Neste trabalho estudamos a aplicabilidade dos conceitos de autoconsistência de R. Hagedorn e de não-extensividade de acordo com a estatística de Tsallis. Estes dois conceitos podem ser associados de acordo com a teoria autoconsistente não-extensiva. A análise dos dados de distribuição de momento tranversal e do espectro de massa de hádrons permite testar a aplicabilidade desses conceitos, e neste trabalho desenvolvemos esta análise para dados obtidos em colisões pp em energias ultrarelativísticas. Os resultados obtidos nessas análises confirmam a idéia de Hagedorn da existência de uma temperatura limite para sistemas hadrônicos e também é observado uma ótima descrição do espectro de massa hadrônico pela da TACNE. Parte dos resultados deste trabalho está publicada na Physical Review D 87, 114022 (2013). / In this work, we study the applicability of the concepts of self-consistency by R. Hagedorn and non-exntensivity according to the Tsallis statistic. These two concepts can be associeted in accordance with the self-consistency non-extensive theory. The analysis of distribution data of transverse momentum and mass spectrum allows hadron test applicability of these concepts, and in this work we developed this analysis for data obtained from pp collisions at ultrarelativistic energies. The results of these analysis support the ideia of the existence of a Hagedorns temperature threshold for hadronic systems and a very good description of the hadroic mass spectrum by the self-consistency non-extensive theory is also verified. Part of this work is published in Physical Review D 87, 114022 (2013).

De nos jours, la quantité de données génétiques séquencées augmente de manière exponentielle sous l'impulsion d'outils de séquençage de plus en plus performants, tels que les outils de séquençage haut débit en particulier. De plus, ces données sont de plus en plus facilement accessibles grâce aux bases de données en ligne. Cette plus grande disponibilité des données ouvre de nouveaux sujets d'étude qui nécessitent de la part des statisticiens et bio-informaticiens de développer des outils adaptés. Par ailleurs, les progrès constants de la statistique, dans des domaines tels que le clustering, la réduction de dimension, ou les régressions entre autres, nécessitent d'être régulièrement adaptés au contexte de la bio-informatique. L’objectif de cette thèse est l’application de techniques avancées de statistiques à des problématiques de bio-informatique. Dans ce manuscrit, nous présentons les résultats de nos travaux concernant le clustering de séquences génétiques via Laplacian eigenmaps et modèle de mélange gaussien, l'étude de la propagation des éléments transposables dans le génome via un processus de branchement, l'analyse de données métagénomiques en écologie via des courbes ROC ou encore la régression polytomique ordonnée pénalisée par la norme l1. / Nowadays, the quantity of sequenced genetic data is increasing exponentially under the impetus of increasingly powerful sequencing tools, such as high-throughput sequencing tools in particular. In addition, these data are increasingly accessible through online databases. This greater availability of data opens up new areas of study that require statisticians and bioinformaticians to develop appropriate tools. In addition, constant statistical progress in areas such as clustering, dimensionality reduction, regressions and others needs to be regularly adapted to the context of bioinformatics. The objective of this thesis is the application of advanced statistical techniques to bioinformatics issues. In this manuscript we present the results of our works concerning the clustering of genetic sequences via Laplacian eigenmaps and Gaussian mixture model, the study of the propagation of transposable elements in the genome via a branching process, the analysis of metagenomic data in ecology via ROC curves or the ordinal polytomous regression penalized by the l1-norm.

