Related papers: Stochastic matrices and majorization in max algebr…
Let $X_1, X_2,\ldots, X_n$ (resp. $Y_1, Y_2,\ldots, Y_n$) be independent random variables such that $X_i$ (resp. $Y_i$) follows generalized exponential distribution with shape parameter $\theta_i$ and scale parameter $\lambda_i$ (resp.…
A dual control problem is presented for the optimal stochastic control of a system governed by partial differential equations. Relationships between the optimal values of the original and the dual problems are investigated and two duality…
Given a real inner product space $V$ and a group $G$ of linear isometries, we construct a family of $G$-invariant real-valued functions on $V$ that we call max filters. In the case where $V=\mathbb{R}^d$ and $G$ is finite, a suitable max…
We propose a new generalization of the Yang-Baxter equation, where the R-matrix depends on cluster $y$-variables in addition to the spectral parameters. We point out that we can construct solutions to this new equation from the…
The present work provides an original framework for random matrix analysis based on revisiting the concentration of measure theory from a probabilistic point of view. By providing various notions of vector concentration ($q$-exponential,…
Convenient parameterizations of matrices in terms of vectors transform (certain classes of) matrix equations into covariant (hence rotation-invariant) vector equations. Certain recently introduced such parameterizations are tersely…
We show that dualization of Stueckelberg-like massive gauge theories and $B\wedge F$ models, follows form a general p-dualization of interacting theories in d spacetime dimensions. This is achieved by a particular choice of the external…
In this work a theory is developed for unifying large classes of nonlinear discrete-time dynamical systems obeying a superposition of a weighted maximum or minimum type. The state vectors and input-output signals evolve on nonlinear spaces…
We study the averaging-based distributed optimization solvers over random networks. We show a general result on the convergence of such schemes using weight-matrices that are row-stochastic almost surely and column-stochastic in expectation…
Multivariate extreme-value analysis is concerned with the extremes in a multivariate random sample, that is, points of which at least some components have exceptionally large values. Mathematical theory suggests the use of max-stable models…
We study integrals over Hermitian supermatrices of arbitrary size $p+q$, that are parametrized by an external field $X$ and a source $Y$, of respective size $m+n$ and $p+q$. We show that these integrals exhibit a simple topological…
We prove the following results: let x,y be (n,n) complex matrices such that x,y,xy have no eigenvalue in ]-infinity,0] and log(xy)=log(x)+log(y). If n=2, or if n>2 and x,y are simultaneously triangularizable, then x,y commute. In both cases…
Random matrix theory has played an important role in various areas of pure mathematics, mathematical physics, and machine learning. From a practical perspective of data science, input data are usually normalized prior to processing. Thus,…
A predominated graph is a pair $(G,D)$, where $G$ is a graph and the vertices in $D\subseteq V(G)$ are considered already dominated. Maker-Breaker domination game critical (MBD critical) predominated graphs are introduced as the…
In this paper semirings with an idempotent addition are considered. These algebraic structures are endowed with a partial order. This allows to consider residuated maps to solve systems of inequalities $A \otimes X \preceq B$. The purpose…
We study duality relations for zeta and M\"{o}bius matrices and monotone conditions on the kernels. We focus on the cases of family of sets and partitions. The conditions for positivity of the dual kernels are stated in terms of the…
This contribution examines optimization problems that involve stochastic dominance constraints. These problems have uncountably many constraints. We develop methods to solve the optimization problem by reducing the constraints to a finite…
The issue of so-called maximal regularity is discussed within a Hilbert space framework for a class of evolutionary equations. Viewing evolutionary equations as a sums of two unbounded operators, showing maximal regularity amounts to…
Well-graded families, extremal systems and maximum systems (the last two in the sense of VC-theory and Sauer-Shelah lemma on VC-dimension) are three important classes of set systems. This paper aims to study the notion of duality in the…
Maximum margin binary classification is one of the most fundamental algorithms in machine learning, yet the role of featurization maps and the high-dimensional asymptotics of the misclassification error for non-Gaussian features are still…