Tractable valuations under uncertainty

I put forward a concise and intuitive formula for the calculation of the valuation for a good in the presence of the expectation that further, related, goods will soon become available. This valuation is tractable in the sense that it does not require the explicit resolution of the consumerís life-time problem.

Conjugacy of piecewise linear Lorenz map that expand on average

For piecewise linear Lorenz map that expand on average, we show that it admits a dichotomy: it is either periodic renormalizable or prime. As a result, such a map is conjugate to a ß-transformation.

A first attempt of geographically-distributed Multi-scale integrated analysis of societal and ecosystem metabolism (MuSIASEM): mapping human time and energy throughput in metropolitan Barcelona

This study presents a first attempt to extend the “Multi-scale integrated analysis of societal and ecosystem metabolism (MuSIASEM)” approach to a spatial dimension using GIS techniques in the Metropolitan area of Barcelona. We use a combination of census and commercial databases along with a detailed land cover map to create a layer of Common Geographic Units that we populate with the local values of human time spent in different activities according to MuSIASEM hierarchical typology. In this way, we mapped the hours of available human time, in regards to the working hours spent in different locations, putting in evidence the gradients in spatial density between the residential location of workers (generating the work supply) and the places where the working hours are actually taking place. We found a strong three-modal pattern of clumps of areas with different combinations of values of time spent on household activities and on paid work. We also measured and mapped spatial segregation between these two activities and put forward the conjecture that this segregation increases with higher energy throughput, as the size of the functional units must be able to cope with the flow of exosomatic energy. Finally, we discuss the effectiveness of the approach by comparing our geographic representation of exosomatic throughput to the one issued from conventional methods.

Quasiconformal maps, analytic capacity, and non linear potentials

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

Near-linear dynamics in KdV with periodic boundary conditions

Near linear evolution in Korteweg de Vries (KdV) equation with periodic boundary conditions is established under the assumption of high frequency initial data. This result is obtained by the method of normal form reduction.

The non-linear Dirichlet problem in Hadamard manifolds

We prove existence theorems for the Dirichlet problem for hypersurfaces of constant special Lagrangian curvature in Hadamard manifolds. The first results are obtained using the continuity method and approximation and then refined using two iterations of the Perron method. The a-priori estimates used in the continuity method are valid in any ambient manifold.

The behavioral relevance and top-down susceptibility of early, low level multisensory interactions in humans

