Algebraic decay of velocity fluctuations near a wall

Computer simulations of the dynamics of a colloidal particle suspended in a fluid confined by an interface show that the asymptotic decay of the velocity correlation functions is algebraic. The exponents of the long-time tails depend on the direction of motion of the particle relative to the surface, as well as on the specific nature of the boundary conditions. In particular, we find that for the angular velocity correlation function, the decay in the presence of a slip surface is faster than the one corresponding to a stick one. An intuitive picture is introduced to explain the various long-time tails, and the simulations are compared with theoretical expressions where available.

Robust Nonlinear Mapping of Soil Contamination Using Support Regression

Spatial data analysis mapping and visualization is of great importance in various fields: environment, pollution, natural hazards and risks, epidemiology, spatial econometrics, etc. A basic task of spatial mapping is to make predictions based on some empirical data (measurements). A number of state-of-the-art methods can be used for the task: deterministic interpolations, methods of geostatistics: the family of kriging estimators (Deutsch and Journel, 1997), machine learning algorithms such as artificial neural networks (ANN) of different architectures, hybrid ANN-geostatistics models (Kanevski and Maignan, 2004; Kanevski et al., 1996), etc. All the methods mentioned above can be used for solving the problem of spatial data mapping. Environmental empirical data are always contaminated/corrupted by noise, and often with noise of unknown nature. That's one of the reasons why deterministic models can be inconsistent, since they treat the measurements as values of some unknown function that should be interpolated. Kriging estimators treat the measurements as the realization of some spatial randomn process. To obtain the estimation with kriging one has to model the spatial structure of the data: spatial correlation function or (semi-)variogram. This task can be complicated if there is not sufficient number of measurements and variogram is sensitive to outliers and extremes. ANN is a powerful tool, but it also suffers from the number of reasons. of a special type ? multiplayer perceptrons ? are often used as a detrending tool in hybrid (ANN+geostatistics) models (Kanevski and Maignank, 2004). Therefore, development and adaptation of the method that would be nonlinear and robust to noise in measurements, would deal with the small empirical datasets and which has solid mathematical background is of great importance. The present paper deals with such model, based on Statistical Learning Theory (SLT) - Support Vector Regression. SLT is a general mathematical framework devoted to the problem of estimation of the dependencies from empirical data (Hastie et al, 2004; Vapnik, 1998). SLT models for classification - Support Vector Machines - have shown good results on different machine learning tasks. The results of SVM classification of spatial data are also promising (Kanevski et al, 2002). The properties of SVM for regression - Support Vector Regression (SVR) are less studied. First results of the application of SVR for spatial mapping of physical quantities were obtained by the authorsin for mapping of medium porosity (Kanevski et al, 1999), and for mapping of radioactively contaminated territories (Kanevski and Canu, 2000). The present paper is devoted to further understanding of the properties of SVR model for spatial data analysis and mapping. Detailed description of the SVR theory can be found in (Cristianini and Shawe-Taylor, 2000; Smola, 1996) and basic equations for the nonlinear modeling are given in section 2. Section 3 discusses the application of SVR for spatial data mapping on the real case study - soil pollution by Cs137 radionuclide. Section 4 discusses the properties of the modelapplied to noised data or data with outliers.

Amplitude envelope synchronization in coupled chaotic oscillators.

A peculiar type of synchronization has been found when two Van der PolDuffing oscillators, evolving in different chaotic attractors, are coupled. As the coupling increases, the frequencies of the two oscillators remain different, while a synchronized modulation of the amplitudes of a signal of each system develops, and a null Lyapunov exponent of the uncoupled systems becomes negative and gradually larger in absolute value. This phenomenon is characterized by an appropriate correlation function between the returns of the signals, and interpreted in terms of the mutual excitation of new frequencies in the oscillators power spectra. This form of synchronization also occurs in other systems, but it shows up mixed with or screened by other forms of synchronization, as illustrated in this paper by means of the examples of the dynamic behavior observed for three other different models of chaotic oscillators.

