Metrics on diagram groups and uniform embeddings in a Hilbert space

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

On uniform conjugators in torsion-free hyperbolic groups

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

Solidarity and uniform rules in bankruptcy problems

The idea of ensuring a guarantee (a minimum amount of the resources) to each agent has recently acquired great relevance, in both social and politi- cal terms. Furthermore, the notion of Solidarity has been treated frequently in redistribution problems to establish that any increment of the resources should be equally distributed taking into account some relevant characteris- tics. In this paper, we combine these two general concepts, guarantee and solidarity, to characterize the uniform rules in bankruptcy problems (Con- strained Equal Awards and Constrained Equal Losses rules). Keywords: Constrained Equal Awards, Constrained Equal Losses, Lower bounds, Bankruptcy problems, Solidarity. JEL classification: C71, D63, D71.

Uniform estimates in the Poincare-Aronszajn theorem on the separation of singularities of analytic functions

We study the possibility of splitting any bounded analytic function $f$ with singularities in a closed set $E\cup F$ as a sum of two bounded analytic functions with singularities in $E$ and $F$ respectively. We obtain some results under geometric restrictions on the sets $E$ and $F$ and we provide some examples showing the sharpness of the positive results.

Candidate counterparts to the soft gamma-ray flare in the direction od LSI+61303

A short duration burst reminiscent of a soft gamma-ray repeater/anomalous X-ray pulsar behaviour was detected in the direction of LS I +61 303 by the Swift satellite. While the association with this well known gamma-ray binary is likely, a different origin cannot be excluded. Aims. We explore the error box of this unexpected flaring event and establish the radio, near-infrared and X-ray sources in our search for any peculiar alternative counterpart. Methods. We carried out a combined analysis of archive Very Large Array radio data of LS I +61 303 sensitive to both compact and extended emission. We also reanalysed previous near infrared observations with the 3.5 m telescope of the Centro Astronómico Hispano Alemán and X-ray observations with the Chandra satellite. Results. Our deep radio maps of the LS I +61 303 environment represent a significant advancement on previous work and 16 compact radio sources in the LS I +61 303 vicinity are detected. For some detections, we also identify near infrared and X-ray counterparts. Extended emission features in the field are also detected and confirmed. The possible connection of some of these sources with the observed flaring event is considered. Based on these data, we are unable to claim a clear association between the Swift-BAT flare and any of the sources reported here. However, this study represents the most sophisticated attempt to determine possible alternative counterparts other than LS I +61 303.

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.

Stability and manipulation in representative democracies

This paper is devoted to the analysis of all constitutions equipped with electoral systems involving two step procedures. First, one candidate is elected in every jurisdiction by the electors in that jurisdiction, according to some aggregation procedure. Second, another aggregation procedure collects the names of the jurisdictional winners in order to designate the final winner. It appears that whenever individuals are allowed to change jurisdiction when casting their ballot, they are able to manipulate the result of the election except in very few cases. When imposing a paretian condition on every jurisdictions voting rule, it is shown that, in the case of any finite number of candidates, any two steps voting rule that is not manipulable by movement of the electors necessarily gives to every voter the power of overruling the unanimity on its own. A characterization of the set of these rules is next provided in the case of two candidates.

The role of fixed delays in neuronal rate models

Fixed delays in neuronal interactions arise through synaptic and dendritic processing. Previous work has shown that such delays, which play an important role in shaping the dynamics of networks of large numbers of spiking neurons with continuous synaptic kinetics, can be taken into account with a rate model through the addition of an explicit, fixed delay. Here we extend this work to account for arbitrary symmetric patterns of synaptic connectivity and generic nonlinear transfer functions. Specifically, we conduct a weakly nonlinear analysis of the dynamical states arising via primary instabilities of the stationary uniform state. In this way we determine analytically how the nature and stability of these states depend on the choice of transfer function and connectivity. While this dependence is, in general, nontrivial, we make use of the smallness of the ratio in the delay in neuronal interactions to the effective time constant of integration to arrive at two general observations of physiological relevance. These are: 1 - fast oscillations are always supercritical for realistic transfer functions. 2 - Traveling waves are preferred over standing waves given plausible patterns of local connectivity.

Failure mechanism under tensile loads in CFRP 0-90º cross-ply laminates containing voids

The failure mechanism of a voided CFRP 0-90° cross-ply laminate under tensile loads applied in one direction was studied in this Final Degree Project. For this purpose, voided coupons were manufactured for being tested and a FEA was done. In both investigations, voids were placed in 90º and 0º direction, in order to understand the void location influence. On the one hand, the behaviour of the voided laminates was investigated through a FEM in order to preview the stress distribution within the material. On the other hand, voided specimens where manufactured by applying blowing agent in between the inner layers. These specimens were tested by a quasi-static step wise tensile test where data showing its real behaviour was collected. Specimens were X-rayed after each step of the test in order to investigate the failure mechanism of the composite. Data from the test was studied so that relations such as strength of the laminates, crack density per stress, void length per first crack at the void and void area per first crack at the specimen could be characterized

