Exponential smoothing algorithms are very attractive for the practical world such as in industry. When considering bivariate exponential smoothing methods, in addition to the properties of univariate methods, additional properties give insight to relationships between the two components of a process, and also to the overall structure of the model. It is important to study these properties, but even with the merits the bivariate exponential smoothing algorithms have, exponential smoothing algorithms are nonstatistical/nonstochastic and to study the properties within exponential smoothing may be worthless. As an alternative approach, the (bivariate) ARIMA and the structural models which are classes of statistical models, are shown to generalize the exponential smoothing algorithms. We study these properties within these classes as they will have implications on exponential smoothing algorithms. Forecast properties are studied using the state space model and the Kalman filter. Comparison of ARIMA and structural model completes the study. / Mathematical Sciences / M. Sc. (Statistics)

En acoustique sous marine, les ´etudes sur les zones en eau peu profondes sontredevenues strat´egiques. Cette th`ese porte sur l’ ´etude de la s´eparation et la d´etectionde trajet dans le cadre des eaux peu profondes tomographie acoustique oc´eanique. Dansune premi´ere ´etape de notre travail, nous avons donn´e un bref aperc¸u sur les techniquesexistantes de traitement acoustique sous-marine afin de trouver la difficult´e toujoursconfront´es `a ce type de m´ethodes. Par cons´equent, nous avons fait une conclusion qu’ilest encore n´e cessaire d’am´eliorer la r´esolution de s´eparation afin de fournir des informationsplus utiles pour l’ ´etape inverse de la tomographie acoustique oc´eanique.Ainsi, une enquˆete sur les mthodes haute r´esolution est effecut´ee. Enfin, nous avonspropos´e une m´ethode `a haute r´esolution appel´ee lissage MUSICAL (MUSIC Active largeband), qui combine le lissage de fr´equence spatiale avec l’algorithme MUSICAL, pourune s´eparation efficace de trajet coh´erentes ou totalement corr´el´es. Cependant, cettem´ethode est bas´ee sur la connaissance a priori du nombre de trajet. Ainsi, nous introduisonsun test (exponential fitting test) (EFT) `a l’aide de courte longueur des ´echantillonspour d´eterminer le nombre de trajets. Ces deux m´ethodes sont appliqu´ees `a la fois desdonn´ees synth´etiques et les donn´ees r´eelles acquises dans un r´eservoir `a petite ´echelle.Leurs performances sont compar´ees avec les m´ethodes conventionnelles pertinentes. / As the studies on shallow-water acoustics became an active field again, this dissertationfocuses on studying the separation and detection of raypaths in the context of shallowwaterocean acoustic tomography. As a first step of our work, we have given a briefreview on the existing array processing techniques in underwater acoustics so as to findthe difficulties still faced by these methods. Consequently, we made a conclusion thatit is still necessary to improve the separation resolution in order to provide more usefulinformation for the inverse step of ocean acoustic tomography. Thus, a survey on highresolutionmethod is provided to discover the technique which can be extended to separatethe raypaths in our application background. Finally, we proposed a high-resolutionmethod called smoothing-MUSICAL (MUSIC Actif Large band), which combines thespatial-frequency smoothing with MUSICAL algorithm, for efficient separation of coherentor fully correlated raypaths. However, this method is based on the prior knowledgeof the number of raypaths. Thus, we introduce an exponential fitting test (EFT)using short-length samples to determine the number of raypaths. These two methodsare both applied to synthetic data and real data acquired in a tank at small scale. Theirperformances are compared with the relevant conventional methods respectively.

