Les statistiques des fluctuations de courant dans un échantillon mésoscopique sous irradiation n'ont jamais été explorées au-delà de la variance et du troisième moment. Nous rapportons la première mesure du quatrième cumulant de bruit dans une jonction tunnel dans le régime classique (c'est-à-dire k [indice inférieur B]T >> h f) en présence d'un courant continu et d'une excitation micro-onde en utilisant deux méthodes. Tout d'abord, nous avons étudié la corrélation entre les fluctuations de puissance à deux fréquences, f [indice inférieur 1] = 4,5 GHz et f [indice inférieur 2] = 7,15 GHz. Cette corrélation existe seulement pour certaines fréquences d'excitation. Nous avons également effectué une mesure directe des statistiques en numérisant le bruit à grande vitesse après conversion vers les basses fréquences. Les résultats obtenus à partir de ces expériences sont en très bon accord avec les prédictions théoriques de la dynamique de bruit. En terme de photons, le quatrième cumulant correspond à une corrélation entre les photons de différentes fréquences. -- The statistics of current fluctuations in a mesoscopic sample under irradiation has never been explored beyond the variance and third moment. We report the first measurement of the fourth cumulant of noise in a tunnel junction in the classical regime (i.e. k[subscript B] T >> hf) in the presence of a d.c and microwave excitation, using two methods. First, we have investigated the correlation between the power fluctuations at two frequencies, f[subscript 1] = 4.5 GHz and f[subscript 2] = 7.15 GHz. This correlation exists only for certain excitation frequencies. We have also performed a direct measurement of the statistics by digitizing the noise at high speed after down conversion. The results obtained from these experiments are in very good agreement with the theoretical predictions of noise dynamics. In terms of photons, the fourth cumulant corresponds to a correlation between photons of different frequencies.

Les cellules vivantes peuvent être considérées comme des systèmes dynamiques. Ses propriétés dynamiques sont essentiellement régulées par des réseaux génétiques. Ce travail de thèse est motivé par l’existence de comportements dynamiques récurrents des réseaux génétiques tels que les oscillations, et s’articule autour de trois études. La première étude concerne le rôle des délais qui sont des ingrédients clés des oscillations. Dans la modélisation déterministe, le délai est modélisé comme délai explicite ou délai réactionnel. En étudiant un réseau génétique comprenant un gène auto-réprimé qui contient divers délais, nos résultats montrent analytiquement le principe de combinaison des divers délais et les influences différentes des délais explicites et réactionnels sur les oscillations. La seconde étude s’intéresse à l’impact des fluctuations moléculaires. Nous proposons un développement de cumulants de l’équation maîtresse et l’appliquons au circuit de gène auto-réprimé. Nous trouvons que les fluctuations modifient significativement les moyennes des quantités moléculaires prévues par les modèles déterministes, et induisent les oscillations. La troisième étude concerne les effets dynamiques de la pause des RNA Polymérases sur la transcription qui est modélisée par le modèle TASEP. Pour des durées des pauses intermédiaires et longues pour lesquelles l’approche de champ moyen n’est pas validée, nous parvenons néanmoins à une bonne compréhension des différents mécanismes qui contrôlent la dynamique de transcription et obtenons une description quantitative du taux de transcription en bon accord avec les simulations numériques. / Living cells can be viewed as dynamical systems and cellular dynamical properties essentially reply on genetic networks. This thesis work is motivated by one striking dynamical behavior of genetic networks, oscillation, and mainly includes three studies. The first study is about the delay that is one of key ingredients of biological oscillation. In mathematical modeling, delay is usually modeled as explicit delay or reaction delay. By studying a minimal genetic network, a self-repressing gene involving various delays, our analytical results reveal the combination principle of various delays and different dynamical influences of explicit and reaction delays on oscillations. The second study is to investigate the dynamical influences of molecular fluctuations on the oscillatory behavior. We develop a cumulant expansion of the master equation and apply it to the self-repressing gene circuit. We find that fluctuations shift significantly the averages of molecular quantities predicted by deterministic models and induce oscillations. In the third study, we investigate the dynamical effects of RNA Polymerase pausing on transcription in using TASEP model. In the limit case where pause duration is short, we can still construct a mean-field model to analyze the transcription rate and site occupation. In the general case where mean-field approach no long applies, we obtain a good understanding of various mechanisms driving the transcription dynamics over the entire range of pause duration, and in particular a theoretical prediction of transcription rate that agrees well with numerical simulations is given.

