A generalized assignment game

The proposed game is a natural extension of the Shapley and Shubik Assignment Game to the case where each seller owns a set of different objets instead of only one indivisible object. We propose definitions of pairwise stability and group stability that are adapted to our framework. Existence of both pairwise and group stable outcomes is proved. We study the structure of the group stable set and we finally prove that the set of group stable payoffs forms a complete lattice with one optimal group stable payoff for each side of the market.

An Atkinson-Gini family of social evaluation functions

We investigate the properties of a family of social evaluation functions and inequality indices which merge the features of the family of Atkinson (1970) and S-Gini (Donaldson and Weymark (1980, 1983), Yitzhaki (1983) and Kakwani (1980)) indices. Income inequality aversion is captured by decreasing marginal utilities, and aversion to rank inequality is captured by rank-dependent ethical weights, thus providing an ethically-flexible dual basis for the assessment of inequality and equity. These ocial evaluation functions can be interpreted as average utility corrected for the illfare of relative deprivation. They can alternatively be understood as averages of altruistic well-being in a population. They moreover have a simple graphical interpretation.

Self-selection consistent functions

This paper studies collective choice rules whose outcomes consist of a collection of simultaneous decisions, each one of which is the only concern of some group of individuals in society. The need for such rules arises in different contexts, including the establishment of jurisdictions, the location of multiple public facilities, or the election of representative committees. We define a notion of allocation consistency requiring that each partial aspect of the global decision taken by society as a whole should be ratified by the group of agents who are directly concerned with this particular aspect. We investigate the possibility of designing envy-free allocation consistent rules, we also explore whether such rules may also respect the Condorcet criterion.

In whose backyard? A generalized bidding approach

We analyze situations in which a group of agents (and possibly a designer) have to reach a decision that will affect all the agents. Examples of such scenarios are the location of a nuclear reactor or the siting of a major sport event. To address the problem of reaching a decision, we propose a one-stage multi-bidding mechanism where agents compete for the project by submitting bids. All Nash equilibria of this mechanism are efficient. Moreover, the payoffs attained in equilibrium by the agents satisfy intuitively appealing lower bounds..

Generalized property R and the Schoenflies Conjecture

There is a relation between the generalized Property R Conjecture and the Schoenflies Conjecture that suggests a new line of attack on the latter. The new approach gives a quick proof of the genus 2 Schoenflies Conjecture and suffices to prove the genus 3 case, even in the absence of new progress on the generalized Property R Conjecture.

Generalized backward doubly stochastic differential equations and SPDEs with nonlinear Neumann boundary conditions

In this paper, a new class of generalized backward doubly stochastic differential equations is investigated. This class involves an integral with respect to an adapted continuous increasing process. A probabilistic representation for viscosity solutions of semi-linear stochastic partial differential equations with a Neumann boundary condition is given.

Cubic spline population density functions and subcentre delimitation. The case of Barcelona

The presence of subcentres cannot be captured by an exponential function. Cubic spline functions seem more appropriate to depict the polycentricity pattern of modern urban systems. Using data from Barcelona Metropolitan Region, two possible population subcentre delimitation procedures are discussed. One, taking an estimated derivative equal to zero, the other, a density gradient equal to zero. It is argued that, in using a cubic spline function, a delimitation strategy based on derivatives is more appropriate than one based on gradients because the estimated density can be negative in sections with very low densities and few observations, leading to sudden changes in estimated gradients. It is also argued that using as a criteria for subcentre delimitation a second derivative with value zero allow us to capture a more restricted subcentre area than using as a criteria a first derivative zero. This methodology can also be used for intermediate ring delimitation.

The mean dehn functions of Abelian groups

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The Cuntz semigroup, the Elliott conjecture, and dimension functions on C*-Algebras

We prove that the Cuntz semigroup is recovered functorially from the Elliott invariant for a large class of C¤-algebras. In particular, our results apply to the largest class of simple C¤-algebras for which K-theoretic classification can be hoped for. This work has three significant consequences. First, it provides new conceptual insight into Elliott's classification program, proving that the usual form of the Elliott conjecture is equivalent, among Z-stable algebras, to a conjecture which is in general substantially weaker and for which there are no known counterexamples. Second and third, it resolves, for the class of algebras above, two conjectures of Blackadar and Handelman concerning the basic structure of dimension functions on C¤-algebras. We also prove in passing that the Kuntz-Pedersen semigroup is recovered functorially from the Elliott invariant for all simple unital C¤-algebras of interest.