La positivité gamma d’une suite combinatoire unifie à la fois l’unimodalité et la symétrie de cette suite. Trouver des nouvelles familles d’objets dont les polynômes énumératives ont une positivité gamma est un défi et un sujet important en combinatoire et géométrie. Il a attiré beaucoup d’attention ces derniers temps en raison de la conjecture de Gal, qui affirme que le gamma-vecteur a des coefficients positifs pour n’importe quel polytope simple. Souvent, le h-polynôme pour les polytopes simpliciaux de signification combinatoire peut être donné en tant que fonction génératrice sur un ensemble d’objets combinatoires apparentés par rapport à une statistique telle que le nombre des descentes, dont les polynômes énumératifs sur les permutations sont des polynômes Eulériens. Ce travail traite des propriétés gamma de plusieurs polynômes énumératifs de permutations tels que les polynômes Eulériens et les polynômes de Narayana. Cette thèse contient cinq chapitres / The gamma positivity of a combinatorial sequence unifies both unimodality and symmetry. Finding new family of objets whose enumerative sequences have gamma positivity is a challenge and important topic in recent years. it has received considerable attention in recent times because of Gal’s conjecture, which asserts that the gamma-vector has nonnegative entries for any flag simple polytope. Often times, the h-polynomial for simplicial polytopes of combinatorial signification can be given as a generating function over a related set of combinatorial objects with respect to some statistic like the descent numbers, whose enumerative polynomials on permutations are Eulerian polynomials.This work deals with the gamma properties of several enumerative polynomials of permutation such as Eulerian polynomials and Narayana polynomials. This thesis contains five chapters

Les salmonelles sont la première cause bactérienne d'infections d'origine alimentaire en France. Ces pathogènes zoonotiques sont présents dans de nombreuses sources animales et font l'objet d'une lutte dès l'élevage. Ainsi, identifier la contribution relative des différentes sources aux cas humains est essentiel pour mettre en place une politique de lutte efficace. L'outil bayésien d'attribution par typage microbiologique qui permet de déterminer le nombre de cas liés à chaque source est pour cela particulièrement adapté. Le principe du modèle consiste à comparer la distribution de types microbiologiques (sérotypes et sous-types), parmi les cas humains et dans les sources animales, en pondérant par les quantités des sources consommées et en tenant compte des spécificités des sources et des types. Les objectifs des travaux de thèse étaient d'identifier et collecter les données nécessaires pour appliquer un tel modèle et d'évaluer sa robustesse et l'impact de la qualité des données sur les résultats. Le système de surveillance français des salmonelles a pour cela été décrit et analysé, et une base de données suffisante pour appliquer le modèle a été constituée. L'application du modèle dans divers pays européens a montré les limites de l'approche. Comme attendu, le modèle est très sensible à l'information a priori informative que sa structure surparamétrée rend nécessaire. Nous avons proposé une paramétrisation plus adaptée basée sur les données. L'application du modèle à des données de surveillance passive (proportions) et actives (prévalences) a alors montré la robustesse du modèle. Ainsi, mettre en place une démarche d'attribution est possible en France. Les limites méthodologiques sont à explorer plus avant, mais les perspectives d'utilisation, notamment pour attribuer les cas en fonction de la résistance aux antibiotiques, justifient les efforts requis.

<p>In this dissertation I study substantially the effects of disembodied technical change on the total factor productivity and inputs demand in U.S. Apparel industry during 1958-1996. A time series input-output data set over the sector employs to estimate an error corrected model of a four-factor transcendental logarithmic cost function. The empirical results indicate technical impact on the total factor productivity at the rate of 9% on average. Technical progress has in addition a biased effect on factor augmenting in the sector.</p>

In this dissertation I study substantially the effects of disembodied technical change on the total factor productivity and inputs demand in U.S. Apparel industry during 1958-1996. A time series input-output data set over the sector employs to estimate an error corrected model of a four-factor transcendental logarithmic cost function. The empirical results indicate technical impact on the total factor productivity at the rate of 9% on average. Technical progress has in addition a biased effect on factor augmenting in the sector.