This paper proposes a cumulant based classification means to identify waveforms for a blind receiver in the presence of time varying channels, which is built from the work done on cumulants in static channels currently in the literature. Results show the classification accuracy is on the order or better than current methods in use in static channels that do not vary over an observation period. This is accomplished by making use of second through tenth order cumulants in a signature vector that the search engine platform has the means of differentiating. A receiver can then blindly identify waveforms accurately in the presence of multipath Rayleigh fading with AWGN noise. Channel learning occurs prior to classification in order to identify the consistent distortion pattern for a waveform that is observable in the signature vector. Then using a database look-up method, the observed waveform is identified as belonging to a particular cluster based on the observed signature vector. If the distortion patterns are collected from a variety of channel types, the database can then classify both the waveform and the rough channel type that the waveform passed through. If the exact channel model or channel parameters is known and used as a limiter, significant improvement on the waveform classification can be achieved. Greater accuracy comes from using the exact channel model as the limiter. / Master of Science

Les statistiques des fluctuations de courant dans un ??chantillon m??soscopique sous irradiation n'ont jamais ??t?? explor??es au-del?? de la variance et du troisi??me moment. Nous rapportons la premi??re mesure du quatri??me cumulant de bruit dans une jonction tunnel dans le r??gime classique (c'est-??-dire k [indice inf??rieur B]T >> h f) en pr??sence d'un courant continu et d'une excitation micro-onde en utilisant deux m??thodes. Tout d'abord, nous avons ??tudi?? la corr??lation entre les fluctuations de puissance ?? deux fr??quences, f [indice inf??rieur 1] = 4,5 GHz et f [indice inf??rieur 2] = 7,15 GHz. Cette corr??lation existe seulement pour certaines fr??quences d'excitation. Nous avons ??galement effectu?? une mesure directe des statistiques en num??risant le bruit ?? grande vitesse apr??s conversion vers les basses fr??quences. Les r??sultats obtenus ?? partir de ces exp??riences sont en tr??s bon accord avec les pr??dictions th??oriques de la dynamique de bruit. En terme de photons, le quatri??me cumulant correspond ?? une corr??lation entre les photons de diff??rentes fr??quences. -- The statistics of current fluctuations in a mesoscopic sample under irradiation has never been explored beyond the variance and third moment. We report the first measurement of the fourth cumulant of noise in a tunnel junction in the classical regime (i.e. k[subscript B] T >> hf) in the presence of a d.c and microwave excitation, using two methods. First, we have investigated the correlation between the power fluctuations at two frequencies, f[subscript 1] = 4.5 GHz and f[subscript 2] = 7.15 GHz. This correlation exists only for certain excitation frequencies. We have also performed a direct measurement of the statistics by digitizing the noise at high speed after down conversion. The results obtained from these experiments are in very good agreement with the theoretical predictions of noise dynamics. In terms of photons, the fourth cumulant corresponds to a correlation between photons of different frequencies.

Data for which the number of predictors exponentially exceeds the number of observations is becoming increasingly prevalent in fields such as bioinformatics, medical imaging, computer vision, And social network analysis. One of the leading questions statisticians must answer when confronted with such “big data” is how to reduce a set of exponentially many predictors down to a set of a mere few predictors which have a truly causative effect on the response being modelled. This process is often referred to as feature screening. In this work we propose three new methods for feature screening. The first method we propose (TC-SIS) is specifically intended for use with data having both categorical response and predictors. The second method we propose (JCIS) is meant for feature screening for interactions between predictors. JCIS is rare among interaction screening methods in that it does not require first finding a set of causative main effects before screening for interactive effects. Our final method (GenCorr) is intended for use with data having a multivariate response. GenCorr is the only method for multivariate screening which can screen for both causative main effects and causative interactions. Each of these aforementioned methods will be shown to possess both theoretical robustness as well as empirical agility.

This paper describes the implementation of a scanning signal detector and automatic modulation classification system. The classification technique is a completely blind method, with no prior knowledge of the signal's center frequency, bandwidth, or symbol rate. An energy detector forms the initial approximations of the signal parameters. The energy detector used in the wideband sweep is reused to obtain fine estimates of the center frequency and bandwidth of the signal. The subsequent steps reduce the effect of frequency offset and sample timing error, resulting in a constellation of the modulation of interest. The cumulant of the constellation is compared to a set of known ideal cumulant values, forming the classification estimate. The algorithm uses two platforms that together provide high speed parallel processing and flexible run-time operation. High-rate spectral scanning using an energy detector is run in parallel with a variable down sampling path; both are highly pipelined structures, which allows for high data throughput. A pair of processing cores is used to record spectral usage and signal characteristics as well as perform the actual classification. The resulting classification system can accurately identify modulations below 5 dB of signal-to-noise ratio (SNR) for some cases of the phase shift keying family of modulations but requires a much higher SNR to accurately classify higher-order modulations. These estimates tend toward classifying all signals as binary phase shift keying because of limits of the noise power estimation part of the cumulant normalization process. Other effects due to frequency offset and synchronization timing are discussed. / Master of Science

