Registered Data

[CT047]

[01172] Spatio-structural partial differential equation (PDE) modelling for single-cell cancer data

  • Session Date & Time : 2D (Aug.22, 15:30-17:10)
  • Type : Contributed Talk
  • Abstract : Melanoma routinely develops resistance to targeted therapies, leading to unfavourable prognosis for patients. We introduce a novel approach to modelling single-cell RNA-seq data obtained from melanoma tumours, using partial differential equations (PDEs) to represent the tumour as a spatio-structural population. We show how non-spatial data can be used to predict spatially heterogeneous distributions of cell types, within the tumour, and explore combination therapies and treatment strategies to overcome traditional patterns of resistance.
  • Classification : 35Q92, 37N25, 62P10, 92-10, 35G20, Mathematical Oncology, PDEs
  • Author(s) :
    • Arran Hodgkinson (Queen's University Belfast)
    • Arran Hodgkinson (Queen's University Belfast)
    • Dumitru Trucu (University of Dundee)
    • Matthieu Lacroix (Institut de Recherche en Cancerologie de Montpellier)
    • Laurent Le Cam (Institut de Recherche en Cancerologie de Montpellier)
    • Ovidiu Radulescu (Universite de Montpellier)

[00081] Strong stationarity for a highly nonsmooth optimization problem with control constraints

  • Session Date & Time : 2D (Aug.22, 15:30-17:10)
  • Type : Contributed Talk
  • 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.
  • Classification : 35Q93, 49K20
  • Author(s) :
    • Livia Betz (Faculty of Mathematics Würzburg)

[00536] Solving inverse and forward problems in the water quality model by neutral networks

  • Session Date & Time : 2D (Aug.22, 15:30-17:10)
  • Type : Contributed Talk
  • Abstract : In this talk, we study the forward and inverse problems in BOD-DO models and present the Physic Inform Neural Network method to solve these problems. We first introduce the fully deep neural network and some well-known results about the approximation of fully deep neural networks to functions of classes. Then, we present the Physic Inform Neural Network method to solve the forward and inverse problems in BOD-DO models. We apply the method to solve some specific numerical examples. The method can be generalized for complex river quality models, e.g., 2D or 3D OD-DO models or river quality models with more the two indicators. For complex river systems, we can use segmentation techniques to divide the river into some segments and in each segment, we can use the proposed method to solve the forward and inverse problems.
  • Classification : 35Q93, 49J50, 37N40
  • Author(s) :
    • Muoi Quy Pham (The University of Danang - University of Science and Education)

[00386] Optimizing the Location of Exit Doors for a Safer Crowd Evacuation

  • Session Date & Time : 2D (Aug.22, 15:30-17:10)
  • Type : Contributed Talk
  • 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.
  • Classification : 35Qxx, 49Mxx, 65Kxx
  • 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)

[00393] Mathematical Modelling of Bilayered Cathodes for Lithium-Ion Batteries

  • Session Date & Time : 2D (Aug.22, 15:30-17:10)
  • Type : Contributed Talk
  • 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, which 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.
  • Classification : 35Qxx, 37Nxx
  • Author(s) :
    • Eloise Tredenick (University of Oxford)