Implementation, elimination of weakly dominated strategies and evolutionary dynamics

This paper is concerned with the realism of mechanisms that implementsocial choice functions in the traditional sense. Will agents actually playthe equilibrium assumed by the analysis? As an example, we study theconvergence and stability properties of Sj\"ostr\"om's (1994) mechanism, onthe assumption that boundedly rational players find their way to equilibriumusing monotonic learning dynamics and also with fictitious play. Thismechanism implements most social choice functions in economic environmentsusing as a solution concept the iterated elimination of weakly dominatedstrategies (only one round of deletion of weakly dominated strategies isneeded). There are, however, many sets of Nash equilibria whose payoffs maybe very different from those desired by the social choice function. Withmonotonic dynamics we show that many equilibria in all the sets ofequilibria we describe are the limit points of trajectories that havecompletely mixed initial conditions. The initial conditions that lead tothese equilibria need not be very close to the limiting point. Furthermore,even if the dynamics converge to the ``right'' set of equilibria, it stillcan converge to quite a poor outcome in welfare terms. With fictitious play,if the agents have completely mixed prior beliefs, beliefs and play convergeto the outcome the planner wants to implement.

Free and fragmenting filling length

The filling length of an edge-circuit η in the Cayley 2-complex of a finite presentation of a group is the minimal integer length L such that there is a combinatorial null-homotopy of η down to a base point through loops of length at most L. We introduce similar notions in which the full-homotopy is not required to fix a base point, and in which the contracting loop is allowed to bifurcate. We exhibit a group in which the resulting filling invariants exhibit dramatically different behaviour to the standard notion of filling length. We also define the corresponding filling invariants for Riemannian manifolds and translate our results to this setting.

Polítiques, pràctiques i estratègies d'inserció: una mirada des de les trajectòries de les dones immigrades

Aquesta recerca, amb l’objectiu general de conèixer i analitzar els processos d’inserció al mercat laboral, les estratègies i pràctiques d’inserció, i els àmbits d’ocupació de les dones immigrades en la societat de recepció, es va plantejar com a finalitat proposar línies d'actuació i pràctiques d'atenció vers aquest col•lectiu. Sota l’eix 1 del Pacte Nacional, apunta a garantir la igualtat de drets i l’accés al mercat laboral de les persones, des de la tranversalitat del gènere. Mitjançant l’aplicació d'entrevistes semiestructurades per tal de construir "trajectòries d’immigració" de dones, i obtenir una mirada sociohistòrica i dinàmica del procés de d’inserció laboral a la societat de recepció, es va portar a terme la recerca amb la participació de 17 dones immigrades al territori català. Entre els resultats, cal destacar que: en quant als relats d’origen destaca la diversitat de motius de la immigració, posant en qüestió les tesis purament economicistes, i en relació amb les polítiques i pràctiques d’inserció laboral, podem confirmar que els esforços dels recursos d’atenció tendeixen a encertar a les dones en els nínxols laborals més precaritzats, i sobre tot generitzats. Per altre banda, l’estudi ens ha permet apropar-nos a les estratègies que fan servir les dones per a sortejar les limitacions, sobre tot legals, que es troben a la societat de recepció. Aquestes accions ens permeten analitzar l’agència de les dones immigrades i la importància de les xarxes socials i de la participació, per a una inserció sociolaboral més plena. A més de les conclusions i recomanacions contingudes en aquest document, s'ha elaborat un material didàctic que es composa de: 1. Documental "Per compte aliè" en el qual hi ha les històries d'inserció de 5 dones i; 2. Guia de 12 tallers de treball com a proposta d’intervenció, destinats als col•lectius i serveis que treballen per a la inserció.

Dynamical Systems approach to Saffman-Taylor fingering. A Dynamical Solvability Scenario

A dynamical systems approach to competition of Saffman-Taylor fingers in a Hele-Shaw channel is developed. This is based on global analysis of the phase space flow of the low-dimensional ordinary-differential-equation sets associated with the classes of exact solutions of the problem without surface tension. Some simple examples are studied in detail. A general proof of the existence of finite-time singularities for broad classes of solutions is given. Solutions leading to finite-time interface pinchoff are also identified. The existence of a continuum of multifinger fixed points and its dynamical implications are discussed. We conclude that exact zero-surface tension solutions taken in a global sense as families of trajectories in phase space are unphysical because the multifinger fixed points are nonhyperbolic, and an unfolding does not exist within the same class of solutions. Hyperbolicity (saddle-point structure) of the multifinger fixed points is argued to be essential to the physically correct qualitative description of finger competition. The restoring of hyperbolicity by surface tension is proposed as the key point to formulate a generic dynamical solvability scenario for interfacial pattern selection.

The Zariski-Lefschetz principle for higher homotopy groups of nongeneric pencils

We prove a general Zariski-van Kampen-Lefschetz type theorem for higher homotopy groups of generic and nongeneric pencils on singular open complex spaces.

