Nash multiplicities and isolated points of maximum multiplicity

Let X be an algebraic variety defined over a field of characteristic zero, and let ξ ∈ Max mult(X) be a point in the closed subset of maximum multiplicity of X. We provide a criterion, given in terms of arcs, to determine whether ξ is isolated in Max mult(X). More precisely, we use invariants of arcs derived from the Nash multiplicity sequence to characterize when ξ is an isolated point in Max mult(X)

An algebraic approach to product-form stationary distributions for some reaction networks

Exact results for product-form stationary distributions of Markov chains are of interest in different fields. In stochastic reaction networks (CRNs), stationary distributions are mostly known in special cases where they are of product-form. However, there is no full characterization of the classes of networks whose stationary distributions have product-form. We develop an algebraic approach to product-form stationary distributions in the framework of CRNs. Under certain hypotheses on linearity and decomposition of the state space for conservative CRNs, this gives sufficient and necessary algebraic conditions for product-form stationary distributions. Correspondingly, we obtain a semialgebraic subset of the parameter space that captures rates where, under the corresponding hypotheses, CRNs have product-form. We employ the developed theory to CRNs and some models of statistical mechanics, besides sketching the pertinence in other models from applied probability.The work of the first author was supported by the European Union's Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie IF grant 794627. The work of the second author was supported by Swiss National Science Foundations Early Postdoctoral Mobility grant P2FRP2 188023.Publicad

An algebraic approach to product-form stationary distributions for some reaction networks

Exact results for product-form stationary distributions of Markov chains are of interest in different fields. In stochastic reaction networks (CRNs), stationary distributions are mostly known in special cases where they are of product-form. However, there is no full characterization of the classes of networks whose stationary distributions have product-form. We develop an algebraic approach to product-form stationary distributions in the framework of CRNs. Under certain hypotheses on linearity and decomposition of the state space for conservative ergodic CRNs, this gives sufficient and necessary algebraic conditions for product-form stationary distributions. Correspondingly we obtain a semialgebraic subset of the parameter space that captures rates where, under the corresponding hypotheses, CRNs have product-form. We employ the developed theory to CRNs and some models of statistical mechanics, besides sketching the pertinence in other models from applied probability.Comment: Accepted for publication in SIAM Journal on Applied Dynamical System

Mayoría de edad a los 18 años. Breve análisis de la Ley 26.579

En el presente artículo se analizan algunas de las consecuencias jurídicas derivadas de la sanción de la Ley Nacional 26.579, por la que se consagró en nuestro ordenamiento la mayoría de edad a los 18 años. Se destacan las consecuencias que ese adelantamiento en la adquisición de plena capacidad civil produce en cuanto a diversas instituciones civiles, tales como la emancipación, la patria potestad, la tutela y la obligación alimentaria paterna. Se analizan, también, algunas de las repercusiones de la nueva norma en el ámbito de otras ramas del derecho, tales como el derecho de daños, el comercial, el previsional y el penal, efectuándose una valoración crítica de la norma

Nash multiplicity sequences and Hironaka's order function

When X is a d-dimensional variety defined over a field k of characteristic zero, a constructive resolution of singularities can be achieved by successively lowering the maximum multiplicity via blow ups at smooth equimultiple centers. This is done by stratifying the maximum multiplicity locus of X by means of the so called resolution functions. The most important of these functions is what we know as Hironaka’s order function in dimension d. Actually, this function can be defined for varieties when the base field is perfect; however if the characteristic of k is positive, the function is, in general, too coarse and does not provide enough information so as to define a resolution. It is very natural to ask what the meaning of this function is in this case, and to try to find refinements that could lead, ultimately, to a resolution. In this paper we show that Hironaka’s order function in dimension d can be read in terms of the Nash multiplicity sequences introduced by Lejeune-Jalabert. Therefore, the function is intrinsic to the variety and has a geometrical meaning in terms of its space of arcs.The authors were partially supported by MTM2015-68524-P. The third author was supported by BES-2013-062656

