Two algorithms to find a power integral basis

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Enrutament i control de flux en xarxes híbrides satèl·lit-terrestre

Les xarxes híbrides satèl·lit-terrestre ofereixen connectivitat a zones remotes i aïllades i permeten resoldre nombrosos problemes de comunicacions. No obstant, presenten diversos reptes, ja que realitzen la comunicació per un canal mòbil terrestre i un canal satèl·lit contigu. Un d'aquests reptes és trobar mecanismes per realitzar eficientment l'enrutament i el control de flux, de manera conjunta. L'objectiu d'aquest projecte és simular i estudiar algorismes existents que resolguin aquests problemes, així com proposar-ne de nous, mitjançant diverses tècniques d'optimització convexa. A partir de les simulacions realitzades en aquest estudi, s'han analitzat àmpliament els diversos problemes d'enrutament i control de flux, i s'han avaluat els resultats obtinguts i les prestacions dels algorismes emprats. En concret, s'han implementat de manera satisfactòria algorismes basats en el mètode de descomposició dual, el mètode de subgradient, el mètode de Newton i el mètode de la barrera logarítmica, entre d'altres, per tal de resoldre els problemes d'enrutament i control de flux plantejats.

Integració de tècniques per a la comprovació eficient de restriccions d'integritat en la generació de programari per entorns web

Estudi elaborat a partir d’una estada al Politecnico de Milano, Itàlia, entre gener i juny del 2006. Un dels principals objectius de l’Enginyeria del Programari és automatitzar el màxim possible el procés de desenvolupament del programari, reduint costos mitjançant la generació automàtica del programari a partir de la seva especificació. Per assolir-ho, entre altres, cal resoldre el problema de la comprovació eficient de restriccions, que són una part fonamental de l’especificació del programari. Aquest és precisament l’àmbit en què s’està desenvolupant una tesi que presentarà un mètode que poden integrar totes les eines generadores de codi per tal d’assolir una implementació eficient de les restriccions d’integritat. En l’actual fase del projecte s’ha treballat per validar el mètode de la tesi, optimitzant-lo pel cas específic de les aplicacions web i estendre’l per poder tractar també aplicacions basades en workflows. Pel que fa a l’optimització del mètode per aplicacions web, s’han definit una sèrie de paràmetres que permeten configurar la implementació del mètode tenint en compte les necessitats específiques de rendiment de cada aplicació web en particular. Respecte als workflows (cada cop més populars i que s’usen com a definició d’alt nivell per a les aplicacions a desenvolupar) s’ha estudiat quins són els tipus de restriccions que impliquen i com després es pot aplicar el mètode de la tesi sobre aquestes restriccions per tal de generar de forma eficient també les aplicacions basades en workflows.

A Model-to-model analysis of the repeated Prisoners' Dilemma: genetic algorithms vs. evolutionary dynamics

We study the properties of the well known Replicator Dynamics when applied to a finitely repeated version of the Prisoners' Dilemma game. We characterize the behavior of such dynamics under strongly simplifying assumptions (i.e. only 3 strategies are available) and show that the basin of attraction of defection shrinks as the number of repetitions increases. After discussing the difficulties involved in trying to relax the 'strongly simplifying assumptions' above, we approach the same model by means of simulations based on genetic algorithms. The resulting simulations describe a behavior of the system very close to the one predicted by the replicator dynamics without imposing any of the assumptions of the analytical model. Our main conclusion is that analytical and computational models are good complements for research in social sciences. Indeed, while on the one hand computational models are extremely useful to extend the scope of the analysis to complex scenar

Fast numerical algorithms for the computation of invariant tori in Hamiltonian systems

In this paper, we develop numerical algorithms that use small requirements of storage and operations for the computation of invariant tori in Hamiltonian systems (exact symplectic maps and Hamiltonian vector fields). The algorithms are based on the parameterization method and follow closely the proof of the KAM theorem given in [LGJV05] and [FLS07]. They essentially consist in solving a functional equation satisfied by the invariant tori by using a Newton method. Using some geometric identities, it is possible to perform a Newton step using little storage and few operations. In this paper we focus on the numerical issues of the algorithms (speed, storage and stability) and we refer to the mentioned papers for the rigorous results. We show how to compute efficiently both maximal invariant tori and whiskered tori, together with the associated invariant stable and unstable manifolds of whiskered tori. Moreover, we present fast algorithms for the iteration of the quasi-periodic cocycles and the computation of the invariant bundles, which is a preliminary step for the computation of invariant whiskered tori. Since quasi-periodic cocycles appear in other contexts, this section may be of independent interest. The numerical methods presented here allow to compute in a unified way primary and secondary invariant KAM tori. Secondary tori are invariant tori which can be contracted to a periodic orbit. We present some preliminary results that ensure that the methods are indeed implementable and fast. We postpone to a future paper optimized implementations and results on the breakdown of invariant tori.

