Stable coalition structures with fixed decision scheme

This paper studies the stability of a finite local public goods economy in horizontal differentiation, where a jurisdiction's choice of the public good is given by an exogenous decision scheme. In this paper, we characterize the class of decision schemes that ensure the existence of an equilibrium with free mobility (that we call Tiebout equilibrium) for monotone distribution of players. This class contains all the decision schemes whose choice lies between the Rawlsian decision scheme and the median voter with mid-distance of the two median voters when there are ties. We show that for non-monotone distribution, there is no decision scheme that can ensure the stability of coalitions. In the last part of the paper, we prove the non-emptiness of the core of this coalition formation game

Non compact euclidean cone 3-manifolds with cone angles less than 2∏

We study of noncompact Euclidean cone manifolds with cone angles less than c&2π and singular locus a submanifold. More precisely, we describe its structure outside a compact set. As a corol lary we classify those with cone angles & 2π/3 and those with cone angles = 2π/3.

Convergence of the mass-transport steepest descent scheme for the sub-critical Patlak-Keller-Segel model

Variational steepest descent approximation schemes for the modified Patlak-Keller-Segel equation with a logarithmic interaction kernel in any dimension are considered. We prove the convergence of the suitably interpolated in time implicit Euler scheme, defined in terms of the Euclidean Wasserstein distance, associated to this equation for sub-critical masses. As a consequence, we recover the recent result about the global in time existence of weak-solutions to the modified Patlak-Keller-Segel equation for the logarithmic interaction kernel in any dimension in the sub-critical case. Moreover, we show how this method performs numerically in one dimension. In this particular case, this numerical scheme corresponds to a standard implicit Euler method for the pseudo-inverse of the cumulative distribution function. We demonstrate its capabilities to reproduce easily without the need of mesh-refinement the blow-up of solutions for super-critical masses.

Parametric analysis of different compact tension specimens for fracture toughness characterisation in woven composite materials

Estudi elaborat a partir d’una estada a l’ Imperial College London, entre juliol i novembre de 2006. En aquest treball s’ha investigat la geometria més apropiada per a la caracterització de la tenacitat a fractura intralaminar de materials compòsits laminats amb teixit. L’objectiu és assegurar la propagació de l’esquerda sense que la proveta falli abans per cap altre mecanisme de dany per tal de permetre la caracterització experimental de la tenacitat a fractura intralaminar de materials compòsits laminats amb teixit. Amb aquesta fi, s’ha dut a terme l’anàlisi paramètrica de diferents tipus de provetes mitjançant el mètode dels elements finits (FE) combinat amb la virtual crack closure technique (VCCT). Les geometries de les provetes analitzades corresponen a la proveta de l’assaig compact tension (CT) i diferents variacions com la extended compact tension (ECT), la proveta widened compact tension (WCT), tapered compact tension (TCT) i doubly-tapered compact tension (2TCT). Com a resultat d’aquestes anàlisis s’han derivat diferents conclusions per obtenir la geometria de proveta més apropiada per a la caracterització de la tenacitat a fractura intralaminar de materials compòsits laminats amb teixit. A més, també s’han dut a terme una sèrie d’assaigs experimentals per tal de validar els resultats de les anàlisis paramètriques. La concordança trobada entre els resultats numèrics i experimentals és bona tot i la presència d’efectes no previstos durant els assaigs experimentals.

Persistent bundles over a two dimensional compact set

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

Stabilized Petrov-Galerkin methods for the convection-diffusion-reaction and the Helmholtz equations

