A geometric chracterization of the nucleolus of the assignment game

Maschler et al. (1979) caracteritzen geomètricament la intersecció del kernel i del core en els jocs cooperatius, demostrant que les distribucions que pertanyen a ambdós conjunts es troben en el punt mig d’un cert rang de negociació entre parelles de jugadors. En el cas dels jocs d’assignació, aquesta caracterització vol dir que el kernel només conté aquells elements del core on el màxim que un jugador pot transferir a una parella òptima és igual al màxim que aquesta parella li pot transferir, sense sortir-se’n del core. En aquest treball demostrem que el nucleolus d’un joc d’assignació queda caracteritzat si requerim que aquesta propietat de bisecció es compleixi no només per parelles, sinó també per coalicions entre sectors aparellades òptimament.

A geometric chracterization of the nucleolus of the assignment game

Maschler et al. (1979) caracteritzen geomètricament la intersecció del kernel i del core en els jocs cooperatius, demostrant que les distribucions que pertanyen a ambdós conjunts es troben en el punt mig d’un cert rang de negociació entre parelles de jugadors. En el cas dels jocs d’assignació, aquesta caracterització vol dir que el kernel només conté aquells elements del core on el màxim que un jugador pot transferir a una parella òptima és igual al màxim que aquesta parella li pot transferir, sense sortir-se’n del core. En aquest treball demostrem que el nucleolus d’un joc d’assignació queda caracteritzat si requerim que aquesta propietat de bisecció es compleixi no només per parelles, sinó també per coalicions entre sectors aparellades òptimament.

The differentiable chain functor is not homotopy equivalent to the continuous chain functor

Let $S_*$ and $S_*^\{infty}$ be the functors of continuous and differentiable singular chains on the category of differentiable manifolds. We prove that the natural transformation $i: S_*^\infty \rightarrow S_*$, which induces homology equivalences over each manifold, is not a natural homotopy equivalence.

On the bicanonical map of irregular varieties

From the point of view of uniform bounds for the birationality of pluricanonical maps, irregular varieties of general type and maximal Albanese dimension behave similarly to curves. In fact Chen-Hacon showed that, at least when their holomorphic Euler characteristic is positive, the tricanonical map of such varieties is always birational. In this paper we study the bicanonical map. We consider the natural subclass of varieties of maximal Albanese dimension formed by primitive varieties of Albanese general type. We prove that the only such varieties with non-birational bicanonical map are the natural higher-dimensional generalization to this context of curves of genus $2$: varieties birationally equivalent to the theta-divisor of an indecomposable principally polarized abelian variety. The proof is based on the (generalized) Fourier-Mukai transform.

Monoidal functors, acyclic models and chain operads

We prove that for a topological operad $P$ the operad of oriented cubical singular chains, $C^{\ord}_\ast(P)$, and the operad of simplicial singular chains, $S_\ast(P)$, are weakly equivalent. As a consequence, $C^{\ord}_\ast(P\nsemi\mathbb{Q})$ is formal if and only if $S_\ast(P\nsemi\mathbb{Q})$ is formal, thus linking together some formality results which are spread out in the literature. The proof is based on an acyclic models theorem for monoidal functors. We give different variants of the acyclic models theorem and apply the contravariant case to study the cohomology theories for simplicial sets defined by $R$-simplicial differential graded algebras.

Dynamics of integrable birational maps preserving genus 0 foliations

Pòster presentat al congrés NPDDS2014

Predation on common tern eggs by the yellow-legged gull at the Ebro Delta

The Ebro Delta holds a large seabird community, including a common tern (Sterna hirundo) local population of 3,085 pairs in 2000 which breeds scattered in several colonies. At El Canalot colony, 1,178 (1999) and 1,156 pairs (2000) of this species bred distributed in 32 and 38 sub-colonies respectively. These sub-colonies varied in size from 1 to 223 pairs and were placed near the main breeding colonies of yellow-legged gulls (Larus cachinnans) and Audouin´s gulls (L. audouinii), which are potential egg-predators of terns. We studied egg predation during 1999 (6 sub-colonies) and 2000 (27 sub-colonies). Overall, we found that 10.6% of the nests in 1999 and 16.7% in 2000 suffered partial or total egg predation, being total in 81.1% of the predatory events. Predation was significantly higher in small sub-colonies (< 11 pairs): 49.4% in 1999 and 75.5% in 2000. Only attacks from yellow-legged gulls were observed, and defence behaviour of terns was significantly more frequent against this gull species (40.5 hours of observation), suggesting that in most cases the egg predation recorded was due to this species. Probability of egg predation was significantly and negatively correlated with distance to the nearest yellow-legged gull sub-colony, although this relationship was no more significant after adjustment for sub-colony size. On the other hand, distance to the nearest Audouin´s gull sub-colony did not show any effect. Our results suggest that the impact of large gulls (at least yellow-legged gulls) upon smaller seabirds breeding in the area might be important, especially when they are breeding in small sub-colonies. Further studies are needed to analyse the general impact of large gulls upon the breeding populations of other colonial bird species in the area.

