniot conditions we derive the Riemann invariats for shock and contact wave. Furthermore, a high-resolution, non-oscillatory semi-discrete central-upwind scheme is presented. The scheme extends existing central-upwind semi-discrete numerical methods for hyperbolic balance laws. We validate the exact solution with the numerical approach.
• Author(s) :
• Sarswati Shah (Universidad Nacional Autónoma de México)
• Gerardo Hernandez-Duenas (Universidad Nacional Autónoma de México)

## [00942] First Steps Towards Simulation of Valve in Valve Transcatheter Aortic Valve Implantation (ViV-TAVI)

• Abstract : Bioprosthetic aortic valves have been widely used to replace diseased native valves. Due to the device’s limited durability, the number of patients in need of a second replacement is increasing. ViV-TAVI emerged as one of the alternatives for those cases. This study required the use of 3D geometries and the FEM method to model the novel VinV protocol. Linear elastic, hyperelastic and shape-memory alloy models were used to reproduce the behavior of the involved geometries.
• Author(s) :
• Marcos Loureiro-Ga (University of Vigo)
• Cesar Veiga (Instituto de Investigación Sanitaria Galicia Sur)
• Generosa Fdez-Manin (University of Vigo)
• Jose Antonio Baz (Cardiology Departement – SERGAS)
• Victor Alfonso Jimenez (Cardiology Departement – SERGAS)
• Andrés Iñiguez (Cardiology Departement – SERGAS)

## [00943] Similarity solutions for shock wave in non-ideal gas

• Abstract : The solution using the Lie group of symmetry method for the problem of propagating magnetogasdynamic strong cylindrical shock wave in a self-gravitating non-ideal gas with the axial magnetic field for isothermal flow. Numerical computations were performed for power law and exponential law shock paths, to see the behaviour of flow variables. The study provides how the variations in the various parameter taken in this study affect the propagation of shock and the flow behind it.
• Author(s) :
• Nandita . (Dept. of Applied Mathematics & Scientific Computing, IIT Roorkee, Roorkee,India 247667)

## [00944] Modelling of healthcare-acquired infection spread in regional healthcare systems

• Abstract : A network-compartmental model for simulation of healthcare-associated infection spread in healthcare systems is presented. The model accounts for transmission of the pathogen by inter-hospital patient transfers and colonized patients’ readmission. Estimates for basic reproduction number per hospital-community pairs are calculated for multidrug-resistant Enterobacteriaceae for selected German regions. Inter-hospital transfer network is created from anonymized German health-insurance datasets. By numerical simulations, we examine interventions to reduce spread of the pathogen within the healthcare network.
• Author(s) :
• Konrad Sakowski (Institute of Applied Mathematics and Mechanics, University of Warsaw)
• Monika Joanna Piotrowska (Institute of Applied Mathematics and Mechanics, University of Warsaw)
• Agata Lonc (Institute of Applied Mathematics and Mechanics, University of Warsaw)
• Johannes Horn (Institute for Medical Epidemiology, Biometrics, and Informatics, Interdisciplinary Center for Health Sciences, Medical Faculty of the Martin Luther University Halle-Wittenberg, Halle (Saale))
• Rafael Mikolajczyk (Institute for Medical Epidemiology, Biometrics, and Informatics, Interdisciplinary Center for Health Sciences, Medical Faculty of the Martin Luther University Halle-Wittenberg, Halle (Saale))
• André Karch (Institute of Epidemiology and Social Medicine, University of Münster)
• Paweł Brachaczek (University of Warsaw)
• Mirjam Kretzschmar (University Medical Center Utrecht, Utrecht University)

## [00945] NUMERICAL ANALYSIS OF A NONLINEAR DISCRETE DUALITY FINITE VOLUME SCHEME FOR LERAY-LIONS TYPE ELLIPTIC PROBLEMS IN ORLICZ SPACES

• Abstract : In this work, we develop a finite volume approximation for general
nonlinear Leray-Lions problems in the Orlicz-Sobolev framework. We prove the existence and uniqueness and
some a priori estimate of the approximate solution. We establish a discrete version of Poincar'{e} inequality and a result of discrete
compactness which allows us to prove the convergence towards the weak solution of the continuous problem.
Some numerical tests are provided on general meshes.
• Author(s) :
• Mohamed RHOUDAF ( University Moulay Ismail- Meknes)

## [00946] Escape kinetics of self-propelled particle from a circular cavity

• Abstract : We numerically investigate the mean exit time of self-propelled Janus particle from a circular cavity with single or multiple exit windows. Our simulation results witness distinct escape mechanisms depending upon the relative amplitudes of the thermal length and self-propulsion length compared to the cavity and pore sizes. We show that the exit rate can be maximized for an optimal self-propulsion persistence length, which depends on the damping strength, self-propulsion velocity, and cavity size.
• Author(s) :
• Tanwi Debnath (University of Calcutta)

## [00947] Statistical analysis of neonatal mortality predictors in Ghana

• Abstract : In this study, we identify and investigate the main factors influencing newborn mortality in the Ghanaian locality and predict the occurrence of future infant mortality based on the 2017 Demographic and Health Survey data using logistic regression. Our work shows that the child’s weight and sex have a strong correlation with its survival. The study reveals that mortality is more than 50% greater in underweight children and also, 62.7% infant deaths happen in infant males.
• Author(s) :
• Elizabeth Dufie Amankwah (Kwame Nkrumah University of Science and Technology)
• Juliet Amegble Richardson (Kwame Nkrumah University of Science and Technology)
• Solomon Kyei Mensah (Kwame Nkrumah University of Science and Technology)

## [00948] Existence results for elliptic (p,q)-Laplacian problems with nonlinear boundary conditions

• Abstract : In this presentation, we study the existence of solutions for a (p, q)-Laplacian Steklov problem .
The main result of our research is to prove the existence of solutions for a (p, q)-Laplacian Steklov problem, using the Ricceri’s three critical points theorem.

• Author(s) :
• Mariya Sadiki (University of Moulay Ismail)

## [00954] Dynamic Modeling and Optimization of Mixed Hydrogen-Natural Gas Flow in Pipeline Networks

• Abstract : We present a dynamic model for the mixing and transport of hydrogen-natural gas blends in a pipeline network. The dynamic model is derived by lumping the partial differential equations to yield a differential algebraic system. The derived system accommodates spatio-temporally heterogeneous gas injections, and is more complex and numerically ill-conditioned than the case of a single gas. Multiple reformulations for the nonlinear and non-smooth equations of mixing are compared using standard optimization solvers.
• Author(s) :
• Saif Kazi (Los Alamos National Laboratory)
• Anatoly Zlotnik (Los Alamos National Laboratory)
• Kaarthik Sundar (Los Alamos National Laboratory)
• Shriram Srinivasan (Los Alamos National Laboratory)

## [00956] Inner Structure of Attractors for a Nonlocal Chafee-Infante Problem

• Abstract : The structure of the global attractor for the multivalued semiflow generated by a nonlocal reaction-diffusion
equation in which we cannot guarantee the uniqueness of the Cauchy problem is studied. The existence and
properties of stationary points are analysed. Also, the study of the stability and connections between them
are carried out, establishing that the semiflow is a dynamic gradient. As a consequence, the attractor
consists of the stationary points and their heteroclinic connections.
• Author(s) :
• RUBEN CABALLERO (UNIVERSIDAD MIGUEL HERNANDEZ DE ELCHE)

## [00958] Existence results and numerical approximation for a quasilinear elliptic system

• Abstract : We analyse the existence and the numerical simulation of a capacity solution to a coupled nonlinear elliptic system with a quadratic growth in the gradient and a non-uniformly elliptic problem in the context of anisotropic Sobolev spaces. The system may be regarded as a generalization of the so-called thermistor problem.
• Author(s) :
• Hajar Talbi (Moulay Ismail University)

## [00962] Discontinuous Galerkin method for a high order nonlocal conservation law

• Abstract : We consider a Direct Discontinuous Galerkin (DDG) method for solving a time dependent partial differential equation with convection-diffusion terms and a fractional operator of order $alpha in (1,2)$. This equation was introduced to describe dunes morphodynamics and was then used for signal processing. For the DDG method, suitable numerical fluxes are introduced. We prove nonlinear stability estimates along with convergence results. Numerical experiments are given to illustrate behaviors of solutions and to verify convergence order.
• Author(s) :
• Afaf Bouharguane
• Afaf Bouharguane (University of Bordeaux)
• Nour Seloula (University of Caen)

## [00964] The Valuation of Real Options for Risky Barrier to Entry with Hybrid Stochastic and Local Volatility and Stochastic Investment Costs

• Abstract : Real options are sorts of investment choices which support agents in making better decisions in management strategic cases as well as reducing uncertainty in investment simultaneously. In this paper, we present the new model for investors to handle uncertain environments in investment flexibly: First, we adopt a hybrid stochastic and local volatility model to efficiently describe the external uncertain environment affecting the value of the project in decision making cases, and we set up the investment cost as geometric Brownian motion to illustrate the value of the opportunity costs which arise from things given up by choosing to invest in complex decision making circumstances. We derive partial differential equations for the value of real options and then use asymptotic analysis to obtain analytical solutions for that of the real options. In addition, we analyze the price accuracy of the approximated formulas compared to the solutions obtained from Monte-Carlo simulation. Finally, we investigate the effects of various parameters related to stochastic volatility on real options numerically to observe economic implications.
• Author(s) :
• Donghyun Kim (Pusan National University)
• Yong Hyun Shin (Sookmyung Women’s University)
• Ji-Hun Yoon (Pusan National University)

## [00968] Modelling pathogen spreading in a network of hospitals

• Abstract : I will introduce an ODE model describing the spread of multidrug-resistant bacteria in a hospital network. I will present the mathematical properties of the model solutions, including the global stability of steady states. Based on simulations for real-life data, I will describe how the parameters affect the process dynamics at both network and hospital levels. Finally, the relations to other types of models describing similar processes will be discussed.
• Author(s) :
• Agata Lonc (University of Warsaw)
• Monika Joanna Piotrowska (Institute of Applied Mrsaathematics and Mechanics, University of Waw)
• Aleksandra Puchalska (Institute of Applied Mathematics and Mechanics, University of Warsaw)

## [00971] Quantify the classicality of quantum states

• Abstract : In this talk, I will first introduce classicality and quantumness in a given quantum state. As quantumness speeds up quantum algorithms, gauging the “non-quantumness” or so-called “classicality” becomes an important task. Next, I will demonstrate using descent flow on smooth manifolds to resolve the issue. Finally, I will exhibit several numerical experiments to clarify whether our proposed method is reliable and applicable.
• Author(s) :
• BingZe Lu (Mathematics, National Cheng Kung University)
• YuChen Shu (Mathematics, National Cheng Kung University)
• Matthew M. Lin (National Cheng Kung University)

## [00972] Reducing Communication in Federated Learning with Variance Reduction Methods

• Abstract : In Federated Learning $text{(}$FL$text{)}$, inter-client heterogeneity and partial participation of clients at each communication cause client sampling error. We control this client sampling error by developing a novel single-loop variance reduction algorithm. While sampling a small number of clients, the proposed FL algorithms require provably fewer or at least equivalent communication rounds compared to any existing method, for finding first and even second-order stationarypoints in the general nonconvex setting, and under the PL condition.
• Author(s) :
• Kazusato Oko (The University of Tokyo, AIP RIKEN)
• Shunta Akiyama (The University of Tokyo)
• Tomoya Murata ( The University of Tokyo, NTT DATA Mathematical Systems Inc.)
• Taiji Suzuki (The University of Tokyo, AIP RIKEN)

## [00973] Inverse source problem for a seventh-order Korteweg–de Vries equation

• Abstract : In this talk, we establish the boundary stability result concerning the inverse source problem for a seventh-order Korteweg–de Vries (KdV) equation. Initially, we derive a new boundary Carleman estimate for the given system using the Dirichlet–Neumann type boundary conditions. We finally obtain a Lipschitz-type boundary stability estimate of a seventh-order KdV equation using the regularity results of the nonlinear KdV equation and the Bukhgeim-Klibanov method.
• Author(s) :
• Arivazhagan Anbu (Indian Institute of Technology Gandhinagar)
• Arivazhagan Anbu (Indian Institute of Technology Gandhinagar)

## [00979] Optimal radio channel assignment to transmitters in a network

• Abstract : An optimal radio channel assignment to transmitters in a network is modeled by graph labeling approach. A radio labeling of a graph $G$ is a function $f : V(G) rightarrow {0,1,2,ldots}$ satisfying $|f(u)-f(v)| geq diam(G)+1-d(u,v)$, for all $u,v in V(G)$. The radio number $rn(G)$ of $G$ is the minimum span of radio labeling of graph $G$. We give current status of research, including our work, on radio labeling of graphs.
• Author(s) :
• Devsi Dudabhai Bantva (Lukhdhirji Engineering College, MorbiL)

## [00983] Effective time step analysis of numerical schemes for gradient flows

• Abstract : A gradient flow has an important role in PDEs and it has a variety of applications including biological fields. In this talk, we briefly introduce the unconditionally stable numerical schemes for type of gradient flows and analyze them by comparing the real and its rescaled time steps, which has been a critical issue in this field. Some numerical simulations are performed to confirm our result.
• Author(s) :
• Seunggyu Lee (Korea University)

## [00986] Approximation results for Gradient Descent trained Shallow Neural Networks

• Abstract : Neural networks show strong performance for function approximation, but provable guarantees typically rely on hand-picked weights and are therefore not fully practical. The aim for a small number of weights in approximation is opposed to over-parametrization by very wide or even infinitely wide networks in contemporary optimization results. The talk reconciles approximation and optimization results and provides approximation bounds that are guaranteed for gradient descent trained neural networks.
• Author(s) :
• Gerrit Welper (University of Central Florida)
• Russell Gentile (n/a)

