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.

Characterizations of Lojasiewicz inequalities and applications

The classical Lojasiewicz inequality and its extensions for partial differential equation problems (Simon) and to o-minimal structures (Kurdyka) have a considerable impact on the analysis of gradient-like methods and related problems: minimization methods, complexity theory, asymptotic analysis of dissipative partial differential equations, tame geometry. This paper provides alternative characterizations of this type of inequalities for nonsmooth lower semicontinuous functions defined on a metric or a real Hilbert space. In a metric context, we show that a generalized form of the Lojasiewicz inequality (hereby called the Kurdyka- Lojasiewicz inequality) relates to metric regularity and to the Lipschitz continuity of the sublevel mapping, yielding applications to discrete methods (strong convergence of the proximal algorithm). In a Hilbert setting we further establish that asymptotic properties of the semiflow generated by -∂f are strongly linked to this inequality. This is done by introducing the notion of a piecewise subgradient curve: such curves have uniformly bounded lengths if and only if the Kurdyka- Lojasiewicz inequality is satisfied. Further characterizations in terms of talweg lines -a concept linked to the location of the less steepest points at the level sets of f- and integrability conditions are given. In the convex case these results are significantly reinforced, allowing in particular to establish the asymptotic equivalence of discrete gradient methods and continuous gradient curves. On the other hand, a counterexample of a convex C2 function in R2 is constructed to illustrate the fact that, contrary to our intuition, and unless a specific growth condition is satisfied, convex functions may fail to fulfill the Kurdyka- Lojasiewicz inequality.

Exclusive Nightclubs and Lonely Hearts Columns: Nonmonotone Participation in Optional Intermediation

In many decentralised markets, the traders who benefit most from an exchange do not employ intermediaries even though they could easily afford them. At the same time, employing intermediaries is not worthwhile for traders who benefit little from trade. Together, these decisions amount to non-monotone participation choices in intermediation: only traders of middle “type” employ intermediaries, while the rest, the high and the low types, prefer to search for a trading partner directly. We provide a theoretical foundation for this, hitherto unexplained, phenomenon. We build a dynamic matching model, where a trader’s equilibrium bargaining share is a convex increasing function of her type. We also show that this is indeed a necessary condition for the existence of non-monotone equilibria.

Correlated equilibria, good and bad: an experimental study

We report results from an experiment that explores the empirical validity of correlated equilibrium, an important generalization of the Nash equilibrium concept. Specifically, we seek to understand the conditions under which subjects playing the game of Chicken will condition their behavior on private, third–party recommendations drawn from known distributions. In a “good–recommendations” treatment, the distribution we use is a correlated equilibrium with payoffs better than any symmetric payoff in the convex hull of Nash equilibrium payoff vectors. In a “bad–recommendations” treatment, the distribution is a correlated equilibrium with payoffs worse than any Nash equilibrium payoff vector. In a “Nash–recommendations” treatment, the distribution is a convex combination of Nash equilibrium outcomes (which is also a correlated equilibrium), and in a fourth “very–good–recommendations” treatment, the distribution yields high payoffs, but is not a correlated equilibrium. We compare behavior in all of these treatments to the case where subjects do not receive recommendations. We find that when recommendations are not given to subjects, behavior is very close to mixed–strategy Nash equilibrium play. When recommendations are given, behavior does differ from mixed–strategy Nash equilibrium, with the nature of the differ- ences varying according to the treatment. Our main finding is that subjects will follow third–party recommendations only if those recommendations derive from a correlated equilibrium, and further, if that correlated equilibrium is payoff–enhancing relative to the available Nash equilibria.

Geometria integral i convexitat en espais de curvatura holomorfa constant

En aquest treball es tracten qüestions de la geometria integral clàssica a l'espai hiperbòlic i projectiu complex i a l'espai hermític estàndard, els anomenats espais de curvatura holomorfa constant. La geometria integral clàssica estudia, entre d'altres, l'expressió en termes geomètrics de la mesura de plans que tallen un domini convex fixat de l'espai euclidià. Aquesta expressió es dóna en termes de les integrals de curvatura mitja. Un dels resultats principals d'aquest treball expressa la mesura de plans complexos que tallen un domini fixat a l'espai hiperbòlic complex, en termes del que definim com volums intrínsecs hermítics, que generalitzen les integrals de curvatura mitja. Una altra de les preguntes que tracta la geometria integral clàssica és: donat un domini convex i l'espai de plans, com s'expressa la integral de la s-èssima integral de curvatura mitja del convex intersecció entre un pla i el convex fixat? A l'espai euclidià, a l'espai projectiu i hiperbòlic reals, aquesta integral correspon amb la s-èssima integral de curvatura mitja del convex inicial: se satisfà una propietat de reproductibitat, que no es té en els espais de curvatura holomorfa constant. En el treball donem l'expressió explícita de la integral de la curvatura mitja quan integrem sobre l'espai de plans complexos. L'expressem en termes de la integral de curvatura mitja del domini inicial i de la integral de la curvatura normal en una direcció especial: l'obtinguda en aplicar l'estructura complexa al vector normal. La motivació per estudiar els espais de curvatura holomorfa constant i, en particular, l'espai hiperbòlic complex, es troba en l'estudi del següent problema clàssic en geometria. Quin valor pren el quocient entre l'àrea i el perímetre per a successions de figures convexes del pla que creixen tendint a omplir-lo? Fins ara es coneixia el comportament d'aquest quocient en els espais de curvatura seccional negativa i que a l'espai hiperbòlic real les fites obtingudes són òptimes. Aquí provem que a l'espai hiperbòlic complex, les cotes generals no són òptimes i optimitzem la superior.