Different trajectories of exosomatic energy metabolism for Brazil, Chile and Venezuela: using the MSIASM approach

Economic development goes hand in hand with an increase in the consumption of natural resources. Some analysts use material flows to describe such relationship [Eurostat 2001, Weisz et al., 2006], or exergy [Ayres et al., 2003]. Instead this paper will use a characterisation of the exosomatic energy metabolism based on expected benchmark values to describe possible constraints to economic development posed by available human time and energy. The aim of the paper is to identify types of exosomatic energy metabolism of different societies to interpret its consequences for economic development. This is done with the application of the accounting methodology called Multi-Scale Integrated Analysis of Societal Metabolism (MSIASM) to the particular case of energy metabolism for the analysis of the economies of Brazil, Chile and Venezuela.

On the homotopy theory of spectral categories

"Vegeu el resum a l'inici del document del fitxer adjunt."

Euler characteristics of categories and homotopy colimits

"Vegeu el resum a l'inici del document del fitxer adjunt."

A study of the labour market trajectories in the Grand Duchy of Luxembourg

We present an analysis of the register of all unemployment episodes in the Grand Duchy of Luxembourg over a recent period of 55 months. We apply propensity score matching to account forthe systematic differences among the groups of subjects (registrants) and unemployment spells.We devise graphical and tabular summaries for describing the sequences of employment states ofthe members of the labour force who register at Agence pour le d?veloppement de l'emploi, theLuxembourg Public Unemployment Agency. Some employment-related information about themis collected by linking their records to the national register of social security contributions, maintained by Inspection g?n?rale de la s?curit? sociale. A class of univariate indices for characterisingthe sequences of labour force states is defined.

Classical line shapes based on analytical solutions of bimolecular trajectories in collision induced emission. II. Reactive collisions

The classical theory of collision induced emission (CIE) from pairs of dissimilar rare gas atoms was developed in Paper I [D. Reguera and G. Birnbaum, J. Chem. Phys. 125, 184304 (2006)] from a knowledge of the straight line collision trajectory and the assumption that the magnitude of the dipole could be represented by an exponential function of the inter-nuclear distance. This theory is extended here to deal with other functional forms of the induced dipole as revealed by ab initio calculations. Accurate analytical expression for the CIE can be obtained by least square fitting of the ab initio values of the dipole as a function of inter-atomic separation using a sum of exponentials and then proceeding as in Paper I. However, we also show how the multi-exponential fit can be replaced by a simpler fit using only two analytic functions. Our analysis is applied to the polar molecules HF and HBr. Unlike the rare gas atoms considered previously, these atomic pairs form stable bound diatomic molecules. We show that, interestingly, the spectra of these reactive molecules are characterized by the presence of multiple peaks. We also discuss the CIE arising from half collisions in excited electronic states, which in principle could be probed in photo-dissociation experiments.

The orthogonal subcategory problem in homotopy theory

It is known that, in a locally presentable category, localization exists with respect to every set of morphisms, while the statement that localization with respect to every (possibly proper) class of morphisms exists in locally presentable categories is equivalent to a large-cardinal axiom from set theory. One proves similarly, on one hand, that homotopy localization exists with respect to sets of maps in every cofibrantly generated, left proper, simplicial model category M whose underlying category is locally presentable. On the other hand, as we show in this article, the existence of localization with respect to possibly proper classes of maps in a model category M satisfying the above assumptions is implied by a large-cardinal axiom called Vopënka's principle, although we do not know if the reverse implication holds. We also show that, under the same assumptions on M, every endofunctor of M that is idempotent up to homotopy is equivalent to localization with respect to some class S of maps, and if Vopënka's principle holds then S can be chosen to be a set. There are examples showing that the latter need not be true if M is not cofibrantly generated. The above assumptions on M are satisfied by simplicial sets and symmetric spectra over simplicial sets, among many other model categories.

Homotopy limits for 2-categories

We study homotopy limits for 2-categories using the theory of Quillen model categories. In order to do so, we establish the existence of projective and injective model structures on diagram 2-categories. Using these results, we describe the homotopical behaviour not only of conical limits but also of weighted limits. Finally, pseudo-limits are related to homotopy limits.

Weighted limits in simplicial homotopy theory

We extend the theory of Quillen adjunctions by combining ideas of homotopical algebra and of enriched category theory. Our results describe how the formulas for homotopy colimits of Bousfield and Kan arise from general formulas describing the derived functor of the weighted colimit functor.

Homotopy exponents for large H-Spaces

We show that H-spaces with finitely generated cohomology, as an algebra or as an algebra over the Steenrod algebra, have homotopy exponents at all primes. This provides a positive answer to a question of Stanley.

Localization of algebras over coloured operads

We give sufficient conditions for homotopical localization functors to preserve algebras over coloured operads in monoidal model categories. Our approach encompasses a number of previous results about preservation of structures under localizations, such as loop spaces or infinite loop spaces, and provides new results of the same kind. For instance, under suitable assumptions, homotopical localizations preserve ring spectra (in the strict sense, not only up to homotopy), modules over ring spectra, and algebras over commutative ring spectra, as well as ring maps, module maps, and algebra maps. It is principally the treatment of module spectra and their maps that led us to the use of coloured operads (also called enriched multicategories) in this context.