## [00987] Role of applied mathematics on optimum MR damper location for LQG controlled framed structure

• Abstract :
This work addresses a Linear Quadratic Gaussian Design (LQG) based semi-active control algorithm for vibration reduction of building structures. The controlled damper force required by the structure has been calculated from an MR damper. A building frame has been selected to illustrate the performance of the proposed algorithm. Four different earthquake acceleration data has been used as input vibration data to the numerical frame
• Author(s) :
• MANIKANDAN RAJASEKARAN (DEPARTMENT OF APPLIED MATHEMATICS BHARATHIYAR UNIVERSITY COIMBATORE TAMIL NADU INDIA)
• PAYEL CHAUDRI (IIT KHARAGPUR)
• SAKTHIVEL R (PROFESSOR DEPARTMENT OF APPLIED MATHEMATICS BHARATHIYAR UNIVERSITY COIMBATORE TAMIL NADU INDIA)

## [00990] BGK model for two-component gases near a global Maxwellian

• Abstract : In this talk, we establish the existence of the unique global-in-time classical solutions to the two-component BGK model when the initial data is a small perturbation of global equilibrium. The main difference between this model compared to the classic mixture Boltzmann equation is that the rate of interchange of momentum and energy between the two species is controllable through two free parameters.
Based on the energy method, we carefully analyze the dissipative nature of the linearized multi-component relaxation operator and observe that the partial dissipation from the intra-species and the inter-species linearized relaxation operators are combined in a complementary manner to give rise to the desired dissipation estimate of the model. Furthermore, the dissipation estimate depends on the momentum interchange rate and the energy interchange rate. So the larger interchange rate leads to stronger dissipation, and therefore, faster convergence to the global equilibrium. This is joint work with C. Klingenberg, M. Pirner, and S.-B. Yun.
• Author(s) :
• Gi-Chan Bae (Seoul National University)
• Christian Klingenberg (Würzburg University)
• Marlies Pirner (Würzburg University)
• Seok-Bae Yun (Sungkyunkwan University)

## [00991] Applied mathematics applications in ocean engineering

• Abstract : A novel controller technique using nonlinear quadratic regulatory framework is proposed, the
algorithm perform the parameterization of the nonlinear model of the system such that the
linearized model remains transversal everywhere to nonlinear model leading to control of original
model. By transversality, linearized and nonlinear solutions intersect at only grid points on time
axis without using Taylor-like expansions and shown its applicability in SWT
• Author(s) :
• MANIKANDAN RAJASEKARAN (UGC-DR DS KOTHARI POST DOCTORAL FELLOW DEPARTMENT OF APPLIED MATHEMATICS BHARATHIYAR UNIVERSITY COIMBATORE TAMIL NADU INDIA)
• SATARUPA DEY (Assistant Professor and Head Department of Botany Shyampur Siddheswari Mahavidyalaya (Affiliated to University of Calcutta) West Bengal India)
• SAKTHIVEL R (DEPARTMENT OF APPLIED MATHEMATICS BHARATHIYAR UNIVERSITY COIMBATORE TAMIL NADU INDIA)

## [00995] Convergence of a Normal Map-Based Prox-SGD Method for Stochastic Composite Optimization

• Abstract : In this talk, we present a novel stochastic normal map-based algorithm (nor-SGD) for nonconvex composite-type optimization problems and discuss its asymptotic convergence properties. We first analyze the global convergence behavior of nor-SGD and show that every accumulation point of the generated sequence of iterates is a stationary point almost surely and in an expectation sense. The obtained results hold under standard assumptions and extend the more limited convergence guarantees of nonconvex prox-SGD. In addition, based on the Kurdyka-Lojasiewicz (KL) framework and utilizing an adaptive time window mechanism, we establish almost sure convergence of the iterates and derive convergence rates that depend on the KL exponent and the step size dynamics. The techniques studied in this work can be potentially applied to other families of stochastic and simulation-based algorithms.
• Author(s) :
• Andre Milzarek (The Chinese University of Hong Kong, Shenzhen)
• Junwen Qiu (The Chinese University of Hong Kong, Shenzhen)

## [00996] A Decentralized Approach for Dynamic Graph Clustering

• Abstract : Interconnected networks characterized by interacting agents can be represented by weighted graphs, with the weight indicating their connection strength. Graph clustering arises naturally in these networks to assist decision making and co-ordination. Among the clustering methods, spectral clustering has emerged as a powerful tool but suffers from slow convergence for large dynamic graphs. Thus, we propose a fast incremental approach for dynamic graphs as an extension of its equivalent decentralized approach based on wave propagation.
• Author(s) :
• Alice Zhu
• Hongyu Zhu (Raytheon Technologies Research Center)
• Tuhin Sahai (Raytheon Technologies Research Center)

## [00997] A Normal Map-Based Perspective on Second Order Theory for Composite Problems: Second Order Conditions, Metric Regularity, and Nonsingularity

• Abstract : Strong metric subregularity and strong metric regularity of the natural residual and the normal map are of particular importance in the convergence analysis of first-order and second-order algorithms for composite-type optimization problems. In this talk, we characterize the strong metric subregularity of the natural residual and the normal map for a general class of nonsmooth nonconvex composite functions and establish the equivalence between these conditions, the strong metric subregularity of the subdifferential, and the quadratic growth condition. Furthermore, if the nonsmooth part of the objective function has a strictly decomposable structure, then strong metric regularity of the subdifferential is shown to be equivalent to strong metric regularity of natural residual and the normal map and to a counterpart of the so-called strong second-order sufficient conditions. Finally, we provide a link of these conditions to nonsingularity of the generalized Jacobians of the normal map and natural residual.
• Author(s) :
• Wenqing Ouyang (The Chinese University of HongKong(Shenzhen))
• Andre Manfred Milzarek (The Chinese University of Hong Kong, Shenzhen)

## [00998] An Optimal Consumption-Portfolio Strategy and Housing Choice Problem with a Loan-to-Value Ratio

• Abstract : This paper promotes a housing choice problem with a loan-to-value ratio by an extended dynamic programming approach. Before purchasing a house, an individual agent rents a house to live in. After purchasing a house, the agent owns a house and uses it as collateral for borrowing. One main contribution is that the loan-to-value ratio has positive effects on an individual agent’s decisions both before and after the time of purchasing a house. We find that an individual agent with a higher loan-to-value ratio delays the time to buy a house and purchases a larger house. We provide closed-form solutions for each optimal policy. We also demonstrate the solutions numerically and discuss the economic implications.
• Author(s) :
• Qi Li (Pusan National University)
• Seryoong Ahn (Pukyong National University)
• Ji-Hun Yoon (Pusan National University)

## [00999] High-order energy stable schemes for the phase-field model by the Convex Splitting Runge-Kutta methods

• Abstract : The Convex Splitting Runge-Kutta method is a high-order energy stable scheme for gradient flow which is a combination of the well-known convex splitting method and the multi-stage Runge-Kutta method. In this talk, we will discuss the applications and challenges of CSRK via extensive examples of the phase-field model.
• Author(s) :
• Jaemin Shin (Chungbuk National University)
• Hyun Geun Lee (Kwangwoon University)
• June-Yub Lee (Ewha Womans University)

## [01001] Recent developments on low-discrepancy point sets for Markov chain quasi-Monte Carlo

• Abstract : We consider the problem of estimating expectations by using Markov chain Monte Carlo methods and improving the accuracy by replacing IID uniform random points with quasi-Monte Carlo (QMC) points. In this talk, we present short-period Tausworthe generators for Markov chain QMC optimized in terms of the t-value, which is a criterion of uniformity widely used in the study of QMC methods. In addition, we show the effectiveness in some numerical examples using Gibbs sampling.
• Author(s) :
• Shin Harase (Ritsumeikan University)

## [01005] Nonlinear Disturbance Observer-Based Control Design for Markovian Jump Systems

• Abstract : This paper addresses the anti-disturbance control problem for time-delayed Markovian jump nonlinear systems with modeled and unmodeled disturbances. Specifically, the modeled disturbance is generated by a nonlinear exogenous system and estimated using a nonlinear disturbance observer. A mode-dependent asymmetric Lyapunov-Krasovskii functional is used to derive sufficient conditions for the existence of the proposed controller and disturbance observer. A numerical example is included to demonstrate the efficacy of the theoretical results developed.
• Author(s) :
• KAVIARASAN BOOMIPALAGAN (CHUNGBUK NATIONAL UNIVERSITY)
• OH-MIN KWON (CHUNGBUK NATIONAL UNIVERSITY)

## [01006] VMS-based Stabilized FE Analysis of Time-dependent Coupled Unified Stokes-Brinkman-Transport Model

• Abstract : We present a Variational Multi-Scale (VMS)-based stabilized FE analysis for completely unified unsteady Stokes-Brinkman model with standard continuity and Beavers-Joseph-Saffman interface conditions, strongly coupled with transient transport equation. The fluids’ viscosities depend on the solute concentration. A simplified algebraic subgrid multiscale approach with time-dependent sub-scales is employed. A fully-implicit Euler scheme is used for time-discretization. We analyse the stability and convergence properties of the method. Appropriate numerical experiments are conducted to verify the method’s credibility.
• Author(s) :
• Manisha Chowdhury (Indian Institute of Technology Jodhpur)
• B.V. Rathish Kumar (Indian Institute of Technology Kanpur)

## [01008] EID estimator-based Control Design for Singular Polynomial Fuzzy Systems

• Abstract : This paper studied the disturbance rejection problem for singular polynomial fuzzy system based on equivalent-input-disturbance-estimator-based control approach. The proposed approach is used to compensate the influences of unknown lumped disturbance. To cope the robust stability problems, the augmented closed-loop system is constructed that includes dynamics of the system, observer, and low-pass filter. Lyapunov stability theory is used to develop stability conditions for the resulting system. Finally, numerical examples are provided to validate the theoretical result.
• Author(s) :
• Selvaraj Palanisamy (Chungbuk National University)
• Kwon Oh-Min (Chungbuk National University)

## [01009] A phase transition of various retention rules from multivariate analysis for big datasets.

• Abstract : Estimating the number of significant components(factors, resp.) from principal component analysis(explanatory factor analysis, resp.) in datasets of finance/biology is essential. However, statistical software’s default estimation method behaves pathologically for big datasets. We analyze the phase transition of the default rule as to the intra-class correlation of various data-generation models, and introduce a more acceptable estimation by random matrix theory for large sample correlation matrices. We also compare our rule to retention rules proposed to date.
• Author(s) :
• Atina Husnaqilati Atina (Department Mathematics Tohoku University )

## [01010] Superconvergent Scheme for a System of Green Fredholm Integral Equations

• Abstract : In this study, we consider a system of second kind linear Fredholm integral equations with Green’s type kernel function. We propose a piecewise polynomial based Galerkin and iterated Galerkin methods to solve the integral model. We carry out the convergence and error analysis for the proposed methods and establish the superconvergence results for iterated Galerkin method. The theoretical results are supported by numerical tests.
• Author(s) :
• Rakesh Kumar (Indian Institute of Technology, Kanpur (India))
• Kapil Kant (Indian Institute of Technology, Kanpur (India))
• B.V. Rathish Kumar (Indian Institute of Technology, Kanpur (India))

## [01012] Uncertainty and disturbance estimator design for interval type-2 fuzzy systems

• Abstract : This article investigates the uncertainty and disturbance estimator-based control problem for the interval type-2 fuzzy systems. By designing the appropriate filter, the proposed control designs can estimate system uncertainties and external disturbances accurately. By using the Lyapunov-Krasovskii stability theorem, the required stability conditions and the control gain matrices for the system under consideration are obtained. Finally, an illustrative example is demonstrated to verify the feasibility of the proposed control method.
• Author(s) :
• KAVIKUMAR RAMASAMY (CHUNGBUK NATIONAL UNIVERSITY)
• KWON OH-MIN (CHUNGBUK NATIONAL UNIVERSITY)

## [01013] Satellite Data Assimilation through Community Land Model to improve Rice Crop Dynamics

• Abstract : The aim of the proposed talk is to discuss evaluation of existing form of Dynamic Generalized Vegetation Model (DGVM) of Community Land Model (CLM) in terms of its bio-geophysics and processes for major agro-ecosystems such as in rice-rice crop rotation in India. Development of new crop-specific growth modules to bring out new version of DGVM suitable for Indian sub-tropics will be explored. This will be followed by its evaluation with respect to surface fluxes. The new modelling system will represent explicit crop growth processes in a terrestrial ecosystem model operable in a stand-alone mode or embedded in a climate model equipped with satellite remote sensing-based data assimilation for large-area prediction of intra-seasonal and inter-annual variability of crop phenology, growth, yield and fluxes of energy, moisture and carbon in the rice based systems at regional scale.
• Author(s) :
• Mahesh Kumar (Sardar Vallabhbhai National Institute of Technology, Surat, India)
• Ranjan Kumar Jana (Sardar Vallabhbhai National Institute of Technology, Surat, India)

## [01014] Fault detection asynchronous filter design for Markovian jump fuzzy systems under cyber attacks

• Abstract : This work is concerned with the issue of fault detection asynchronous filter design for a class of discrete-time
Markovian jump fuzzy systems with cyber attacks. Precisely, the cyber attacks phenomenon in the network environment satisfies the Bernoulli distribution. Finally, the applicability and usefulness of the proposed filter design method is verified through a practical example.
• Author(s) :
• Sakthivel Ramalingam (Chungbuk National University)
• Oh-Min Kwon (Chungbuk National University)