Capacity of MIMO Channels: asymptotic evaluation under correlated fading

This paper investigates the asymptotic uniform power allocation capacity of frequency nonselective multiple-inputmultiple-output channels with fading correlation at either thetransmitter or the receiver. We consider the asymptotic situation,where the number of inputs and outputs increase without boundat the same rate. A simple uniparametric model for the fadingcorrelation function is proposed and the asymptotic capacity perantenna is derived in closed form. Although the proposed correlationmodel is introduced only for mathematical convenience, itis shown that its shape is very close to an exponentially decayingcorrelation function. The asymptotic expression obtained providesa simple and yet useful way of relating the actual fadingcorrelation to the asymptotic capacity per antenna from a purelyanalytical point of view. For example, the asymptotic expressionsindicate that fading correlation is more harmful when arising atthe side with less antennas. Moreover, fading correlation does notinfluence the rate of growth of the asymptotic capacity per receiveantenna with high Eb /N0.

Thomas-Fermi theory for atomic nuclei revisited

The recently developed semiclassical variational Wigner-Kirkwood (VWK) approach is applied to finite nuclei using external potentials and self-consistent mean fields derived from Skyrme inter-actions and from relativistic mean field theory. VWK consist s of the Thomas-Fermi part plus a pure, perturbative h 2 correction. In external potentials, VWK passes through the average of the quantal values of the accumulated level density and total en energy as a function of the Fermi energy. However, there is a problem of overbinding when the energy per particle is displayed as a function of the particle number. The situation is analyzed comparing spherical and deformed harmonic oscillator potentials. In the self-consistent case, we show for Skyrme forces that VWK binding energies are very close to those obtained from extended Thomas-Fermi functionals of h 4 order, pointing to the rapid convergence of the VWK theory. This satisfying result, however, does not cure the overbinding problem, i.e., the semiclassical energies show more binding than they should. This feature is more pronounced in the case of Skyrme forces than with the relativistic mean field approach. However, even in the latter case the shell correction energy for e.g.208 Pb turns out to be only ∼ −6 MeV what is about a factor two or three off the generally accepted value. As an adhoc remedy, increasing the kinetic energy by 2.5%, leads to shell correction energies well acceptable throughout the periodic table. The general importance of the present studies for other finite Fermi systems, self-bound or in external potentials, is pointed out.

An Interface Damage Model for the Simulation of Delamination Under Variable-Mode Ratio in Composite Materials

A thermodynamically consistent damage model for the simulation of progressive delamination under variable mode ratio is presented. The model is formulated in the context of the Damage Mechanics. The constitutive equation that results from the definition of the free energy as a function of a damage variable is used to model the initiation and propagation of delamination. A new delamination initiation criterion is developed to assure that the formulation can account for changes in the loading mode in a thermodynamically consistent way. The formulation proposed accounts for crack closure effets avoiding interfacial penetration of two adjacent layers aftercomplete decohesion. The model is implemented in a finite element formulation. The numerical predictions given by the model are compared with experimental results

Resonant tunneling effects in semiconductor heterostructures

The thesis is devoted to a theoretical study of resonant tunneling phenomena in semiconductor heterostructures and nanostructures. It considers several problems relevant to modern solid state physics. Namely these are tunneling between 2D electron layers with spin-orbit interaction, tunnel injection into molecular solid material, resonant tunnel coupling of a bound state with continuum and resonant indirect exchange interaction mediated by a remote conducting channel. A manifestation of spin-orbit interaction in the tunneling between two 2D electron layers is considered. General expression is obtained for the tunneling current with account of Rashba and Dresselhaus types of spin-orbit interaction and elastic scattering. It is demonstrated that the tunneling conductance is very sensitive to relation between Rashba and Dresselhaus contributions and opens possibility to determine the spin-orbit interaction parameters and electron quantum lifetime in direct tunneling experiments with no external magnetic field applied. A microscopic mechanism of hole injection from metallic electrode into organic molecular solid (OMS) in high electric field is proposed for the case when the molecules ionization energy exceeds work function of the metal. It is shown that the main contribution to the injection current comes from direct isoenergetic transitions from localized states in OMS to empty states in the metal. Strong dependence of the injection current on applied voltage originates from variation of the number of empty states available in the metal rather than from distortion of the interface barrier. A theory of tunnel coupling between an impurity bound state and the 2D delocalized states in the quantum well (QW) is developed. The problem is formulated in terms of Anderson-Fano model as configuration interaction between the carrier bound state at the impurity and the continuum of delocalized states in the QW. An effect of this interaction on the interband optical transitions in the QW is analyzed. The results are discussed regarding the series of experiments on the GaAs structures with a -Mn layer. A new mechanism of ferromagnetism in diluted magnetic semiconductor heterosructures is considered, namely the resonant enhancement of indirect exchange interaction between paramagnetic centers via a spatially separated conducting channel. The underlying physical model is similar to the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction; however, an important difference relevant to the low-dimensional structures is a resonant hybridization of a bound state at the paramagnetic ion with the continuum of delocalized states in the conducting channel. An approach is developed, which unlike RKKY is not based on the perturbation theory and demonstrates that the resonant hybridization leads to a strong enhancement of the indirect exchange. This finding is discussed in the context of the known experimental data supporting the phenomenon.

