Sur les familles des lois de fonction de hasard unimodale (applications en fiabilité et analyse de survie)

En fiabilité et en analyse de survie, les distributions qui ont une fonction de hasard unimodale ne sont pas nombreuses, qu'on peut citer: Gaussienne inverse ,log-normale, log-logistique, de Birnbaum-Saunders, de Weibull exponentielle et de Weibullgénéralisée. Dans cette thèse, nous développons les tests modifiés du Chi-deux pour ces distributions tout en comparant la distribution Gaussienne inverse avec les autres. Ensuite nousconstruisons le modèle AFT basé sur la distribution Gaussienne inverse et les systèmes redondants basés sur les distributions de fonction de hasard unimodale.In reliability and survival analysis, distributions that have a unimodalor $\cap-$shape hazard rate function are not too many, they include: the inverse Gaussian,log-normal, log-logistic, Birnbaum-Saunders, exponential Weibull and power generalized Weibulldistributions. In this thesis, we develop the modified Chi-squared tests for these distributions,and we give a comparative study between the inverse Gaussian distribution and the otherdistributions, then we realize simulations. We also construct the AFT model based on the inverseGaussian distribution and redundant systems based on distributions having a unimodal hazard ratefunction.BORDEAUX1-Bib.electronique (335229901) / SudocSudocFranceF

A Generalized Framework for Quantifying the Dynamics of EEG Event-Related Desynchronization

Brains were built by evolution to react swiftly to environmental challenges. Thus, sensory stimuli must be processed ad hoc, i.e., independent—to a large extent—from the momentary brain state incidentally prevailing during stimulus occurrence. Accordingly, computational neuroscience strives to model the robust processing of stimuli in the presence of dynamical cortical states. A pivotal feature of ongoing brain activity is the regional predominance of EEG eigenrhythms, such as the occipital alpha or the pericentral mu rhythm, both peaking spectrally at 10 Hz. Here, we establish a novel generalized concept to measure event-related desynchronization (ERD), which allows one to model neural oscillatory dynamics also in the presence of dynamical cortical states. Specifically, we demonstrate that a somatosensory stimulus causes a stereotypic sequence of first an ERD and then an ensuing amplitude overshoot (event-related synchronization), which at a dynamical cortical state becomes evident only if the natural relaxation dynamics of unperturbed EEG rhythms is utilized as reference dynamics. Moreover, this computational approach also encompasses the more general notion of a “conditional ERD,” through which candidate explanatory variables can be scrutinized with regard to their possible impact on a particular oscillatory dynamics under study. Thus, the generalized ERD represents a powerful novel analysis tool for extending our understanding of inter-trial variability of evoked responses and therefore the robust processing of environmental stimuli

Lamotrigine and levetiracetam exert a similar modulation of TMS-evoked EEG potentials

Objective: Antiepileptic drug (AED) treatment failures may occur because there is insufficient drug in the brain or because of a lack of relevant therapeutic response. Until now there is no possibility to measure these factors. It has been recently shown that the combination of transcranial magnetic stimulation and electroencephalography (TMS-EEG) can measure the effects of drugs in healthy volunteers. TMS-evoked EEG potentials (TEPs) comprise a series of positive and negative deflections which can be specifically modulated by drugs with a well-known mode of action targeting inhibitory neurotransmission. Hence, we hypothesised that TMS-EEG can detect effects of two widely used AEDs, lamotrigine and levetiracetam, in healthy volunteers. Methods: Fifteen healthy subjects participated in a pseudo randomized, placebo-controlled, double-blind, crossover design, using a single oral dose of lamotrigine (300mg) and levetiracetam (3000mg). TEPs were recorded before and 120 min after drug intake and the effects of drugs on the amplitudes of TEP components were statistically evaluated. Results: A non-parametric cluster-based permutation analysis of TEP amplitudes showed that both AEDs increased the amplitude of the negative potential at 45ms after stimulation (N45) and suppressed the positive peak at 180ms (P180). This is the first demonstration of AED-induced modulation of TMS-EEG measures. Significance: Despite the different mechanism of action that lamotrigine and levetiracetam exert at molecular level, both AEDs impact the TMS-EEG response in a similar way. These TMS-EEG fingerprints observed in healthy subjects are candidate predictive markers of treatment response in patients on monotherapy with lamotrigine and levetiracetam

On approximation of Gaussian integrals

In this article we compare the difference between an absolute moment of any Gaussian measure on the Hilbert space and the corresponding moment of its projection onto some finite-dimensional subspace.Gaussian measure Hilbert space Banach space Infinite-dimensional Gaussian integral

Fiabilité et analyse de survie (le modèle semi-paramétrique de dégradation)

On a développé le modèle de dégradation général dans un environnement dynamique appliqué en fiabilité et analyse de survie. On a proposé les estimateurs semi paramétriques et nous avons étudié ses propriétés asymptotiques. On a présenté une nouvelle généralisation de la famille Weibull. Nous avons testé Weibull contre Weibull généralisé en utilisant Nikulin-Moore statistique basé sur les classes de Neyman-Pearson, ensuite nous avons étudié le test d'ajustement et de kullback-lieber pour les données censurées.We consider the general degradation path model in dynamic environment. We proposed semi parametric estimators and we studied their asympthotic properties. We present a new extension of weibull families. We consider goodness-of-fit test for weibull against generalized weibull, applied Nikulin-Moore statistic. We compared chi-squared test and kullback-lieber test in the case of censored data.BORDEAUX2-BU Santé (330632101) / SudocSudocFranceF

Statistique inférentielle pour le modèle de Cauchy et le modèle de vie accélérée Crur

BORDEAUX1-BU Sciences-Talence (335222101) / SudocSudocFranceF