## [01016] Approximate formula for indefinite convolutions by the DE-Sinc method

• Abstract : Approximate formula for indefinite convolutions by means of the Sinc approximation has been proposed by Stenger. The formula is based on his Sinc indefinite integration formula combined with the single-exponential transformation. Recently, the Sinc indefinite integration formula was improved by replacing the single-exponential transformation with the double-exponential transformation. Based on the improved formula, this study proposes a new approximate formula for indefinite convolutions.
• Author(s) :
• Tomoaki Okayama (Hiroshima City University)

## [01017] Feature Collisions in Neural Networks: Theory and Practice

• Abstract : Deep neural networks are behind many breakthroughs in the last decade, but much of their behavior remains poorly understood. In particular, under some conditions, neural networks can be insensitive to changes of large magnitude, in which case the features are said to collide. We will discuss necessary conditions for such feature collisions to occur, and we will introduce the null-space method, a numerical approach to create data points with colliding features for many vision tasks.
• Author(s) :
• Utku Ozbulak (Ghent University)
• Joris Vankerschaver (Ghent University)

## [01018] VMS Stablized FEA of M-NS Equations For Nano Thermal Fluid

• Abstract : In this paper, we present a variable multiscale stabilised finite element metthod for NS equations with
thermal transport for hybrid nano fluid flow. In particular algebraic approach of approximating the
subscales has been considered and then the stabilization parameters are derived using Fourier analysis.
Following that, we have derived an apriori error estimates. Also we have analysed the flow, velocity,
pressure and temperature distribution over the bench mark problems viz. Multiply driven cavity flow.
• Author(s) :
• Dipak Kumar Sahoo (Indian Institute of Technology, Kanpur)
• B. V. Rathish Kumar (Indian Institute of Technology, Kanpur)
• Anil Rathi (Indian Institute of Technology, Kanpur)

## [01020] Singularly perturbed integro-differential equation with a discontinuous source term

• Abstract : The singular perturbation Fredholm integro-differential equation has been examined with a discontinuous source term using computational numerical techniques. To solve the problem, an exponentially-fitted numerical method on a Shishkin mesh has been used. It is demonstrated that the method is uniformly convergent concerning the singular perturbation parameter. The theoretical findings are validated through the numerical outcomes.
• Author(s) :
• Ajay Singh Rathore (National Institute of Technology Tiruchirappalli.)
• Shanthi Vembu (National Institute of Technology Tiruchirappalli.)

## [01021] A mixed finite element approach to a non-isothermal flow vegetation model

• Abstract : We consider a vegetation root-soil model which couples Richards PDE in the soil domain and saturated flow in the roots domain. Scenarios when the flow depends on soil temperature is included. A mixed finite element method is applied to obtain numerical solutions, and the well-posedness for its weak formulation and error estimates are studied. We provide numerical examples using tomography data of root domains and study convergence errors to validate our theoretical results.
• Author(s) :
• Malgorzata Peszynska (Oregon State University)
• Nachuan Zhang (Oregon State University)

## [01022] Self similar solutions of fuzzy fractional vibration equation

• Abstract : In this work, we consider the one dimensional fuzzy fractional vibration equation of large membrane. In order to find the self similar solution, we use scaling transformation to transform the fuzzy fractional vibration equation into the ordinary fractional differential equation with variable coefficients. Numerical examples are presented to show the effectiveness of developed theoretical results. The computation has been carried out using the MATHEMATICA software.

• Author(s) :
• PRAKASH PERIASAMY (Periyar University, Salem – 636 011 INDIA)

## [01025] EXISTENCE OF OPTIMAL CONTROL FOR TIME VARYING STOCHASTIC DIFFERENTIAL EQUATIONS

• Abstract : The work deals with the control problem for linear stochastic time varying system driven by square integrable stochastic process with zero mean and continuous sample paths. The cost functional is considered to be quadratic in the system state and the control. The completion of squares technique is used to establish the existence of optimal control under the family of non-adapted admissible control.
• Author(s) :
• Murugan Suvinthra (Bharathiar University)

## [01027] A Discussion on Numerical Methods to Solve Structural Engineering Problems

• Abstract : A number of numerical methods are developed by researchers to solve the linear/nonlinear, ordinary differential equations (ODEs) / partial differential equations (PDEs) developed for structural analysis such as vibration/bending/buckling/wave-propagation analysis in plates. The present talk is focused on a discussion of numerical approaches and their accuracy and convergence for plate vibrations i.e., linear PDE which can be extended as semi-analytic approaches to solving the nonlinear PDE during critical vibration analysis of plates.
• Author(s) :
• Rahul Saini (H N B Garhwal Central University, Srinagar, Uttarakhand, India )

## [01030] A 3D linearity-preserving cell-centered finite volume scheme with extended least square interpolation for anisotropic diffusion equations

• Abstract : In this talk, we study a cell-centered finite volume scheme for anisotropic diffusion problems on unstructured polyhedral meshes through a certain linearity-preserving approach. The main feature of our new scheme is that the vertex unknowns are interpolated by the least square technique combined with graph search algorithm to handle arbitrary discontinuities. The search algorithm is local, and for the problem with continuous diffusion coefficients, the resulting interpolation algorithm naturally degenerates into the classical least squares algorithm. Numerical experiments show that our scheme achieves nearly second order accuracy on general unstructured grids in case that the diffusion tensor is taken to be anisotropic and heterogeneous.
• Author(s) :
• Longshan Luo (Institute of Applied Physics and Computational Mathematics)

## [01031] Anti-disturbance synchronization of polytopic uncertain complex dynamical networks under attacks

• Abstract : A truncated prediction feedback approach and a disturbance observer-based method are used to solve a synchronization problem for polytopic uncertain complex dynamical networks with input time delay and deception attacks. Deception attacks are introduced into the communication channel and modelled using a Bernoulli stochastic variable. Utilizing the Lyapunov-Krasovskii functional, a new set of sufficient conditions is obtained in the form of linear matrix inequalities. Eventually, the proposed theoretical results will be verified through numerical simulations.
• Author(s) :
• Sakthivel Natarajan (Bharathiar University)

## [01032] Memory event-triggered finite-time fault control for neural networks system

• Abstract : By wielding METS, this topic explores finite-time issue for neural networks comprise to actuator failures and deception attack. By engaging Lyapunov function and integral inequality technique, sufficient conditions in the structure of linear matrix inequality assures the asymptotic mean-square finite-time boundedness of the considered model. Ultimately, the capability of the proposed control design is demonstrated through two numerical examples.
• Author(s) :
• Karthick SA (National Tsing Hua University)
• Bor-Sen Chen (National Tsing Hua University)

## [01038] Study of transitional stresses in rotating disc of materials with different Poisson Ratio under varying temperature

• Abstract : The present paper is devoted to a study of stress distribution in rotating disc of different materials with variable Poisson ratio. Seth’s transition theory is applied to the problems of elastic-plastic stresses in a rotating disc.Yield criteria and the associated flow rule are not taken into consideration for this study that forms the bases for the development of many researchers investigation. The obtained results allied in the direction of rotating disc made of an incompressible materials required higher angular speed for initial yielding as compared to disc made of gold, nickel and cast iron. At the internal surface of the compressible materials however, the circumferential stresses are showing higher values as compared to incompressible materials i.e. gold, nickel and cast iron required maximum circumferential stresses as compared to rubber material (incompressible). Also rotating disc required maximum stresses for the fully plastic state as compared to the initial yielding state.
• Author(s) :
• Jatinder Kaur (Chandigarh University Mohali , Chandigarh )
• Sonia – (Chandigarh University Mohali , Chandigarh )

## [01039] A model of cerebrospinal fluid flow in the cranial subarachnoid space

• Abstract : Cerebrospinal fluid fills the subarachnoid space (SAS), which covers the spinal cord and the brain. During the cardiac cycle, it pulsates due to time-varying brain displacements. In this work, we study oscillating and steady streaming flow in cranial SAS in order to understand the mixing processes and waste clearance. We develop a theoretical model of the flow using lubrication theory. The model suggests that steady streaming plays an important role in mixing.
• Author(s) :
• Mariia Dvoriashyna (University of Oxord)
• Alain Goriely (University of Oxford)

## [01041] Dynamical Behaviours of a Stochastic Leptospirosis Model with Saturated Incidence Rate

• Abstract : Leptospirosis is a zoonotic bacterial disease that is endemic and having high incidence rate in tropical and subtropical regions especially after flooding or heavy rainfall. The objective is to investigate the asymptotic behaviour of a stochastic Leptospirosis model with saturated incidence rate in terms of basic reproduction number using Lyapunov functions. As a first step, a biologically well-posed model perturbed by multiplicative Gaussian noise will be proposed. The existence of a stationary distribution and the ergodicity of solutions of the proposed model will also be established.
• Author(s) :
• SELSHA S (Research Scholar, Govt College Chittur)

## [01042] Preconditioners of Reduced Dimension for Vector Field Problems

• Abstract : When designing preconditioners based on domain decomposition methods, the coarse space
plays a key role. In order to keep the scalability, the coarse space of low computational complexity
is essential. We introduce a new coarse space of reduced dimension for vector field
problems. Numerical results for the problems in three dimensions are also presented.
• Author(s) :
• Duk-Soon Oh (Chungnam National University)

## [01046] Flow past a mounted wedge: The three fold structure

• Abstract : This talk is concerned with the simulation of flow past a wedge mounted on a wall for channel Reynolds number $Re_c = 6873$ in accelerated flow medium. All three stages of vortex shedding for the accelerated flow, leading to the exceedingly intricate three-fold structure has been captured very accurately. Transition to turbulence have also been resolved which is indicated by the existence of coherent structures.
• Author(s) :
• Jiten C Kalita (Indian Institute of Technology Guwahati)

## [01048] Analysis of a Poisson–Nernst–Planck–Fermi model for ion transport in biological channels and nanopores

• Abstract : We analyse a Poisson-Nernst-Planck-Fermi model to describe the evolution of a mixture of finite size ions in liquid electrolytes, which move through biological membranes or nanopores. The global-in-time existence of bounded weak solutions and the weak-strong uniqueness result are proved, via entropy and relative entropy, respectively. Furthermore, an implicit Euler finite-volume scheme for the model is analysed and some simulations are shown.
• Author(s) :
• Annamaria Massimini (TU Wien)
• Ansgar Jüngel (TU Wien)

## [01049] A numerical study of a moving boundary problem during the phase change process

• Abstract : Here, we present a mathematical model of a parabolic partial differential equation in a time-dependent domain for a phase change process. This non-linear problem includes moving phase change material and a size-dependent thermal conductivity. A numerical solution of the problem is proposed by using finite difference scheme. We also present the consistency, stability and convergency of the scheme for the considered problem. For a particular case, we propose the comparison of our result with the exact solution to show the accuracy of the proposed numerical solution, and it is observed that our calculated results are sufficiently closed to the exact results. The effects of various parameters on the phase change process are also discussed.
• Author(s) :
• Rajeev . (Indian Institute of Technology BHU Varanasi India )

## [01051] Moderate Deviations for Shell Model of Turbulence

• Abstract : This work establishes the central limit theorem and moderate deviation principle for stochastic shell model of turbulence driven by multiplicative noise. The method of weak convergence introduced by Budhiraja and Dupuis has been followed in order to establish our results. The equivalence of Laplace principle and large deviation principle under Polish spaces contributes to reduce the complexity.
• Author(s) :
• Sridevi C.S. (Bharathiar University, Coimbatore, Tamil nadu)

## [01052] Large systems of linear equations in particle transport problems

• Abstract : This work discusses solutions of large linear systems of algebraic equations relevant to establish a solution to the discrete ordinates approximation of the two-dimensional linear Boltzmann equation. Direct and iterative methods are investigated, along with domain decomposition techniques and parallel implementation. The type of the quadrature scheme describing the directions and the class of problems to be solved, neutron or radiation problems, directly affect the final choice of the numerical algorithm.
• Author(s) :
• Rudnei Dias da Cunha (Universidade Federal do Rio Grande do Sul)
• Liliane Basso Barichello (Universidade Federal do Rio Grande do Sul)

## [01053] Radial Basis for Solving high-dimensional PDEs in Option Pricing

• Abstract : A Radial Basis Function is used to solve the partial differential equations arising for option pricing problems in very high dimension. For such problems, classical grid-based finite-difference approaches fail to give any numerical solution as the memory requirements grow exponentially with the number of dimensions. Our numerical results are compared to both analytical solutions as well as Monte Carlo Simulations to demonstrate the efficiency of the proposed radial basis approximation.
• Author(s) :
• Désiré Yannick TANGMAN (University of Mauritius)

## [01056] Statistical methodology for functional meta-analysis of sex-based disparities in neurological diseases

• Abstract : Sex-based differences in diverse health scenarios and diseases have been acknowledged for many years but still not thorough-fully analysed. We propose a statistical methodology combining transcriptomics data from different spurces which allows to unveil those disparities at the level of differentially expressed genes and differentially enriched functions. The methodology uses linear models, meta-analysing the results through the logFC, and has been successfully applied to various diseases such as Multiple Sclerosis, Alzheimer’s and Parkinson’s diseases.
• Author(s) :
• Marta R. Hidalgo (CIPF)
• Francisco Garcia-Garcia (CIPF)
• Borja Gomez-Cabañes (CIPF)
• Carla Perpiña-Clerigues (CIPF)
• Irene Soler-Saez (CIPF)
• Fernando Gordillo-González (CIPF)
• Gonzalo Anton-Bernat (Universitat de València)
• Rubén Grillo-Risco (CIPF)
• Jose Francisco Català-Senent (INCLIVA)

## [01057] Hypergraph Attention Graph Convolution Network for Precision Medicine

• Abstract : Graph neural networks have achieved prominent results recently in many research fields. However, the existing GCN approaches encountered large challenges when handling some issues with heterogeneous graphs of a huge number of nodes, and multiple types of relations. A good example of such issues can be the relational networks of adverse events and drugs from the area of precision medicine. We propose the Hypergraph Attention convolution mechanism as a promising remedy and is worth further studies.
• Author(s) :
• ZHOUMING XU (The University of Hong Kong)

## [01059] EVENT-TRIGGERED CONTROL FOR PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS WITH CYBER-ATTACKS

• Abstract : An event-triggered control for parabolic-type partial differential equations subject to disturbances and cyber-attacks is addressed in this talk. To attenuate the disturbances an H∞ performance is considered. By designing an appropriate Lyapunov-Krasovskii functional the stabilization conditions for the considered parabolic type partial differential equations are obtained in the form of linear matrix inequalities. Finally, a numerical example is provided to verify the efficiency of the derived theoretical results.
• Author(s) :
• Parivallal Arumugam (Sungkyunkwan University)

## [01061] Computation of control for fractional nonlinear systems using Tikhonov regularization

• Abstract : Determining the control steering the dynamical system is equally important as it is to examine the controllability of a control system. This study computes the control for the approximately controllable nonlinear system governed by Caputo derivatives. By using operator theoretic formulations, the problem of computing the control gets converted into an ill-posed problem which is solved for stable approximations using Tikhonov regularization. An example is presented demonstrating the error and truncated control graphs using MATHEMATICA.

