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.

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.

On moduli of smoothness of fractional order

In this paper we consider the properties of moduli of smoothness of fractional order. The main result of the paper describes the equivalence of the modulus of smoothness and a function from some class.

Limit Cycles for a class of three dimensional polynomial differential systems

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The mean dehn functions of Abelian groups

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┴N as an Abstract Elementary Class

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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.

A class of stochastic games with infinitely many interacting agents related to Glauber dynamics on random graphs

We introduce and study a class of infinite-horizon nonzero-sum non-cooperative stochastic games with infinitely many interacting agents using ideas of statistical mechanics. First we show, in the general case of asymmetric interactions, the existence of a strategy that allows any player to eliminate losses after a finite random time. In the special case of symmetric interactions, we also prove that, as time goes to infinity, the game converges to a Nash equilibrium. Moreover, assuming that all agents adopt the same strategy, using arguments related to those leading to perfect simulation algorithms, spatial mixing and ergodicity are proved. In turn, ergodicity allows us to prove “fixation”, i.e. that players will adopt a constant strategy after a finite time. The resulting dynamics is related to zerotemperature Glauber dynamics on random graphs of possibly infinite volume.

On locally finite transitive two-ended digraphs

Projecte de recerca elaborat a partir d’una estada al Department de Matemàtica Aplicada de la Montanuniversität Leoben, Àustria, entre agost i desembre del 2006. L’ objectiu ha estat fer recerca sobre digrafs infinits amb dos finals, connexos i localment finits, i, en particular, en digrafs amb dos finals i altament arc-transitius. Malnic, Marusic et al. van introduir un nou tipus de relació d’equivalència en els vèrtexs d’un dígraf, anomenades relacions d’assolibilitat, que generalitzen i tenen el seu origen en un problema posat per Cameron et al., on les classes de la relació d’equivalència eren vèrtexs que pertanyien a un camí alternat del dígraf . Malnic et al. en el mencionat article van establir connexions ben estretes entre aquestes relacions d’assolibilitat i l'estructura de finals i creixement dels digrafs localment finits i transitius. En aquest treball, s’ha caracteritzat per complet aquestes relacions d’assolibitat en el cas de dígrafs localment finits i transitius amb exactament dos finals, en termes de la descomposició en números primers del número de línies que genera el digraf amb dos finals. A més, es nega la Conjectura 1 sostinguda per Seifter que afirmava que un digraf connex localment finit amb més d’un final era necessàriament o be 0-, 1- o altament arc-transitiu. Seifer havia donat una solució parcial a la conjectura pel cas de digrafs regulars amb grau primer que tinguin un conjunt de tall connex. En aquest treball, es descriu una família infinita de dígrafs regulars de grau dos, amb dos finals, exactament 2-arc transitius i no 3-arc transitius. Així, es nega la Conjectura de Seifter en el cas general, fins i tot per grau primer. Tot i així, la solució parcial donada per Seifter en el seu article és en cert sentit la millor possible i l'existència un conjunt de tall connex essencial.

Heteroclinic orbits for a class of Hamiltonian systems on Riemannian manifolds

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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).

Generalized multiresolution analyses with given multiplicity functions

Generalized multiresolution analyses are increasing sequences of subspaces of a Hilbert space H that fail to be multiresolution analyses in the sense of wavelet theory because the core subspace does not have an orthonormal basis generated by a fixed scaling function. Previous authors have studied a multiplicity function m which, loosely speaking, measures the failure of the GMRA to be an MRA. When the Hilbert space H is L2(Rn), the possible multiplicity functions have been characterized by Baggett and Merrill. Here we start with a function m satisfying a consistency condition which is known to be necessary, and build a GMRA in an abstract Hilbert space with multiplicity function m.