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Many real-world complex systems are best modeled by multiplex networks of interacting network layers. The multiplex network study is one of the newest and hottest themes in the statistical physics of complex networks. Pioneering studies…
A family of quaternary sequences over Z4 is defined based on the Ding-Helleseth generalized cyclotomic classes modulo pq for two distinct odd primes p and q. The linear complexity is determined by computing the defining polynomial of the…
In this paper, we introduce and study a new extragradient iterative process for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of a variational inequality for an…
We look at thin interpolating sequences and the role they play in uniform algebras, Hardy spaces, and model spaces.
Multisets are sets that allow repetition of elements. As such, multisets pave the way to a number of interesting possibilities of theoretical and applied nature. In the present work, after revising the main aspects of traditional sets, we…
We study the worst-case complexity of a non-monotone line search framework that covers a wide variety of known techniques published in the literature. In this framework, the non-monotonicity is controlled by a sequence of nonnegative…
The aim of this paper is to investigate the intersection problem between two linear sets in the projective line over a finite field. In particular, we analyze the intersection between two clubs with eventually different maximum fields of…
We recast homogeneous linear recurrence sequences with fixed coefficients in terms of partial Bell polynomials, and use their properties to obtain various combinatorial identities and multifold convolution formulas. Our approach relies on a…
We define recurrence matrices and study a few properties (links with automatic sequences, branch groups etc.) of them.
The main results of this paper are generalizations some classical theorems about transversals for families of finite sets to some cases of families of infinite sets.
We study the complexity of functions computable by deep feedforward neural networks with piecewise linear activations in terms of the symmetries and the number of linear regions that they have. Deep networks are able to sequentially map…
We study the expressive power of polynomial recursive sequences, a nonlinear extension of the well-known class of linear recursive sequences. These sequences arise naturally in the study of nonlinear extensions of weighted automata, where…
Let $ \prod_{i=1}^d (X-\alpha_i Y) \in{\mathbb C}[X,Y]$ be a binary form and let $\epsilon_1,\dots,\epsilon_d$ be nonzero complex numbers. We consider the family of binary forms $ \prod_{i=1}^d (X-\alpha_i \epsilon_i^aY)$, $a\in {\mathbb…
Let $S$ be a finite set of points in the plane and let $\mathcal{T}(S)$ be the set of intersection points between pairs of lines passing through any two points in $S$. We characterize all configurations of points $S$ such that iteration of…
With every family of finitely many subsets of a finite-dimensional vector space over the Galois-field with two elements we associate a cyclic transversal polytope. It turns out that those polytopes generalize several well-known polytopes…
The objective of this paper is to introduce and study a complicated nonlinear system, called coupled variational-hemivariational inequalities, which is described by a highly nonlinear coupled system of inequalities on Banach spaces. We…
Mixture models are one of the most widely used statistical tools when dealing with data from heterogeneous populations. This paper considers the long-standing debate over finite mixture and infinite mixtures and brings the two modelling…
We consider composite loss functions for multiclass prediction comprising a proper (i.e., Fisher-consistent) loss over probability distributions and an inverse link function. We establish conditions for their (strong) convexity and explore…
We count the number of irreducible polynomials in several variables of a given degree over a finite field. The results are expressed in terms of a generating series, an exact formula and an asymptotic approximation. We also consider the…
This paper presents a new approach for analysing structural properties of time series from complex systems. Starting from the concept of recurrences in phase space, the recurrence matrix of a time series is interpreted as the adjacency…