• Author(s) :
• Lavina Sahijwani (Indian Institute of Technology Roorkee, India)
• N. Sukavanam (Indian Institute of Technology Roorkee, India)
• D. N. Pandey (Indian Institute of Technology Roorkee, India)

## [01062] An anisotropic PDE model for Image Segmentation

• Abstract : An anisotropic PDE model for the classification of grey scale images has been proposed. A fully automatic classification of any image is achieved by a suitably designed multi-modal well potential function. The model is solved by the spectrally accurate pseudo-spectral method and has been successfully tested on several bench-mark problems for its superior performance measured in terms on standard metrics like SNR, PSNR, SSIM etc.
• Author(s) :
• Rathish Kumar Venkatesulu Bayya (Indian Institute of Technology Kanpur)

## [01066] Probability of Disease Extinction or Outbreak in a Stochastic Epidemic Model for Zika Virus Dynamics in Humans

• Abstract : In this presentation, we consider a stochastic Zika virus transmission model. The stochastic model predicts the possibility of disease extinction even though the deterministic model predicts a continuous infection without any prevention. We derived the extinction probability using the Galton-Watson branching process. Finally, we derived the implicit equation of expected time to disease extinction and illustrated graphically the effect of the model parameters on the expected time to extinction.
• Author(s) :
• Partha Sarathi Mandal (National Institute of Technology Patna)

## [01067] Stoneley wave propagation at the interface between two initially stressed medium with interface energy

• Abstract : The present study investigates the propagation of Stoneley waves at interface of two distinct imperfectly bonded solid half-spaces considering strain and kinetic energies localized at interface. Gurtin−Murdoch (1975) and Eremeyev (2016) approaches are used to derive interface strain energy density, stress tensor, kinetic energy density accounting for non-perfect interface. Comparative analysis of dispersion curves is done numerically and presented through graphs. The findings have applications in geosciences for non-destructive characterization of thin inter-phases between solids.
• Author(s) :
• Arindam Nath (Department of Mathematics, School of Sciences, NIT Andhra Pradesh, India)
• Sudarshan Dhua (Department of Mathematics, School of Sciences, NIT Andhra Pradesh, India)

## [01069] Global existence and stability of three species predator-prey system with prey-taxis

• Abstract : In this paper, we study the initial-boundary value problem of a three species predator-prey system with prey-taxis which describes the indirect prey interactions through a shared predator in a bounded domain $Omega subset mathbb{R}^n (ngeq 1)$with smooth boundary and homogeneous Neumann boundary conditions. The model parameters are assumed to be positive constants. We first prove the global existence of classical solutions under suitable assumptions on the prey-taxis coefficients $chi_1,chi_2$ and $d$. Moreover, we establish the global stability of the prey-only state and coexistence steady states by using Lyapunov functionals and LaSalle’s invariance principle.
• Author(s) :
• GURUSAMY ARUMUGAM (The Hong Kong Polytechnic University )

## [01075] Implementation of Mathematical Proof and Argumentation Learning Activities in Langsa

• Abstract : This study aims to implement learning designs for mastering mathematical proof and argumentation abilities in pre-service mathematics teachers enrolling in one public university in Langsa City, Aceh, Indonesia. Learning activities consist of four core stages, i.e., proofreading, writing resumes, exercises in proving, then reflection and evaluation. The results demonstrated an increase in students’ mathematical proof and argumentation abilities from mediocre to excellent.
• Author(s) :
• Iden Rainal Ihsan (Universitas Samudra)
• Natanael Karjanto (Sungkyunkwan University)
• Guntur Maulana Muhammad (Universitas Samudra)

## [01076] Herglotz’s Variational Problem involving distributed-order fractional derivatives with arbitrary kernels

• Abstract : In this talk we extend the study of fractional variational problems of Herglotz type for the case where the Lagrangian function depends on distributed-order fractional derivatives with arbitrary smooth kernels,
the endpoints conditions, and a real parameter.
The fact that the Lagrangian depends on the boundary conditions and an arbitrary parameter is not an
artificial generalization, as this formulation is important in many problems, such as in physics and
economics.
• Author(s) :
• Natália Martins (University of Aveiro)

## [01078] DNN-based hybrid ensemble learning strategy for XSS detection and defense

• Abstract : Due to the high level of intelligence displayed by attackers, existing web-based security applications have failed. When attackers make changes to an organization’s data, it is one of the most dangerous attacks (XSS). Combining ML and DL frameworks is proposed as a way to detect and defend against XSS assaults with high accuracy and efficiency. Using this representation, a new method is developed for integrating stacking ensembles into web-based software, which is called “hybrid stacking”.
• Author(s) :
• Seethalakshmi Perumal (MIT Campus, Anna University – Chennai)

## [01079] Higher order numerical scheme to approximation generalized Caputo fractional derivatives and its application

• Abstract : In this paper, a high-order numerical scheme is established to approximate the generalized Caputo fractional derivative using Lagrange interpolation formula. Order of convergence for this scheme is obtained as (4 − α), where α ∈ (0, 1) is the order of generalized Caputo fractional derivative. The local truncation error of the approximation is also obtained. Further, the developed scheme is used to solve the generalized fractional advection-diffusion equation. Stability and convergence are also discussed for the difference scheme. In the last, numerical examples are discussed to illustrate the theoretical results.
• Author(s) :
• Sarita kumari (Indian Institute of technology (Banaras Hindu University))
• Dr. Rajesh Kumar Pandey (Indian Institute of Technology (BHU) Varanasi)

## [01082] Analysis of traffic flow models by triangulation of min-plus matrices

• Abstract : Cellular automata model for traffic flow can be described in terms of min-plus linear systems. In this talk, we focus on the triangulation of a min-plus matrix, which is defined based on the roots of characteristic polynomial and the algebraic eigenvectors associated with the roots. It plays an important role in the analysis of the asymptotic behavior of the model. Further the algebraic eigenvectors are shown to give us preferable initial states.
• Author(s) :
• Yuki Nishida (Tokyo University of Science)
• Sennosuke Watanabe (The University of Fukuchiyama)
• Yoshihide Watanabe (Doshisha University)

## [01083] The existence and the numerical approximation to a nonlinear coupled system in anisotropic Orlicz-Sobolev spaces

• Abstract : We study the existence of a capacity solution for a nonlinear elliptic coupled system
in anisotropic Orlicz-Sobolev spaces. The unknowns are the temperature inside a semiconductor material, and the electric potential. This system may be considered as a generalization of the steady-state thermistor problem. The numerical solution is also analyzed by means of the least squares method in combination with a conjugate gradient technique.
• Author(s) :
• Hakima Ouyahya (Moulay Ismail University)

## [01084] Linear instability of pipe Poiseuille flow of shear-thinning White–Metzner fluid

• Abstract : It has been investigated that the pressure-driven pipe flow of Oldroyd-B fluid is linearly unstable to an axisymmetric centre mode (Chaudhary et al., JFM, vol. 908, 2021, A11). Understanding the effects of elasticity and shear thinning, which are not accounted for in Oldroyd-B fluids and are often evident in White-Metzner fluid, is crucial for developing a comprehensive theory on the linear instability of viscoelastic pipe flow. We have found that the shear thinning trigger centre mode instability at smaller Reynolds number. Furthermore, there may be a possibility of purely elastic wall mode instability due to strong variations of the normal forces close to the wall as demonstrated by the flow of shear thinning polymer solutions in channel (Groisman et al., Nature, vol. 405, 2000, 53-55). The mechanism of this elastic shear-thinning instability will be discussed.
• Author(s) :
• Arshan Khan (Indian Institute of Technology Delhi, India)
• Paresh Chokshi (Indian Institute of Technology Delhi, India)

## [01087] Ferrohydrodynamic Mixed Convective Flow of a Rotating Disk with Vertical Motion

• Abstract : A mathematical model of an electrically non-conducting nano-ferrofluid over a rotating disk subject to vertical disk motion and low oscillating magnetic field with heat transfer is framed. The coupled ferrohydrodynamic equations of motion and the magnetization equation is solved using finite difference method with collocation technique and artificial intelligence algorithm. Novel results are obtained for ferroparticle concentration and magnetization parameter subject to entropy optimization.
• Author(s) :
• Gayathri Palanisamy (PSG College of Arts & Science, Coimbatore)

## [01089] Revisiting Subgradient Method Beyond Global Lipschitz Continuity

• Abstract : Subgradient method is one of the most fundamental algorithmic schemes for nonsmooth optimization. Most of the existing complexity and convergence results for this algorithm are derived based on global Lipschitz continuity assumption. In this work, we extend the typical complexity results for subgradient method to convex and weakly convex minimization without assuming global Lipschitz continuity. Specifically, we establish $O(1/sqrt{T})$ bound in terms of the suboptimality gap “$f(x) – f^*$” for convex case and $O(1/{T}^{1/4})$ bound in terms of the gradient of the Moreau envelope function for weakly convex case. Moreover, we provide convergence results with proper diminishing rules on the step sizes. In particular, when $f$ is convex, we show that the weighted average of the iterates has a $O(log(k)/sqrt{k})$ rate of convergence in terms of suboptimality gap. With an additional quadratic growth condition, the rate is improved to $O(1/k)$ in terms of squared distance to the optimal solution set. When $f$ is weakly convex, asymptotic convergence is derived. The central idea is that the dynamics of properly chosen step sizes rule fully controls the movement of the subgradient method, which leads to boundedness of the iterates. Then, a trajectory-based analysis and local Lipschitz continuity can be employed to establish the desired results. To further illustrate the wide applicability of our framework, we extend the complexity results to truncated, incremental, and proximal subgradient methods for non-Lipschitz functions.
• Author(s) :
• Xiao Li (The Chinese University of Hong Kong, Shenzhen)

## [01090] A high order approximation scheme for non-linear time fractional reaction-diffusion equation

• Abstract : We discuss a high order numerical scheme for the non-linear time fractional reaction-diffusion equation of order $alphain (0, 1)$. A cubic approximation and compact finite difference schemes are used to approximate the time-fractional and spatial derivatives respectively. The numerical scheme achieves convergence rate of order $4-alpha$ in the temporal direction and $4$ in the spatial direction. Further, numerical experimentation is performed to demonstrate the authenticity of the proposed numerical scheme.
• Author(s) :
• Rajesh Kumar Pandey (Indian Institute of Technology (BHU) Varanasi)
• Deeksha Singh (Indian Institute of Technology (BHU) Varanasi)

## [01093] Optimizing Functionals with dependence on fractional derivatives with variable order

• Abstract : In this work we combine two ideas: fractional derivatives of variable order and fractional derivatives depending on another function. With such operators, we develop a variational problem theory by presenting necessary conditions of optimization. The fundamental problem will be addressed, proving an Euler-Lagrange equation, and then other versions will be considered such as the isoperimetric problem or the Herglotz problem. We provide a numerical tool to solve fractional problems dealing with such fractional derivatives.
• Author(s) :
• Ricardo Almeida (University of Aveiro)

## [01094] Variational iteration Method for Shallow Water Waves

• Abstract : Variational iteration method, VIM, is employed to solve analytic solutions of shallow water wave equations. For its linearized models we compute a periodic numerical example, and a symbolic one with unprescribed initial conditions and parameters. Both examples are found their explicit exact solutions by VIM. Then we turn to some nonlinear models and obtain their highly accurate approximate solutions. We concluded that VIM is very effective for shallow water wave problems and other nonlinear PDEs.
• Author(s) :
• Tzon-Tzer Lu (Department of Applied Mathematics, National Sun Yat-sen University)

## [01097] Versal deformations as a tool of matrix analysis

• Abstract : Reductions of matrices or matrix pencils to canonical forms are unstable operations: both the corresponding canonical forms and the reduction transformations depend discontinuously on the entries of an original matrix or pencil. This issue complicates the use of canonical forms for numerical purposes. Therefore V.I. Arnold introduced a notion of versal deformations. We will discuss versal deformations and their use in codimension computations, investigation of possible changes in eigenstructures, and reduction to structured perturbations.
• Author(s) :
• Andrii Dmytryshyn (Örebro University)
• Andrii Dmytryshyn (Örebro University)