Abstract (English)General backgroundMultisensory stimuli are easier to recognize, can improve learning and a processed faster compared to unisensory ones. As such, the ability an organism has to extract and synthesize relevant sensory inputs across multiple sensory modalities shapes his perception of and interaction with the environment. A major question in the scientific field is how the brain extracts and fuses relevant information to create a unified perceptual representation (but also how it segregates unrelated information). This fusion between the senses has been termed "multisensory integration", a notion that derives from seminal animal single-cell studies performed in the superior colliculus, a subcortical structure shown to create a multisensory output differing from the sum of its unisensory inputs. At the cortical level, integration of multisensory information is traditionally deferred to higher classical associative cortical regions within the frontal, temporal and parietal lobes, after extensive processing within the sensory-specific and segregated pathways. However, many anatomical, electrophysiological and neuroimaging findings now speak for multisensory convergence and interactions as a distributed process beginning much earlier than previously appreciated and within the initial stages of sensory processing.The work presented in this thesis is aimed at studying the neural basis and mechanisms of how the human brain combines sensory information between the senses of hearing and touch. Early latency non-linear auditory-somatosensory neural response interactions have been repeatedly observed in humans and non-human primates. Whether these early, low-level interactions are directly influencing behavioral outcomes remains an open question as they have been observed under diverse experimental circumstances such as anesthesia, passive stimulation, as well as speeded reaction time tasks. Under laboratory settings, it has been demonstrated that simple reaction times to auditory-somatosensory stimuli are facilitated over their unisensory counterparts both when delivered to the same spatial location or not, suggesting that audi- tory-somatosensory integration must occur in cerebral regions with large-scale spatial representations. However experiments that required the spatial processing of the stimuli have observed effects limited to spatially aligned conditions or varying depending on which body part was stimulated. Whether those divergences stem from task requirements and/or the need for spatial processing has not been firmly established.Hypotheses and experimental resultsIn a first study, we hypothesized that auditory-somatosensory early non-linear multisensory neural response interactions are relevant to behavior. Performing a median split according to reaction time of a subset of behavioral and electroencephalographic data, we found that the earliest non-linear multisensory interactions measured within the EEG signal (i.e. between 40-83ms post-stimulus onset) were specific to fast reaction times indicating a direct correlation of early neural response interactions and behavior.In a second study, we hypothesized that the relevance of spatial information for task performance has an impact on behavioral measures of auditory-somatosensory integration. Across two psychophysical experiments we show that facilitated detection occurs even when attending to spatial information, with no modulation according to spatial alignment of the stimuli. On the other hand, discrimination performance with probes, quantified using sensitivity (d'), is impaired following multisensory trials in general and significantly more so following misaligned multisensory trials.In a third study, we hypothesized that behavioral improvements might vary depending which body part is stimulated. Preliminary results suggest a possible dissociation between behavioral improvements andERPs. RTs to multisensory stimuli were modulated by space only in the case when somatosensory stimuli were delivered to the neck whereas multisensory ERPs were modulated by spatial alignment for both types of somatosensory stimuli.ConclusionThis thesis provides insight into the functional role played by early, low-level multisensory interac-tions. Combining psychophysics and electrical neuroimaging techniques we demonstrate the behavioral re-levance of early and low-level interactions in the normal human system. Moreover, we show that these early interactions are hermetic to top-down influences on spatial processing suggesting their occurrence within cerebral regions having access to large-scale spatial representations. We finally highlight specific interactions between auditory space and somatosensory stimulation on different body parts. Gaining an in-depth understanding of how multisensory integration normally operates is of central importance as it will ultimately permit us to consider how the impaired brain could benefit from rehabilitation with multisensory stimula-Abstract (French)Background théoriqueDes stimuli multisensoriels sont plus faciles à reconnaître, peuvent améliorer l'apprentissage et sont traités plus rapidement comparé à des stimuli unisensoriels. Ainsi, la capacité qu'un organisme possède à extraire et à synthétiser avec ses différentes modalités sensorielles des inputs sensoriels pertinents, façonne sa perception et son interaction avec l'environnement. Une question