Nous étudions le modèle de la marche aléatoire branchante. Nous obtenons d'abord des résultats concernant le processus ponctuel formé par les particules extrémales, résolvant ainsi une conjecture de Brunet et Derrida 2010 [36]. Ensuite, nous établissons la dérivée au point critique de la limite des martingales additives complétant ainsi l'étude initiée par Biggins [23]. Ces deux travaux reposent sur les techniques modernes de décompositions épinales de la marche aléatoire branchante, originairement développées par Chauvin, Rouault et Wakolbinger [41], Lyons, Pemantle et Peres [74], Lyons [73] et Biggins et Kyprianou [24]. Le dernier chapitre de la thèse porte sur un champ Gaussien log-correle introduit par Kahane 1985 [61]. Via de récents travaux comme ceux de Allez, Rhodes et Vargas [11], Duplantier, Rhodes, Sheeld et Vargas [46] [47], ce modèle a connu un important regain d'intérêt. La construction du chaos multiplicatif Gaussien dans le cas critique a notamment été prouvée dans [46]. S'inspirant des techniques utilisées pour la marche aléatoire branchante nous résolvons une conjecture de [46] concernant le maximum de ce champ Gaussien. / We study the model of the branching random walk. First we obtain some results concerning thepoint process formed by the extremal particles, proving a Brunet and Derrida's conjecture [36] as well. Thenwe establish the derivative of the additive martingale limit at the critical point, completing the study initiatedby Biggins [23]. These two works rely on the spinal decomposition of the branching random walk, originallyintroduced by Chauvin, Rouault and Wakolbinger [41], Lyons, Pemantle and Peres [74], Lyons [73] and Bigginsand Kyprianou [24].The last chapter of the thesis deals with a log-correlated Gaussian field introduced by Kahane [61]. Thismodel was recently revived in particular by Allez, Rhodes and Vargas [11], and Duplantier, Rhodes, Shefield andVargas [46] [47]. Inspired by the techniques used for branching random walk we solved a conjecture of Duplantier,Rhodes, Shefield and Vargas [46], on the maximum of this Gaussian field.

Given a square with integer side length n, we ask for the number of different ways to divide it into sub-squares, considering only the list of parts. We enumerate all possible lists and check whether a placement with those squares is possible. In order to do this, we propose a new algorithm for creating perfect square packings.

Yes / A simple method is reported for the estimation of in vivo air-tissue partition coefficients of VOCs and of in vitro blood-tissue partition coefficients for volatile organic compounds and other compounds. Linear free energy relationships for tissues such as brain, muscle, liver, lung, kidney, heart, skin and fat are available and once the Abraham descriptors are known for a compound, no more than simple arithmetic is required to estimate air-tissue and blood-tissue partitions.

Yes / Literature data on solubilities of adamantane in organic solvents have been used to obtain properties, or descriptors, of adamantane. There is much less data on substituted adamantanes but we have been able to obtain descriptors for some 40 substituted adamantanes. These descriptors can then be used to estimate a wide range of physicochemical, environmental and other properties of the adamantanes. For the first time, the water-solvent partition coefficient and the gas-solvent partition coefficient into a large range of solvents, can be estimated, the latter being equivalent to Henry's Law constants. A variety of other important properties can also be estimated. These include vapor pressures, enthalpies of vaporization and sublimation, partitions from air and from blood into biological tissues, and skin permeability from water. The descriptors themselves are not exceptional. Adamantane itself has a rather low dipolarity, zero hydrogen bond acidity and a very low hydrogen bond basicity, in common with other multicyclic aliphatic compounds. These lead to adamantane being a very hydrophobic compound, as is evident from our estimated water-octanol partition coefficient.

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System virtualization technology is widely used in computing nowadays. In embedded domain, it is used as a solution to resource sharing among independent applications. One of the areas is to apply virtualization technique to real-time embedded systems with timing constraints. Multi-level adaptive hierarchical scheduling (AdHierSched) framework is a virtualized real-time framework, which runs in the Linux operating system. Šis virtualized framework has ability to adapt the CPU partition sizes according to their need through monitoring their demand during run-time, which yields more appropriate processor assignment. However, the performance of the virtualized framework is still unknown when the budget borrowing mechanism is enabled. To this end, in this thesis, we explore a new direction for performing the adaptation of CPU partition. We design and implement a budget borrowing mechanism for dynamic adaptation of resource parameters in AdHierSched framework. Extensive simulations are performed in this thesis, which are used to study and compare di‚erent adaptation mechanisms with our approach. From the results of experiments, we conclude that when the framework works only with budget borrowing controller, the results are not as good as only running a budget controller in the AdHierSched framework. However, while running both of the controllers at the same time, the experiments results are good enough. We also analyze the overhead of the framework at the end of the evaluation. Finally, we conclude the thesis by presenting the possible future work.

We examine the task of feature selection, which is a method of forming simplified descriptions of complex data for use in probabilistic classifiers. Feature selection typically requires a numerical measure or metric of the desirability of a given set of features. The thesis considers a number of existing metrics, with particular attention to those based on entropy and other quantities derived from information theory. A useful new perspective on feature selection is provided by the concepts of partitioning and encoding of data by a feature set. The ideas of partitioning and encoding, together with the theoretical shortcomings of existing metrics, motivate a new class of feature selection metrics based on conditional entropy. The simplest of the new metrics is referred to as expected partition entropy or EPE. Performances of the new and existing metrics are compared by experiments with a simplified form of part-of-speech tagging and with classification of Reuters news stories by topic. In order to conduct the experiments, a new class of accelerated feature selection search algorithms is introduced; a member of this class is found to provide significantly increased speed with minimal loss in performance, as measured by feature selection metrics and accuracy on test data. The comparative performance of existing metrics is also analysed, giving rise to a new general conjecture regarding the wrapper class of metrics. Each wrapper is inherently tied to a specific type of classifier. The experimental results support the idea that a wrapper selects feature sets which perform well in conjunction with its own particular classifier, but this good performance cannot be expected to carry over to other types of model. The new metrics introduced in this thesis prove to have substantial advantages over a representative selection of other feature selection mechanisms: Mutual information, frequency-based cutoff, the Koller-Sahami information loss measure, and two different types of wrapper method. Feature selection using the new metrics easily outperforms other filter-based methods such as mutual information; additionally, our approach attains comparable performance to a wrapper method, but at a fraction of the computational expense. Finally, members of the new class of metrics succeed in a case where the Koller-Sahami metric fails to provide a meaningful criterion for feature selection.

Assuming the axiom of determinacy, we give a new proof of the strong partition relation on ω1. Further, we present a streamlined proof that J<λ+(a) (the ideal of sets which force cof Π α < λ) is generated from J<λ+(a) by adding a singleton. Combining these results with a polarized partition relation on ω1

Laczkovich proved from ZF that, given a countable sequence of Borel sets on a perfect Polish space, if the limit superior along every subsequence was uncountable, then there was a particular subsequence whose intersection actually contained a perfect subset. Komjath later expanded the result to hold for analytic sets. In this paper, by adding AD and sometimes V=L(R) to our assumptions, we will extend the result further. This generalization will include the increasing of the length of the sequence to certain uncountable regular cardinals as well as removing any descriptive requirements on the sets.

In this paper we present a fuzzy voting scheme for cluster algorithms. This fuzzy voting method allows us to combine several runs of cluster algorithms resulting in a common fuzzy partition. This helps us to overcome instabilities of the cluster algorithms and results in a better clustering. / Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"