## [01101] Supersonic Pre-Transitional Disturbances in Boundary Layers on Porous Surfaces

• Abstract : The effect of wall permeability on the response of pre-transitional supersonic boundary layers subject to low-amplitude, free-stream vortical disturbances is investigated via asymptotic methods and numerically. Equally-spaced cylindrical pores couple the pressure and wall-normal velocity fluctuations when the spanwise diffusion is negligible, thereby reducing the growth of low-frequency laminar streaks and Görtler vortices on concave porous walls. Highly-oblique Tollmien-Schlichting waves that develop further downstream are instead enhanced. This finding is confirmed by a triple-deck analysis.
• Author(s) :
• Ludovico Fossà (The University of Sheffield)
• Pierre Ricco (The University of Sheffield)

## [01102] Independent Study in Designing Mathematics Learning Using GeoGebra AR

• Abstract : This research examines the implementation of one program from the Indonesian Ministry of Education, Culture, Research, and Technology, i.e., independent studies, in the Department of Mathematics Education at a public university in Langsa, Aceh, Indonesia. The activities focused on compiling learning designs that apply the GeoGebra Augmented Reality (AR) to geometrical concepts in secondary schools by adopting the ADDIE Model. The aim is for pre-service mathematics teachers to explore learning activities independently in mastering Technological Pedagogical Content Knowledge (TPACK) when teaching mathematics. Our findings suggest the implementation of such an independent study because of its advantages and program improvisation as a form of program development.
• Author(s) :
• Guntur Maulana Muhammad (Universitas Samudra)
• Natanael Karjanto (Sungkyunkwan University)
• Iden Rainal Ihsan (Universitas Samudra)

## [01103] Mechanoelectric effects in cardiac function

• Abstract : To date the role of the different mechanoelectric feedback $($MEF$)$ mechanisms is not clear in the cardiac function. Using a multiscale $($from cellular to organ level$)$ 3D-0D closed loop fluid-electromechanical framework implemented in the Cardiac Arrhythmia Research Package $($CARP$)$ software, we perform computer simulations to explore the effect of two MEF mechanisms in healthy cardiac function and under the Left Bundle Branch Block pathology.
• Author(s) :
• Argyrios Petras (RICAM-Johann Radon Institute for Computational and Applied Mathematics)
• Matthias AF Gsell (Medical University of Graz)
• Christoph M Augustin (Medical University of Graz)
• Jairo J Rodriguez Padilla (Centre Inria d’Université Côte d’Azur)
• Alexander Jung (Medical University of Graz)
• Marina Strocchi (King’s College London)
• Frits Prinzen (Maastricht University)
• Steven Niederer (King’s College London)
• Gernot Plank (Medical University of Graz)
• Edward J Vigmond (Liryc, Electrophysiology and Heart Modeling Institute)

## [01104] Generation of $hp$-FEM Massive Databases for Deep Learning Inversion

• Abstract : Deep Neural Networks are employed in many geophysical applications to characterize the Earth’s subsurface. However, they often need to solve hundreds of thousands of complex and expensive forward problems to produce the training dataset.

This work presents a robust approach to producing massive databases at a reduced computational cost. In particular, we build a single $hp$-adapted mesh that accurately solves many FEM problems for any combination of parameters within a given range.

• Author(s) :
• Julen Alvarez-Aramberri (University of the Basque Country (UPV/EHU))
• Vincent Darrigrand (CNRS-IRIT, Toulouse)
• Felipe Vinicio Caro (Basque Center for Applied Mathematics (BCAM), University of the Basque Country (UPV/EHU))
• David Pardo (University of the Basque Country (UPV-EHU), Basque Center for Applied Mathematics (BCAM), Ikerbasque)

## [01105] SIPG Method for boundary control problems governed by parabolic PDEs

• Abstract : We present a posteriori error analysis of adaptive finite element approximations for parabolic boundary control problems with bilateral box constraints that act on a Neumann boundary. The discretization is followed by using the symmetric interior penalty Galerkin (SIPG) technique. Both reliable and efficient residual-based error estimators are deduced. The implementation of these error estimators serves as a guide for the adaptive mesh refinement process. The numerical experiment shows the effectiveness of the derived estimators.
• Author(s) :
• Ram Manohar (Indian Institute of Technology Kanpur)
• Rathish Kumar Venkatesulu Bayya (Indian Institute of Technology Kanpur)
• Kedarnath Buda (Indian Institute of Technology Kanpur)
• Rajen Kumar Sinha (Indian Institute of Technology Guwahati)

## [01106] An alternative approach to generating the Covid-19 dynamics

• Abstract : The dynamics of the mysterious Covid-19 spread are interesting for further exploration and investigation. We propose a generating dynamic operator of cumulative case functions to recover all the dynamics of the SEIR model. This approach can also provide estimates of unrecorded cases based on the dynamics of the Covid-19 test, IFR, CFR, and recorded cases. This approach directly measures daily transmission indicators, which can be used effectively for day-to-day epidemic control.
• Author(s) :
• Kamal Khairudin Sukandar (Institut Teknologi Bandung)
• Andy Leonardo Louismono (Institut Teknologi Bandung)
• Metra Volisa (Institut Teknologi Bandung)
• Rudy Kusdiantara (Institut Teknologi Bandung)
• Muhammad Fakhruddin (The Republic of Indonesia Defense University)
• Nuning Nuraini (Institut Teknologi Bandung)
• Edy Soewono (Institut Teknologi Bandung)

## [01108] Harmonic Instability and Modal Transition in Ultra-Long Marine Risers

• Abstract : Recent results on the dynamics of beams under self-weight imply the existence of dynamic compression in ultra-large marine structures, possibly causing the coexistence of compressive and anti-compressive vibration modes. This results in a harmonic phase-transition as the mode-shapes flip qualitatively, leading to extreme curvatures and numerical instability. For this talk we’ll present sharp estimates for the bottom tensions required for the safe operation of marine risers through an analogy with quantum systems with turning points.
• Author(s) :
• Arthur Bizzi (IMPA)
• Arthur Bizzi (IMPA)

## [01109] Harmonic Instability and Modal Transition in Ultra-Long Marine Risers

• Abstract : Recent results on the dynamics of beams under self-weight imply the existence of dynamic compression in ultra-large marine structures, possibly causing the coexistence of compressive and anti-compressive vibration modes. This results in a harmonic phase-transition as the mode-shapes flip qualitatively, leading to extreme curvatures and numerical instability. For this talk we’ll present sharp estimates for the bottom tensions required for the safe operation of marine risers through an analogy with quantum systems with turning points.
• Author(s) :
• Arthur Bizzi (IMPA)
• Arthur Bizzi (IMPA)

## [01110] Patient-specific simulation of veno-venous Extra Corporeal Membrane Oxygenation (ECMO)

• Abstract : Veno-Venous ECMO is a well-established procedure used in Intensive Care Units for patients with pulmonary failure. The patient blood is drained via a cannula in the inferior vena cava, oxygenated and reinserted via another cannula in the superior vena cava. Still, its efficacy is very limited, mainly due to recirculation between the two cannulas. In this talk we present a patient-specific, CFD-based computational model to assess the efficacy of the procedure and quantify recirculation.
• Author(s) :
• Massimiliano Leoni (RICAM)
• Johannes Szasz (Kepler University Klinikum)
• Jens Meier (Kepler University Klinikum)
• Luca Gerardo Giorda (Johannes Kepler University Linz)

## [01113] Acoustic Scattering Highly Efficient Iterative Method with high Order ABC

• Abstract : In this paper, we have developed a highly efficient numerical method for acoustic multiple scattering. This novel method consists of a high order local absorbing boundary condition combined with an isogeometric finite element and finite differences methods. By employing high order NURB basis, a globally high order method results. In our numerical experiments, we obtain errors close to machine precision by appropriate implementation of p- and h-refinement. We include numerical results which demonstrate the improved accuracy and efficiency of this new formulation compared with similar methods.
• Author(s) :
• Vianey Roman Villamizar (Brigham Young University)
• Vianey Roman Villamizar (Brigham Young UniversityBrigham Young University)
• Tahsin Khajah (University of Texas at Tyler)
• Jonathan Hale (University of Wisconsin at Madison)

## [01114] Modeling Covid-19 Cases and Vaccination Interplay through Time-Varying Copula Approach

• Abstract : Currently, the Indonesian government has made various efforts to reduce the number of Covid-19 cases, one of which is through administering vaccines. This study aims to model the interplay between the number of Covid-19 cases and the number of citizens who have been vaccinated, especially in term of the temporal relationship, using the time-varying copula approach.
• Author(s) :
• Atina Ahdika (Universitas Islam Indonesia)

## [01115] Torsional surfce wave in a piezoelectric fiber-reinforced composite layer in context of surface/interface theory

• Abstract : The present paper investigates surface/interface theory-based torsional surface wave propagation in a Piezo-fiber-reinforced composite (PFRC) layer overlying a functionally graded substrate. When the external characteristic length is comparable to the characteristic length, surface/interface effects become prominent. The dispersion equation has been derived by analytical method. Numerically the effects of volume fraction and surface/interface parameters are analyzed and presented graphically. The results can be found helpful for the development and production of smart materials.
• Author(s) :
• Sudarshan Dhua (Department of Mathematics, School of Sciences, NIT Andhra Pradesh)
• Subrata Mondal (Department of Mathematics, School of Sciences, NIT Andhra Pradesh)

## [01116] Finite-time dynamic event-triggered consensus for multi-agent systems under multiple attacks

• Abstract : This paper addresses the problem of resilient finite-time consensus for multi-agent systems (MASs) under a dynamic event-triggered mechanism and multiple cyber-attacks. The proposed attack strategy includes scaling, replay, and DoS attacks that occur stochastically in a unified framework. Sufficient conditions for consensus of MASs are derived using linear matrix inequalities and Lyapunov stability theory, which ensure the exponentially mean-square finite-time stability. Eventually, the effectiveness of the obtained results is verified through autonomous mobile robots.
• Author(s) :
• Sathishkumar Murugesan (National Cheng Kung University)
• Yen-Chen Liu (National Cheng Kung University)

## [01118] Finite Element Analysis of a Non-equilibrium Model for Hybrid Nano-Fluid

• Abstract : A theoretical and computational finite element study of modified Navier-Stokes
Equations coupled with energy conservation governing the flow and heat transfer
in complex domain with hybrid nanofluid is carried out. The apriori error
estimates providing the convergence analysis for the finite element scheme is
derived in the H1-norm. The effect of hybrid nano-particle’s volume fraction,
Rayleigh Number, Prandtl Number, Darcy number, porosity are analyzed to trace
the physics related to flow and heat transfer.

• Author(s) :
• SANGITA DEY (Ph.D Student of Indian Institute of Technology Kanpur)
• Rathish Kumar Venkatesulu Bayya (Indian Institute of Technology Kanpur)

## [01119] Miscible Flows Based On Darcy-Stokes-Brinkman Model: Existence and Uniqueness

• Abstract : Flows in a porous or vuggy medium are encountered in several physical phenomena, including oil recovery. A vast literature use the unsteady Brinkman and continuity equations for numerical modeling of such flow systems. We couple these equations with a convection-diffusion equation for the solute concentration to take the miscibility of fluids into account. For the first time, we show the well-posedness of this problem by employing regularized Galerkin method and hemivaritional inequalities.
• Author(s) :
• Sahil Kundu (Indian Institute of Technology Ropar,Ropar, India)
• Manoranjan Mishra (Indian Institute of Technology Ropar, India)
• Surya Narayan Maharana (Indian Institute of Technology Ropar)

## [01122] A mathematical model of microtubule assembly and polarity in dendrites

• Abstract : The microtubule cytoskeleton is responsible for sustained, long-range intracellular transport of mRNAs and proteins in neurons. However, microtubules must also be dynamic and rearrange their orientation, or polarity, in response to injuries. While mechanisms that control the minus-end out microtubule orientation in Drosophila dendrites have been identified experimentally, it is unknown how these mechanisms maintain both dynamic rearrangement and sustained function. To better understand these mechanisms, we introduce a spatially-explicit mathematical model of dendritic microtubule dynamics using parameters informed by experimental data. We explore several hypotheses of microtubule growth using a stochastic model, and validate such mechanisms with fluorescence experiments. By incorporating biological experiments, our modeling framework can uncover the impact of various mechanisms and parameters on the emergent dynamics and polarity of microtubules in Drosophila dendrites.
• Author(s) :
• Anna Nelson (Duke University )
• Veronica Ciocanel (Duke University)
• Scott McKinley (Tulane University)

## [01133] Surface wave propagation in coated poro-elastic layer due to point source

• Abstract : The impact of an internal energy source on an anisotropic fluid-saturated poro-elastic layer over a non-homogeneous semi-infinite medium is presented. The poroelastic layer is coated with a thin elastic layer. The Fourier transform and Green’s function techniques are applied to analyse the velocity profile of Love-type wave propagation. Error analysis between phase velocity with and without damping has been shown. It is found that the dispersiveness is caused by the non-homogeneity of the semi-infinite medium.
• Author(s) :
• Dipendu Pramanik (Department of Mathematics, Indian Institute of Technology Indore)
• Santanu Manna (Department of Mathematics, Indian Institute of Technology Indore)

## [01134] A propagating edge wave on a crack plate

• Abstract : The study analyzes the characteristics of the bending edge wave on a semi-infinite Kirchhoff plate having a stationary crack on the plate and supported by an elastic foundation. The non-local elasticity theory is used to investigate the effect of non-local stress on the propagation of edge waves on the crack plate. Due to the presence of the crack, the stress intensity factor related to the edge wave propagation will be discussed via numerical analysis.
• Author(s) :
• Rahul Som (Department of Mathematics, Indian Institute of Technology Indore, India )
• Santanu Manna (Assistant Professor, Indian Institute of Technology Indore)