Dimension and degeneracy of solutions of parametric polynomial systems arising from reaction networks

We study the generic dimension of the solution set over C^*, R^* and R_{>0} of parametric polynomial systems that consist of linear combinations of monomials scaled by free parameters. We establish a relation between this dimension, Zariski denseness of the set of parameters for which the system has solutions, and the existence of nondegenerate solutions, which enables fast dimension computations. Systems of this form are used to describe the steady states of reaction networks modeled with mass-action kinetics, and as a corollary of our results, we prove that weakly reversible networks have finitely many steady states for generic reaction rate constants and total concentrations

Contact loci and Hironaka's order

We study contact loci sets of arcs and the behavior of Hironaka’s order function defined in constructive Resolution of singularities. We show that this function can be read in terms of the irreducible components of the contact loci sets at a singular point of an algebraic variety.The authors were partially supported by MTM2015-68524-P; The first author was partially supported from the Spanish Ministry of Economy and Competitiveness, through the "Severo Ochoa" Programme for Centres of Excellence in R&D (SEV-2015-0554)

Hacia la conciencia cuántica a partir del efecto fotoeléctrico

En este artículo se indaga acerca de los recursos que emplean los estudiantes cuando tienen que responder a interrogantes cuyo contenido se refiere a fenómenos intangibles desde el punto de vista sensorial que vinculan el mundo a distintas escalas, tal como es el caso de la interacción de la radiación electromagnética con la materia. El estudio se realizó sobre tres situaciones problemáticas de efecto fotoeléctrico, y a partir de su análisis se pudieron diferenciar claramente cinco categorías de respuestas que nos dirigen a reflexionar acerca de la construcción de un concepto esencial de las ciencias naturales, como es el de energía, y su relación con el de interacción radiación-materia, dualidad onda-partícula, cuanto, entre otros. Se evidencia una malla de subjetividades que actúa como soporte de la formación de conceptos hacia cuya objetividad apuntan los esfuerzos del proceso de enseñanza.En aquest article s'indaga sobre els recursos que empren els estudiants quan han de respondre a interrogants el contingut dels quals es refereix a fenòmens intangibles des del punt de vista sensorial que vinculen el món a diferents escales, tal com és el cas de la interacció de la radiació electromagnètica amb la matèria. L'estudi es va realitzar sobre tres situacions problemàtiques d'efecte fotoelèctric, i a partir de la seva anàlisi es van poder diferenciar clarament cinc categories de respostes que ens dirigeixen a reflexionar sobre la construcció d'un concepte essencial de les ciències naturals, com és el d'energia, i la seva relació amb el d'interacció radiació-matèria, dualitat ona-partícula, quant, entre d'altres. S'evidencia una malla de subjectivitats que actua com a suport de la formació de conceptes cap a l'objectivitat dels quals apunten els esforços del procés d'ensenyament.This article inquires about the resources that students employ when they answer to questions related to non tangible phenomena that relate the world in different scales. Such is the case of the electromagnetic radiation and matter interaction. This research was focused on three problem situations related to the photoelectric effect and five categories were identified within their answers making us think about the construction of a main concept of the natural sciences such as energy and its relationship with the ideas of radiation-matter interaction, wave-particle duality, quantum, among others. It is evidenced a net of subjectivities is generated so that it works as the support for the objective concept formation that is the ultimate goal of the process of teaching

Algorithmic Resolution of Singularities and Nash multiplicity sequences

Tesis doctoral inédita leída en la Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Matemáticas. Fecha de lectura: 19-01-201

Prevalencia de Úlceras en Neda y diferencias entre la población rural y urbana.

Resumen del trabajo Este trabajo consiste en un estudio descriptivo transversal, es decir, un estudio que analiza un fenómeno en un periodo de tiempo corto (Febrero 2014-Mayo 2014), en este caso, el fenómeno se trata del estado de las úlceras vasculares en miembros inferiores de los pacientes que acuden al centro de Salud de Neda.Traballo fin de grao (UDC.FEP). Enfermaría. Curso 2013/201