majeure dans le domaine scientifique est comment le cerveau parvient à extraire et à fusionner des stimuli pour créer une représentation percep- tuelle cohérente (mais aussi comment il isole les stimuli sans rapport). Cette fusion entre les sens est appelée "intégration multisensorielle", une notion qui provient de travaux effectués dans le colliculus supérieur chez l'animal, une structure sous-corticale possédant des neurones produisant une sortie multisensorielle différant de la somme des entrées unisensorielles. Traditionnellement, l'intégration d'informations multisen- sorielles au niveau cortical est considérée comme se produisant tardivement dans les aires associatives supérieures dans les lobes frontaux, temporaux et pariétaux, suite à un traitement extensif au sein de régions unisensorielles primaires. Cependant, plusieurs découvertes anatomiques, électrophysiologiques et de neuroimageries remettent en question ce postulat, suggérant l'existence d'une convergence et d'interactions multisensorielles précoces.Les travaux présentés dans cette thèse sont destinés à mieux comprendre les bases neuronales et les mécanismes impliqués dans la combinaison d'informations sensorielles entre les sens de l'audition et du toucher chez l'homme. Des interactions neuronales non-linéaires précoces audio-somatosensorielles ont été observées à maintes reprises chez l'homme et le singe dans des circonstances aussi variées que sous anes- thésie, avec stimulation passive, et lors de tâches nécessitant un comportement (une détection simple de stimuli, par exemple). Ainsi, le rôle fonctionnel joué par ces interactions à une étape du traitement de l'information si précoce demeure une question ouverte. Il a également été démontré que les temps de réaction en réponse à des stimuli audio-somatosensoriels sont facilités par rapport à leurs homologues unisensoriels indépendamment de leur position spatiale. Ce résultat suggère que l'intégration audio- somatosensorielle se produit dans des régions cérébrales possédant des représentations spatiales à large échelle. Cependant, des expériences qui ont exigé un traitement spatial des stimuli ont produits des effets limités à des conditions où les stimuli multisensoriels étaient, alignés dans l'espace ou encore comme pouvant varier selon la partie de corps stimulée. Il n'a pas été établi à ce jour si ces divergences pourraient être dues aux contraintes liées à la tâche et/ou à la nécessité d'un traitement de l'information spatiale.Hypothèse et résultats expérimentauxDans une première étude, nous avons émis l'hypothèse que les interactions audio- somatosensorielles précoces sont pertinentes pour le comportement. En effectuant un partage des temps de réaction par rapport à la médiane d'un sous-ensemble de données comportementales et électroencépha- lographiques, nous avons constaté que les interactions multisensorielles qui se produisent à des latences précoces (entre 40-83ms) sont spécifique aux temps de réaction rapides indiquant une corrélation directe entre ces interactions neuronales précoces et le comportement.Dans une deuxième étude, nous avons émis l'hypothèse que si l'information spatiale devient perti-nente pour la tâche, elle pourrait exercer une influence sur des mesures comportementales de l'intégration audio-somatosensorielles. Dans deux expériences psychophysiques, nous montrons que même si les participants prêtent attention à l'information spatiale, une facilitation de la détection se produit et ce toujours indépendamment de la configuration spatiale des stimuli. Cependant, la performance de discrimination, quantifiée à l'aide d'un index de sensibilité (d') est altérée suite aux essais multisensoriels en général et de manière plus significative pour les essais multisensoriels non-alignés dans l'espace.Dans une troisième étude, nous avons émis l'hypothèse que des améliorations comportementales pourraient différer selon la partie du corps qui est stimulée (la main vs. la nuque). Des résultats préliminaires suggèrent une dissociation possible entre une facilitation comportementale et les potentiels évoqués. Les temps de réactions étaient influencés par la configuration spatiale uniquement dans le cas ou les stimuli somatosensoriels étaient sur la nuque alors que les potentiels évoqués étaient modulés par l'alignement spatial pour les deux types de stimuli somatosensorielles.ConclusionCette thèse apporte des éléments nouveaux concernant le rôle fonctionnel joué par les interactions multisensorielles précoces de bas niveau. En combinant la psychophysique et la neuroimagerie électrique, nous démontrons la pertinence comportementale des ces interactions dans le système humain normal. Par ailleurs, nous montrons que ces interactions précoces sont hermétiques aux influences dites «top-down» sur le traitement spatial suggérant leur occurrence dans des régions cérébrales ayant accès à des représentations spatiales de grande échelle. Nous soulignons enfin des interactions spécifiques entre l'espace auditif et la stimulation somatosensorielle sur différentes parties du corps. Approfondir la connaissance concernant les bases neuronales et les mécanismes impliqués dans l'intégration multisensorielle dans le système normale est d'une importance centrale car elle permettra d'examiner et de mieux comprendre comment le cerveau déficient pourrait bénéficier d'une réhabilitation avec la stimulation multisensorielle.

