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Across the sciences, the statistical analysis of networks is central to the production of knowledge on relational phenomena. Because of their ability to model the structural generation of networks, exponential random graph models are a…
High precision calculations in perturbative QFT often require evaluation of big collection of Feynman integrals. Complexity of this task can be greatly reduced via the usage of linear identities among Feynman integrals. Based on…
Introduced in the mid-1970's as an intermediate step in proving a long-standing conjecture on arithmetic progressions, Szemer\'edi's regularity lemma has emerged over time as a fundamental tool in different branches of graph theory,…
Networks and their higher order generalizations, such as hypernetworks or multiplex networks are ever more popular models in the applied sciences. However, methods developed for the study of their structural properties go little beyond the…
The law of large numbers is one of the most fundamental results in Probability Theory. In the case of independent sequences, there are some known characterizations; for instance, in the independent and identically distributed setting it is…
Let $m, n$ be positive integers such that $m>1$ divides $n$. In this paper, we introduce a special class of piecewise-affine permutations of the finite set $[1, n]:=\{1, \ldots, n\}$ with the property that the reduction $\pmod m$ of $m$…
We propose a probabilistic formulation that enables sequential detection of multiple change points in a network setting. We present a class of sequential detection rules for certain functionals of change points (minimum among a subset), and…
This paper mainly studies nonnegativity decision of forms based on variable substitutions. Unlike existing research, the paper regards simplex subdivisions as new perspectives to study variable substitutions, gives some subdivisions of the…
Recently, it has been shown that many functions on sets can be represented by sum decompositions. These decompositons easily lend themselves to neural approximations, extending the applicability of neural nets to set-valued inputs---Deep…
A set A of natural numbers is finitely embeddable in another such set B if every finite subset of A has a rightward translate that is a subset of B. This notion of finite embeddability arose in combinatorial number theory, but in this paper…
Renyi's "thinning" operation on a discrete random variable is a natural discrete analog of the scaling operation for continuous random variables. The properties of thinning are investigated in an information-theoretic context, especially in…
Learning latent representations from long text sequences is an important first step in many natural language processing applications. Recurrent Neural Networks (RNNs) have become a cornerstone for this challenging task. However, the quality…
Given a Dedekind incomplete ordered field, a pair of convergent nets of gaps which are respectively increasing or decreasing to the same point is used to obtain a further equivalent criterion for Dedekind completeness of ordered fields:…
Mixed superposition rules, i.e., functions describing the general solution of a system of first-order differential equations in terms of a generic family of particular solutions of first-order systems and some constants, are studied. The…
Given any two sequences of complex numbers, we establish simple relations between their binomial convolution and the binomial convolution of their individual binomial transforms. We employ these relations to derive new identities involving…
We establish a connection between two results in the literature on probabilistic semantics: a formulation of De Finetti's theorem in the language of category theory due to Jacobs and Staton, and the generic construction of the free…
In the first part of this paper, we generalize the results of the author \cite{Liu,Liu2} from the random flow case to the random semiflow case, i.e. we obtain Conley decomposition theorem for infinite dimensional random dynamical systems.…
The theory of patterns formation for a reaction-diffusion system defined on a multiplex is developed by means of a perturbative approach. The intra-layer diffusion constants act as small parameter in the expansion and the unperturbed state…
In image processing, classical methods minimize a suitable functional that balances between computational feasibility (convexity of the functional is ideal) and suitable penalties reflecting the desired image decomposition. The fact that…
Simple methods permit to generalize the concepts of iteration and of recursive processes. We shall see briefly on several examples what these methods generate. In additive sequences, we shall encounter not only the golden or the silver…