Related papers: Divergence functions in Information Geometry
This paper lays the foundations for a unified framework for numerically and computationally applying methods drawn from a range of currently distinct geometrical approaches to statistical modelling. In so doing, it extends information…
Starting from the Colombeau's full generalized functions, the sharp topologies and the notion of generalized points, we introduce a new kind differential calculus (for functions between totally disconnected spaces). We study generalized…
In this paper, a simple proof of the divergence theorem is given by using the Dirac operator and noncommutative residues. Then we extend the divergence theorem to compact manifolds with boundary by the noncommutative residue of the…
Algebras of generalized functions offer possibilities beyond the purely distributional approach in modelling singular quantities in non-smooth differential geometry. This article presents an introductory survey of recent developments in…
The aim of these notes is to present an accessible overview of some topics in classical algebraic geometry which have applications to aspects of discrete integrable systems. Precisely, we focus on surface theory on the algebraic geometry…
Some integral properties of Jack polynomials, hypergeometric functions and invariant polynomials are studied for real normed division algebras.
In this paper, we obtain some new upper bounds for differantiable mappings whose q-th powers are geometrically convex and monotonically decreasing by using the H\"older inequality, Power mean inequality and properties of modulus.
In this paper, we tackle unresolved inquiries by Ferreira et al. \cite{bruno} in their recent publication, ``Functional Identity on Division Algebras". We delve into the intricate behavior of additive functions on matrix algebras over…
The theoretical computing of special values assumed by the hypergeometric functions has a high interest not only on its own, but also in sight of the remarkable implications to both pure Mathematics and Mathematical Physics. Accordingly, in…
Contrast functions play a fundamental role in information geometry, providing a means for generating the geometric structures of a statistical manifold: a pseudo-Riemannian metric and a pair of torsion-free conjugate affine connections.…
In this position paper, we promote the study of function spaces parameterized by machine learning models through the lens of algebraic geometry. To this end, we focus on algebraic models, such as neural networks with polynomial activations,…
We geometrically study the Legendre duality relation that plays an important role in statistical physics with the standard or generalized entropies. For this purpose, we introduce dualistic structure defined by information geometry, and…
A review of theoretical models of diffractive structure functions in deep inelastic scattering (DIS) is presented with a view to highlighting distinctive features, that may be distinguished experimentally. In particular, predictions for the…
It is shown that generalized trigonometric functions and generalized hyperbolic functions can be transformed from each other. As an application of this transformation, a number of properties for one immediately lead to the corresponding…
A deformed differential calculus is developed based on an associative star-product. In two dimensions the Hamiltonian vector fields model the algebra of pseudo-differential operator, as used in the theory of integrable systems. Thus one…
We introduce a novel formulation for geometry on discrete points. It is based on a universal differential calculus, which gives a geometric description of a discrete set by the algebra of functions. We expand this mathematical framework so…
Ideas from deformation quantization applied to algebras with one generator lead to methods to treat a nonlinear flat connection. It provides us elements of algebras to be parallel sections. The moduli space of the parallel sections is…
Information geometry is used to quantify the amount of information integration within multiple terminals of a causal dynamical system. Integrated information quantifies how much information is lost when a system is split into parts and…
We study some type of mappings with finite distortion $f:D\rightarrow D^{\prime},$ $D, D^{\prime}\subset{\Bbb R}^n,$ $n\ge 2,$ which admit branch points. It is proved some inequality playing essential role at investigation of some problems…
In this review we discuss what is known about semiorthogonal decompositions of derived categories of algebraic varieties. We review existing constructions, especially the homological projective duality approach, and discuss some related…