Mixed Hodge structures and vector bundles on the projective Plane I

We describe an equivalence of categories between the category of mixed Hodge structures and a category of vector bundles on the toric complex projective plane which verify some semistability condition. We then apply this correspondence to define an invariant which generalises the notion of R-split mixed Hodge structure and compute extensions in the category of mixed Hodge structures in terms of extensions of the corresponding vector bundles. We also give a relative version of this correspondence and apply it to define stratifications of the bases of the variations of mixed Hodge structure.

Can genetic algorithms explain experimental anomalies? An application to common property resources

It is common to find in experimental data persistent oscillations in the aggregate outcomes and high levels of heterogeneity in individual behavior. Furthermore, it is not unusual to find significant deviations from aggregate Nash equilibrium predictions. In this paper, we employ an evolutionary model with boundedly rational agents to explain these findings. We use data from common property resource experiments (Casari and Plott, 2003). Instead of positing individual-specific utility functions, we model decision makers as selfish and identical. Agent interaction is simulated using an individual learning genetic algorithm, where agents have constraints in their working memory, a limited ability to maximize, and experiment with new strategies. We show that the model replicates most of the patterns that can be found in common property resource experiments.

Optimal regulation of specialized medical care in a mixed system

We study the optimal public intervention in setting minimum standards of formation for specialized medical care. The abilities the physicians obtain by means of their training allow them to improve their performance as providers of cure and earn some monopoly rents.. Our aim is to characterize the most efficient regulation in this field taking into account different regulatory frameworks. We find that the existing situation in some countries, in which the amount of specialization is controlled, and the costs of this process of specialization are publicly financed, can be supported as the best possible intervention.

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.

Real rank zero algebras have the corona factorization property

The purpose of this short note is to prove that a stable separable C*-algebra with real rank zero has the so-called corona factorization property, that is, all the full multiplier projections are properly in finite. Enroute to our result, we consider conditions under which a real rank zero C*-algebra admits an injection of the compact operators (a question already considered in [21]).

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.

Pure motives, mixed motives and extensions of motives associated to singular surfaces

We first recall the construction of the Chow motive modelling intersection cohomology of a proper surface X and study its fundamental properties. Using Voevodsky's category of effective geometrical motives, we then study the motive of the exceptional divisor D in a non-singular blow-up of X. If all geometric irreducible components of D are of genus zero, then Voevodsky's formalism allows us to construct certain one-extensions of Chow motives, as canonical subquotients of the motive with compact support of the smooth part of X. Specializing to Hilbert-Blumenthal surfaces, we recover a motivic interpretation of a recent construction of A. Caspar.

Subgroups of small index in Aut(Fn) and Kazhdan's property (T)

We give a series of interesting subgroups of finite index in Aut(Fn). One of them has index 42 in Aut(F3) and infinite abelianization. This implies that Aut(F3) does not have Kazhdan’s property (T) (see [3] and [6] for another proofs). We proved also that every subgroup of finite index in Aut(Fn), n &= 3, which contains the subgroup of IA-automorphisms, has a finite abelianization.

A mixed finite element method for nonlinear diffusion equations

We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model.

A mixed splicing procedure for economic time series

This note develops a flexible methodology for splicing economic time series that avoids the extreme assumptions implicit in the procedures most commonly used in the literature. It allows the user to split the required correction to the older of the series being linked between its levels and growth rates on the basis what he knows or conjectures about the persistence of the factors that account for the discrepancy between the two series that emerges at their linking point. The time profile of the correction is derived from the assumption that the error in the older series reflects the inadequate coverage of emerging sectors or activities that grow faster than the aggregate.

Endogenous Mergers of Complements with Mixed Bundling

This paper studies endogenous mergers of complements with mixed bundling, by allowing both for joint and separate consumption. After merger, partner fi…rms decrease the price of the bundled system. Besides, when markets for individual components are suffi…ciently important, partner …firms raise prices of stand-alone products, exploiting their monopoly power in local markets and making substitute 'mix-and-match' composite products less attractive to consumers. Even though these effects favor the pro…fitability of mergers, merging is not always an equilibrium outcome. The reason is that outsiders respond by cutting their prices to retain their market share, and mergers can be unprofitable when competition is intense. From a welfare analysis, we observe that the number of mergers observed in equilibrium may be either excessive (when markets for individual components are important) or suboptimal (when markets for individual components are less important). Keywords: complements; merger; mixed bundling; separate consumption JEL classi…fication: L13; L41; D43

On finite unions and finite products with the D-property

We show that the product of a subparacompact C-scattered space and a Lindelöf D-space is D. In addition, we show that every regular locally D-space which is the union of a finite collection of subparacompact spaces and metacompact spaces has the D-property. Also, we extend this result from the class of locally D-spaces to the wider class of D-scattered spaces. All the results are shown in a direct way.

On slicewise monotone parameterized problems and optimal proof systems for TAUT

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

Reduction theorems for operators on the cones of monotone functions

For a quasilinear operator on the semiaxis a reduction theorem is proved on the cones of monotone functions in Lp - Lq setting for 0 < q < ∞, 1<= p < ∞. The case 0 < p < 1 is also studied for operators with additional properties. In particular, we obtain critera for three-weight inequalities for the Hardy-type operators with Oinarov' kernel on monotone functions in the case 0 < q < p <= 1.

Opening Education Beyond the Property Relation: From Commons to Communism

Open Education, and specifically the OER movement, seeks to provide universal access to knowledge, undermining the historical enclosure and the increasing privatisation of the public education system. In this paper we examine this aspiration by submitting the implicit theoretical assumptions of Open Education to the test of critical political economy. We acknowledge the Open Education movement's revolutionary potential but outline the inherent limitations of its current focus on the commons (property relations) rather than the social relations of capitalist production (wage work, the company) and because of this, argue that it will only achieve limited, rather than revolutionary, impact.