Daniel Hernández Serrano

• University of Salamanca

We propose a stochastic model that describes of epidemics over simplicial complex networks (SSCM) in which higher-order unforeseen or random interactions may occur. Its dynamics obeys a stochastic differential equation (SDE) based on the mean field approach of the simplicial social contagion model. In this stochastic regime the only possible equili...

The aim of these notes is three fold. First we introduce virtual cyclic cellular automata and show that the inverse of a reversible (2R+1)-cyclic cellular automaton with periodic boundary conditions is a virtual cyclic cellular automaton. These virtual automata have two special characteristics: they have active and non active cells at specific step...

In this work the notion of linear cellular automata on trees with loops is introduced and the reversibility problem in some particular cases is tackled. The explicit expressions of the inverse cellular automata are computed.

Many real networks in social sciences, biological and biomedical sciences or computer science have an inherent structure of simplicial complexes reflecting many-body interactions. Therefore, to analyse topological and dynamical properties of simplicial complex networks centrality measures for simplices need to be proposed. Many of the classical com...

Network Science provides a universal formalism for modelling and studying complex systems based on pairwise interactions between agents. However, many real networks in the social, biological or computer sciences involve interactions among more than two agents, having thus an inherent structure of a simplicial complex. The relevance of an agent in a...

Reversibility of cellular automata (CA) has been an extensively studied problem from both a theoretical and a practical point of view. It is known when a (2R+1)-cyclic cellular automaton with periodic boundary conditions (p.b.c.) is reversible (see Siap et al., 2013) but, as far as we know, no explicit expression is given for its inverse cellular a...

The aim of this work is to completely solve the reversibility problem for symmetric linear cellular automata with radius r = 3 and null boundary conditions. The main result obtained is the explicit computation of the local transition functions of the inverse cellular automata. This allows introduction of possible and interesting applications in dig...

Many real networks in social sciences, biological and biomedical sciences or computer science have an inherent structure of simplicial complexes reflecting many-body interactions. Using the recently introduced higher order notions of adjacency and degree for simplices in a simplicial complex, we define new centrality measures in simplicial complexe...

Many real networks in social, biological or computer sciences have an inherent structure of a simplicial complex, which reflects the multi interactions among agents (and groups of agents) and constitutes the basics of Topological Data Analysis. Normally, the relevance of an agent in a network of graphs is given in terms of the number of edges incid...

The purpose of this paper is to give a twisted version of the Eynard-Orantin topological recursion by a 2D Topological Quantum Field Theory. We define a kernel for a 2D TQFT and use an algebraic definition for a topological recursion to define how to twist a standard topological recursion by a 2D TQFT. The A-model side enumerative problem consists...

We study mirror symmetry for orbifold Hurwitz numbers. We show that the Laplace transform of orbifold Hurwitz numbers satisfy a differential recursion, which is then proved to be equivalent to the integral recursion of Eynard and Orantin with spectral curve given by the r-Lambert curve. We argue that the r-Lambert curve also arises in the infinite...

The aim of this paper is to offer an algebraic definition of infinite determinants of finite potent endomorphisms using linear algebra techniques. It generalizes Grothendieck's determinant for finite rank endomorphisms and is equivalent to the classic analytic definitions. The theory can be interpreted as a multiplicative analogue to Tate's formali...

In this paper we show the existence of a group acting infinitesimally transitively on the moduli space of pointed-curves and vector bundles (with formal trivialization data) and whose Lie algebra is an algebra of differential operators. The central extension of this Lie algebra induced by the determinant bundle on the Sato Grassmannian is precisely...

Using the technique of the Fourier-Mukai transform we give an explicit set of generators of the ideal defining an algebraic curve as a subscheme of its Jacobian. Essentially, these ideals are generated by the Fay's trisecant identities.

This paper is devoted to the study of the uniformization of the moduli space of pairs (X, E) consisting of an algebraic curve and a vector bundle on it. For this goal, we study the moduli space of 5-tuples (X, x, z, E, \phi), consisting of a genus g curve, a point on it, a local coordinate, a rank n degree d vector bundle and a formal trivializatio...

The aim of this paper is to offer an algebraic definition of infinite determinants of finite potent endomorphisms. It generalizes Grothendieck's determinant for finite rank endomorphisms on infinite-dimensional vector spaces, and is equivalent to the classic analytic definitions. Moreover, the theory can be interpreted as a multiplicative analogue...

In this paper the moduli space of Higgs pairs over a fixed smooth projective curve with extra formal data is defined and is endowed with a scheme structure. We introduce a relative version of the Krichever map using a fibration of Sato Grassmannians and show that this map is injective. This, together with the characterization of the points of the i...

Este trabajo hace un estudio detallado de la construcción de Krichever para diversos espacios de moduli, que hemos elegido motivados por el Programa de Abelianización de Hitchin. En el año 1988, Hitchin descubre una aplicación que va del espacio cotangente al moduli de fibrados (sobre una superficie de Riemann fija) a un espacio de secciones global...