A parameter-free approach for solving combinatorial optimization problems through biased randomization of efficient heuristics

This paper discusses the use of probabilistic or randomized algorithms for solving combinatorial optimization problems. Our approach employs non-uniform probability distributions to add a biased random behavior to classical heuristics so a large set of alternative good solutions can be quickly obtained in a natural way and without complex conguration processes. This procedure is especially useful in problems where properties such as non-smoothness or non-convexity lead to a highly irregular solution space, for which the traditional optimization methods, both of exact and approximate nature, may fail to reach their full potential. The results obtained are promising enough to suggest that randomizing classical heuristics is a powerful method that can be successfully applied in a variety of cases.

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).

On slicewise monotone parameterized problems and optimal proof systems for TAUT

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

Application of the combined integral method to Stefan problems

In this paper we present a new, accurate form of the heat balance integral method, termed the Combined Integral Method (or CIM). The application of this method to Stefan problems is discussed. For simple test cases the results are compared with exact and asymptotic limits. In particular, it is shown that the CIM is more accurate than the second order, large Stefan number, perturbation solution for a wide range of Stefan numbers. In the initial examples it is shown that the CIM reduces the standard problem, consisting of a PDE defined over a domain specified by an ODE, to the solution of one or two algebraic equations. The latter examples, where the boundary temperature varies with time, reduce to a set of three first order ODEs.

Improving the accuracy of heat balance integral methods applied to thermal problems with time dependent boundary conditions

In this paper the two main drawbacks of the heat balance integral methods are examined. Firstly we investigate the choice of approximating function. For a standard polynomial form it is shown that combining the Heat Balance and Refined Integral methods to determine the power of the highest order term will either lead to the same, or more often, greatly improved accuracy on standard methods. Secondly we examine thermal problems with a time-dependent boundary condition. In doing so we develop a logarithmic approximating function. This new function allows us to model moving peaks in the temperature profile, a feature that previous heat balance methods cannot capture. If the boundary temperature varies so that at some time t & 0 it equals the far-field temperature, then standard methods predict that the temperature is everywhere at this constant value. The new method predicts the correct behaviour. It is also shown that this function provides even more accurate results, when coupled with the new CIM, than the polynomial profile. Analysis primarily focuses on a specified constant boundary temperature and is then extended to constant flux, Newton cooling and time dependent boundary conditions.

An axiomatic justification of mediation in bankruptcy problems.

This paper provides a natural way of reaching an agreement between two prominent proposals in a bankruptcy problem. Particularly, using the fact that such problems can be faced from two different points of views, awards and losses, we justify the average of any pair of dual bankruptcy rules through the definition a double recursive process. Finally, by considering three posible sets of equity principles that a particular society may agree on, we retrieve the average of old and well known bankruptcy rules, the Constrained Equal Awards and the Constrained Equal Losses rules, Piniles’ rule and its dual rule, and the Constrained Egalitarian rule and its dual rule. Keywords: Bankruptcy problems, Midpoint, Bounds, Duality, Recursivity. JEL classification: C71, D63, D71.

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.

