Information geometry最新文献_第2页

On the geometric mechanics of assignment flows for metric data labeling 度量数据标注分配流的几何力学研究

Information geometry Pub Date : 2023-11-03 DOI: 10.1007/s41884-023-00120-1

Fabrizio Savarino, Peter Albers, Christoph Schnörr

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引用次数: 0

Conelike radiant structures 锥形辐射结构

Information geometry Pub Date : 2023-10-04 DOI: 10.1007/s41884-023-00115-y

Daniel J. F. Fox

{"title":"Conelike radiant structures","authors":"Daniel J. F. Fox","doi":"10.1007/s41884-023-00115-y","DOIUrl":"https://doi.org/10.1007/s41884-023-00115-y","url":null,"abstract":"Abstract Analogues of the classical affine-projective correspondence are developed in the context of statistical manifolds compatible with a radiant vector field. These utilize a formulation of Einstein equations for special statistical structures that generalizes the usual Einstein equations for pseudo-Riemannian metrics and is of independent interest. A conelike radiant structure is a not necessarily flat affine connection equipped with a family of surfaces that behave like the intersections of the planes through the origin with a convex cone in a real vector space. A radiant structure is a torsion-free affine connection and a vector field whose covariant derivative is the identity endomorphism. A radiant structure is conelike if for every point and every two-dimensional subspace containing the radiant vector field there is a totally geodesic surface passing through the point and tangent to the subspace. Such structures exist on the total space of any principal bundle with one-dimensional fiber and on any Lie group with a quadratic structure on its Lie algebra. The affine connection of a conelike radiant structure can be normalized in a canonical way to have antisymmetric Ricci tensor. Applied to a conelike radiant structure on the total space of a principal bundle with one-dimensional fiber this yields a generalization of the classical Thomas connection of a projective structure. The compatibility of radiant and conelike structures with metrics is investigated and yields a construction of connections for which the symmetrized Ricci curvature is a constant multiple of a compatible metric that generalizes well-known constructions of Riemannian and Lorentzian Einstein–Weyl structures over Kähler–Einstein manifolds having nonzero scalar curvature. A formulation of Einstein equations for special statistical manifolds is given that generalizes the Einstein–Weyl equations and encompasses these more general examples. There are constructed left-invariant conelike radiant structures on a Lie group endowed with a left-invariant nondegenerate bilinear form, and the case of three-dimensional unimodular Lie groups is described in detail.","PeriodicalId":93762,"journal":{"name":"Information geometry","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135547708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Publisher Correction: Object embedding using an information geometrical perspective 发布者更正:使用信息几何透视图嵌入对象

Information geometry Pub Date : 2023-08-24 DOI: 10.1007/s41884-023-00118-9

Taiki Sugiura, Noboru Murata

引用次数: 0

Object embedding using an information geometrical perspective 基于信息几何视角的对象嵌入

Information geometry Pub Date : 2023-07-27 DOI: 10.1007/s41884-023-00114-z

Taiki Sugiura, Noboru Murata

引用次数: 0

Doubly autoparallel structure and curvature integrals 二重自平行结构与曲率积分

Information geometry Pub Date : 2023-07-27 DOI: 10.1007/s41884-023-00116-x

A. Ohara, H. Ishi, T. Tsuchiya