相关论文: Geometric statistics with subspace structure prese…
We describe the geometry of generic heterotic backgrounds preserving minimal supersymmetry in four dimensions using the language of generalised geometry. They are characterised by an $SU(3)\times Spin(6+n)$ structure within…
Based on the computation of a superset of the implicit support, implicitization of a parametrically given hyper-surface is reduced to computing the nullspace of a numeric matrix. Our approach exploits the sparseness of the given parametric…
Wasserstein distance, especially among symmetric positive-definite matrices, has broad and deep influences on development of artificial intelligence (AI) and other branches of computer science. A natural idea is to describe the geometry of…
A key technique of machine learning and computer vision is to embed discrete weighted graphs into continuous spaces for further downstream processing. Embedding discrete hierarchical structures in hyperbolic geometry has proven very…
First, we derive explicit computable expressions of structured backward errors of approximate eigenelements of structured matrix polynomials including symmetric, skew-symmetric, Hermitian, skew-Hermitian, even and odd polynomials. We also…
In this paper, we compute the Stokes matrices of a special quantum confluent hypergeometric system with Poincar\'e rank one. The sources of the interests in the Stokes phenomenon of such system are from representation theory and the theory…
The efficient representation of random fields on geometrically complex domains is crucial for Bayesian modelling in engineering and machine learning. Today's prevalent random field representations are either intended for unbounded domains…
The Hellinger-Kantorovich (HK) space provides a natural geometry for nonnegative measures with varying total mass, but its differential-geometric structure is less well understood than that of the closely related Wasserstein space of…
This paper is devoted to the study of preservation of eigenvalues, Jordan structure and complementary invariant subspaces of structured matrices under structured perturbations. Perturbations and structure-preserving perturbations are…
Leveraging on the underlying low-dimensional structure of data, low-rank and sparse modeling approaches have achieved great success in a wide range of applications. However, in many applications the data can display structures beyond simply…
We consider planar directed last-passage percolation on the square lattice with general i.i.d. weights and study the geometry of the full set of semi-infinite geodesics in a typical realization of the random environment. The structure of…
In this paper, we perform a detailed investigation on the various geometrical properties of trapped surfaces and the boundaries of trapped region in general relativity. This treatment extends earlier work on LRS II spacetimes to a general 4…
We extend finding geometrically-significant preserved quantities by solving specific PDEs to the affine transformations and subgroups. This can be viewed not only as a purely geometrical problem but also as a subcase of finding physical…
Despite the obvious similarities between the metrics used in topological data analysis and those of optimal transport, an optimal-transport based formalism to study persistence diagrams and similar topological descriptors has yet to come.…
Spatial transcriptomics studies are becoming increasingly large and commonplace, necessitating simultaneous analysis of a large number of spatially resolved variables. Correspondingly, a diverse range of methodologies have been proposed to…
This survey contains a selection of topics unified by the concept of positive semi-definiteness (of matrices or kernels), reflecting natural constraints imposed on discrete data (graphs or networks) or continuous objects (probability or…
We discuss here geometric structures of condensed matters by means of a fundamental topological method. Any geometric pattern can be universally represented by a decomposition space of a topological space consisting of the infinite product…
In this paper, we propose a topology optimization (TO) framework where the design is parameterized by a set of convex polygons. Extending feature mapping methods in TO, the representation allows for direct extraction of the geometry. In…
We define a new topological summary for data that we call the persistence landscape. Since this summary lies in a vector space, it is easy to combine with tools from statistics and machine learning, in contrast to the standard topological…
Recent advances suggest that encoding images through Symmetric Positive Definite (SPD) matrices and then interpreting such matrices as points on Riemannian manifolds can lead to increased classification performance. Taking into account…