PREDICTING DIFFUSIVITIES IN DENSE FLUIDS

In this work the Weeks-Chandler-Andersen (WCA) perturbation theory coupled with the Enskog’s solution of the Boltzmann equation for dense hard-sphere fluids is employed for estimating diffusion coefficients in compressed pure liquids and fluids and dense fluid mixtures. The effect of density correction on the estimation of diffusivities is analyzed using the Carnahan-Starling pair correlation function and the correlation of Speedy and Harris which have been proposed as models of self-diffusion coefficient of hard-sphere fluids. The approach presented here is based on the smooth hard-sphere theory without any binary adjustable parameters and can be readily used for estimating diffusivities in multicomponent fluid mixtures. It is shown that the correlated and the predicted diffusivities are in good agreement with the experimental data and much better than estimates of Wilke-Chang equation.

The alpha2C-adrenoceptor as a neuropsychiatric drug tar-get - PET studies in human subjects

Positron emission tomography imaging has both academic and applied uses in revealing the distribution and density of different molecular targets in the central nervous system. Following the significant progress made with the dopamine D2 receptor, advances have been made in developing PET tracers to allow analysis of receptor occupancy of many other receptor types as well as evaluating changes in endogenous synaptic transmitter concentrations of transmitters e.g. serotonin and noradrenaline. Noradrenergic receptors are divided into α1-, α2- and β-adrenoceptor subfamilies, in humans each of which is composed of three receptor subtypes. The α2-adrenoceptors have an important presynaptic auto-inhibitory function on noradrenaline release but they also have postsynaptic roles in modulating the release of other neurotransmitters, such as serotonin and dopamine. One of the subtypes, the α2C-adrenoceptor, has been detected at distinct locations in the central nervous system, most notably the dorsal striatum. Several serious neurological conditions causing dementia, Alzheimer’s disease and Parkinson’s disease have been linked to disturbed noradrenergic signaling. Furthermore, altered noradrenergic signaling has also been implicated in conditions like ADHD, depression, anxiety and schizophrenia. In order to benefit future research into these central nervous system disorders as well as being useful in the clinical development of drugs affecting brain noradrenergic neurotransmission, validation work of a novel tracer for positron emission tomography studies in humans was performed. Altogether 85 PET imaging experiments were performed during four separate clinical trials. The repeatability of [11C]ORM-13070 binding was tested in healthy individuals, followed by a study to evaluate the dose-dependent displacement of [11C]ORM-13070 from α2C-adrenoceptors by a competing ligand, and the final two studies examined the sensitivity of [11C]ORM-13070 binding to reflect changes in endogenous noradrenaline levels. The repeatability of [11C]ORM-13070 binding was very high. The binding properties of the tracer allowed for a reliable estimation of α2C-AR occupancy by using the reference tissue ratio method with low test-retest variability. [11C]ORM-13070 was dose-dependently displaced from its specific binding sites by the subtype-nonselective α2-adrenoceptor antagonist atipamezole, and thus it proved suitable for use in clinical drug development of novel α2C-adrenoceptor ligands e.g. to determine the best doses and dosing intervals for clinical trials. Convincing experimental evidence was gained to support the suitability of [11C]ORM-13070 for detecting an increase in endogenous synaptic noradrenaline in the human brain. Tracer binding in the thalamus tended to increase in accordance with reduced activity of noradrenergic projections from the locus coeruleus, although statistical significance was not reached. Thus, the investigation was unable to fully validate [11C]ORM-13070 for the detection of pharmacologically evoked reductions in noradrenaline levels.

