# Registered Data

Contents

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

# [CT070]

**Session Time & Room****Classification**

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

**Session Time & Room**:__2C__(Aug.22, 13:20-15:00) @__F411__**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__**Format**: Talk at Waseda University**Author(s)**:**Hiroyuki Nishimoto**(Kochi University)

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

**Session Time & Room**:__2C__(Aug.22, 13:20-15:00) @__F411__**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__**Format**: Talk at Waseda University**Author(s)**:**Yusuke Ono**(Keio University)- Linyu Peng (Keio University)

## [01548] Quadratically Regularized Bilevel Optimal Transport

**Session Time & Room**:__2C__(Aug.22, 13:20-15:00) @__F411__**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__**Format**: Talk at Waseda University**Author(s)**:**Sebastian Hillbrecht**(Technische Universität Dortmund)- Christian Meyer (Technische Universität Dortmund)
- Paul Manns (Technische Universität Dortmund)

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

**Session Time & Room**:__2C__(Aug.22, 13:20-15:00) @__F411__**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__**Format**: Talk at Waseda University**Author(s)**:**Rosalio Jr Gaid Artes**(Mindanao State University - Tawi-Tawi College of Technology and Oceanography)