## [01137] Stability and Dispersion analysis for Rayleigh-type waves in non-local media

• Abstract : We present the non-local elastic behavior of Rayleigh-type surface waves in a layered media comprising an inhomogeneous medium and a fiber-reinforced layer. The dispersion equation is derived using an approximate asymptotic displacement solution of the governing wave equation. Using the Finite Difference Scheme, the stability conditions are determined for the equations of group velocity and phase velocity.The effects of various defining parameters on propagation are discussed and graphically depicted.
• Author(s) :
• Manasa Bhat (Department of Mathematics, Indian Institute of Technology Indore.)
• Santanu Manna (Department of Mathematics, Indian Institute of Technology Indore)

## [01139] Adaptive sampling and transfer learning techniques for solution of PDEs

• Abstract : An adaptive sampling technique applied to the deep Galerkin method (DGM), and separately a transfer learning algorithm also applied to DGM is examined, aimed to improve, and speed up the training of the deep neural network when learning the solution of partial differential equations (PDEs). The proposed algorithms improve the DGM method. The adaptive sampling scheme implementation is natural and efficient. Tests applied to selected PDEs discussing the robustness of our methods are presented.
• Author(s) :
• Andreas Aristotelous (The University of Akron)

## [01141] On tensor-based training of neural networks

• Abstract : In this work by resorting to the continuous ‘model’ of a shallow neural network, we present a novel training approach, that is based on a suitable approximate solution of a Fredholm integral equation of the first kind. Here, we concentrate on least-squares collocation, functional tensor networks and alternating ridge regression. Application of the algorithm to some supervised learning tasks is on par with other state-of-the-art approaches.
• Author(s) :
• Patrick Gelß ( Zuse Institute Berlin)
• Aizhan Issagali ( Freie Universität Berlin)
• Ralf Kornhuber (Freie Universität Berlin)

## [01147] A convergent numerical scheme to a McKendrick-von Foerster equation with diffusion

• Abstract : This talk presents a numerical scheme for a nonlinear McKendrick–von Foerster equation with diffusion in age (MV-D) with the Dirichlet boundary condition. The main idea for deriving the scheme is to use discretization based on the method of characteristics to the convection part, and the finite difference method to the rest of the terms. The nonlocal terms are dealt with the quadrature methods. As a result, an implicit scheme is obtained for the boundary value problem under consideration. The consistency and the convergence of the proposed numerical scheme are established. Moreover, numerical simulations are presented to validate the theoretical results.
• Author(s) :
• Suman Kumar Tumuluri (University of Hyderabad)

## [01150] Optimizing Tool Assignment Using Smart Lockers

• Abstract : A logistics operator adopted smart lockers to distribute 150 commercial tools such as tablets and scanners to employees, working in 3 shifts. The lockers gather significant data like tools deficiencies, breakdowns, usage time, punctuality. The assignment policy to deliver tools must minimize downtime using two figure of merit, one classifying employees according to their ability to handle tools, and another measuring the frequency of deficiencies and breakdowns. The proposal is inspired in genetic algorithms.
• Author(s) :
• Jose Alberto Fonseca (Instituto de Telecomunicações – Universidade de Aveiro)
• Joaquim Ferreira (Instituto de Telecomunicacoes, Universidade de Aveiro)
• Ricardo Bandeira (Microio,Lda)
• Fernanda Coutinho (Instituto Superior de Engenharia de Coimbra – IPP)

## [01151] Structure-Preserving Neural Networks for Hamiltonian Systems

• Abstract : When solving Hamiltonian systems using numerical integrators, preserving the symplectic structure is crucial. We analyze whether the same is true if neural networks (NN) are used. In order to include the symplectic structure in the NN’s topology we formulate a generalized framework for two well-known NN topologies and discover a novel topology outperforming all others. We find that symplectic NNs generalize better and give more accurate long-term predictions than physics-unaware NNs.
• Author(s) :
• Philipp Horn (Eindhoven University of Technology)
• Barry Koren (Eindhoven University of Technology)
• Veronica Saz Ulibarrena (Leiden University)
• Simon Portegies Zwart (Leiden University)

## [01153] Analysis of driver’s behavior and average flow on traffic dynamics

• Abstract : In this work, a new lattice model is proposed by considering the driver’s behavior (timid or aggressive) and downstream average flow on traffic dynamics. The stability condition is determined through stability analysis. Nonlinear analysis forms the modified Korteweg-de Vries (mKdV) equation to describe traffic density wave propagation near the critical point. Theoretical results are verified with numerical simulations, and it is concluded that driver behavior and average flow can stabilize traffic flow dynamics.
• Author(s) :
• Nikita Madaan (Thapar Institute of Engineering and Technology)
• Sonia – (Chandigarh University)

## [01154] Optimal bounds on the fundamental spectral gap with single-well potentials

• Abstract : We characterize the potential-energy functions $V(x)$ that
minimize the gap $Gamma$
between the two lowest
Sturm-Liouville eigenvalues for
[
H(p,V) u := -frac{d}{dx}
]
boundary conditions are imposed at end points, and $V$
is subject to various assumptions, especially convexity or having a “single-well” form.
In the classic case where $p=1$ we recover with different arguments the result of Lavine that
$Gamma$ is uniquely minimized among convex $V$ by the constant, and in the case of
single-well potentials, with no restrictions on the position of the minimum,
we obtain a new, sharp bound, that $Gamma > 2.04575dots$.
• Author(s) :
• Zakaria El Allali (Mohammed First University , Oujda, Morocco)
• Evans Harrell (Georgia Institute of Technology)

## [01155] Optimal bounds on the fundamental spectral gap with single-well potentials

• Abstract : We characterize the potential-energy functions $V(x)$ that
minimize the gap $Gamma$
between the two lowest
Sturm-Liouville eigenvalues for
[
H(p,V) u := -frac{d}{dx}
]
boundary conditions are imposed at end points, and $V$
is subject to various assumptions, especially convexity or having a “single-well” form.
In the classic case where $p=1$ we recover with different arguments the result of Lavine that
$Gamma$ is uniquely minimized among convex $V$ by the constant, and in the case of
single-well potentials, with no restrictions on the position of the minimum,
we obtain a new, sharp bound, that $Gamma > 2.04575dots$.
• Author(s) :
• Zakaria El Allali (Mohammed First University , Oujda, Morocco)
• Evans Harrell (Georgia Institute of Technology)

## [01156] Row completion of polynomial matrices

• Abstract : Perturbation problems arise frequently in applications, as in structural changes of the dynamics of a system or in pole placement problems in control theory.

Perturbation problems of matrices are closely related to completion problems. We present a solution to the row-completion problem of a polynomial matrix, prescribing the eigenstructure of the resulting matrix and maintaining the degree.

• Author(s) :
• Agustzane Amparan (Universidad del País Vasco, UPV/EHU)
• Itziar Baragaña (Universidad del País Vasco, UPV/EHU)
• Silvia Marcaida (Universidad del País Vasco, UPV/EHU)
• Alicia Roca (Universitat Politècnica de València )

## [01157] The boundary domain integral method for boundary value problems with variable coefficients

• Abstract : The boundary domain integral equation method is an important tool to formulate (in terms of integral operators) boundary value problems with variable coefficients. Although the theory of boundary domain integral equations has been largely developed, there is a lack of results in numerical implementations.
The aim of this talk is to enumerate the different boundary domain formulations for several boundary conditions and present discretizations of the integral equation systems and comparisons between the numerical behavior of the approximated solutions.
• Author(s) :
• Nahuel Domingo Caruso (National University of Rosario – CIFASIS-CONICET)
• Carlos Fresneda-Portillo (Universidad Loyola Andalucía (Spain))

## [01159] A multiscale framework for rigid bodies in Stokes flow with applications to nanocellulose

• Abstract : The dynamics of rod-like nanocellulose chrystals in an aqueous suspension is modelled with the rigid multiblob method for Stokes flow, with particle interactions from an accurate potential obtained from molecular dynamics data fed to a neural network. Tools to control the error from the hydrodynamic interactions and from discretising the overdamped Langevin equation, describing the Brownian motion of the particles, enable predictions of physical properties difficult to measure in the lab.
• Author(s) :
• Anna Broms (KTH Royal Institute of Technology)
• Anna-Karin Tornberg (KTH Royal Institute of Technology)
• Mattias Sandberg (KTH Royal Institute of Technology)

## [01162] Higher-Order Numerical Approximation of Coupled System of Singularly Perturbed Time-Delay Parabolic PDEs on Generalized Adaptive Mesh

• Abstract : We consider a coupled system of singularly perturbed convection-diffusion parabolic PDEs with time-delay and having small diffusion parameters of different orders of magnitude. Due to the occurrence of the overlapping boundary layers, generating efficient numerical approximation becomes a challenging task. To accomplish this goal, the governing system of equations is approximated on a generalized S-mesh, a general form of the piecewise-uniform Shishkin mesh, by employing an implicit-Euler method in the time direction together with the upwind finite difference scheme in the spatial direction. At first, we prove that the numerical solution converges uniformly in maximum-norm with faster convergence rate on the generalized S-mesh than the standard Shishkin mesh. Afterwards, we establish higher-order uniform convergence of the resulting numerical solution by applying the Richardson extrapolation technique. The theoretical outcomes are finally supported by the extensive numerical experiments.
• Author(s) :
• KAUSHIK MUKHERJEE (Indian Institute of Space Science and Technology (IIST), Thiruvananthapuram)
• Sonu Bose (Indian Institute of Space Science and Technology (IIST), Thiruvananthapuram)

## [01163] An infinite class of shocks for compressible Euler

• Abstract : We consider the two dimensional compressible Euler equations with azimuthal symmetry and construct an infinite class of shocks by establishing shock formation for a new Hölder family of so-called pre-shocks for all nonnegative integers. Moreover, a precise description of the dominant Riemann variable in the Hölder space is given in the form of a fractional series expansion.
• Author(s) :
• Calum Rickard (University of California, Davis)
• Sameer Iyer (University of California, Davis)
• Steve Shkoller (University of California, Davis)
• Vlad Vicol (New York University)

## [01164] Infection spreading in tissue as a delayed reaction diffusion wave

• Abstract : In this work, we have discussed the stationary solution of a delayed reaction diffusion system for the concentrations of uninfected cells, infected cells, and virus cells. We have also discussed the existence of waves for the corresponding monotone system and found the minimal wave speed of the system. We have observed that when the death rates of uninfected and infected cells were the same, the virus propagation gradually decreases, but when the death rates are different, the wave propagation initially increases and then decreases. It is also observed that as the time delay increases the initial oscillations also increases. Next, we convert the system into a single diffusion equation using a quasi-stationary approximation, study the existence of the wave, and find the analytical expression for the minimal wave speed. We have also performed comprehensive simulations to compare and validate the results for both cases.
• Author(s) :
• Moitri Sen (National Institute of Technology Patna)
• Saddam Hussain (National Institute of Technology Patna)
• Vitaly Volpert (Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1)

## [01171] The role of the autoregulation mechanism in hypertension and hypotension in humans

• Abstract : We present a nonlinear model for the propagation of the pressure and flow velocity waves in the human cardiovascular system, including deep learning tools with available physiological data. This model is used for understanding the system-level dynamics of the pressure and flow rates. This time-domain analysis is best to describe time-dependent controls, collectively known as the autoregulation mechanism. We discuss an application of our model to the study of the hypertension and hypotension.
• Author(s) :

## [01176] Analysis of Girl Child School Dropout With Multiple Regression

• Abstract : Home factors, social and school environment factors are attributed to the causes of girl child school-dropout in Ghana. Mitigating school dropout menace calls for a scientific approach in determining the most contributory factors. Sampling respondents from Junior High Schools and stakeholders in the Tano North District of the Brong Ahafo Region in Ghana, a multiple regression model was constructed to determine the most contributory factor of girl child school dropout in order to advise on government policies.
• Author(s) :
• Emmanuel Apraku Amankwah (University of Energy and Natural Resources)

## [01179] Applications of a Tiled Monte Carlo Algorithm to the Computation of Matrix Functions

• Abstract : We extend our prior work on Monte Carlo algorithms for solving large linear systems to compute other matrix functions such as exponential and logarithm. Our recent algorithm that computes with matrix tiles is shown to guarantee convergence for sufficiently large tiles. We compute matrix functions by summing a polynomial approximation (e.g. Taylor, Chebyshev). We investigate the convergence conditions for each function and optimize the algorithm by adjusting the parameters.
• Author(s) :
• Hyeji Choi (Stony Brook University)

## [01182] Optimizing the manufacturing process of a cutting machine in iron industry

• Abstract : In this talk we discuss a multi-criteria optimization framework designed for the cooperation with a prominent company, leader in the production of automatic machines employed in iron manufacturing. The optimized machine process counts several steps, starting by cutting the bars at specified lengths and moving them into two temporary buffers. Afterwards, bars are relocated through pliers to parallel depots through a lengthwise movement and gathered by order to facilitate the subsequent transfer to downstream steps.
• Author(s) :
• Andrea Pizzuti (Università Politecnica delle Marche)
• Fabrizio Marinelli (Università Politecnica delle Marche)

## [01184] Harmonic Instability and Uncontrollability of Heavy Rayleigh Beams

• Abstract : Recent results imply the coexistence of compressive and anti-compressive vibration modes for massive Rayleigh beams, leading to a harmonic phase-transition within the structure. As a result, the underlying wave operators switch between causal and anti-causal, a phenomenon which is entirely absent from the usual Euler-Bernoulli simplification. For this talk, we’ll discuss the wide-ranging implications of this for the control of flexible structures, specially the partial loss of controllabity and observability.
• Author(s) :
• Arthur Bizzi (IMPA)
• Arthur Bizzi (IMPA)