Low frequency Raman scattering in amorphous materials: fused quartz, "pyrex" boro-silicate glass and soda-lime silicate glass

Raman scattering in the region 20 to 100 cm -1 for fused quartz, "pyrex" boro-silicate glass, and soft soda-lime silicate glass was investigated. The Raman spectra for the fused quartz and the pyrex glass were obtained at room temperature using the 488 nm exciting line of a Coherent Radiation argon-ion laser at powers up to 550 mW. For the soft soda-lime glass the 514.5 nm exciting line at powers up to 660 mW was used because of a weak fluorescence which masked the Stokes Raman spectrum. In addition it is demonstrated that the low-frequency Raman coupling constant can be described by a model proposed by Martin and Brenig (MB). By fitting the predicted spectra based on the model with a Gaussian, Poisson, and Lorentzian forms of the correlation function, the structural correlation radius (SCR) was determined for each glass. It was found that to achieve the best possible fit· from each of the three correlation functions a value of the SCR between 0.80 and 0.90 nm was required for both quartz and pyrex glass but for the soft soda-lime silicate glass the required value of the SCR. was between 0.50 and 0.60 nm .. Our results support the claim of Malinovsky and Sokolov (1986) that the MB model based on a Poisson correlation function provides a universal fit to the experimental VH (vertical and horizontal polarizations) spectrum for any glass regardless of its chemical composition. The only deficiency of the MB model is its failure to fit the experimental depolarization spectra.

Régulation de l'activité transcriptionnelle de PPARgamma via l'activation des récepteurs CD36 et GHS-R1a : potentiel anti-athérosclérotique

Les sécrétines peptidiques de l’hormone de croissance (GHRPs) constituent une classe de peptides synthétiques capables de stimuler la sécrétion de l’hormone de croissance (GH). Cette activité est médiée par leur liaison à un récepteur couplé aux protéines G : le récepteur des sécrétines de l’hormone de croissance (GHS-R1a), identifié subséquemment comme le récepteur de la ghréline. La ghréline est un peptide de 28 acides aminés sécrété principalement par les cellules de la muqueuse de l’estomac, qui exerce de nombreux effets périphériques indépendamment de la sécrétion de l’hormone de croissance. Les effets indépendants de la sécrétion de GH incluent, entre autres, des actions sur le contrôle de la prise de nourriture, le métabolisme énergétique, la fonction cardiaque, le système immunitaire et la prolifération cellulaire. L’étude de la distribution périphérique des sites de liaison des GHRPs nous a permis d’identifier un second site, le CD36, un récepteur scavenger exprimé dans plusieurs tissus dont le myocarde, l’endothélium de la microvasculature et les monocytes/macrophages. Le CD36 exprimé à la surface du macrophage joue un rôle clé dans l’initiation du développement de l’athérosclérose par la liaison et l’internalisation des lipoprotéines de faible densité oxydées (LDLox) dans l’espace sous-endothélial de l’artère. L’hexaréline, un analogue GHRP, a été développé comme agent thérapeutique pour stimuler la sécrétion de l’hormone de croissance par l’hypophyse. Sa propriété de liaison aux récepteurs GHS-R1a et CD36 situés en périphérie et particulièrement sa capacité d’interférer avec la liaison des LDLox par le CD36 nous ont incité à évaluer la capacité de l’hexaréline à moduler le métabolisme lipidique du macrophage. L’objectif principal de ce projet a été de déterminer les effets de l’activation des récepteurs CD36 et GHS-R1a, par l’hexaréline et la ghréline, le ligand endogène du GHS-R1a, sur la physiologie du macrophage et de déterminer son potentiel anti-athérosclérotique. Les résultats montrent premièrement que l’hexaréline et la ghréline augmentent l’expression des transporteurs ABCA1 et ABCG1, impliqués dans le transport inverse du cholestérol, via un mécanisme contrôlé par le récepteur nucléaire PPARγ. La régulation de l’activité transcriptionnelle de PPARγ par l’activation des récepteurs CD36 et GHS-R1a se fait indépendamment de la présence du domaine de liaison du ligand (LBD) de PPARγ et est conséquente de changements dans l’état de phosphorylation de PPARγ. Une étude plus approfondie de la signalisation résultant de la liaison de la ghréline sur le GHS-R1a révèle que PPARγ est activé par un mécanisme de concertation entre les voies de signalisation Gαq/PI3-K/Akt et Fyn/Dok-1/ERK au niveau du macrophage. Le rôle de PPARγ dans la régulation du métabolisme lipidique par l’hexaréline a été démontré par l’utilisation de macrophages de souris hétérozygotes pour le gène de Ppar gamma, qui présentent une forte diminution de l’activation des gènes de la cascade métabolique PPARγ-LXRα-transporteurs ABC en réponse à l’hexaréline. L’injection quotidienne d’hexaréline à un modèle de souris prédisposées au développement de l’athérosclérose, les souris déficientes en apoE sous une diète riche en cholestérol et en lipides, se traduit également en une diminution significative de la présence de lésions athérosclérotiques correspondant à une augmentation de l’expression des gènes cibles de PPARγ et LXRα dans les macrophages péritonéaux provenant des animaux traités à l’hexaréline. L’ensemble des résultats obtenus dans cette thèse identifie certains nouveaux mécanismes impliqués dans la régulation de PPARγ et du métabolisme du cholestérol dans le macrophage via les récepteurs CD36 et GHS-R1a. Ils pourraient servir de cibles thérapeutiques dans une perspective de traitement des maladies cardiovasculaires.