In sedimentary basins, rock thermal conductivity can vary both laterally and vertically, thus altering the basin’s thermal structure locally and regionally. Knowledge of the thermal conductivity of geological formations and its spatial variations is essential, not only for quantifying basin evolution and hydrocarbon maturation processes, but also for understanding geothermal conditions in a geological setting. In conjunction with the temperature gradient, thermal conductivity represents the basic input parameter for the determination of the heat-flow density; which, in turn, is applied as a major input parameter in thermal modeling at different scales. Drill-core samples, which are necessary to determine thermal properties by laboratory measurements, are rarely available and often limited to previously explored reservoir formations. Thus, thermal conductivities of Mesozoic rocks in the North German Basin (NGB) are largely unknown. In contrast, geophysical borehole measurements are often available for the entire drilled sequence. Therefore, prediction equations to determine thermal conductivity based on well-log data are desirable. In this study rock thermal conductivity was investigated on different scales by (1) providing thermal-conductivity measurements on Mesozoic rocks, (2) evaluating and improving commonly applied mixing models which were used to estimate matrix and pore-filled rock thermal conductivities, and (3) developing new well-log based equations to predict thermal conductivity in boreholes without core control. Laboratory measurements are performed on sedimentary rock of major geothermal reservoirs in the Northeast German Basin (NEGB) (Aalenian, Rhaethian-Liassic, Stuttgart Fm., and Middle Buntsandstein). Samples are obtained from eight deep geothermal wells that approach depths of up to 2,500 m. Bulk thermal conductivities of Mesozoic sandstones range between 2.1 and 3.9 W/(m∙K), while matrix thermal conductivity ranges between 3.4 and 7.4 W/(m∙K). Local heat flow for the Stralsund location averages 76 mW/m², which is in good agreement to values reported previously for the NEGB. For the first time, in-situ bulk thermal conductivity is indirectly calculated for entire borehole profiles in the NEGB using the determined surface heat flow and measured temperature data. Average bulk thermal conductivity, derived for geological formations within the Mesozoic section, ranges between 1.5 and 3.1 W/(m∙K). The measurement of both dry- and water-saturated thermal conductivities allow further evaluation of different two-component mixing models which are often applied in geothermal calculations (e.g., arithmetic mean, geometric mean, harmonic mean, Hashin-Shtrikman mean, and effective-medium theory mean). It is found that the geometric-mean model shows the best correlation between calculated and measured bulk thermal conductivity. However, by applying new model-dependent correction, equations the quality of fit could be significantly improved and the error diffusion of each model reduced. The ‘corrected’ geometric mean provides the most satisfying results and constitutes a universally applicable model for sedimentary rocks. Furthermore, lithotype-specific and model-independent conversion equations are developed permitting a calculation of water-saturated thermal conductivity from dry-measured thermal conductivity and porosity within an error range of 5 to 10%. The limited availability of core samples and the expensive core-based laboratory measurements make it worthwhile to use petrophysical well logs to determine thermal conductivity for sedimentary rocks. The approach followed in this study is based on the detailed analyses of the relationships between thermal conductivity of rock-forming minerals, which are most abundant in sedimentary rocks, and the properties measured by standard logging tools. By using multivariate statistics separately for clastic, carbonate and evaporite rocks, the findings from these analyses allow the development of prediction equations from large artificial data sets that predict matrix thermal conductivity within an error of 4 to 11%. These equations are validated successfully on a comprehensive subsurface data set from the NGB. In comparison to the application of earlier published approaches formation-dependent developed for certain areas, the new developed equations show a significant error reduction of up to 50%. These results are used to infer rock thermal conductivity for entire borehole profiles. By inversion of corrected in-situ thermal-conductivity profiles, temperature profiles are calculated and compared to measured high-precision temperature logs. The resulting uncertainty in temperature prediction averages < 5%, which reveals the excellent temperature prediction capabilities using the presented approach. In conclusion, data and methods are provided to achieve a much more detailed parameterization