Cette thèse se situe dans le cadre de l'analyse théorique et numérique de modèles en séparation de phase qui tiennent compte d'effets d'anisotropie. Ceci est pertinent, par exemple, pour l'évolution de cristaux dans leur matrice liquide pour lesquels ces effets d'anisotropie sont très forts. On étudie l'existence, l'unicité et la régularité de la solution des équations de Cahn-Hilliard et d'Allen-Cahn ainsi que son comportement asymptotique en terme d'existence d'un attracteur global de dimension fractale finie. La première partie de la thèse concerne certains modèles de séparation de phase qui, en particulier, décrivent la formation de motifs dendritiques. D'abord, on étudie les équations de Cahn-Hilliard et d'Allen-Cahn qui prennent en compte les effets d'anisotropie forts en dimension un avec des conditions de type Neumann sur le bord et une non linéarité régulière de type polynomial. En particulier, ces modèles contiennent un terme supplémentaire appelé régularisation de Willmore. Ensuite, on étudie ces modèles avec des conditions de type périodique (respectivement, Dirichlet) sur le bord pour l'équation de Cahn-Hilliard (respectivement, d'Allen-Cahn) mais en dimension spatiales plus élevées. Finalement, on étudie la dynamique des équations de Cahn-Hilliard et d'Allen-Cahn visqueux avec des conditions de type Neumann et Dirichlet respectivement sur le bord et une non linéarité régulière et en plus, la présence de simulations numériques qui montrent les effets du terme de viscosité sur l'anisotropie et l'isotropie dans l'équation de Cahn-Hilliard. Dans le dernier chapitre, on étudie le comportement en temps long en termes d'attracteurs de dimension finie, d'une classe d'équations doublement non linéaires de type Allen-Cahn avec des conditions de type Dirichlet sur le bord et une non linéarité singulière. / This thesis is situated in the context of the theoretical and numerical analysis of models in phase separation which take into account the anisotropic effects. This is relevant, for example, for the development of crystals in their liquid matrix for which the effects of anisotropy are very strong. We study the existence, uniqueness and the regularity of the solution of Cahn-Hilliard and Alen-Cahn equations and the asymptotic behavior in terms of the existence of a global attractor with finite fractal dimension. The first part of the thesis concerns some models in phase separation which, in particular, describe the formation of dendritic patterns. We start by study- ing the anisotropic Cahn-Hilliard and Allen-Cahn equations in one space dimension both associated with Neumann boundary conditions and a regular nonlinearity. In particular, these two models contain an additional term called Willmore regularization. Furthermore, we study these two models with Periodic (respectively, Dirichlet) boundary conditions for the Cahn-Hilliard (respectively, Allen-Cahn) equation but in higher space dimensions. Finally, we study the dynamics of the viscous Cahn-Hilliard and Allen-Cahn equations with Neumann and Dirichlet boundary conditions respectively and a regular nonlinearity in the presence of the Willmore regularization term and we also give some numerical simulations which show the effects of the viscosity term on the anisotropic and isotropic Cahn-Hilliard equations. In the last chapter, we study the long time behavior, in terms of finite dimensional attractors, of a class of doubly nonlinear Allen-Cahn equations with Dirichlet boundary conditions and singular potentials.