Characterisation of neutron spectra in mixed high energy fields in lineal accelerators: response functions validation

Actualment, la resposta de la majoria d’instrumentació operacional i dels dosímetres personals utilitzats en radioprotecció per a la dosimetria neutrònica és altament dependent de l’energia dels espectres neutrònics a analitzar, especialment amb camps neutrònics amb una important component intermitja. En conseqüència, la interpretació de les lectures d’aquests aparells es complicada si no es té un coneixement previ de la distribució espectral de la fluència neutrònica en els punts d’interès. El Grup de Física de les Radiacions de la Universitat Autònoma de Barcelona (GFR-UAB) ha desenvolupat en els últims anys un espectròmetre de neutrons basat en un Sistema d’Esferes Bonner (BSS) amb un contador proporcional d’3He com a detector actiu. Els principals avantatges dels espectròmetres de neutrons per BSS són: la seva resposta isotròpica, la possibilitat de discriminar la component neutrònica de la gamma en camps mixtos, i la seva alta sensibilitat neutrònica als nivells de dosi analitzats. Amb aquestes característiques, els espectròmetres neutrònics per BSS compleixen amb els estándards de les últimes recomanacions de la ICRP i poden ser utilitzats també en el camp de la dosimetria neutrònica per a la mesura de dosis en el rang d’energia que va dels tèrmics fins als 20 MeV, en nou ordres de magnitud. En el marc de la col•laboració entre el GFR - UAB i el Laboratorio Nazionale di Frascati – Istituto Nazionale di Fisica Nucleare (LNF-INFN), ha tingut lloc una experiència comparativa d’espectrometria per BSS amb els feixos quasi monoenergètics de 2.5 MeV i 14 MeV del Fast Neutron Generator de l’ENEA. En l’exercici s’ha determinat l’espectre neutrònic a diferents distàncies del blanc de l’accelerador, aprofitant el codi FRUIT recentment desenvolupat pel grup LNF. Els resultats obtinguts mostren una bona coherència entre els dos espectròmetres i les dades mesurades i simulades.

Calibration of CES functions for real-world multisectoral modeling

We show how to calibrate CES production and utility functions when indirect taxation affecting inputs and consumption is present. These calibrated functions can then be used in computable general equilibrium models. Taxation modifies the standard calibration procedures since any taxed good has two associated prices and a choice of reference value units has to be made. We also provide an example of computer code to solve the calibration of CES utilities under two alternate normalizations. To our knowledge, this paper fills a methodological gap in the CGE literature.

Generalized factor models: a bayesian approach

There is recent interest in the generalization of classical factor models in which the idiosyncratic factors are assumed to be orthogonal and there are identification restrictions on cross-sectional and time dimensions. In this study, we describe and implement a Bayesian approach to generalized factor models. A flexible framework is developed to determine the variations attributed to common and idiosyncratic factors. We also propose a unique methodology to select the (generalized) factor model that best fits a given set of data. Applying the proposed methodology to the simulated data and the foreign exchange rate data, we provide a comparative analysis between the classical and generalized factor models. We find that when there is a shift from classical to generalized, there are significant changes in the estimates of the structures of the covariance and correlation matrices while there are less dramatic changes in the estimates of the factor loadings and the variation attributed to common factors.

Characterizations of Lojasiewicz inequalities and applications

The classical Lojasiewicz inequality and its extensions for partial differential equation problems (Simon) and to o-minimal structures (Kurdyka) have a considerable impact on the analysis of gradient-like methods and related problems: minimization methods, complexity theory, asymptotic analysis of dissipative partial differential equations, tame geometry. This paper provides alternative characterizations of this type of inequalities for nonsmooth lower semicontinuous functions defined on a metric or a real Hilbert space. In a metric context, we show that a generalized form of the Lojasiewicz inequality (hereby called the Kurdyka- Lojasiewicz inequality) relates to metric regularity and to the Lipschitz continuity of the sublevel mapping, yielding applications to discrete methods (strong convergence of the proximal algorithm). In a Hilbert setting we further establish that asymptotic properties of the semiflow generated by -∂f are strongly linked to this inequality. This is done by introducing the notion of a piecewise subgradient curve: such curves have uniformly bounded lengths if and only if the Kurdyka- Lojasiewicz inequality is satisfied. Further characterizations in terms of talweg lines -a concept linked to the location of the less steepest points at the level sets of f- and integrability conditions are given. In the convex case these results are significantly reinforced, allowing in particular to establish the asymptotic equivalence of discrete gradient methods and continuous gradient curves. On the other hand, a counterexample of a convex C2 function in R2 is constructed to illustrate the fact that, contrary to our intuition, and unless a specific growth condition is satisfied, convex functions may fail to fulfill the Kurdyka- Lojasiewicz inequality.

Foundations for contest success functions

In the literature the outcome of contests is either interpreted as win probabilities or as shares of the prize. With this in mind, we examine two approaches to contest success functions. In the first we analyze the implications of contestants' incomplete information concerning the "type" of the contest administrator. While in the case of two contestants this approach can rationalize prominent contest success functions, we show that it runs into difficulties when there are more agents. Our second approach interprets contest success functions as sharing rules and establishes a connection to bargaining and claims problems which is independent of the number of contestants. Both approaches provide foundations for popular contest success functions and guidelines for the definition of new ones. Keywords: Endogenous Contests, Contest Success Function. JEL Classification: C72 (Noncooperative Games), D72 (Economic Models of Political Processes: Rent-Seeking, Elections), D74 (Conflict; Conflict Resolution; Alliances).

Analytic approximation of matrix functions in Lp

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