Resource management research in Passive Optical Networks (PON)

Next Generation Access Networks (NGAN) are the new step forward to deliver broadband services and to facilitate the integration of different technologies. It is plausible to assume that, from a technological standpoint, the Future Internet will be composed of long-range high-speed optical networks; a number of wireless networks at the edge; and, in between, several access technologies, among which, the Passive Optical Networks (xPON) are very likely to succeed, due to their simplicity, low-cost, and increased bandwidth. Among the different PON technologies, the Ethernet-PON (EPON) is the most promising alternative to satisfy operator and user needs, due to its cost, flexibility and interoperability with other technologies. One of the most interesting challenges in such technologies relates to the scheduling and allocation of resources in the upstream (shared) channel. The aim of this research project is to study and evaluate current contributions and propose new efficient solutions to address the resource allocation issues in Next Generation EPON (NG-EPON). Key issues in this context are future end-user needs, integrated quality of service (QoS) support and optimized service provisioning for real time and elastic flows. This project will unveil research opportunities, issue recommendations and propose novel mechanisms associated with the convergence within heterogeneous access networks and will thus serve as a basis for long-term research projects in this direction. The project has served as a platform for the generation of new concepts and solutions that were published in national and international conferences, scientific journals and also in book chapter. We expect some more research publications in addition to the ones mentioned to be generated in a few months.

Opportunities for a cultural specific approach in the computational description of music

The current research in Music Information Retrieval (MIR) is showing the potential that the Information Technologies can have in music related applications. Amajor research challenge in that direction is how to automaticallydescribe/annotate audio recordings and how to use the resulting descriptions to discover and appreciate music in new ways. But music is a complex phenomenonand the description of an audio recording has to deal with this complexity. For example, each musicculture has specificities and emphasizes different musicaland communication aspects, thus the musical recordings of each culture should be described differently. At the same time these cultural specificities give us the opportunity to pay attention to musical concepts andfacets that, despite being present in most world musics, are not easily noticed by listeners. In this paper we present some of the work done in the CompMusic project, including ideas and specific examples on how to take advantage of the cultural specificities of differentmusical repertoires. We will use examples from the art music traditions of India, Turkey and China.

Equilibrium asset prices and savings of heterogeneous agents in the presence of incomplete markets and portfolio constraints

We study the quantitative properties of a dynamic general equilibrium model in which agents face both idiosyncratic and aggregate income risk, state-dependent borrowing constraints that bind in some but not all periods and markets are incomplete. Optimal individual consumption-savings plans and equilibrium asset prices are computed under various assumptions about income uncertainty. Then we investigate whether our general equilibrium model with incomplete markets replicates two empirical observations: the high correlation between individual consumption and individual income, and the equity premium puzzle. We find that, when the driving processes are calibrated according to the data from wage income in different sectors of the US economy, the results move in the direction of explaining these observations, but the model falls short of explaining the observed correlations quantitatively. If the incomes of agents are assumed independent of each other, the observations can be explained quantitatively.

Wage structures and family economies in the Catalan textile industry in an age of nascent capitalism

This paper deals with changes in managerial practices in Catalonia in anage of nascent capitalism (1830-1925) and adaptive family strategies inorder to face the absence of state welfare. During the 19 t h Century andin the absence of recorded labor contracts, human resources of the firmwere organized by means of implicit contracts and informal labor markets.With the advent of scientific organization of labor, wage per hour workedbegan to be recorded. This is why in the 1920s the perfect competitionmodel applies to our case. On the other hand, in the same period, and inthe absence of state welfare, ideas stemming from cooperative game theoryapply to the pattern of household income formation. Kin related networkswere used to improve the living standards of the household. In thisparticular direction we also show that there was a demonstration effectby means of which migrant s living standards were higher than those ofnatives.

Dissipation in quasistatically driven disordered systems

This work presents an analysis of hysteresis and dissipation in quasistatically driven disordered systems. The study is based on the random field Ising model with fluctuationless dynamics. It enables us to sort out the fraction of the energy input by the driving field stored in the system and the fraction dissipated in every step of the transformation. The dissipation is directly related to the occurrence of avalanches, and does not scale with the size of Barkhausen magnetization jumps. In addition, the change in magnetic field between avalanches provides a measure of the energy barriers between consecutive metastable states

Exchange-correlation effects on quantum wires with spin-orbit interactions under the influence of in-plane magnetic fields.

Within the noncollinear local spin-density approximation, we have studied the ground state structure of a parabolically confined quantum wire submitted to an in-plane magnetic field, including both Rashba and Dresselhaus spin-orbit interactions. We have explored a wide range of linear electronic densities in the weak (strong) coupling regimes that appear when the ratio of spin-orbit to confining energy is small (large). These results are used to obtain the conductance of the wire. In the strong coupling limit, the interplay between the applied magnetic field¿irrespective of the in-plane direction, the exchange-correlation energy, and the spin-orbit energy-produces anomalous plateaus in the conductance vs linear density plots that are otherwise absent, or washes out plateaus that appear when the exchange-correlation energy is not taken into account.