Durante o desenvolvimento do sistema nervoso, as oscilações da concentração de cálcio intracelular livre resultam na proliferação celular, migração e diferenciação neuronal. Nesta tese foram investigadas a participação dos receptores ionotrópicos purinérgicos dos tipos P2X2 e P2X4 seletivos ao influxo de cálcio durante a diferenciação neuronal in vitro das células de carcinoma embrionário murino P19. Identificamos o padrão diferencial de expressão de receptores purinérgicos nas células indiferenciadas e neurônios P19. O receptor P2X4 é expresso durante toda a diferenciação neuronal e o receptor P2X2 é detectado na fase tardia da diferenciação em neurônios. Através de ensaios farmacológicos, foi possível identificar a participação dos receptores metabotropicos P2Y e do receptor P2X4 na formação dos corpos embriônicos, na proliferação celular e ou na determinação do fenótipo de progenitor neural. Durante a maturação neuronal os receptores P2X2 e P2Y1 participam da determinação do fenótipo neuronal glutamatérgico NMDA e os receptores P2X2 e P2Y2 no fenótipo neuronal colinérgico. A ausência de inibidores específicos e seletivos aos receptores purinérgicos levou-nos a empregar a técnica SELEX (Systematic Evolution of Ligands by EXponential enrichment) a fim de identificar inibidores seletivos aos receptores P2X2 e P2X4. A técnica envolve a utilização da biblioteca combinatória randômica de RNA 2\'- F pirimidina modificadas resistentes a nucleases. Após 9 ciclos de seleção in vitro de SELEX (ciclo 9-P2X4), as sequências selecionadas mostraram-se seletivas a ligação somente ao receptor P2X4 e não aos receptores P2X2 ou P2X7 através de ensaios de ligação radioligante-receptor. Por patch clamping na configuração whole cell recording identificou-se que além de seletividade ao receptor, que a aplicação do RNA ciclo 9- P2X4 promoveu inibição da corrente ativada pelo ATP somente nos receptores P2X4 e não em P2X2 em celulas 1321N1 astrocitoma transfectadas. A incubação do RNA ciclo 9-P2X4 na concentração de 200 nM com as células no estágio indiferenciado inibiu a formação dos corpos embriônicos. Já utilização de 25 nM, resultou em mudanças morfológicas nas células diferenciadas. Estes dados corroboram com os dados farmacológicos que identificaram a participação do receptor P2X4 na diferenciação precoce. Após 11 ciclos P2X2 de seleção, identificou-se sequências com especificidade de ligação aos receptores P2X2. Aptâmeros, moleculas de RNA com sequência identificada e com alta afinidade ao alvo da seleção, foram isolados de ambas as bibliotecas, ciclo 9 P2X4 e ciclo 11 P2X2. A co-aplicação destes aptâmeros e ATP em ensaios de whole-cell recording resultou na inibição de 30 a 80% da corrente ativada pelo ATP nos receptores P2X2 ou P2X4. Estes testes em células PC12 de rato, que expressa os receptores endógenos, resultou em inibição da corrente ativada pelo ATP de modo semelhante. Além de termos desenvolvido aptâmeros como ferramentas para elucidar as funções dos receptores P2X2 e P2X4 durante o desenvolvimento, diferenciação, em processos fisiológicos e patológicos, estas moléculas resistentes a nucleases são as primeiras identificadas capazes de reconhecer, discernir e inibir dois subtipos de receptores purinérgicos sendo promissores para utilização terapêutica. / During the development of the nervous system, oscillations of intracellular calcium concentrations activate programs of gene expression resulting in proliferation, migration and neuronal differentiation of embryonic cells. In this thesis, the participation of ionotropic P2X2 and P2X4 receptor subtypes, whose receptor channels are highly permeable for calcium influx in the cells, was studied during the process of neuronal differentiation. We have identified differential gene expression of purinergic receptors in undifferentiated and neuronal-differentiated P19 cells. P2X4 receptor expression was present along neuronal differentiation of P19 cells, whereas P2X2 receptor expression was only detected when P19 cells became neurons. Based on purinergic receptor pharmacology we have determined the participation of P2X4 receptors in addition to metabotropic P2Y2 receptors in the formation of embryonic bodies as prerequisites for phenotype determination of P19 neural progenitor cells. Final neuronal maturation of P19 cells in the presence or absence of agonists or antagonists of purinergic receptors implicated the involvement of P2X2, P2Y1, and P2Y2 in the determination of the final neuronal phenotype, such as expression of NMDA-glutamate and cholinergic receptors. In order to further evaluate the functions of these P2X receptors and due to the absence of specific inhibitors for these receptor subtypes, we have used the SELEX technique (Systematic Evolution of Ligands by EXponential enrichment) to select for specific inhibitors for P2X2 and P2X4 receptors. The 2\' -F-pyrimidine modified, nuclease- resistant combinatorial SELEX RNA pool enriched with inhibitors of P2X4 receptors following nine cycles of in vitro selection (cycle 9-P2X4) specifically interacted with P2X4 receptors and not with P2X2 or P2X7 receptors as verified in radioligand-receptor binding studies. Moreover, whole-cell recording measurements using astrocytoma cells expressing recombinant rat P2X2 or P2X4 receptors showed inhibition of P2X4 but not of P2X2 receptors by the selected RNA molecules. RNA molecules selected in vitro in 11 reiterative SELEX cycles using the P2X2 receptor as target specifically bound to membrane extracts containing recombinant P2X2 receptors. From both selected RNA libraries (against P2X4 and P2X2 receptors) aptamers, as RNA molecules with identified sequences and high-affinity binding, were identified by cloning and DNA sequencing. The presence of these aptamers in whole-cell recording experiments resulted in 30-80% inhibition of ATP-induced receptor activity and did not provoke any inhibitory effects on P2X receptors which had not been used as selection target. The activity of the aptamers selected using recombinant receptors as targets in inhibiting wild-type P2X4 or P2X2 receptors was verified in whole-cell recording experiments with PC12 cells which endogenously express both receptor subtypes. In addition of having developed aptamers as tools to elucidate P2X2 and P2X4 receptor functions during neuronal differentiation, these nuclease-resistant aptamers are suitable for in vivo use and may turn into therapeutics in the inhibition of purinergic receptor participation in pathophysiological conditions.

