Related papers: The Gaussian entropy map in valued fields
We define the class of multivariate group entropies as a novel set of information - theoretical measures, which extends significantly the family of group entropies. We propose new examples related to the "super-exponential" universality…
Non-Gaussian bosonic states are ubiquitous in interacting light--matter systems, many-body platforms, and relativistic quantum field settings, but their quantitative characterization is hindered by the infinite-dimensional Hilbert space and…
We derive mean-field information Hessian matrices on finite graphs. The "information" refers to entropy functions on the probability simplex. And the "mean-field" means nonlinear weight functions of probabilities supported on graphs. These…
In this short note, we present a theorem concerning certain "additive structure" for the level sets of non-degenerate Gaussian fields, which yields the multiple valley phenomenon for extremal fields with exponentially many valleys.
A gauge invariant formulation for the massive axion is considered. The axion acquires mass through a topological term which couples a (pseudo)scalar and a third rank antisymmetric tensor. Duality, local and canonical equivalences with the…
In this article, we offer group-theoretic, field-theoretic, and topological interpretations of the Gaussian binomial coefficients and their sum. For a finite $p$-group $G$ of rank $n$, we show that the Gaussian binomial coefficient…
We study algebraic, combinatorial and topological properties of the set of preorders on a group, and the set of valuations on a field. We show strong analogies between these two kinds of sets and develop a dictionary for these ones. Among…
Methods that learn representations of nodes in a graph play a critical role in network analysis since they enable many downstream learning tasks. We propose Graph2Gauss - an approach that can efficiently learn versatile node embeddings on…
As in random matrix theories, eigenvector/value distributions are important quantities of random tensors in their applications. Recently, real eigenvector/value distributions of Gaussian random tensors have been explicitly computed by…
We describe the immediate extensions of a one dimensional valuation ring $V$ which could be embedded in some separation of a ultrapower of $V$ with respect to a certain ultrafilter. For such extensions holds a kind of Artin's approximation.
This paper is devoted to the problem of sampling Gaussian fields in high dimension. Solutions exist for two specific structures of inverse covariance : sparse and circulant. The proposed approach is valid in a more general case and…
Hadwiger integrals employ the intrinsic volumes as measures for integration of real-valued functions. We provide a formula for the expected values of Hadwiger integrals of Gaussian-related random fields. The expected Hadwiger integrals of…
Though the underlying fields associated with vector-valued environmental data are continuous, observations themselves are discrete. For example, climate models typically output grid-based representations of wind fields or ocean currents,…
We give a notion of entropy for general gemetric structures, which generalizes well-known notions of topological entropy of vector fields and geometric entropy of foliations, and which can also be applied to singular objects, e.g. singular…
A definable set $X$ in the first-order language of rings defines a family of random vectors: for each finite field $\mathbb{F}_q$, let the distribution be supported and uniform on the $\mathbb{F}_q$-rational points of $X$. We employ results…
We discuss D-dimensional scalar field interacting with a scale invariant random metric which is either a Gaussian field or a square of a Gaussian field. The metric depends on d-dimensional coordinates (where d is less than D). By a…
We perform a systematic study of the image of the Gauss map for complete minimal surfaces in Euclidean four-space. In particular, we give a geometric interpretation of the maximal number of exceptional values of the Gauss map of a complete…
We study the value distribution and extreme values of eigenfunctions for the ``quantized cat map''. This is the quantization of a hyperbolic linear map of the torus. In a previous paper it was observed that there are quantum symmetries of…
This paper investigates Gaussian Markov random field approximations to nonstationary Gaussian fields using graph representations of stochastic partial differential equations. We establish approximation error guarantees building on the…
Feature attribution maps are a popular approach to highlight the most important pixels in an image for a given prediction of a model. Despite a recent growth in popularity and available methods, little attention is given to the objective…