## [01185] Harmonic Instability and Uncontrollability of Heavy Rayleigh Beams

• Abstract : Recent results imply the coexistence of compressive and anti-compressive vibration modes for massive Rayleigh beams, leading to a harmonic phase-transition within the structure. As a result, the underlying wave operators switch between causal and anti-causal, a phenomenon which is entirely absent from the usual Euler-Bernoulli simplification. For this talk, we’ll discuss the wide-ranging implications of this for the control of flexible structures, specially the partial loss of controllabity and observability.
• Author(s) :
• Arthur Bizzi (IMPA)
• Arthur Bizzi (IMPA)

## [01192] Application of MUSIC Algorithm in Microwave Imaging Without Switching Device

• Abstract : Although the MUltiple SIgnal Classification (MUSIC) algorithm has demonstrated suitability as a microwave imaging technique for identifying unknown anomalies, there is a fundamental limit that it requires a switching device to be used which permits a dipole antenna for signal transmission and reception. In this contribution, we design a MUSIC-type imaging function and explore its mathematical structure. Considering the investigated structure, we confirm that the imaging performance is highly dependent on the antenna arrangement and suggest an optimal antenna arrangement to improve the imaging performance. Simulation results with real-data are displayed to support the theoretical result.
• Author(s) :
• Won-Kwang Park (Kookmin University)

## [01193] Cost-effectiveness and Public Health Impact of HPV Vaccination Strategies with consideration of cross-immunity in Japan

• Abstract : We assessed the epidemiological and economic impact of potential health advantages of the HPV vaccination in Japan among girls and boys of ages 12–16. An age-structured mathematical model of HPV transmission was constructed. Compared to halted vaccination, girls-only vaccination programs with either 4vHPV or 9vHPV are cost-effective, but gender-neutral vaccination programs are less so. Adding boys to an existing successful girls-only program is not cost-effective since men are protected by herd immunity.
• Author(s) :
• Wongyeong Choi (Soongsil University)
• Eunha Shim (Soongsil University)

## [01201] How differential geometry and extremum seeking systems reveal the decades- long mystery of optimized flight of soaring birds

• Abstract : The optimized flight physics of soaring birds such as albatrosses have always been fascinating to biologists, physicists, mathematicians, and engineers. How can soaring birds fly in that effective way without spending almost any energy? The decades-long literature of the problem have not been successful in providing frameworks that can work in real time similar to the birds themselves. Recently, a breakthrough took place in providing a simple, real time extremum seeking method that characterize this phenomenon and implement it in real time. Mathematical analysts using differential geometric methods have been successful in supporting this new results.
• Author(s) :
• Sameh Eisa (University of Cincinnati )

## [01203] Existence and regularity results for nonlinear elliptic equations with degenerate coercivity

• Abstract : In this research we drive the existence and regularity results for solutions of some nonlinear degenerate Dirichlet problems containing two lower order terms, the fi rst is a nonlinear convection term satisfying an optimal growth conditions and without any hypothesis of coercivity and the second is a zero order perturbation term, which called the hardy potential, that creates an obstruction to the existence of a solution. Not also that for right hand side,
it is assumed that to be an L^m-function with m⩾1.
• Author(s) :
• Fessel Achhoud (MISI Laboratory Hassan First University of Settat)
• Abdelkader Bouajaja (MISI Laboratory Hassan First University of Settat)

## [01204] Observer-based control for nonlinear time-delayed system under delay fractionising approach

• Abstract : In this research, an observer-based control for a time delay system is developed. The main goal of the research is to derive tractable conditions for stability analysis with reduced conservatism. By using the Lyapunov-Krasovskii approach, delay fractionising and matrix inequality techniques, a robust observer-based control strategy is proposed so that conditions which ensures stochastic stability of the system are obtained. Finally, numerical examples provide evidence for giving the desired result with the proposed control.
• Author(s) :
• Maya Joby (KCG College of Technology)
• Srimanta Santra (Technion-Israel Institute of Technology)

## [01205] Finite-Time Analysis of Single-Timescale Actor Critic

• Abstract : Actor Critic (AC) is a popular class of reinforcement algorithms. Despites its remarkable success in practice, the convergence property of AC is largely unexplored. Most of the existing convergence results are derived based on either double-loop update or two-timescale step sizes rule. In this talk, we presents the latest sample complexity result of practical single-timescale AC algorithm, where the actor and critic are updated alternatively with step sizes being of the same order.
• Author(s) :
• Qijun Luo (The Chinese University of Hong Kong Shenzhen)
• Xiao Li (The Chinese University of Hong Kong, Shenzhen)

## [01206] Fast Algorithms for Maxwell’s Equations for Three-Dimensional Photonic Crystals

• Abstract : In this article, we propose the Fast Algorithms for Maxwell’s Equations (FAME) package for solving Maxwell’s equations for modeling three-dimensional photonic crystals. FAME combines the null-space free method with fast Fourier transform (FFT)-based matrix-vector multiplications to solve the generalized eigenvalue problems (GEPs) arising from Yee’s discretization. Numerical results demonstrate the potential of our proposed package to enable large-scale numerical simulations for novel physical discoveries and engineering applications of photonic crystals.
• Author(s) :
• Xing-Long Lyu (Southeast University)
• Tiexiang Li (Southeast University)
• Tsung-Ming Huang (National Taiwan Normal University)
• Jia-Wei Lin (National Yang Ming Chiao Tung University)
• Heng Tian (Sichuan University of Science and Engineering)
• Wen-Wei Lin (National Yang Ming Chiao Tung University)

## [01207] Optimal analysis of ecological-economic model with fishing tax and tourist entry-fee

• Abstract : A market-based fishing strategy in a multi-species fishery with a fair taxation policy may provide long-term sustainable growth. Fishery-based ecotourism with an entry fee for the tourist may further contribute to the financial improvement of the local people. Here we have proposed and analyzed a harvesting model that integrates fishery and fishery-based ecotourism with the open market economy theory. We determine the optimal fishing tax and entry fee that maximizes the social benefit.
• Author(s) :

## [01208] On bundles of matrix pencils under strict equivalence

• Abstract : Bundles of matrix pencils under strict equivalence are sets of pencils having the same Kronecker canonical form, up to the eigenvalues: namely, they are unions of orbits. The notion of bundle was introduced by Arnold in 1971, and it has been extensively used since then. In this talk, we review and/or formalize some notions and results on bundles of pencils and provide a characterization for the inclusion relation between their closures in the standard topology.
• Author(s) :

## [01209] Detecting CoVid 19 using Topology

• Abstract : In this worldwide spread of SARS-CoV-2 (COVID-19) infection, it is of utmost importance to detect the disease early, especially in the hot spots of this epidemic. The computed tomography (CT)-scan image is preferred to the  (RT-PCR) due to its effective results. We use persistent homology, a technique from the topological data analysis (TDA) for this purpose to quantify the topological properties of  CT-scan images, to imitate an eye of a professional medical practitioner.
• Author(s) :
• Muhammad Imran Qureshi (King Fahd University of Petroleum and Minerals)
• Sohail Iqbal (COMSATS University Islamabad)
• hafiz Ahmed (COMSATS University Islamabad)
• Talha Qaiser (Imperial College)
• Nasir Rajpout (University of Warwick)

## [01210] Adaptive Observer for Cyber-Physical Systems under Sensor Attacks with Delays

• Abstract : This paper addresses the issue of adaptive observer-based control for a class of cyber-physical systems under sensor attacks. First, based on the available input and output data sets is formulated with two objectives: attack detection and attack isolation. Then, with the subspace approach, a data-driven attack detection policy is presented, wherein the attack detector is designed directly by the process data. Moreover, the attention is focused on designing an adaptive observer-based state feedback controller which ensures that, for all input delay and sensor attacks, the resulting error system is exponentially stable.
• Author(s) :
• SRIMANTA SANTRA (KIOS Centre of Excellence at the University of Cyprus,Aglatzia, Nic osia , Cyprus.)
• Maya Joby (KCG College of Technology)
• Sathishkumar Murugesan (National Cheng Kung University)

## [01216] Neural network in option pricing

• Abstract : Black-Scholes model is the universally accepted model for computing option prices. While its is robust and easy to use, it has many flaws. Moreover, it failed spectacularly in 1987 during the wall street crash. This has led to proliferation of many extensions to the Black-Scholes model. Most extensions focus on relaxing the constant volatility assumption by incorporating randomness in the volatility. Whilst it provides slightly better estimation to option prices, it is computationally expensive to implement. Moreover, most of these models do not have closed-form solutions

With advancement in computational techniques, neural network has been increasingly used to price options. Not only, does it outperform conventional stochastic volatility models, it does not require assumption on the statistical characteristics of assets and volatility distribution. A typical neural network consists of three layers: input, hidden, and output. It uses a supervised learning method based on the generalisation of the least mean square error (LMS) algorithm. A gradient descent method is used to minimise the cost function, which is the mean square difference between the target and actual net output. More advanced neural networks (deep learning architectures), such as a Recurrent Neural Network (RNN) and its variant Long Short-Term Memory (LSTM), are useful for taking care of the time-series nature of financial data. The general architecture of the convolutional neural network-based LSTM model includes an input layer, one or more convolutional layers, long short-term memory layer(s), dense layer(s), and an output layer. In this research, we will attempt to predict Strait Times Index (STI) which is one of the most regularly traded options in Singapore Exchange (SGX).

After pre-processing and cleaning the data, the input (stock price, time to maturity and volatility and output (option prices) , variables will be extracted for training and testing the models. Various hyperparameters (optimizers, learning rate, hidden layers, activation functions, etc.) will be optimised to generate the best model for the prediction of the option pricing. A comparison of the accuracy of the prediction of option pricing will be performed for three models, namely convolutional neural network-based LSTM, Multilayer Perceptron neural network N and the Black Scholes option pricing model. Different metrics (root mean squared error, mean absolute error, and mean absolute percentage error) will be used to compare the performance of the models.

• Author(s) :
• Abby Chee Hong Tan (Universiti Brunei Darussalam)

## [01223] Descent hybrid four-term conjugate gradient methods for unconstrained optimization

• Abstract : Conjugate gradient method (CGM) is widely acclaimed to be efficient for solving large-scale unconstrained optimization problems. This study proposes new modified schemes that contains four terms based on the linear combination of the update parameters of classical or early methods depending on the popular two- and three-term CGMs.
Under some certain assumptions, descent and convergence properties were established. The results of the new schemes showed superior performance over the existing ones.
• Author(s) :
• Idowu Ademola Osinuga (Federal University of Agriculture, Abeokuta, Nigeria )
• Moses Oluwasegun Olubiyi (Federal University of Agriculture, Abeokuta)
• Semiu Akinpelu Ayinde (Babcock University, Ilishan-Remo)

## [01224] Collision-induced amplitude dynamics of 2D solitons in a perturbed saturable nonlinear medium

• Abstract : We study the amplitude dynamics of two-dimensional (2D) fast solitons in an interaction under a framework of coupled (2+1)D nonlinear Schrodinger equations with a saturable nonlinearity and weak perturbation. We derive a theoretical expression for the collision-induced amplitude dynamics in a fast collision of two 2D solitons. Our perturbative approach is mainly based on the analysis of the collision-induced change in the envelope of the perturbed 2D soliton. The theoretical results are validated by numerical simulations with the coupled perturbed nonlinear Schrodinger equations with saturable nonlinearity.
• Author(s) :
• Quan Minh Nguyen (International University, Vietnam National University Ho Chi Minh City)
• Toan Thanh Huynh (Department of Mathematics, University of Medicine and Pharmacy at Ho Chi Minh City, Ho Chi Minh City)

## [01226] Health Care: Robotic Dog for Navigation of a Rehabilitation Robot

• Abstract : One of the more recent technological advancements is assistive robots, which can improve patient-centered care in the health sector. This paper presents a unique set of continuous nonlinear control laws derived from a Lyapunov-based control scheme for navigation of an assistive robot and a rehabilitation wheelchair robot together modeled as a new autonomous robotic dog and rehabilitation wheelchair system. The computer simulations also present a qualitative analysis of the effectiveness of the control laws.
• Author(s) :
• Bibhya Nand Sharma (The University of the South Pacific )
• Sandeep Kumar (The University of the South Pacific )

## [01232] A MESH-LESS, RAY-BASED DEEP NEURAL NETWORK METHOD FOR THE HELMHOLTZ EQUATION WITH HIGH FREQUENCY

• Abstract : We develop a mesh-less, ray-based deep neural network method to solve the Helmholtz equation with high frequency. This method does not use an adaptive mesh refinement method, nor does it design a numerical scheme using some specially designed basis function to calculate the numerical solution, but it has the advantages of easy implementation and no mesh. We have carried out various numerical examples to prove the accuracy and efficiency of the proposed nnumerical method.
• Author(s) :
• andy L yang (DutchFork High school)

## [01233] A Study of the Spectra-Cutoff Imaging Method of Multiple Scattering in Isotropic Point-Like Discrete Random Media

• Abstract : Imaging in random media is an important and interesting subject of inverse problems, relevant to a wide range of physical and engineering contexts, such as seismic imaging, remote sensing, medical imaging, wireless communications, and nondestructive testing.

In this talk, we show that imaging becomes difficult to perform in random media when multiple scattering is too strong to cause image distortion arising from the underlying interactions of multiply scattered waves at resonance frequencies.

