Spatio-temporal patterns driven by autocatalytic internal reaction noise

The influence that intrinsic local density fluctuations can have on solutions of mean-field reaction-diffusion models is investigated numerically by means of the spatial patterns arising from two species that react and diffuse in the presence of strong internal reaction noise. The dynamics of the Gray-Scott (GS) model with constant external source is first cast in terms of a continuum field theory representing the corresponding master equation. We then derive a Langevin description of the field theory and use these stochastic differential equations in our simulations. The nature of the multiplicative noise is specified exactly without recourse to assumptions and turns out to be of the same order as the reaction itself, and thus cannot be treated as a small perturbation. Many of the complex patterns obtained in the absence of noise for the GS model are completely obliterated by these strong internal fluctuations, but we find novel spatial patterns induced by this reaction noise in regions of parameter space that otherwise correspond to homogeneous solutions when fluctuations are not included.Comment: 12 pages, 18 figure

Almost-extreme Khovanov spectra

We introduce a functor from the cube to the Burnside 2-category and prove that it is equivalent to the Khovanov spectrum given by Lipshitz and Sarkar in the almost-extreme quantum grading. We provide a decomposition of this functor into simplicial complexes. This decomposition allows us to compute the homotopy type of the almost-extreme Khovanov spectra of diagrams without alternating pairsBoth authors were supported by the Spanish projects MTM2016-76453-C2, MDM-2014-0445 and FEDER. The first author was partially supported by project PID2019-108936GB-C21. The second author was partially supported by projects PID2020-117971GB-C21, US-1263032, and IJC2019-040519-I/A

La visión de la Administración

La universidad española goza de virtudes y, naturalmente, de debilidades que deberían ser abordadas. España se encuentra en el noveno puesto de producción científica y no es baladí que dos terceras partes de la producción científica de España se realicen en universidades. Apoyar la excelencia de nuestra ciencia, desarrollada en el marco universitario, y del personal investigador es una prioridad para el gobierno, como muestran las últimas iniciativas políticas que se repasan en este artículo

Dynamic Renormalization Group and Noise Induced Transitions in a Reaction Diffusion Model

We investigate how additive weak noise (correlated as well as uncorrelated) modifies the parameters of the Gray-Scott (GS) reaction diffusion system by performing numerical simulations and applying a Renormalization Group (RG) analysis in the neighborhood of the spatial scale where biochemical reactions take place. One can obtain the same sequence of spatial-temporal patterns by means of two equivalent routes: (i) by increasing only the noise intensity and keeping all other model parameters fixed, or (ii) keeping the noise fixed, and adjusting certain model parameters to their running scale-dependent values as predicted by the RG. This explicit demonstration validates the dynamic RG transformation for finite scales in a two-dimensional stochastic model and provides further physical insight into the coarse-graining analysis proposed by this scheme. Through several study cases we explore the role of noise and its temporal correlation in self-organization and propose a way to drive the system into a new desired state in a controlled way.Comment: 8 pages, 21 figure

Weight decompositions of Thom spaces of vector bundles in rational homotopy

Motivated by the theory of representability classes by submanifolds, we study the rational homotopy theory of Thom spaces of vector bundles. We first give a Thom isomorphism at the level of rational homotopy, extending work of Félix-Oprea-Tanré by removing hypothesis of nilpotency of the base and orientability of the bundle. Then, we use the theory of weight decompositions in rational homotopy to give a criterion of representability of classes by submanifolds, generalising results of Papadima. Along the way, we study issues of formality and give formulas for Massey products of Thom spaces. Lastly, we link the theory of weight decompositions with mixed Hodge theory and apply our results to motivic Thom spaces

La Inspección Educativa de Galicia: caminos recorridos y estrategias de futuro

As is well known, the social sciences are concerned with organizing and interpreting the knowledge resulting from the reflection of societies on themselves. As an integral part of society and members of a collective, analyzing the past will help us understand the present and project the future. Following that pattern, we will review the brief history of the Galician Education Inspectorate to later analyze its current situation and make some proposals that may contribute to its improvement.Como es bien conocido, las ciencias sociales se ocupan de organizar e interpretar los conocimientos resultantes de la reflexión de las sociedades sobre sí mismas. Como parte integrante de la sociedad y miembros de un colectivo analizar el pasado nos ayudará a entender el presente y a proyectar el futuro. Siguiendo esa pauta, repasaremos la breve historia de la Inspección de Educación de Galicia para después analizar su situación actual y hacer algunas propuestas que puedan contribuir a su mejora