Registered Data

[CT071]

[02394] Gaussian distributions on Riemannian symmetric spaces of non-positive curvature

  • Session Date & Time : 5D (Aug.25, 15:30-17:10)
  • Type : Contributed Talk
  • Abstract : Learning from data that live in Riemannian manifolds has become central to many applications, ranging from radar signal processing to neuroscience. In this talk, we present a generalisation of Gaussian distributions to Riemannian symmetric spaces of non-positive curvature, which include hyperbolic spaces, as well as spaces of real, complex and quaternion positive definite matrices, and spaces of structured Toeplitz or block-Toeplitz positive definite matrices and discuss applications to geometric statistics on such spaces.
  • Classification : 53C22, 53B20, 53B50, 53C80, 53C35, Geometric statistics, probability on manifolds
  • Author(s) :
    • Cyrus Mostajeran (Nanyang Technological University)
    • Salem Said (Université Grenoble-Alpes)

[00489] Curvature related properties of Finsler manifolds and applications

  • Session Date & Time : 5D (Aug.25, 15:30-17:10)
  • Type : Contributed Talk
  • 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.
  • Classification : 53C60
  • Author(s) :
    • Sorin Sabau (Tokai University)

[01100] Intuitionistic fuzzy weakly π generalized closed set

  • Session Date & Time : 5D (Aug.25, 15:30-17:10)
  • Type : Contributed Talk
  • Abstract : The present work deals with the new class of intuitionistic fuzzy set, “Intuitionistic fuzzy weakly π generalized closed set” in topological spaces. Their characterizations, various properties and their inter-relationship have been illustrated.
  • Classification : 54Axx, 54Exx, 54Gxx
  • Author(s) :
    • Vaithiyalingam K (Sri Vasavi College , Bharathiar University )

[01209] Detecting CoVid 19 using Topology

  • Session Date & Time : 5D (Aug.25, 15:30-17:10)
  • Type : Contributed Talk
  • 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.
  • Classification : 55-08, Data Analysis
  • 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)

[01680] Dual Graph Based n-Holes Detecting for Persistent Homology of Data

  • Session Date & Time : 5D (Aug.25, 15:30-17:10)
  • Type : Contributed Talk
  • Abstract : Persistent homology studies the relation between $n$-holes and their boundaries in the triangulated, combinatorial representations of the data over the entire range of parameter $\epsilon$ for data triangulation. We discovered sufficiency condition that each $n$-hole is enclosed in a set of $n$-simplices. Exploiting this ‘simplex boundedness property’, this paper develops a method for analyzing persistent homology via a dual graph based optimization model for detecting newly generated minimal $n$-holes on Rips complex filtration.
  • Classification : 55-08, 55-11, 05-08, 90C10
  • Author(s) :
    • Taekgeun Jung (Korea University)
    • Hong Seo Ryoo (Korea University)