We present two new stabilized high-resolution numerical methods for the convection–diffusion–reaction (CDR) and the Helmholtz equations respectively. The work embarks upon a priori analysis of some consistency recovery procedures for some stabilization methods belonging to the Petrov–Galerkin framework. It was found that the use of some standard practices (e.g. M-Matrices theory) for the design of essentially non-oscillatory numerical methods is not feasible when consistency recovery methods are employed. Hence, with respect to convective stabilization, such recovery methods are not preferred. Next, we present the design of a high-resolution Petrov–Galerkin (HRPG) method for the 1D CDR problem. The problem is studied from a fresh point of view, including practical implications on the formulation of the maximum principle, M-Matrices theory, monotonicity and total variation diminishing (TVD) finite volume schemes. The current method is next in line to earlier methods that may be viewed as an upwinding plus a discontinuity-capturing operator. Finally, some remarks are made on the extension of the HRPG method to multidimensions. Next, we present a new numerical scheme for the Helmholtz equation resulting in quasi-exact solutions. The focus is on the approximation of the solution to the Helmholtz equation in the interior of the domain using compact stencils. Piecewise linear/bilinear polynomial interpolation are considered on a structured mesh/grid. The only a priori requirement is to provide a mesh/grid resolution of at least eight elements per wavelength. No stabilization parameters are involved in the definition of the scheme. The scheme consists of taking the average of the equation stencils obtained by the standard Galerkin finite element method and the classical finite difference method. Dispersion analysis in 1D and 2D illustrate the quasi-exact properties of this scheme. Finally, some remarks are made on the extension of the scheme to unstructured meshes by designing a method within the Petrov–Galerkin framework.

A quality-based cost distribution charging scheme for QoS multicast networks

This paper presents a new charging scheme for cost distribution along a point-to-multipoint connection when destination nodes are responsible for the cost. The scheme focus on QoS considerations and a complete range of choices is presented. These choices go from a safe scheme for the network operator to a fair scheme to the customer. The in-between cases are also covered. Specific and general problems, like the incidence of users disconnecting dynamically is also discussed. The aim of this scheme is to encourage the users to disperse the resource demand instead of having a large number of direct connections to the source of the data, which would result in a higher than necessary bandwidth use from the source. This would benefit the overall performance of the network. The implementation of this task must balance between the necessity to offer a competitive service and the risk of not recovering such service cost for the network operator. Throughout this paper reference to multicast charging is made without making any reference to any specific category of service. The proposed scheme is also evaluated with the criteria set proposed in the European ATM charging project CANCAN

A behavior-based scheme using reinforcement learning for autonomous underwater vehicles

This paper presents a hybrid behavior-based scheme using reinforcement learning for high-level control of autonomous underwater vehicles (AUVs). Two main features of the presented approach are hybrid behavior coordination and semi on-line neural-Q_learning (SONQL). Hybrid behavior coordination takes advantages of robustness and modularity in the competitive approach as well as efficient trajectories in the cooperative approach. SONQL, a new continuous approach of the Q_learning algorithm with a multilayer neural network is used to learn behavior state/action mapping online. Experimental results show the feasibility of the presented approach for AUVs

Medium access control messaging scheme for cognitive radio networks

Los sistemas de radio cognitivos son una solución a la deficiente distribución del espectro inalámbrico de frecuencias. Usando acceso dinámico al medio, los usuarios secundarios pueden comunicarse en canales de frecuencia disponibles, mientras los usuarios asignados no están usando dichos canales. Un buen sistema de mensajería de control es necesario para que los usuarios secundarios no interfieran con los usuarios primarios en las redes de radio cognitivas. Para redes en donde los usuarios son heterogéneos en frecuencia, es decir, no poseen los mismos canales de frecuencia para comunicarse, el grupo de canales utilizado para transmitir información de control debe elegirse cuidadosamente. Por esta razón, en esta tesis se estudian las ideas básicas de los esquemas de mensajería de control usados en las redes de radio cognitivas y se presenta un esquema adecuado para un control adecuado para usuarios heterogéneos en canales de frecuencia. Para ello, primero se presenta una nueva taxonomía para clasificar las estrategias de mensajería de control, identificando las principales características que debe cumplir un esquema de control para sistemas heterogéneos en frecuencia. Luego, se revisan diversas técnicas matemáticas para escoger el mínimo número de canales por los cuales se transmite la información de control. Después, se introduce un modelo de un esquema de mensajería de control que use el mínimo número de canales y que utilice las características de los sistemas heterogéneos en frecuencia. Por último, se comparan diversos esquemas de mensajería de control en términos de la eficiencia de transmisión.