of thermal models. / Die thermische Modellierung des geologischen Untergrundes ist ein wichtiges Werkzeug bei der Erkundung und Bewertung tiefliegender Ressourcen sedimentärer Becken (e.g., Kohlenwasserstoffe, Wärme). Die laterale und vertikale Temperaturverteilung im Untergrund wird, neben der Wärmestromdichte und der radiogenen Wärmeproduktion, hauptsächlich durch die Wärmeleitfähigkeit (WLF) der abgelagerten Gesteinsschichten bestimmt. Diese Parameter stellen die wesentlichen Eingangsgrößen für thermische Modelle dar. Die vorliegende Dissertation befasst sich mit der Bestimmung der Gesteins-WLF auf verschiedenen Skalen. Dies umfasst (1) laborative WLF-Messungen an mesozoischen Bohrkernproben, (2) die Evaluierung und Verbesserung der Prognosefähigkeit von Mischgesetzten zur Berechnung von Matrix- und Gesamt-WLF sedimentärer Gesteine, sowie (3) die Entwicklung neuer Prognosegleichungen unter Nutzung bohrlochgeophysikalischer Messungen und multivariater Analysemethoden im NGB. Im Nordostdeutschen Becken (NEGB) wurden für die wichtigsten geothermischen Reservoire des Mesozoikums (Aalen, Rhät-Lias-Komplex, Stuttgart Formation, Mittlerer Buntsandstein) Bohrkerne geothermischer Tiefbohrungen (bis 2.500 m Tiefe) auf Ihre thermischen und petrophysikalischen Eigenschaften hin untersucht. Die WLF mesozoischer Sandsteine schwankt im Mittel zwischen 2,1 und 3,9 W/(m∙K), die WLF der Gesteinsmatrix hingegen im Mittel zwischen 3,4 und 7,4 W/(m∙K). Neu berechnete Werte zur Oberflächenwärmestromdichte (e.g., 76 mW/m², Stralsund) stehen im Einklang mit den Ergebnissen früherer Studien im NEGB. Erstmals im NDB wurde für das mesozoisch/känozoischen Intervall am Standort Stralsund ein in-situ WLF-Profil berechnet. In-situ Formations-WLF, für als potentielle Modelschichten interessante, stratigraphische Intervalle, variieren im Mittel zwischen 1,5 und 3,1 W/(m∙K) und bilden eine gute Grundlage für kleinskalige (lokale) thermische Modelle. Auf Grund der in aller Regel nur eingeschränkt verfügbaren Bohrkernproben sowie des hohen laborativen Aufwandes zur Bestimmung der WLF waren alternative Methoden gesucht. Die Auswertung petrophysikalischer Bohrlochmessungen mittels mathematischer-statistischer Methoden stellt einen lang genutzten und erprobten Ansatz dar, welcher in seiner Anwendbarkeit jedoch auf die aufgeschlossenen Gesteinsbereiche (Genese, Geologie, Stratigraphie, etc.) beschränkt ist. Daher wurde ein leicht modifizierter Ansatz entwickelt. Die thermophysikalischen Eigenschaften der 15 wichtigsten gesteinsbildenden Minerale (in Sedimentgesteinen) wurden statistisch analysiert und aus variablen Mischungen dieser Basisminerale ein umfangreicher, synthetischer Datensatz generiert. Dieser wurde mittels multivariater Statistik bearbeitet, in dessen Ergebnis Regressionsgleichungen zur Prognose der Matrix-WLF für drei Gesteinsgruppen (klastisch, karbonatisch, evaporitisch) abgeleitet wurden. In einem zweiten Schritt wurden für ein Echtdatenset (laborativ gemessene WLF und Standardbohrlochmessungen) empirische Prognosegleichungen für die Berechnung der Gesamt-WLF entwickelt. Die berechneten WLF zeigen im Vergleich zu gemessenen WLF Fehler zwischen 5% und 11%. Die Anwendung neu entwickelter, sowie in der Literatur publizierter Verfahren auf den NGB-Datensatz zeigt, dass mit den neu aufgestellten Gleichungen stets der geringste Prognosefehler erreicht wird. Die Inversion neu berechneter WLF-Profile erlaubt die Ableitung synthetischer Temperaturprofile, deren Vergleich zu gemessenen Gesteinstemperaturen in einen mittleren Fehler von < 5% resultiert. Im Rahmen geothermischer Berechnungen werden zur Umrechnung zwischen Matrix- und Gesamt-WLF häufig Zwei-Komponenten-Mischmodelle genutzt (Arithmetisches Mittel, Harmonische Mittel, Geometrisches Mittel, Hashin-Shtrikman Mittel, Effektives-Medium Mittel). Ein umfangreicher Datensatz aus trocken- und gesättigt-gemessenen WLF und Porosität erlaubt die Evaluierung dieser Modelle hinsichtlich Ihrer Prognosefähigkeit. Diese variiert für die untersuchten Modelle stark (Fehler: 5 – 53%), wobei das geometrische Mittel die größte, quantitativ aber weiterhin unbefriedigende Übereinstimmungen zeigt. Die Entwicklung und Anwendung mischmodelspezifischer Korrekturgleichungen führt zu deutlich reduzierten Fehlern. Das korrigierte geometrische Mittel zeigt dabei, bei deutlich reduzierter Fehlerstreubreite, erneut die größte Übereinstimmung zwischen berechneten und gemessenen Werten und scheint ein universell anwendbares Mischmodel für sedimentäre Gesteine zu sein. Die Entwicklung modelunabhängiger, gesteinstypbezogener Konvertierungsgleichungen ermöglicht die Abschätzung der wassergesättigten Gesamt-WLF aus trocken-gemessener WLF und Porosität mit einem mittleren Fehler < 9%. Die präsentierten Daten und die neu entwickelten Methoden erlauben künftig eine detailliertere und präzisere Parametrisierung thermischer Modelle sedimentärer Becken.