Sur le théorème locale des cycles invariants

Si on considère une famille de variétés projectives complexes non singulières, c"est un fait aujourd'hui bien connu que les possibles variétés singulières vers lesquelles peut dégénerer cette famille doivent vérifier certaines contraintes, parmi lesquelles une importante relation entre la cohomologie de la fibre singulière, la cohomologie de la fibre générique et la monodromie de la famille, qui est precise par le théorème local des cycles invariants prouvé par Clemens, Deligne et Steenbrink ([1], [4], [13]) : tous les cocycles de la fibre générique qui sont invariants par la monodromie autour d¡une fibre singulière proviennent par spécialisation de la cohomologie de cette fibre singulière.

Review of Rewriting Terror: The 9/11 Terrorists in American Fiction (Juanjo Bermúdez de Castro, 2012)

In the wake of the terrorist attacks of September 11, 2001, many authors of fiction, filmmakers, journalists, public figures and scholars have attempted to narrate, recreate, explain, reflect on, and theorize about the event and its aftermath.

Vacancy-assisted domain-growth in asymmetric binary alloys: A Monte Carlo Study

A Monte Carlo simulation study of the vacancy-assisted domain growth in asymmetric binary alloys is presented. The system is modeled using a three-state ABV Hamiltonian which includes an asymmetry term. Our simulated system is a stoichiometric two-dimensional binary alloy with a single vacancy which evolves according to the vacancy-atom exchange mechanism. We obtain that, compared to the symmetric case, the ordering process slows down dramatically. Concerning the asymptotic behavior it is algebraic and characterized by the Allen-Cahn growth exponent x51/2. The late stages of the evolution are preceded by a transient regime strongly affected by both the temperature and the degree of asymmetry of the alloy. The results are discussed and compared to those obtained for the symmetric case.

Garvey-Kelson relations for nuclear charge radii

The Garvey-Kelson relations (GKRs) are algebraic expressions originally developed to predict nuclear masses. In this letter we show that the GKRs provide a fruitful framework for the prediction of other physical observables that also display a slowly-varying dynamics. Based on this concept, we extend the GKRs to the study of nuclear charge radii. The GKRs are tested on 455 out of the approximately 800 nuclei whose charge radius is experimentally known. We find a rms deviation between the GK predictions and the experimental values of only 0.01 fm. This should be contrasted against some of the most successful microscopic models that yield rms deviations almost three times as large. Predictions -with reliable uncertainties- are provided for 116 nuclei whose charge radius is presently unknown.

The normal distribution in some constrained sample spaces

Phenomena with a constrained sample space appear frequently in practice. This is the case e.g. with strictly positive data, or with compositional data, like percentages or proportions. If the natural measure of difference is not the absolute one, simple algebraic properties show that it is more convenient to work with a geometry different from the usual Euclidean geometry in real space, and with a measure different from the usual Lebesgue measure, leading to alternative models which better fit the phenomenon under study. The general approach is presented and illustrated using the normal distribution, both on the positive real line and on the D-part simplex. The original ideas of McAlister in his introduction to the lognormal distribution in 1879, are recovered and updated

A Fair and Secure Cluster Formation Process for Ad Hoc Networks

An efficient approach for organizing large ad hoc networks is to divide the nodesinto multiple clusters and designate, for each cluster, a clusterhead which is responsible forholding intercluster control information. The role of a clusterhead entails rights and duties.On the one hand, it has a dominant position in front of the others because it manages theconnectivity and has access to other node¿s sensitive information. But on the other hand, theclusterhead role also has some associated costs. Hence, in order to prevent malicious nodesfrom taking control of the group in a fraudulent way and avoid selfish attacks from suitablenodes, the clusterhead needs to be elected in a secure way. In this paper we present a novelsolution that guarantees the clusterhead is elected in a cheat-proof manner.