L2−estimates for the DG IIPG-0 scheme

We discuss the optimality in L2 of a variant of the Incomplete Discontinuous Galerkin Interior Penalty method (IIPG) for second order linear elliptic problems. We prove optimal estimate, in two and three dimensions, for the lowest order case under suitable regularity assumptions on the data and on the mesh. We also provide numerical evidence, in one dimension, of the necessity of the regularity assumptions.

Additional compact formulas for vibrational dynamic dipole polarizabilities and hyperpolarizabilities

Compact expressions, complete through second order in electrical and/or mechanical anharmonicity, are given for the dynamic dipole vibrational polarizability and dynamic first and second vibrational hyperpolarizabilities. Certain contributions not previously formulated are now included

On the computational security of a distributed key distribution scheme

In a distributed key distribution scheme, a set of servers helps a set of users in a group to securely obtain a common key. Security means that an adversary who corrupts some servers and some users has no information about the key of a noncorrupted group. In this work, we formalize the security analysis of one such scheme which was not considered in the original proposal. We prove the scheme is secure in the random oracle model, assuming that the Decisional Diffie-Hellman (DDH) problem is hard to solve. We also detail a possible modification of that scheme and the one in which allows us to prove the security of the schemes without assuming that a specific hash function behaves as a random oracle. As usual, this improvement in the security of the schemes is at the cost of an efficiency loss.

A new compact linear programming formulation for choice network revenue management

The choice network revenue management model incorporates customer purchase behavioras a function of the offered products, and is the appropriate model for airline and hotel networkrevenue management, dynamic sales of bundles, and dynamic assortment optimization.The optimization problem is a stochastic dynamic program and is intractable. A certainty-equivalencerelaxation of the dynamic program, called the choice deterministic linear program(CDLP) is usually used to generate dyamic controls. Recently, a compact linear programmingformulation of this linear program was given for the multi-segment multinomial-logit (MNL)model of customer choice with non-overlapping consideration sets. Our objective is to obtaina tighter bound than this formulation while retaining the appealing properties of a compactlinear programming representation. To this end, it is natural to consider the affine relaxationof the dynamic program. We first show that the affine relaxation is NP-complete even for asingle-segment MNL model. Nevertheless, by analyzing the affine relaxation we derive a newcompact linear program that approximates the dynamic programming value function betterthan CDLP, provably between the CDLP value and the affine relaxation, and often comingclose to the latter in our numerical experiments. When the segment consideration sets overlap,we show that some strong equalities called product cuts developed for the CDLP remain validfor our new formulation. Finally we perform extensive numerical comparisons on the variousbounds to evaluate their performance.

Compact matrix expressions for generalized Wald tests of equality of moment vectors

Asymptotic chi-squared test statistics for testing the equality ofmoment vectors are developed. The test statistics proposed aregeneralizedWald test statistics that specialize for different settings by inserting andappropriate asymptotic variance matrix of sample moments. Scaled teststatisticsare also considered for dealing with situations of non-iid sampling. Thespecializationwill be carried out for testing the equality of multinomial populations, andtheequality of variance and correlation matrices for both normal andnon-normaldata. When testing the equality of correlation matrices, a scaled versionofthe normal theory chi-squared statistic is proven to be an asymptoticallyexactchi-squared statistic in the case of elliptical data.

A zero-delay sequential scheme for lossy coding of individual sequences

We consider adaptive sequential lossy coding of bounded individual sequences when the performance is measured by the sequentially accumulated mean squared distortion. Theencoder and the decoder are connected via a noiseless channel of capacity $R$ and both are assumed to have zero delay. No probabilistic assumptions are made on how the sequence to be encoded is generated. For any bounded sequence of length $n$, the distortion redundancy is defined as the normalized cumulative distortion of the sequential scheme minus the normalized cumulative distortion of the best scalarquantizer of rate $R$ which is matched to this particular sequence. We demonstrate the existence of a zero-delay sequential scheme which uses common randomization in the encoder and the decoder such that the normalized maximum distortion redundancy converges to zero at a rate $n^{-1/5}\log n$ as the length of the encoded sequence $n$ increases without bound.