Caractérisation des complexes ribonucléoprotéiques de Staufen1 et Staufen2

Dans la cellule, chaque ARNm se doit d’être régulé finement au niveau transcriptionnel, bien entendu, mais également au niveau de sa traduction, de sa dégradation ainsi que de sa localisation intracellulaire, et ce, afin de permettre l’expression de chaque produit protéique au moment et à l’endroit précis où son action est requise. Lorsqu’un mécanisme physiologique est mis de l’avant dans la cellule, il arrive souvent que plusieurs ARNm se doivent d’être régulés simultanément. L’un des moyens permettant d’orchestrer un tel processus est de réguler l’action d’une protéine commune associée à chacun de ces ARNm, via un mécanisme post-traductionnel par exemple. Ainsi l’expression d’un groupe précis d’ARNm peut être régulée finement dans le temps et dans l’espace selon les facteurs protéiques auxquels il est associé. Dans l’optique d’étudier certains de ces complexes ribonucléoprotéiques (mRNP), nous nous sommes intéressés aux isoformes et paralogues de Staufen, une protéine à domaine de liaison à l’ARN double-brin (dsRBD) impliquée dans de nombreux aspects de la régulation post-transcriptionnelle, tels la dégradation, la traduction ou encore la localisation d’ARNm. Chez la drosophile, un seul gène Staufen est exprimé alors que chez les mammifères, il existe deux paralogues de la protéine, soit Stau1 et Stau2, tous deux possédant divers isoformes produits suite à l’épissage alternatif de leur gène. Stau1 et Stau2 sont identiques à 50%. Les deux isoformes de Stau2, Stau259 et Stau262 ne diffèrent qu’en leur extrémité N-terminale. En effet, alors que Stau259 arbore un dsRBD1 tronqué, celui de Stau262 est complet. Ces observations introduisent une problématique très intéressante à laquelle nous nous sommes attaqué : ces différentes protéines, quoique très semblables, font-elles partie de complexes ribonucléoprotéiques distincts ayant des fonctions propres à chacun ou, au contraire, vu cette similarité de séquence, travaillent-elles de concert au sein des mêmes complexes ribonucléoprotéiques? Afin d’adresser cette question, nous avons entrepris d’isoler, à partir de cellules HEK293T, les différents complexes de Stau1 et Stau2 par la technique d’immunoprécipitation. Nous avons isolé les ARNm associés à chaque protéine, les avons identifiés grâce aux micropuces d’ADN et avons confirmé nos résultats par RT-PCR. Malgré la présence d’une population commune d’ARNm associée à Stau1 et Stau2, la majorité des transcrits identifiés furent spécifiques à chaque orthologue. Cependant, nous avons remarqué que les diverses populations d’ARNm participaient aux mêmes mécanismes de régulation, ce qui suggère que ces deux protéines possèdent des rôles complémentaires dans la mise en œuvre de divers phénomènes cellulaires. Au contraire, les transcrits associés à Stau259 et Stau262 sont davantage similaires, indiquant que celles-ci auraient des fonctions plutôt semblables. Ces résultats sont très intéressants, car pour la première fois, nous avons identifié des populations d’ARNm associées aux isoformes Stau155, Stau259 et Stau262. De plus, nous les avons analysées en parallèle afin d’en faire ressortir les populations spécifiques à chacune de ces protéines. Ensuite, connaissant l’importance de Stau2 dans le transport dendritique d’ARNm, nous avons cherché à caractériser les complexes ribonucléoprotéiques neuronaux associés à celle-ci. Dans un premier temps et à l’aide de la technique d’immunoprécipitation, nous avons identifié une population d’ARNm neuronaux associés à Stau2. Plus de 1700 ARNm montraient une présence d’au moins huit fois supérieure dans le précipité obtenu avec l’anticorps anti-Stau2 par rapport à celui obtenu avec le sérum pré-immun. Ces ARNm codent pour des protéines impliquées