La philosophie de cette thèse est de dire que nos plus grandes chances de trouver et de caractériser les ingrédients essentiels du modèle cosmologique passe par l'élargissement de l'éventail des méthodes que l'on peut utiliser dans le but de trouver une nouvelle physique. Bien qu'il soit d'une importance primordiale de continuer à affiner, à de-biaiser et à rendre plus puissantes, les stratégies qui ont contribué à établir le modèle de concordance, il est également crucial de remettre en question, avec de nouvelles méthodes, tous les secteurs de l'actuel paradigme cosmologique. Cette thèse, par conséquent, s'engage dans le défi de développer des sondes cosmologiques nouvelle et performantes qui visent à optimiser les résultats scientifiques des futures grand sondages de galaxies. L'objectif est double. Du côté théorique, je cherche à mettre au point de nouvelles stratégies de test qui sont peu (voire pas du tout) affectées par des incertitudes astrophysiques ou par des modèles phénoménologiques qui ne sont pas complet . Cela rendra les interprétations cosmologiques plus facile et plus sûr. Du côté des observations, l'objectif est d'évaluer les performances des stratégies proposées en utilisant les données actuelles, dans le but de démontrer leur potentiel pour les futures grandes missions cosmologiques tels que BigBoss et EUCLID. / The philosophy of this thesis is that our best chances of finding and characterizing the essential ingredients of a well grounded cosmological model is by enlarging the arsenal of methods with which we can hunt for new physics. While it is of paramount importance to continue to refine, de-bias and power, the very same testing strategies that contributed to establish the concordance model, it is also crucial to challenge, with new methods, all the sectors of the current cosmological paradigm. This thesis, therefore, engages in the challenge of developing new and performant cosmic probes that aim at optimizing the scientific output of future large redshift surveys. The goal is twofold. From the theoretical side, I aim at developing new testing strategies that are minimally (if not at all) affected by astrophysical uncertainties or by not fully motivated phenomenological models. This will make cosmological interpretations easier and safer. From the observational side, the goal is to gauge the performances of the proposed strategies using current, state of the art, redshift data, and to demonstrate their potential for the future large cosmological missions such as BigBOSS and EUCLID.

We determine the dynamical structure factors of two gapped correlated electron systems, namely the Ising model in a strong transverse field and the two-leg spin-1/2 Heisenberg ladder in the limit of strong rung coupling. We consider the low-temperature limit, employing a variety of analytical and numerical techniques. The coherent modes of single-particle excitations, which are delta functions at zero temperature, are shown to broaden asymmetrically in energy with increasing temperature. Firstly, we apply a low-temperature “resummation” inspired by the Dyson equation to a linked-cluster expansion of the two-leg Heisenberg ladder. We include matrix elements to second order in the interaction between states containing up to two particles. A low-frequency response similar to the “Villain mode” is also observed. Next, we apply a cumulant expansion technique to the transverse field Ising model. We resolve the issue of negative spectral weight caused by double pole in the leading self-energy diagram by including a resummation of terms obtained from the six-point function, demonstrating that the perturbation series in 2n-spin correlation functions can be extended to higher orders. The result generalises to higher dimensions and the analytic calculation is compared to a numerical Pade approximant. We outline the extension of this method to the strong coupling ladder. Finally, we compare the previous results to numerical data obtained by full diagonalisation of finite chains and numerical evaluation of the Pfaffian, a method specific to the transverse field Ising chain. The latter method is used for a phenomenological study of the asymmetric broadening as well as an evaluation of fitting functions for the broadened lineshapes.

The novelty and originality of the work consists in the fact that in order to obtain asymptotic expansions with optimal values of the remainder terms in the zone of large deviations, along with the cumulant method the classical method of characteristic functions has to be used. In addition, when solving the problems stated in the work, other than the well known results in the problems of limit theorems of the probability theory and mathematical statistics, we have to estimate constants. Technically it is frequently rather a complicated task. The results obtained in the work have good opportunities to be applied in probability theory, mathematical statistics, econometric, etc. That is illustrated in the last section of the work in which theorems of large deviations are proved in the summation of weighted random variables with weights as well as discounted limit theorems.

Response and stability of vessel rolling motion with strongly nonlinear softening stiffness will be studied in this dissertation using the methods of stochastic dynamical systems. As one of the most classic stability failure modes of vessel dynamics, large amplitude rolling motion in random beam waves has been studied in the past decades by many different research groups. Due to the strongly nonlinear softening stiffness and the stochastic excitation, there is still no general approach to predict the large amplitude rolling response and capsizing phenomena. We studied the rolling problem respectively using the shaping filter technique, stochastic averaging of the energy envelope and the stochastic Melnikov function. The shaping filter technique introduces some additional Gaussian filter variables to transform Gaussian white noise to colored noise in order to satisfy the Markov properties. In addition, we developed an automatic cumulant neglect tool to predict the response of the high dimensional dynamical system with higher order neglect. However, if the system has any jump phenomena, the cumulant neglect method may fail to predict the true response. The stochastic averaging of the energy envelope and the Melnikov function both have been applied to the rolling problem before, it is our first attempt to apply both approaches to the same vessel and compare their efficiency and capability. The inverse of the mean first passage time based on Markov theory and rate of phase space flux based on the stochastic Melnikov function are defined as two different, but analogous capsizing criteria. The effects of linear and nonlinear damping and wave characteristic frequency are studied to compare these two criteria. Further investigation of the relationship between the Markov and Melnikov based method is needed to explain the difference and similarity between the two capsizing criteria.