Clarke critical values of subanalytic Lipschitz continuous functions

We prove that any subanalytic locally Lipschitz function has the Sard property. Such functions are typically nonsmooth and their lack of regularity necessitates the choice of some generalized notion of gradient and of critical point. In our framework these notions are defined in terms of the Clarke and of the convex-stable subdifferentials. The main result of this note asserts that for any subanalytic locally Lipschitz function the set of its Clarke critical values is locally finite. The proof relies on Pawlucki's extension of the Puiseuxlemma. In the last section we give an example of a continuous subanalytic function which is not constant on a segment of "broadly critical" points, that is, points for which we can find arbitrarily short convex combinations of gradients at nearby points.

Elicited bid functions in (a)symmetric first-price auctions

We report on a series of experiments that examine bidding behavior in first-price sealed bid auctions with symmetric and asymmetric bidders. To study the extent of strategic behavior, we use an experimental design that elicits bidders' complete bid functions in each round (auction) of the experiment. In the aggregate, behavior is consistent with the basic equilibrium predictions for risk neutral or homogenous risk averse bidders (extent of bid shading, average seller's revenues and deviations from equilibrium). However, when we look at the extent of best reply behavior and the shape of bid functions, we find that individual behavior is not in line with the received equilibrium models, although it exhibits strategic sophistication.

Increasing quasiconcave production and utility functions with diminishing returns to scale

In microeconomic analysis functions with diminishing returns to scale (DRS) have frequently been employed. Various properties of increasing quasiconcave aggregator functions with DRS are derived. Furthermore duality in the classical sense as well as of a new type is studied for such aggregator functions in production and consumer theory. In particular representation theorems for direct and indirect aggregator functions are obtained. These involve only small sets of generator functions. The study is carried out in the contemporary framework of abstract convexity and abstract concavity.

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.

Endogenous population subgroups: the best population partition and optimal number of groups

The aim of this paper is to suggest a method to find endogenously the points that group the individuals of a given distribution in k clusters, where k is endogenously determined. These points are the cut-points. Thus, we need to determine a partition of the N individuals into a number k of groups, in such way that individuals in the same group are as alike as possible, but as distinct as possible from individuals in other groups. This method can be applied to endogenously identify k groups in income distributions: possible applications can be poverty

Shellability of noncrossing partition lattices

We give a case-free proof that the lattice of noncrossing partitions associated to any finite real reflection group is EL-shellable. Shellability of these lattices was open for the groups of type Dn and those of exceptional type and rank at least three.

Inverse Problems for multiple invariant curves

Planar polynomial vector fields which admit invariant algebraic curves, Darboux integrating factors or Darboux first integrals are of special interest. In the present paper we solve the inverse problem for invariant algebraic curves with a given multiplicity and for integrating factors, under generic assumptions regarding the (multiple) invariant algebraic curves involved. In particular we prove, in this generic scenario, that the existence of a Darboux integrating factor implies Darboux integrability. Furthermore we construct examples where the genericity assumption does not hold and indicate that the situation is different for these.

The mean dehn functions of Abelian groups

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

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.

Well-posedness and invariant measures for HJM models with deterministic volatility and Lévy noise

We give sufficient conditions for existence, uniqueness and ergodicity of invariant measures for Musiela's stochastic partial differential equation with deterministic volatility and a Hilbert space valued driving Lévy noise. Conditions for the absence of arbitrage and for the existence of mild solutions are also discussed.

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.

Invariants de matrius Hadamard en MAGMA

L'objectiu d'aquest projecte ha estat generalitzar i integrar la funcionalitat de dos projectes anteriors que ampliaven el tractament que oferia el Magma respecte a les matrius de Hadamard. Hem implementat funcions genèriques que permeten construir noves matrius Hadamard de qualsevol mida per a cada rang i dimensió de nucli, i així ampliar la seva base de dades. També hem optimitzat la funció que calcula el nucli, i hem desenvolupat funcions que calculen la invariant Symmetric Hamming Distance Enumerator (SH-DE) proposada per Kai-Tai Fang i Gennian Gei que és més sensible per a la detecció de la no equivalència de les matrius Hadamard.