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 numerical algorithm for finding solutions of a generalized Nash equilibrium problem

A family of nonempty closed convex sets is built by using the data of the Generalized Nash equilibrium problem (GNEP). The sets are selected iteratively such that the intersection of the selected sets contains solutions of the GNEP. The algorithm introduced by Iusem-Sosa (2003) is adapted to obtain solutions of the GNEP. Finally some numerical experiments are given to illustrate the numerical behavior of the algorithm.

The distribution of intestinal helminth infections in a rural village in Guatemala

Fecal egg count scores were used to investigate the distribution and abundance of intestinal helminths in the population of a rural village. Prevalences of the major helminths were 41% with Ascaris lumbricoides 60% with Trichuris trichiura and 50% with Necator americanus. All three parasites showed a highly aggregated distribution among hosts. Age/prevalence and age/intensity profiles were typical for both A. lumbricoides and T. trichiura with the highest worm burdens in the 50-10 year old children. For hookworm both prevalence and intensity curves were convex in shape with maximum infection levels in the 30-40 year old age class. Infected females had higher burdens of T. trichiura than infected males in all age classes of the population; there were no other effects of host gender. Analysis of associations between parasites within hosts revealed strong correlations between A. lumbricoides and T. lumbricoides and T. trichiura. Individuals with heavy infections of A. lumbricoides and T. trichiura showed highly significant aggregation within households. Associations between a variety of household features and heavy infections with A. lumbricoides and T. trichiura are described.

Iceberg transport technologies in spatial competition. Hotelling reborn

Transport costs in address models of differentiation are usually modeled as separable of the consumption commodity and with a parametric price. However, there are many sectors in an economy where such modeling is not satisfactory either because transportation is supplied under oligopolistic conditions or because there is a difference (loss) between the amount delivered at the point of production and the amount received at the point of consumption. This paper is a first attempt to tackle these issues proposing to study competition in spatial models using an iceberg-like transport cost technology allowing for concave and convex melting functions.

Rigid flat webs on the projective plane

This paper studies global webs on the projective plane with vanishing curvature. The study is based on an interplay of local and global arguments. The main local ingredient is a criterium for the regularity of the curvature at the neighborhood of a generic point of the discriminant. The main global ingredient, the Legendre transform, is an avatar of classical projective duality in the realm of differential equations. We show that the Legendre transform of what we call reduced convex foliations are webs with zero curvature, and we exhibit a countable infinity family of convex foliations which give rise to a family of webs with zero curvature not admitting non-trivial deformations with zero curvature.

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).

A way to play bankruptcy problems.

The commitment among agents has always been a difficult task, especially when they have to decide how to distribute the available amount of a scarce resource among all. On the one hand, there are a multiplicity of possible ways for assigning the available amount; and, on the other hand, each agent is going to propose that distribution which provides her the highest possible award. In this paper, with the purpose of making this agreement easier, firstly we use two different sets of basic properties, called Commonly Accepted Equity Principles, to delimit what agents can propose as reasonable allocations. Secondly, we extend the results obtained by Chun (1989) and Herrero (2003), obtaining new characterizations of old and well known bankruptcy rules. Finally, using the fact that bankruptcy problems can be analyzed from awards and losses, we define a mechanism which provides a new justification of the convex combinations of bankruptcy rules. Keywords: Bankruptcy problems, Unanimous Concessions procedure, Diminishing Claims mechanism, Piniles’ rule, Constrained Egalitarian rule. JEL classification: C71, D63, D71.

Resolution of foveal detachment in dome-shaped macula after treatment by spironolactone: report of two cases and mini-review of the literature.

Dome-shaped macula (DSM) was recently described in myopic patients as a convex protrusion of the macula within a posterior pole staphyloma. The pathogenesis of DSM and the development of associated serous foveal detachment (SFD) remain unclear. The obstruction of choroidal outflow and compressive changes of choroidal capillaries have been proposed as causative factors. In this paper, we report two cases of patients with chronic SFD associated with DSM treated with oral spironolactone. After treatment, there was a complete resolution of SFD in both patients. To the best of our knowledge, this is the first report of successful treatment of SFD in DSM by a mineralocorticoid receptor antagonist.

Decomposable approximations of nuclear C*-algebras

We show that nuclear C*-algebras have a re ned version of the completely positive approximation property, in which the maps that approximately factorize through finite dimensional algebras are convex combinations of order zero maps. We use this to show that a separable nuclear C*-algebra A which is closely contained in a C*-algebra B embeds into B.

A Proportional Approach to Bankruptcy Problems with a guaranteed minimum

In a distribution problem, and specfii cally in bankruptcy issues, the Proportional (P) and the Egalitarian (EA) divisions are two of the most popular ways to resolve the conflict. The Constrained Equal Awards rule (CEA) is introduced in bankruptcy literature to ensure that no agent receives more than her claim, a problem that can arise when using the egalitarian division. We propose an alternative modi cation, by using a convex combination of P and EA. The recursive application of this new rule finishes at the CEA rule. Our solution concept ensures a minimum amount to each agent, and distributes the remaining estate in a proportional way. Keywords: Bankruptcy problems, Proportional rule, Equal Awards, Convex combination of rules, Lorenz dominance. JEL classi fication: C71, D63, D71.