Cette thèse porte sur les équations d’évolution et s’articule autour de trois parties. Dans la première partie, on se propose de se concentrer sur le critère oscillatoire de certaines équations différentielles. Des résultats classiques sur les fonctions presque-périodiques sont rassemblés dans le premier chapitre. Le deuxième chapitre de cette thèse a pour objectif de prouver l’existence d’une solution presque-périodique de Besicovitch d’une équation différentielle de second ordre sur un espace de Hilbert. L’approche utilisée se base sur un formalisme variationnel. La deuxième partie de cette thèse traite le comportement asymptotique des problèmes de Cauchy dans le cas non autonome. Les semi-groupes et les familles d’évolution étant les outils principaux utilisés dans cette partie, le troisième chapitre introduit des résultats importants de cette théorie, notamment ceux permettant de caractériser la stabilité des semigroupes et des familles d’évolution périodiques. Dans le quatrième chapitre de cette contribution, on prouve, en utilisant une approche basée sur les semigroupes, un résultat liant la bornitude de solutions de problèmes de Cauchy périodiques et la stabilité exponentielle uniforme des familles d’évolution issues de ces problèmes. Dans une troisième partie, on focalise l’attention sur quelques résultats sur la dichotomie exponentielle comme une propriété liée au comportement asymptotique des systèmes différentiels. Quelques résultats connus sont, par suite, réunis au cinquième chapitre qui introduit brièvement la notion de dichotomie exponentielle. Dans un dernier chapitre, une caractérisation de la dichotomie exponentielle d’une famille d’évolution en termes de bornitude des solutions de problèmes de Cauchy opératoriels correspondants sera démontrée. / This PhD thesis deals with the evolution equations and is organized in three parts. The first part is devoted to the almost periodic solutions of certain differential equations. Classic results on the almost periodic functions are collected in the first chapter. The second chapter of this thesis aims to prove the existence of an almost-periodic solution of Besicovitch of a second-order differential equation on Hilbert space. The used approach is based on a variational formalism. In the second part of this thesis, we study the asymptotic behavior of Cauchy problems in the non-autonomous case. We give in the third chapter important results on semigroups and evolution families, namely, those allowing to characterize the stability of semigroups and periodic evolution families. We prove in the fourth chapter sufficient conditions for the uniform exponential stability of a strongly continuous, q-periodic evolution family acting on a complex Banach space. The last part in this work focuses the attention on some results on the exponential dichotomy as a property for the asymptotic behavior of the differential systems. Some well-known results are given in the fifth chapter which introduces briefly the concept of the exponential dichotomy. A characterization of the exponential dichotomy for evolution family in terms of boundedness of the solutions to periodic operatorial Cauchy problems will be established.

