Dually flat manifold
WebAug 2, 2024 · For such a manifold, we give a geometric interpretation of its sectional curvature in terms of how the divergence between a pair of primal and dual geodesics differ from the dually flat case. Further results can be found in our follow-up paper [ 27 ] which uncovers a novel relation between optimal transport and information geometry. WebDec 8, 2024 · Simple question on parallel transport in dually flat manifolds. 0. Riemannian connection is flat iff there exists a Euclidean coordinate system. 1. Locality of canonical Bregman divergence on dually flat manifolds. 1. Question about connection coefficient on …
Dually flat manifold
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WebAbstract. Dually flat manifolds constitute fundamental mathematical objects of information geometry. This note establishes several results on the global properties and topology of … WebFeb 2, 2016 · As an important special case, we study a dually flat Riemannian manifold. It may be regarded as a dualistic extension of the Euclidean space. The generalized …
WebMay 8, 2024 · It is known that such a manifold is dually projectively flat with constant negative sectional curvature, and is closely related to the $\mathcal{F}^{(\alpha)}$-family, a generalized exponential family introduced by the second author. Our main result constructs a dual foliation of the statistical manifold, i.e., an orthogonal decomposition ... WebThe concept of the canonical divergence is defined for dually flat statistical manifolds in terms of the Legendre transform between dual affine coordinates. In this article, we introduce a new two ...
WebOct 1, 2014 · Dually flat Finsler metrics arise from α-flat information structures on Riemann-Finsler manifolds. Such Finsler metrics was introduced by Amari-Nagaoka and Z. Shen (See [3, 72]). WebRare short wheelbase flatbed dually! SB 350 Crate motor. 4 Speed tranny w/ Granny. New 373 rear end. Electronic ignition. Edlebrock manifold and carb. Aluminum radiator with electric fan. Train horn. New insulated flooring and mat. New headliner. New glass and weather stripping. New Chrome grill and bumper. New steering wheel. New mirrors. LED ...
WebFeb 2, 2016 · A dually flat manifold is a generalization of a Euclidean space, inheriting useful properties from it. A general non-flat manifold is regarded as a curved submanifold of a …
WebApr 14, 2014 · Information geometry studies the dually flat structure of a manifold, highlighted by the generalized Pythagorean theorem. The present paper studies a class of Bregman divergences called the (ρ,τ)-divergence. A (ρ,τ) -divergence generates a dually flat structure in the manifold of positive measures, as well as in the manifold of positive … initial necklaces for women sterling silverWebA dually flat manifold possesses a beautiful structure: It has two mutually coupled flat affine connections and two convex functions connected by the Legendre transformation. It has a canonical divergence, from which all the geometrical structure is derived. The KL-divergence in probability distributions is automatically derived from the ... mmm stock price history macrotrendsWeblocally dually flat (α,β)-metrics on an n-dimensional manifold M (n≥ 3) [9]. Further in 2014, the authors of [1] discuss characterization of locally dually flat first approximate Matsumoto metric. The first example of non-Riemannian dually flat metrics is the Funk metric given by ([4], 1Received June 13, 2016, Accepted November 8, 2016. initial necklaces for women that are cheapWebThe latter class includes the Bregman divergence , also called “geometric divergence” , which turns out to be identical to the “canonical divergence” on a dually flat manifold expressed in a pair of biorthogonal coordinates; those coordinates are induced by a pair of conjugate convex functions via the Legendre–Fenchel transform [2,20]. initial necklaces with diamondsWebMar 16, 2009 · This work begins with a convex function, and construction of a dually flat manifold, which possesses a Riemannian metric, two types of geodesics, and a … initial necklace with crownhttp://ccj.pku.edu.cn/sxjz/CN/10.11845/sxjz.2024082b mmm stock researchWebDec 8, 2024 · Consider the following partial differential equation for a function $\psi:S\to\mathbb {R}$ : $$\partial_ {i}\psi=\eta_ {i}$$ we may rewrite this as $d\psi=\eta_ … initial necklaces kay jewelers