# Registered Data

Contents

- 1 [CT070]
- 1.1 [01548] Quadratically Regularized Bilevel Optimal Transport
- 1.2 [02087] Best Approximation in Euclidean Space: A Supply Distribution Efficiency Model
- 1.3 [02111] Geometric visual model for linear derivation of elliptical orbits in 3-dimensional space
- 1.4 [02473] Applications of Bures-Wasserstein geometry of HPD matrices to signal detection
- 1.5 [02399] Gravitation of Deformed Charged Spheres

# [CT070]

## [01548] Quadratically Regularized Bilevel Optimal Transport

**Session Date & Time**: 2C (Aug.22, 13:20-15:00)**Type**: Contributed Talk**Abstract**: We study the effect of an $L^2$ regularization to an optimal control problem that is constrained by the Kantorovich problem of optimal transport. We present a class of possible applications by means of a toy problem. Using a reverse approximation argument, we discuss the approximability of solutions of the unregularized problem by a sequence of solutions of the regularized problems.**Classification**:__49Q22__,__90C08__,__49J45__**Author(s)**:**Sebastian Hillbrecht**(Technische Universität Dortmund)

## [02087] Best Approximation in Euclidean Space: A Supply Distribution Efficiency Model

**Session Date & Time**: 2C (Aug.22, 13:20-15:00)**Type**: Contributed Talk**Abstract**: In this paper, we developed a mathematical model for supply distribution efficiency using inverse best approximation by considering Euclidean distance in a Euclidean space. Given a sequence $\langle S_i\rangle_{i=1}^k$ of closed convex subsets of a Euclidean space $E$ and a sequence of natural numbers $\langle n_i\rangle_{i=1}^k$, we determined the best location of a convex set $S$ in $E$ such that the Euclidean distance from $S$ to $S_i$ is at most $n_i$ for each $i\in \{1,2,\ldots,k\}$.**Classification**:__51K05__,__41A45__,__41A29__**Author(s)**:**Rosalio Jr Gaid Artes**(Mindanao State University - Tawi-Tawi College of Technology and Oceanography)

## [02111] Geometric visual model for linear derivation of elliptical orbits in 3-dimensional space

**Session Date & Time**: 2C (Aug.22, 13:20-15:00)**Type**: Contributed Talk**Abstract**: If visual space is defined as a 3-dimensional complex vector space, linear perspective is expressed as an L1-norm constraint with the scale. The vanishing point represents the boundary of visual space, and the L2-norm constraint indicates that visual space is a sphere. A geometric visual model that satisfies these constraints allows linear derivation of elliptical orbits. The solution is simple because it does not involve an infinite series.**Classification**:__51K05__**Author(s)**:**Hiroyuki Nishimoto**(Kochi University)

## [02473] Applications of Bures-Wasserstein geometry of HPD matrices to signal detection

**Session Date & Time**: 2C (Aug.22, 13:20-15:00)**Type**: Contributed Talk**Abstract**: Autocovariance matrices can describe characteristic of time series data. If the data follow the stationary process, the corresponding autocovariance matrix is Hermitian positive definite (HPD). In this talk, we introduce Riemannian geometry of the HPD matrix spaces equipped with the Bures–Wasserstein (BW) metric and propose a detection method by utilizing the geodesic distance to define BW mean and median of HPD matrices. Robustness of the proposed mean and median will also be analyzed.**Classification**:__53B20__,__60G35__,__32M15__**Author(s)**:**Yusuke Ono**(Keio University)- Linyu Peng (Keio University)

## [02399] Gravitation of Deformed Charged Spheres

**Session Date & Time**: 2C (Aug.22, 13:20-15:00)**Type**: Contributed Talk**Abstract**: The Kerr hypothesis in gravitation can be tested by using two approaches namely the top-bottom approach and bottom-up approach. The first one involves introducing the deviations in the Kerr metric through a theoretical model. The second approach involves introducing the deviations in terms of parameters. The metric proposed by Johannsen and Psaltis is one such parametrically deformed Kerr sphere. It reduces to the usual Kerr when one sets the deviation parameters to zero. We construct some generalizations of these spheres including the charged versions and discuss their properties.**Classification**:__53Z05__,__83C15__**Author(s)**:**Khalid Saifullah**(Quaid-i-Azam University, Islamabad )