dans des processus de modifications post-traductionnelles, de traduction, de transport intracellulaire et de métabolisme de l’ARN. De façon intéressante, cette population d’ARNm isolée du cerveau de rat est relativement différente de celle caractérisée des cellules humaines HEK293T. Ceci suggère que la spécificité d’association Stau2-ARNm peut diffèrer d’un tissu à un autre. Dans un deuxième temps, nous avons isolé les protéines présentes dans les complexes ribonucléoprotéiques obtenus de cerveaux de rat et les avons identifiées par analyse en spectrométrie de masse. De cette façon, nous avons identifié au sein des particules de Stau2 des protéines liant l’ARN (PABPC1, hnRNPH1, YB1, hsc70), des protéines du cytosquelette (α- et β-tubuline), de même que la protéine peu caractérisée RUFY3. En poussant davantage la caractérisation, nous avons établi que YB1 et PABPC1 étaient associées à Stau2 grâce à la présence de l’ARN, alors que la protéine hsc70, au contraire, interagissait directement avec celle-ci. Enfin, cette dernière association semble être modulable par l’action de l’ATP. Ce résultat offre de nombreuses possibilités quant à la régulation de la fonction de Stau2 et/ou de son mRNP. Entre autres, cette étude suggère un mécanisme de régulation de la traduction au sein de ces particules. Pour faire suite à la caractérisation des mRNP de Stau, nous avons voulu déterminer au niveau neurophysiologique l’importance de ceux-ci. Comme l’étude de Stau2 avait déjà été entreprise préalablement par un autre laboratoire, nous avons décidé de concentrer notre étude sur le rôle de Stau1. Ainsi, nous avons démontré que celle-ci était nécessaire à la mise en place d’une forme de plasticité synaptique à long terme, la forme tardive de potentialisation à long terme ou L-LTP, dépendante de la transcription et de l’activité des récepteurs NMDA. La transmission de base, de même que la faculté de ces épines à faire de la E-LTP, la forme précoce de potentialisation à long terme, et la dépression à long terme ou LTD sont conservées. Ceci indique que les épines conservent la capacité d’être modulées. Ainsi, l’inhibition de la L-LTP, suite à la sous-expression de Stau1, n’est pas simplement due à la perte d’éléments fonctionnels, mais réside plutôt dans l’incapacité de ceux-ci à induire les changements synaptiques spécifiquement nécessaires à la mise en place de la L-LTP. De plus, au niveau synaptique, la sous-expression de Stau1 réduit à la fois l’amplitude et la fréquence des mEPSC. Ces résultats concordent avec l’observation que la sous-expression de Stau1 augmente significativement la proportion d’épines allongées et filopodales, des épines formant des synapses dites silencieuses. Par le fait même, elle diminue le nombre d’épines fonctionnelles, de forme dite normale. Ainsi, nous avons été en mesure de démontrer que l’absence, au niveau neuronal, de la protéine Stau1 induisait un déficit probable dans la localisation et/ou la traduction d’ARNm responsable de la restructuration de l’épine et de facteurs nécessaires à la mise en place de la L-LTP. En conclusion, nous avons participé à lever le voile sur la composition et l’importance des complexes ribonucléoprotéiques de Stau1 et Stau2. Nous avons identifié des populations distinctes et communes d’ARNm associées aux différents isoformes de Stau, à partir des mRNP présents au sein des cellules HEK293. De plus, nous avons réussi à mettre à l’avant plan certaines composantes des mRNP neuronaux de Stau2, dont un partenaire protéique direct, hsc70, partenaire dont l’association est modulable par l’action de l’ATP, ainsi qu’une population neuronale de transcrits d’ARNm. Enfin, nous avons mis en lumière l’importance de Stau1 dans la morphologie des épines dendritiques ainsi que dans le phénomène de la plasticité synaptique.