Generic optimality conditions for semi-algebraic convex programs

We consider linear optimization over a nonempty convex semi-algebraic feasible region F. Semidefinite programming is an example. If F is compact, then for almost every linear objective there is a unique optimal solution, lying on a unique \active" manifold, around which F is \partly smooth", and the second-order sufficient conditions hold. Perturbing the objective results in smooth variation of the optimal solution. The active manifold consists, locally, of these perturbed optimal solutions; it is independent of the representation of F, and is eventually identified by a variety of iterative algorithms such as proximal and projected gradient schemes. These results extend to unbounded sets F.

Analysis and optimization of the satellite-to-plane link of an aeronautical global system

En aquest projecte s’ha analitzat i optimitzat l’enllaç satèl·lit amb avió per a un sistema aeronàutic global. Aquest nou sistema anomenat ANTARES està dissenyat per a comunicar avions amb estacions base mitjançant un satèl·lit. Aquesta és una iniciativa on hi participen institucions oficials en l’aviació com ara l’ECAC i que és desenvolupat en una col·laboració europea d’universitats i empreses. El treball dut a terme en el projecte compren bàsicament tres aspectes. El disseny i anàlisi de la gestió de recursos. La idoneïtat d’utilitzar correcció d’errors en la capa d’enllaç i en cas que sigui necessària dissenyar una opció de codificació preliminar. Finalment, estudiar i analitzar l’efecte de la interferència co-canal en sistemes multifeix. Tots aquests temes són considerats només per al “forward link”. L’estructura que segueix el projecte és primer presentar les característiques globals del sistema, després centrar-se i analitzar els temes mencionats per a poder donar resultats i extreure conclusions.

An algorithm for semi-infinite polynomial optimization

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On the stability of the optimal value and the optimal set in optimization problems

The paper develops a stability theory for the optimal value and the optimal set mapping of optimization problems posed in a Banach space. The problems considered in this paper have an arbitrary number of inequality constraints involving lower semicontinuous (not necessarily convex) functions and one closed abstract constraint set. The considered perturbations lead to problems of the same type as the nominal one (with the same space of variables and the same number of constraints), where the abstract constraint set can also be perturbed. The spaces of functions involved in the problems (objective and constraints) are equipped with the metric of the uniform convergence on the bounded sets, meanwhile in the space of closed sets we consider, coherently, the Attouch-Wets topology. The paper examines, in a unified way, the lower and upper semicontinuity of the optimal value function, and the closedness, lower and upper semicontinuity (in the sense of Berge) of the optimal set mapping. This paper can be seen as a second part of the stability theory presented in [17], where we studied the stability of the feasible set mapping (completed here with the analysis of the Lipschitz-like property).

Hard instances of algorithms and proof systems

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Approximation algorithms for two-state anti-ferromagnetic spin systems on bounded degree graphs

In a seminal paper [10], Weitz gave a deterministic fully polynomial approximation scheme for counting exponentially weighted independent sets (which is the same as approximating the partition function of the hard-core model from statistical physics) in graphs of degree at most d, up to the critical activity for the uniqueness of the Gibbs measure on the innite d-regular tree. ore recently Sly [8] (see also [1]) showed that this is optimal in the sense that if here is an FPRAS for the hard-core partition function on graphs of maximum egree d for activities larger than the critical activity on the innite d-regular ree then NP = RP. In this paper we extend Weitz's approach to derive a deterministic fully polynomial approximation scheme for the partition function of general two-state anti-ferromagnetic spin systems on graphs of maximum degree d, up to the corresponding critical point on the d-regular tree. The main ingredient of our result is a proof that for two-state anti-ferromagnetic spin systems on the d-regular tree, weak spatial mixing implies strong spatial mixing. his in turn uses a message-decay argument which extends a similar approach proposed recently for the hard-core model by Restrepo et al [7] to the case of general two-state anti-ferromagnetic spin systems.

UOC Algorithms

Aplicació per a iPad a mode de repositori de continguts relacionats amb l'ensenyament d'assignatures d'informàtica.

Enhancing fault management performance of two-step QoS routing algorithms in GMPLS networks

In this paper a novel methodology aimed at minimizing the probability of network failure and the failure impact (in terms of QoS degradation) while optimizing the resource consumption is introduced. A detailed study of MPLS recovery techniques and their GMPLS extensions are also presented. In this scenario, some features for reducing the failure impact and offering minimum failure probabilities at the same time are also analyzed. Novel two-step routing algorithms using this methodology are proposed. Results show that these methods offer high protection levels with optimal resource consumption

Enhancing MPLS QoS routing algorithms by using the network protection degree paradigm

IP based networks still do not have the required degree of reliability required by new multimedia services, achieving such reliability will be crucial in the success or failure of the new Internet generation. Most of existing schemes for QoS routing do not take into consideration parameters concerning the quality of the protection, such as packet loss or restoration time. In this paper, we define a new paradigm to develop new protection strategies for building reliable MPLS networks, based on what we have called the network protection degree (NPD). This NPD consists of an a priori evaluation, the failure sensibility degree (FSD), which provides the failure probability and an a posteriori evaluation, the failure impact degree (FID), to determine the impact on the network in case of failure. Having mathematical formulated these components, we point out the most relevant components. Experimental results demonstrate the benefits of the utilization of the NPD, when used to enhance some current QoS routing algorithms to offer a certain degree of protection