Evolution of decision-making and learning under fluctuating social environments

The capacity to learn to associate sensory perceptions with appropriate motor actions underlies the success of many animal species, from insects to humans. The evolutionary significance of learning has long been a subject of interest for evolutionary biologists who emphasize the bene¬fit yielded by learning under changing environmental conditions, where it is required to flexibly switch from one behavior to another. However, two unsolved questions are particularly impor¬tant for improving our knowledge of the evolutionary advantages provided by learning, and are addressed in the present work. First, because it is possible to learn the wrong behavior when a task is too complex, the learning rules and their underlying psychological characteristics that generate truly adaptive behavior must be identified with greater precision, and must be linked to the specific ecological problems faced by each species. A framework for predicting behavior from the definition of a learning rule is developed here. Learning rules capture cognitive features such as the tendency to explore, or the ability to infer rewards associated to unchosen actions. It is shown that these features interact in a non-intuitive way to generate adaptive behavior in social interactions where individuals affect each other's fitness. Such behavioral predictions are used in an evolutionary model to demonstrate that, surprisingly, simple trial-and-error learn¬ing is not always outcompeted by more computationally demanding inference-based learning, when population members interact in pairwise social interactions. A second question in the evolution of learning is its link with and relative advantage compared to other simpler forms of phenotypic plasticity. After providing a conceptual clarification on the distinction between genetically determined vs. learned responses to environmental stimuli, a new factor in the evo¬lution of learning is proposed: environmental complexity. A simple mathematical model shows that a measure of environmental complexity, the number of possible stimuli in one's environ¬ment, is critical for the evolution of learning. In conclusion, this work opens roads for modeling interactions between evolving species and their environment in order to predict how natural se¬lection shapes animals' cognitive abilities. - La capacité d'apprendre à associer des sensations perceptives à des actions motrices appropriées est sous-jacente au succès évolutif de nombreuses espèces, depuis les insectes jusqu'aux êtres hu¬mains. L'importance évolutive de l'apprentissage est depuis longtemps un sujet d'intérêt pour les biologistes de l'évolution, et ces derniers mettent l'accent sur le bénéfice de l'apprentissage lorsque les conditions environnementales sont changeantes, car dans ce cas il est nécessaire de passer de manière flexible d'un comportement à l'autre. Cependant, deux questions non résolues sont importantes afin d'améliorer notre savoir quant aux avantages évolutifs procurés par l'apprentissage. Premièrement, puisqu'il est possible d'apprendre un comportement incorrect quand une tâche est trop complexe, les règles d'apprentissage qui permettent d'atteindre un com¬portement réellement adaptatif doivent être identifiées avec une plus grande précision, et doivent être mises en relation avec les problèmes écologiques spécifiques rencontrés par chaque espèce. Un cadre théorique ayant pour but de prédire le comportement à partir de la définition d'une règle d'apprentissage est développé ici. Il est démontré que les caractéristiques cognitives, telles que la tendance à explorer ou la capacité d'inférer les récompenses liées à des actions non ex¬périmentées, interagissent de manière non-intuitive dans les interactions sociales pour produire des comportements adaptatifs. Ces prédictions comportementales sont utilisées dans un modèle évolutif afin de démontrer que, de manière surprenante, l'apprentissage simple par essai-et-erreur n'est pas toujours battu par l'apprentissage basé sur l'inférence qui est pourtant plus exigeant en puissance de calcul, lorsque les membres d'une population interagissent socialement par pair. Une deuxième question quant à l'évolution de l'apprentissage concerne son lien et son avantage relatif vis-à-vis d'autres formes plus simples de plasticité phénotypique. Après avoir clarifié la distinction entre réponses aux stimuli génétiquement déterminées ou apprises, un nouveau fac¬teur favorisant l'évolution de l'apprentissage est proposé : la complexité environnementale. Un modèle mathématique permet de montrer qu'une mesure de la complexité environnementale - le nombre de stimuli rencontrés dans l'environnement - a un rôle fondamental pour l'évolution de l'apprentissage. En conclusion, ce travail ouvre de nombreuses perspectives quant à la mo¬délisation des interactions entre les espèces en évolution et leur environnement, dans le but de comprendre comment la sélection naturelle façonne les capacités cognitives des animaux.

The stabilizing effects of the acquired immunity on the schistosomiasis transmission modeling - the sensitivity Analysis

A mathematical model is proposed to analyze the effects of acquired immunity on the transmission of schistosomiasis in the human host. From this model the prevalence curve dependent on four parameters can be obtained. These parameters were estimated fitting the data by the maximum likelihood method. The model showed a good retrieving capacity of real data from two endemic areas of schistosomiasis: Touros, Brazil (Schistosoma mansoni) and Misungwi, Tanzania (S. haematobium). Also, the average worm burden per person and the dispersion of parasite per person in the community can be obtained from the model. In this paper, the stabilizing effects of the acquired immunity assumption in the model are assessed in terms of the epidemiological variables as follows. Regarded to the prevalence curve, we calculate the confidence interval, and related to the average worm burden and the worm dispersion in the community, the sensitivity analysis (the range of the variation) of both variables with respect to their parameters is performed.

Zerebrale Probleme in der pädiatrischen Intensivmedizin [Cerebral problems in pediatric intensive care]

This paper presents a review of different methods enabling the monitoring of cerebral function in neonatal and paediatric intensive care. EEG, evoked potentials, conventional radiological studies, computerized tomography, ultrasound, intracranial pressure measurements, nuclear magnetic resonance, Doppler ultrasound, radioisotope studies, angiography, infra-red spectral analysis and last, but not least, clinical examination produce information regarding the neurological state of the patient which must be critically analysed in order to ensure optimal management of the case. Unfortunately, and in spite of impressive progress in non-invasive monitoring of the cerebral function, we are still forced to make important medical and ethical decisions without precise information about the neurological state of our patients.

Synchronous versus asynchronous modeling of gene regulatory networks.

MOTIVATION: In silico modeling of gene regulatory networks has gained some momentum recently due to increased interest in analyzing the dynamics of biological systems. This has been further facilitated by the increasing availability of experimental data on gene-gene, protein-protein and gene-protein interactions. The two dynamical properties that are often experimentally testable are perturbations and stable steady states. Although a lot of work has been done on the identification of steady states, not much work has been reported on in silico modeling of cellular differentiation processes. RESULTS: In this manuscript, we provide algorithms based on reduced ordered binary decision diagrams (ROBDDs) for Boolean modeling of gene regulatory networks. Algorithms for synchronous and asynchronous transition models have been proposed and their corresponding computational properties have been analyzed. These algorithms allow users to compute cyclic attractors of large networks that are currently not feasible using existing software. Hereby we provide a framework to analyze the effect of multiple gene perturbation protocols, and their effect on cell differentiation processes. These algorithms were validated on the T-helper model showing the correct steady state identification and Th1-Th2 cellular differentiation process. AVAILABILITY: The software binaries for Windows and Linux platforms can be downloaded from http://si2.epfl.ch/~garg/genysis.html.