Predictive and distributed routing balancing (PR-DRB): high speed interconnection networks

Current parallel applications running on clusters require the use of an interconnection network to perform communications among all computing nodes available. Imbalance of communications can produce network congestion, reducing throughput and increasing latency, degrading the overall system performance. On the other hand, parallel applications running on these networks posses representative stages which allow their characterization, as well as repetitive behavior that can be identified on the basis of this characterization. This work presents the Predictive and Distributed Routing Balancing (PR-DRB), a new method developed to gradually control network congestion, based on paths expansion, traffic distribution and effective traffic load, in order to maintain low latency values. PR-DRB monitors messages latencies on intermediate routers, makes decisions about alternative paths and record communication pattern information encountered during congestion situation. Based on the concept of applications repetitiveness, best solution recorded are reapplied when saved communication pattern re-appears. Traffic congestion experiments were conducted in order to evaluate the performance of the method, and improvements were observed.

Gaussian estimates for the density of the non-linear stochastic heat equation in any space dimension

In this paper, we establish lower and upper Gaussian bounds for the probability density of the mild solution to the stochastic heat equation with multiplicative noise and in any space dimension. The driving perturbation is a Gaussian noise which is white in time with some spatially homogeneous covariance. These estimates are obtained using tools of the Malliavin calculus. The most challenging part is the lower bound, which is obtained by adapting a general method developed by Kohatsu-Higa to the underlying spatially homogeneous Gaussian setting. Both lower and upper estimates have the same form: a Gaussian density with a variance which is equal to that of the mild solution of the corresponding linear equation with additive noise.

Linear Aggregation In The Social Accounting Matrix Framework

In economic literature, information deficiencies and computational complexities have traditionally been solved through the aggregation of agents and institutions. In inputoutput modelling, researchers have been interested in the aggregation problem since the beginning of 1950s. Extending the conventional input-output aggregation approach to the social accounting matrix (SAM) models may help to identify the effects caused by the information problems and data deficiencies that usually appear in the SAM framework. This paper develops the theory of aggregation and applies it to the social accounting matrix model of multipliers. First, we define the concept of linear aggregation in a SAM database context. Second, we define the aggregated partitioned matrices of multipliers which are characteristic of the SAM approach. Third, we extend the analysis to other related concepts, such as aggregation bias and consistency in aggregation. Finally, we provide an illustrative example that shows the effects of aggregating a social accounting matrix model.

A linear optimization technique for graph pebbling

Graph pebbling is a network model for studying whether or not a given supply of discrete pebbles can satisfy a given demand via pebbling moves. A pebbling move across an edge of a graph takes two pebbles from one endpoint and places one pebble at the other endpoint; the other pebble is lost in transit as a toll. It has been shown that deciding whether a supply can meet a demand on a graph is NP-complete. The pebbling number of a graph is the smallest t such that every supply of t pebbles can satisfy every demand of one pebble. Deciding if the pebbling number is at most k is NP 2 -complete. In this paper we develop a tool, called theWeight Function Lemma, for computing upper bounds and sometimes exact values for pebbling numbers with the assistance of linear optimization. With this tool we are able to calculate the pebbling numbers of much larger graphs than in previous algorithms, and much more quickly as well. We also obtain results for many families of graphs, in many cases by hand, with much simpler and remarkably shorter proofs than given in previously existing arguments (certificates typically of size at most the number of vertices times the maximum degree), especially for highly symmetric graphs. Here we apply theWeight Function Lemma to several specific graphs, including the Petersen, Lemke, 4th weak Bruhat, Lemke squared, and two random graphs, as well as to a number of infinite families of graphs, such as trees, cycles, graph powers of cycles, cubes, and some generalized Petersen and Coxeter graphs. This partly answers a question of Pachter, et al., by computing the pebbling exponent of cycles to within an asymptotically small range. It is conceivable that this method yields an approximation algorithm for graph pebbling.

Relaxation methods for solving linear inequality systems: Converging results

The problem of finding a feasible solution to a linear inequality system arises in numerous contexts. In [12] an algorithm, called extended relaxation method, that solves the feasibility problem, has been proposed by the authors. Convergence of the algorithm has been proven. In this paper, we onsider a class of extended relaxation methods depending on a parameter and prove their convergence. Numerical experiments have been provided, as well.

A subspace correction method for discontinuous Galerkin discretizations of linear elasticity equations

We study preconditioning techniques for discontinuous Galerkin discretizations of isotropic linear elasticity problems in primal (displacement) formulation. We propose subspace correction methods based on a splitting of the vector valued piecewise linear discontinuous finite element space, that are optimal with respect to the mesh size and the Lamé parameters. The pure displacement, the mixed and the traction free problems are discussed in detail. We present a convergence analysis of the proposed preconditioners and include numerical examples that validate the theory and assess the performance of the preconditioners.