Decomposition spaces in combinatorics

A decomposition space (also called unital 2-Segal space) is a simplicial object satisfying an exactness condition weaker than the Segal condition: just as the Segal condition expresses (up to homotopy) composition, the new condition expresses decomposition. It is a general framework for incidence (co)algebras. In the present contribution, after establishing a formula for the section coefficients, we survey a large supply of examples, emphasising the notion's firm roots in classical combinatorics. The first batch of examples, similar to binomial posets, serves to illustrate two key points: (1) the incidence algebra in question is realised directly from a decomposition space, without a reduction step, and reductions are often given by CULF functors; (2) at the objective level, the convolution algebra is a monoidal structure of species. Specifically, we encounter the usual Cauchy product of species, the shuffle product of L-species, the Dirichlet product of arithmetic species, the Joyal-Street external product of q-species and the Morrison `Cauchy' product of q-species, and in each case a power series representation results from taking cardinality. The external product of q-species exemplifies the fact that Waldhausen's S-construction on an abelian category is a decomposition space, yielding Hall algebras. The next class of examples includes Schmitt's chromatic Hopf algebra, the Fa\`a di Bruno bialgebra, the Butcher-Connes-Kreimer Hopf algebra of trees and several variations from operad theory. Similar structures on posets and directed graphs exemplify a general construction of decomposition spaces from directed restriction species. We finish by computing the M\Preprin

Three Hopf algebras from number theory, physics & topology, and their common background I: operadic & simplicial aspects

We consider three a priori totally different setups for Hopf algebras from number theory, mathematical physics and algebraic topology. These are the Hopf algebra of Goncharov for multiple zeta values, that of Connes-Kreimer for renormalization, and a Hopf algebra constructed by Baues to study double loop spaces. We show that these examples can be successively unified by considering simplicial objects, co-operads with multiplication and Feynman categories at the ultimate level. These considerations open the door to new constructions and reinterpretations of known constructions in a large common framework, which is presented step-by-step with examples throughout. In this first part of two papers, we concentrate on the simplicial and operadic aspectsPeer ReviewedPostprint (author's final draft

Three Hopf algebras and their common simplicial and categorical background

We consider three a priori totally different setups for Hopf algebras from number theory, mathematical physics and algebraic topology. These are the Hopf algebras of Goncharov for multiple zeta values, that of Connes--Kreimer for renormalization, and a Hopf algebra constructed by Baues to study double loop spaces. We show that these examples can be successively unified by considering simplicial objects, cooperads with multiplication and Feynman categories at the ultimate level. These considerations open the door to new constructions and reinterpretation of known constructions in a large common frameworkPreprin

Strategic Communication in the communications environment of today’s organizations

This article seeks to clarify the concept of strategic communication as part of the new communications challenges facing today’s firms (Carrillo et al., 2013). Strategic communication has become an academic and professional working field of major importance. Delineating the issues underlying this area of theoretical and professional work is a challenge for scholars of the communication sciences. A correct definition of the concept should respond to the need to include communication as part of senior management’s essential competences, and should comply with a number of pre-defined, long-term objectives designed to address the interests of each of the company or organization’s stakeholders

Decay rates for a class of diffusive-dominated interaction equations

We analyse qualitative properties of the solutions to a mean-field equation for particles interacting through a pairwise potential while diffusing by Brownian motion. Interaction and diffusion compete with each other depending on the character of the potential. We provide sufficient conditions on the relation between the interaction potential and the initial data for diffusion to be the dominant term. We give decay rates of Sobolev norms showing that asymptotically for large times the behavior is then given by the heat equation. Moreover, we show an optimal rate of convergence in the $L^1$-norm towards the fundamental solution of the heat equation.Comment: 22 page

Resistencia al encamado

Se conoce como encamado el proceso por el que los tallos de las plantas son desplazados de una manera permanente de su posición vertical. Puede culminar en que las plantas se queden dobladas o tumbadas sobre el suelo, y a veces puede llevar rotura de los tallos. Los tallos pueden permanecer rectos en su encamado o adoptar formas curvas. El encamado a menudo no se distribuye uniformemente en el campo afectado, puede afectar solo a ciertas secciones del campo. El grado de encamado, es decir, el grado en que los tallos se desplazan de la perpendicular puede también variar en diferentes lugares dentro del campo. La permanencia, junto con el grado, determina la severidad del encamado. Este proceso afecta principalmente a cultivos pertenecientes a las familias de cereales y leguminosas. Normalmente ocurre después de que las inflorescencias, es decir, espigas, panículas, etc. hayan emergido. Se ha observado que los cereales pueden encamar en cualquier tiempo desde la emergencia de su espiga hasta que los granos han madurado. Y las plantas son más propensas al encamado conforme avanzan en el desarrollo y llegan a la maduración. El encamado puede reducir la producción hasta casi anularla, y causa además diferentes daños en el cultivo, como disminuir la calidad, e incrementa los gastos de la cosecha. El encamado es un fenómeno complejo que está influenciado por muchos factores ambientales, incluyendo el viento, la lluvia, la topografía, el tipo de suelo, las enfermedades e incluso el cultivo previo. Frecuentemente está asociado con condiciones que promueven el crecimiento de la planta como puede ser un abundante abonado

Aprenentatge actiu de conceptes en probabilitat i estadística per a l'enginyeria

Peer Reviewe

Diversity and Genetic structure of the Spanish collection of durum wheat (Triticum turgidum L) landraces

The objectives of this study were to assess diversity and genetic structure of a collection of Spanish durum wheat (Triticum turgidum L) landraces, using SSRs, DArTs and gliadin-markers, and to correlate the distribution of diversity with geographic and climatic features, as well as agro-morphological traits. A high level of diversity was detected in the genotypes analyzed, which were separated into nine populations with a moderate to great genetic divergence among them. The three subspecies taxa, dicoccon, turgidum and durum, present in the collection, largely determined the clustering of the populations. Genotype variation was lower in dicoccon (one major population) and turgidum (two major populations) than in durum (five major populations). Genetic differentiation by the agro-ecological zone of origin was greater in dicoccon and turgidum than in durum. DArT markers revealed two geographic substructures, east-west for dicoccon and northeast-southwest for turgidum. The ssp. durum had a more complex structure, consisting of seven populations with high intra-population variation. DArT markers allowed the detection of subgroups within some populations, with agro-morphological and gliadin differences, and distinct agro-ecological zones of origin. Two different phylogenetic groups were detected; revealing that some durum populations were more related to ssp. turgidum from northern Spain, while others seem to be more related to durum wheats from North Afric