相关论文: Analytic and Geometric Representations of the Gene…
In an earlier paper the authors proved that limits of convergent graph sequences can be described by various structures, including certain 2-variable real functions called graphons, random graph models satisfying certain consistency…
We present a constant and a recursive relation to define a sequence $f_n$ such that the floor of $f_n$ is the $n$th prime. Therefore, this constant generates the complete sequence of primes. We also show this constant is irrational and…
In this paper, we provide a general framework for counting geometric structures in pseudo-random graphs. As applications, our theorems recover and improve several results on the finite field analog of questions originally raised in the…
The Galilean conformal algebra has recently been realised in the study of the non-relativistic limit of the AdS/CFT conjecture. This was obtained by a systematic parametric group contraction of the parent relativistic conformal field…
In this paper we study the Fibonacci numbers and derive some interesting properties and recurrence relations. We prove some charecterizations for $F_p$, where $p$ is a prime of a certain type. We also define period of a Fibonacci sequence…
In this review article we consider linear regression analysis from a geometric perspective, looking at standard methods and outputs in terms of the lengths of the relevant vectors and the angles between these vectors. We show that standard…
For an arbitrary homogeneous linear recurrence sequence of order d with constant coefficients, we derive recurrence relations for all subsequences with indices in arithmetic progression. The coefficients of these recurrences are given…
We determine the asymptotic distribution of the sum of correlated variables described by a matrix product ansatz with finite matrices, considering variables with finite variances. In cases when the correlation length is finite, the law of…
In this article we review recent generalisations of the central limit theorem for the sum of specially correlated (or q-independent) variables, focusing on q greater or equal than 1. Specifically, this kind of correlation turns the…
Convex geometry has recently attracted great attention as a framework to formulate general probabilistic theories. In this framework, convex sets and affine maps represent the state spaces of physical systems and the possible dynamics,…
We consider uniform random permutations drawn from a family enumerated through generating trees. We develop a new general technique to establish a central limit theorem for the number of consecutive occurrences of a fixed pattern in such…
Biological and physical systems often exhibit distinct structures at different spatial/temporal scales. Persistent homology is an algebraic tool that provides a mathematical framework for analyzing the multi-scale structures frequently…
We announce two breakthrough results concerning important questions in the Theory of Computational Complexity. In this expository paper, a systematic and comprehensive geometric characterization of the Subset Sum Problem is presented. We…
This paper explores the asymptotic behaviour of the radii of convexity and uniform convexity for normalized Bessel functions with respect to large order. We provide detailed asymptotic expansions for these radii and establish recurrence…
We introduce the Plancherel measure on the set of partition collections, which parameterize irreducible representations of order n general linear group over a finite field. We prove that as n goes to infinity, the random partitions from the…
Graph compositions generalize both integer compositions and partitions of a finite set. We develop formulas, generating functions and recurrence relations for composition counting functions for several families of graphs.
Convex sets arising in a variety of applications are well-defined for every relevant dimension. Examples include the simplex and the spectraplex that correspond to probability distributions and to quantum states; combinatorial polytopes and…
Periodic lattices are natural generalizations of lattices, which arise naturally in diophantine approximations with rationals of bounded denominators. In this paper, we prove analogues of classical theorems in geometry of numbers for…
We study the generalized Hankel transform of the family of sequences satisfying the recurrence relation $a_{n+1} = \bigl(\alpha + \frac{\beta}{n+\gamma}\bigr) a_n$. We apply the obtained formula to several particular important sequences.…
We provide a rigorous treatment of continuous limits for various generalizations of the pentagram map on polygons in $\mathbb{RP}^d$ by means of quantum calculus. Describing this limit in detail for the case of the short-diagonal pentagram…