Modeling and Analysis of Some Heavy Tailed Time Series

The thesis has covered various aspects of modeling and analysis of finite mean time series with symmetric stable distributed innovations. Time series analysis based on Box and Jenkins methods are the most popular approaches where the models are linear and errors are Gaussian. We highlighted the limitations of classical time series analysis tools and explored some generalized tools and organized the approach parallel to the classical set up. In the present thesis we mainly studied the estimation and prediction of signal plus noise model. Here we assumed the signal and noise follow some models with symmetric stable innovations.We start the thesis with some motivating examples and application areas of alpha stable time series models. Classical time series analysis and corresponding theories based on finite variance models are extensively discussed in second chapter. We also surveyed the existing theories and methods correspond to infinite variance models in the same chapter. We present a linear filtering method for computing the filter weights assigned to the observation for estimating unobserved signal under general noisy environment in third chapter. Here we consider both the signal and the noise as stationary processes with infinite variance innovations. We derived semi infinite, double infinite and asymmetric signal extraction filters based on minimum dispersion criteria. Finite length filters based on Kalman-Levy filters are developed and identified the pattern of the filter weights. Simulation studies show that the proposed methods are competent enough in signal extraction for processes with infinite variance.Parameter estimation of autoregressive signals observed in a symmetric stable noise environment is discussed in fourth chapter. Here we used higher order Yule-Walker type estimation using auto-covariation function and exemplify the methods by simulation and application to Sea surface temperature data. We increased the number of Yule-Walker equations and proposed a ordinary least square estimate to the autoregressive parameters. Singularity problem of the auto-covariation matrix is addressed and derived a modified version of the Generalized Yule-Walker method using singular value decomposition.In fifth chapter of the thesis we introduced partial covariation function as a tool for stable time series analysis where covariance or partial covariance is ill defined. Asymptotic results of the partial auto-covariation is studied and its application in model identification of stable auto-regressive models are discussed. We generalize the Durbin-Levinson algorithm to include infinite variance models in terms of partial auto-covariation function and introduce a new information criteria for consistent order estimation of stable autoregressive model.In chapter six we explore the application of the techniques discussed in the previous chapter in signal processing. Frequency estimation of sinusoidal signal observed in symmetric stable noisy environment is discussed in this context. Here we introduced a parametric spectrum analysis and frequency estimate using power transfer function. Estimate of the power transfer function is obtained using the modified generalized Yule-Walker approach. Another important problem in statistical signal processing is to identify the number of sinusoidal components in an observed signal. We used a modified version of the proposed information criteria for this purpose.

Statistics of avalanches in martensitic transformations, II. Modelling

Using a scaling assumption, we propose a phenomenological model aimed to describe the joint probability distribution of two magnitudes A and T characterizing the spatial and temporal scales of a set of avalanches. The model also describes the correlation function of a sequence of such avalanches. As an example we study the joint distribution of amplitudes and durations of the acoustic emission signals observed in martensitic transformations [Vives et al., preceding paper, Phys. Rev. B 52, 12 644 (1995)].

Notes on PCA, Regularization, Sparsity and Support Vector Machines

We derive a new representation for a function as a linear combination of local correlation kernels at optimal sparse locations and discuss its relation to PCA, regularization, sparsity principles and Support Vector Machines. We first review previous results for the approximation of a function from discrete data (Girosi, 1998) in the context of Vapnik"s feature space and dual representation (Vapnik, 1995). We apply them to show 1) that a standard regularization functional with a stabilizer defined in terms of the correlation function induces a regression function in the span of the feature space of classical Principal Components and 2) that there exist a dual representations of the regression function in terms of a regularization network with a kernel equal to a generalized correlation function. We then describe the main observation of the paper: the dual representation in terms of the correlation function can be sparsified using the Support Vector Machines (Vapnik, 1982) technique and this operation is equivalent to sparsify a large dictionary of basis functions adapted to the task, using a variation of Basis Pursuit De-Noising (Chen, Donoho and Saunders, 1995; see also related work by Donahue and Geiger, 1994; Olshausen and Field, 1995; Lewicki and Sejnowski, 1998). In addition to extending the close relations between regularization, Support Vector Machines and sparsity, our work also illuminates and formalizes the LFA concept of Penev and Atick (1996). We discuss the relation between our results, which are about regression, and the different problem of pattern classification.