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 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

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

Políticas de seguridad, control preventivo y peligrosidad. La construcción del orden social seguritario

En relación con la “Políticas de seguridad” mencionadas en el Título de este trabajo, entiendo que para su comprensión son referentes centrales las expresiones “seguridad pública” y “seguridad ciudadana”. Se recogen así en esta Introducción porque ambas se han utilizado, a veces incluso por el TC, de manera sinónima o atribuyéndoles una mínima diferencia de matiz y una cierta indeterminación. Desde su presencia normativa, BARCELONA LLOP (1997) ha planteado alguna diferencia al señalar que “la seguridad ciudadana” no hace...referencia a cualquier actuación pública susceptible de encuadrarse en el conjunto de la seguridad pública, sino solo aquellas actividades que se insertan en el conjunto de los cometidos ordinarios y normales de las Fuerzas y Cuerpos de Seguridad encontrándose además, en íntima conexión con la protección del libre ejercicio de derechos y libertades... En otro caso cuando los derechos y las libertades no precisan protección frente a conductas agre- soras pero si requieran de actividades públicas tendentes a proteger su indemnidad, será el concepto de seguridad pública, que es más amplio, el que entre en escena, con intervención policial o no”

An alternative approach to the resolution of singularities of toric varieties

Das Problem des Auflösens von Singularitäten besteht daraus, eine singuläre algebraische Varietät als Bild einer anderen glatten algebraischen Varietät X' unter einem eigentlichen birationalen Morphismus zu interpretieren. Dieser birationale Morphismus muss ein Isomorphismus ausserhalb der singulären Punkte von X definieren. \\ Diese Arbeit analysiert das Problem des Auflösens von Singularitäten für algebraische Varietäten, die einen Koordinatenring mit speziellen Eigenschaften besitzen: der Koordinatenring muss eine Algebra über einem algebraisch abgeschlossenen Körper sein und von einer endlichen Menge von Monomen erzeugt sein. Das Ziel ist es, einen Algorithmus zu konstruieren, der für eine solche Varietät eine Auflösung von Singularitäten findet. Um dies zu erreichen, übersetzen wir die Effekte eines Blowups in eine Transformation der Exponenten der Monome, die die Koordinatenring von X erzeugen. Dann betrachten wir ein kombinatorisches Problem. Das Ergebnis dieser Arbeit ist ein kombinatorisches Verfahren, das für Kurven und Hyperflächen von Dimension 2 funktioniert. Weiters folgt eine Diskussion über Schwierigkeiten, die in höherer Dimension auftreten, und wie das Problem angegangen werden könnte.The problem of Resolution of Singularities consists of interpreting an algebraic variety X with singular points as the image by a birational proper morphism of some smooth algebraic variety X'. This morphism must define an isomorphism outside the singular locus of X. The present work analyzes this problem for those affine algebraic varieties whose coordinate ring is an algebra over an algebraically closed field of characteristic zero, generated by a finite set of monomials. The aim is to construct an algorithm that, given such a variety, finds a resolution of its singularities. To do so, we translate the effect of a blowup into a transformation of the exponents of the monomials generating the coordinate ring of X. After that, we deal with a combinatorial problem. The result is a combinatorial procedure which works for curves and for hypersurfaces of dimension 2. A discussion about the difficulties that appear for higher dimensional varieties and how could the problem be addressed in this case follows

Remote Teaching of Chemistry Laboratory Courses during COVID-19

This paper describes the transfer from face-to-face education toemergency remote teaching of chemistry laboratory courses in a bachelor's degree inPharmacy during the COVID-19 pandemic. The virtualization was carried out usingvideos of each experimental practice and questionnaires containing the experimentaldata needed. The contents were integrated into the virtual platform BlackboardCollaborate, where tutorials and remote support from the teachers were provided tosolve the issues raised. The didactic strategy was very positive: it turned the studentsinto active learners, fostering knowledge sharing and promoting the self-management of their learning process. The teachers acted as guides, raisingquestions, and provided continuous feedback to the students that contributed toknowledge assimilation and competence acquisition. The teaching-learning processwas evaluated through a rubric that graded the reports delivered by the students andafinal online test. The impact of this teaching methodology was assessed bycomparing the students'marks with those obtained in the conventional on-site education before the pandemic and feedback fromthe students via surveys. This study provides a unique experience on how a traditional instruction can be adapted to remote teachingin analytical chemistry laboratories, providing new tools that can be used in future pandemics or in other setting

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)

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

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

Monocyte-mediated regulation of genes by the amyloid and prion peptides in SH-SY5Y neuroblastoma cells

El pdf del artículo es la versión manuscrita de autor.Alzheimer's disease as well as prion-related encephalopathies are neurodegenerative disorders of the central nervous system, which cause mental deterioration and progressive dementia. Both pathologies appear to be primarily associated with the pathological accumulation and deposit of β-amyloid or prion peptides in the brain, and it has been even suggested that neurotoxicity induced by these peptides would be associated to essentially similar pathogenic mechanisms, in particular to those that follow the activation of microglial cells. To probe whether the neurotoxic effects induced by the β-amyloid and prion peptides are actually mediated by similar glial-associated mechanisms, we have examined the differential expression of genes in SH-SY5Y neuroblastoma cells incubated with conditioned media from β-amyloid or prion-stimulated THP-1 monocytic cells. According to microarray analysis, not many coincidences are observed and only four genes (Hint3, Psph, Daam1 and c-Jun) appear to be commonly upregulated by both peptides. Furthermore, c-Jun appears to be involved in the cell death mediated by both peptides. © 2011 Elsevier Ltd. All rights reserved.Peer Reviewe