Simultaneous operation of different wireless applications in the same geographical region and the same frequency band gives rise to undesired interference issues. Since licensed (primary) applications have been granted priority access to the frequency spectrum, unlicensed (secondary) services should avoid imposing interference on the primary system. In other words, secondary system’s activity in the same bands should be in a controlled fashion so that the primary system maintains its quality of service (QoS) requirements. In this thesis, we consider collocated point-to-multipoint primary and secondary networks that have simultaneous access to the same frequency band. Particularly, we examine three different levels at which the two networks may coexist: pure interference, asymmetric co-existence, and symmetric co-existence levels. At the pure interference level, both networks operate simultaneously regardless of their interference to each other. At the other two levels, at least one of the networks attempts to mitigate its interference to the other network by deactivating some of its users. Specifically, at the asymmetric co-existence level, the secondary network selectively deactivates its users based on knowledge of the interference and channel gains, whereas at the symmetric level, the primary network also schedules its users in the same way. Our aim is to derive optimal sum-rates (i.e., throughputs) of both networks at each co-existence level as the number of users grows asymptotically and evaluate how the sum-rates scale with the network size. In order to find the asymptotic throughput results, we derive two propositions; one on the asymptotic behaviour of the largest order statistic and one on the asymptotic behaviour of the sum of lower order statistics. As a baseline comparison, we calculate primary and secondary sum-rates for the time division (TD) channel sharing. Then, we compare the asymptotic secondary sum-rate in TD to that under simultaneous channel sharing, while ensuring the primary network maintains the same sum-rate in both cases. Our results indicate that simultaneous channel sharing at both asymmetric and symmetric co-existence levels can outperform TD. Furthermore, this enhancement is achievable when user scheduling in uplink mode is based only on the interference gains to the opposite network and not on a network’s own channel gains. In other words, the optimal secondary sum-rate is achievable by applying a scheduling strategy, referred to as the least interference strategy, for which only the knowledge of interference gains is required and can be performed in a distributed way.

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Simultaneous operation of different wireless applications in the same geographical region and the same frequency band gives rise to undesired interference issues. Since licensed (primary) applications have been granted priority access to the frequency spectrum, unlicensed (secondary) services should avoid imposing interference on the primary system. In other words, secondary system’s activity in the same bands should be in a controlled fashion so that the primary system maintains its quality of service (QoS) requirements. In this thesis, we consider collocated point-to-multipoint primary and secondary networks that have simultaneous access to the same frequency band. Particularly, we examine three different levels at which the two networks may coexist: pure interference, asymmetric co-existence, and symmetric co-existence levels. At the pure interference level, both networks operate simultaneously regardless of their interference to each other. At the other two levels, at least one of the networks attempts to mitigate its interference to the other network by deactivating some of its users. Specifically, at the asymmetric co-existence level, the secondary network selectively deactivates its users based on knowledge of the interference and channel gains, whereas at the symmetric level, the primary network also schedules its users in the same way. Our aim is to derive optimal sum-rates (i.e., throughputs) of both networks at each co-existence level as the number of users grows asymptotically and evaluate how the sum-rates scale with the network size. In order to find the asymptotic throughput results, we derive two propositions; one on the asymptotic behaviour of the largest order statistic and one on the asymptotic behaviour of the sum of lower order statistics. As a baseline comparison, we calculate primary and secondary sum-rates for the time division (TD) channel sharing. Then, we compare the asymptotic secondary sum-rate in TD to that under simultaneous channel sharing, while ensuring the primary network maintains the same sum-rate in both cases. Our results indicate that simultaneous channel sharing at both asymmetric and symmetric co-existence levels can outperform TD. Furthermore, this enhancement is achievable when user scheduling in uplink mode is based only on the interference gains to the opposite network and not on a network’s own channel gains. In other words, the optimal secondary sum-rate is achievable by applying a scheduling strategy, referred to as the least interference strategy, for which only the knowledge of interference gains is required and can be performed in a distributed way.