The Foldy-Lax-Lippmann-Schwinger, (FLLS), formalism, which is employed for the multiply scattered waves, in the frequency domain, in the case of an ensemble of randomly distributed point-like scatterers. The scattering matrix representing the (FLLS) formalism is a non-Hermitian Euclidean random matrix.

According to the eigenvalue distribution of the scattering matrix, we present our approach to restore the distorted images by cutting off the sharp frequency responses in the resonance regime due to strong multiple scattering.

Finally, we show the use of this approach for imaging in discrete random media with numerical simulations and also discuss the limitations and future research direction.

• Author(s) :
• Ray-Hon Sun
• Ray-Hon Sun (Stanford University (for this research work) / Google (now))

## [01239] Convergence analysis of the discrete consensus-based optimization algorithm

• Abstract : We study stochastic convergence of the discrete Consensus-Based Optimization, called CBO algorithm, in almost-sure sense and in expectation. CBO is a mathematical toy example for non-gradient multi-point optimizer which tries to find the global minimum point of a given cost function. The convergence analysis guarantees the termination of the optimization process. The main result is a joint work with Seung-Yeal Ha, Shi Jin, and Doheon Kim.
• Author(s) :
• Dongnam Ko (The Catholic University of Korea)

## [01241] Crossing Sea States in Layered and Stratified Fluids

• Abstract : Crossing sea states are common phenomena in the oceans, and have been suggested as one possible generation mechanism for rogue waves. Modeling studies are conducted for (a) a two-layer fluid with long wave-short wave resonance, and (b) the triad resonance in a continuously stratified fluid with constant buoyancy frequency. Modulation instability will be enhanced. There is a preferred inclination of oblique wave propagation for a maximum growth rate, suggesting the occurrence of rogue waves.
• Author(s) :
• Qing Pan (The University of Hong Kong)

## [01248] Reduction of Computational Cost with Optimal Accurate Approximation for Boundary Layer Originated Two Dimensional Coupled System of Convection Diffusion Reaction Problems

• Abstract : In this talk, I will consider a generalized form of a coupled system of time dependent convection diffusion reaction problems having arbitrary small diffusion terms, which lead to boundary layers. The numerical approximations of these problems require adaptive mesh generation for uniformly convergent approximation. In the present talk, I will provide an algorithm which will reduce the computational cost of the system solver by converting the system of discrete equations to a tridiagonal matrix form. This approach together with an adaptive mesh generation technique will preserve the optimal convergence accuracy. This convergence is proved to be independent of diffusion terms magnitude.
• Author(s) :
• Pratibhamoy Das (Indian Institute of Technology Patna)
• Pratibhamoy Das (Indian Institute of Technology Patna)
• Shridhar Kumar (Indian Institute of Technology Patna)

## [01250] Boundary Stabilization of Polynomial Reaction Diffusion Equations

• Abstract : We show how to stabilize a polynomial reaction diffusion system using boundary control,
integration by parts, completing the square and an infinite dimensional extension of Al’brekht’s
method.
• Author(s) :
• Arthur J Krener (Naval Postgraduate School)

## [01251] Integral Equations Techniques for Floating Flexible Membrane

• Abstract : Scattering of obliquely incident gravity waves by a horizontal floating flexible porous membrane in the water of finite depth having a variable bottom bed is analyzed. A coupled eigenfunction expansion – boundary element method is used for the solution purpose. The effect of sinusoidally varying bottom topography, membrane porosity and heading angle of the incident wave on the Bragg resonance is analyzed.
• Author(s) :
• SANTANU KOLEY (Birla Institute of Technology and Science – Pilani, Hyderabad Campus)

## [01254] Fast SVD-Preconditioned Eigensolver for 3D Phononic Crystals

• Abstract : In this talk, a Fast Linear Elastic Eigenvalue Problem Solver (FLEEPS) is developed to calculate band structures of 3D isotropic phononic crystals. FLEEPS is an iterative eigensolver of quasi-linear complexity to compute the smallest few eigenvalues of the linear elastic eigenvalue problem. The weighted SVD-preconditioned CG method in FLEEPS convergences faster than the AMG-preconditioned CG method by more than 60 times. Band structure calculations of several 3D isotropic phononic crystals demonstrate the strengths of FLEEPS.
• Author(s) :
• Tiexiang Li (Southeast University)
• Heng Tian (Sichuan University of Science and Engineering)
• Xing-Long Lyu (Southeast University)
• Wen-Wei Lin (National Yang Ming Chiao Tung University)

## [01271] Localized and degenerate controls for the incompressible Navier–Stokes system

• Abstract : This talk concerns the global approximate controllability of incompressible Newtonian fluids driven by a physically localized and degenerate interior control. By introducing transported Fourier modes as building blocks, we act on the planar Navier–Stokes system via four scalar controls that depend only on time and appear as coefficients in an effectively constructed driving force supported in a given subdomain. The four unknown parameters can be computed by merely solving a linear transport controllability problem.
• Author(s) :
• Manuel Rissel (New York University Shanghai)
• Vahagn Nersesyan (New York University Shanghai)

## [01281] Optimal network synchronization from a higher-order topological approach

• Abstract : In this talk, we will discuss the optimal network synchronization problem. The totally homogenous network approach will be reviewed, and a higher-order topological approach will be introduced, with some preliminary results reported.
• Author(s) :
• Guanrong (Ron) Chen (City University of Hong Kong )

## [01286] Radiation effect of ND–Ni nanocomposite, water-filled multiport cavity

• Abstract : The control of the thermal radiation influence on free convection of a multiple-port open cavity packed with water supported nanocomposite nanofluid is investigated numerically . One inlet port and two outlet ports are situated on the perpendicular walls. The remaining cavity walls are adiabatic. The heated thin baffle is located inside the cavity. The cavity is crammed with the water-supported nanodiamond–nickel nanocomposite. The governing Navier–stokes equations are written in the term of vorticity stream function transport. An ADI scheme-based finite difference process is used for discretization of the governing equations. The results are discussed graphically with the various parameters of radiation parameter, Reynolds number, Rayleigh number, solid volume fraction, widths of the opening, and locations of baffle position. It reveals that the average heat transfer rate reduces with the baffle placed far from the inlet.
• Author(s) :
• muthtamilselvan murugan (Bharathiar university)

## [01288] A WENO-Based Scheme for Simulating Miscible Viscous-Fingering Instability in Highly Convection-Dominated Regimes

• Abstract : We develop a Diffuse interface numerical method that simulates the miscible Viscous-Fingering instability in highly convection-dominated regimes (Péclet number > 10000). The developed finite volume scheme uses a two-point flux approximation (TPFA) for Darcy law and a fifth-order Weighted Essentially Non-Oscillatory(WENO) approximation for the convection term of the transport equation. The details of the numerical scheme and simulation results that agree excellently with existing numerical or experimental data will be discussed in this talk.
• Author(s) :
• Surya Narayan Maharana (Indian Institute of Technology Ropar)
• Manoranjan Mishra (Indian Institute of Technology Ropar, India)

## [01340] Mathematical finance without probability

• Abstract : We present a non-probabilistic, pathwise approach to continuous-time finance based on causal functional calculus. We introduce a definition of self-financing, free from any integration concept and show that the value of a self-financing portfolio is a pathwise integral and that generic domain of functional calculus is inherently arbitrage-free. We then consider the problem of hedging a path-dependent payoff across a generic set of scenarios. We apply the transition principle of Isaacs in differential games and obtain a verification theorem for the optimal solution, which is characterised by a fully non-linear path-dependent equation. For the Asian option, we obtain explicit solution.
• Author(s) :
• Henry Chiu (Imperial College London)

## [01345] Novel Lyapunov-type Inequality Involving Riesz Fractional Derivative

• Abstract : In this work, we obtained necessary condition for the existence of solutions to a fractional boundary value problem involving Riesz fractional derivative, which is defined as a two-sided fractional operator. The approach proposed in this work is based on the reduction of the problem considered to a singular integral equation, then we derive the Lyapunov-type inequalities in a weighted Lebesgue space.
• Author(s) :
• Rabah Khaldi (Badji Mokhtar Annaba University)
• Assia Guezane Laakoud (Badji Mokhtar Annaba University)

## [01348] Existence and nonexistence of solutions of thin-film equations with variable exponent spaces

• Abstract : This works aims at presenting a thin film problem involving variable exponent sources in a bounded domain. Which deals with the existence and nonexistence of solutions under subcritical initial energy. Also determine the global existence of solutions, exponential decay and finite time blow-up of solutions under specific conditions for the proposed model.
• Author(s) :
• GNANAVEL Soundararajan (Central University of Kerala)
• GNANAVEL SOUNDARARAJAN (Central University of Kerala)

## [01364] Time-Delay Systems: An Overview

• Abstract : Time-delay naturally arises in many real-world systems, due to the fact that the instantaneous rate of change of such systems does not only depend on their current time but rather on their previous history as well. Hence, time-delays are ubiquitous, their introduction often leads to suppression of oscillations, multistability and chaotic motion in the dynamical systems. This talk presents some models with different kinds of time-delays such as discrete, distributed and combination of both discrete and distributed time-delays with special emphasis on the reason of incorporating such delays into the system
• Author(s) :
• Bootan Rahman (University of Kurdistan Hewler (UKH))

## [01392] Solving a fractional pantograph delay equation

• Abstract : We study a pantograph delay equation involving a fractional derivative. Our approach relies basically on the reduction of the considered problem to an equivalent integral equation, then by using fixed point theorems, we prove the existence results. We also discussed the fractional Ambartsumian differential equation, that describes in the classical case the absorption of light by the interstellar matter.
• Author(s) :
• Assia Guezane Laakoud (Badji Mokhtar Annaba University)
• Rabah Khaldi (Badji Mokhtar Annaba University)

## [01401] Mass-Transfer on Ultrasound-Assisted Biodiesel Production from J.Oil through Process optimization

• Abstract : A three-step transesterification process using ultrasound is performed through mathematical modeling in presence of KOH catalyst for Production of Biodiesel. We investigated mass transfer effect between Jatropha oil and methanol considering ultrasound with temperature and oil-to-methanol molar ratio through Reynold’s and Schmidt’s Number. Application of optimal control approach maximize the production of biodiesel at minimum cost reveals that 98% biodiesel yield at 48 kHz, methanol-to-oil molar ratio 5:1 with 50oC through analytical and numerical analysis.

• Author(s) :
• PRITI KUMAR ROY (JADAVPUR UNIVERSITY)
• SK MOSARAF AHAMMED (Jadavpur University)

## [01405] Isotonic Regression Estimators of Order Restricted Parameters of a General Bivariate Model

• Abstract : We consider component-wise estimation of order-restricted location/scale parameters of a general bivariate distribution. To find improvements over the best location/scale equivariant estimators (BLEE/BSEE) of µ1 and µ2, we study isotonic regression of suitable location/scale equivariant estimators (LEE/SEE) with general weights. We consider two suitable classes of isotonic regression estimators of µ1 and µ2. We characterize admissible estimators within these classes and identify estimators that dominate the BLEE/BSEE of µ1 and µ2. Our study unifies and extends several studies reported in the literature for specific probability distributions having independent marginals. Additionally, some new and interesting results are obtained.
• Author(s) :
• Naresh Garg (IIT Kanpur)
• Neeraj Misra (IIT Kanpur)

## [01414] Solving multidimensional elliptic problems in unbounded domains using quasi-rational functions

• Abstract : The recent discovery of a family of multidimensional functions ([1,2]) has led to the design of an efficient numerical method for solving elliptical problems in unbounded domains, without truncation. In this talk we present the method, the proof of its convergence and some highly promising numerical results. Applications of the method are numerous and are currently being explored.
Ref.:
1. Arar and Boulmezaoud, J. Math. Anal. Appl. 400 (2013).
2. Boulmezaoud and al., M2AN 50 (2016).
• Author(s) :
• Tahar Zamene BOULMEZAOUD (University of Versailles SQY and University of Paris-Saclay)

## [01464] Fractional norm regularization under a generative deep learning framework for image restoration

• Abstract : Fractional norm regularization has been extensively used in various scientific applications. The usual integer norms are not sufficient to retains many important information inherent in the underlying images. In this study, we intent to incorporate fractional norms in the loss function of a generative model designed to handle various distortion present in the input images. A variational framework using a fractional norm has to be designed to handle various kinds of distortions in the data.
• Author(s) :
• Jidesh Pacheeri Padikkal (National Institute of Technology Karnataka, Surathkal)
• Bini A A (National Institute of Technology Calicut)

## [01476] Self-Organized Criticality on Stochastic Networks

• Abstract : Many systems in nature seem to be poised at criticality. Self-organized criticality $(SOC)$ suggests a mechanism by which the dynamics of the system intrinsically evolve into a critical state without any parameter tuning. We will describe the concept of SOC and present a new route obtained through temporal fluctuations in stochastic networks with applications to epidemic models over dynamic scale-free graphs, offering a possible explanation for why some epidemics, which we expect to disappear, don’t.
• Author(s) :
• Inbar Seroussi (Tei-Aviv University)
• Gil Ariel (Bar-Ilan University)

## [01524] Radon measure solutions to compressible Euler equations and applications

• Abstract : We proposed a definition of Radon measure solutions to the compressible Euler equations with general constitutive relations. With this definition, we proved the Newton-Busemann law for stationary hypersonic flow passing bodies, constructed delta shock solutions to the Riemann problems of the rectilinear barotropic Euler equations, justified the interpretation of delta shocks as free pistons. This shows the possibility of treating solid-fluid interaction problems by simpler Cauchy problems with solutions in the class of Radon measures.
• Author(s) :
• Hairong Yuan (East China Normal University )
• Aifang Qu (Shanghai Normal University )