This study estimated soybean yield responses to K fertilizer using trials data from 18 sites in Mississippi from 2011-2016. Eight response functions were fitted, including linear, linear plateau, quadratic, quadratic-plateau, square root quadratic, spherical plateau, exponential, and exponential-plateau functions. The ratio of high responsive, low responsive, and no responsive sites to K rates is 3:3:12 respectively. The response functions led to different predicted optimal K rates, and the best response function for each site was determined by the Vuong closeness test and economic loss analysis. The predicted economically optimal K rates are 157, 73, and 0 lb/acre for high, low, and no response sites respectively, and the average optimal K rate is 55 lb/acre. Compared to the currently used regional uniform K fertilizer rate of 80 lb/acre, the response-based K rates are expected to generate soybean production gain of about $14 per acre for Mississippi soybean producers.

No description available.

No description available.

The behaviour of free-surface gravity waves on small Froude number fluid flow past some obstacle cannot be determined using ordinary asymptotic power series methods, as the amplitude of the waves is exponentially small. An exponential asymptotic method is used by Chapman and Vanden-Broeck (2006) to consider the problem of two-dimensional, steady flow past a submerged obstacle in the small Froude number limit, finding that a steady downstream wavetrainis switched on rapidly across a curve known as a Stokes line. Here, equivalent wavetrains on three-dimensional and unsteady flow configurations are considered, and Stokes switching causedby the interaction between exponentially small free-surface components is shown to play an important role in both cases. The behaviour of free-surface gravity waves is introduced by considering the problem of steady free-surface flow due to a line source. A steady wavetrain is shown to exist in the far field, and the behaviour of these waves is compared to existing numerical results. The problem of unsteady flow over a step is subsequently investigated, with the flow behaviour formulated in terms of Lagrangian coordinates so that the position of the free surface is fixed. Initially, the problem is linearized in the step-height, and the steady wavetrain is shown to spread downstream over time. The position of the wavefront is determined by considering the full Stokes structure present in the problem. The equivalent fully-nonlinear problem is then considered, with the position of the Stokes lines, and hence the wavefront, being determined numerically. Finally, linearized three-dimensional free-surface flow past an obstacle is considered in both the steady and unsteady case. The surface is shown to contain downstream longitudinal and transverse waves. These waves are shown to propagate downstream in the unsteady case, with the position of the wavefront again determined by considering the full Stokes structure of the problem.

We study stochastic heat equations of the forms $[\partial_t u-\sL u]\d t\d x=\lambda\int_\R\sigma(u,h)\tilde{N}(\d t,\d x,\d h),$ and $[\partial_t u-\sL u]\d t\d x=\lambda\int_{\R^d}\sigma(u,h)N(\d t,\d x,\d h)$. Here, $u(0,x)=u_0(x)$ is a non-random initial function, $N$ a Poisson random measure with its intensity $\d t\d x\nu(\d h)$ and $\nu(\d h)$ a L\'vy measure; $\tilde$ is the compensated Poisson random measure and $\sL$ a generator of a L\'{e}vy process. The function $\sigma:\R\rightarrow\R$ is Lipschitz continuous and $\lambda>0$ the noise level. The above discontinuous noise driven equations are not always easy to handle. They are discontinuous analogues of the equation introduced in \cite{Foondun} and also more general than those considered in \cite{Saint}. We do not only compare the growth moments of the two equations with each other but also compare them with growth moments of the class of equations studied in \cite{Foondun}. Some of our results are significant generalisations of those given in \cite{Saint} while the rest are completely new. Second and first growth moments properties and estimates were obtained under some linear growth conditions on $\sigma$. We also consider $\sL:=-(-\Delta)^{\alpha/2}$, the generator of $\alpha$-stable processes and use some explicit bounds on its corresponding fractional heat kernel to obtain more precise results. We also show that when the solutions satisfy some non-linear growth conditions on $\sigma$, the solutions cease to exist for both compensated and non-compensated noise terms for different conditions on the initial function $u_0(x)$. We consider also fractional heat equations of the form $ \partial_t u(t,x)=-(-\Delta)^{\alpha/2}u(t,x)+\lambda\sigma(u(t,x)\dot{F}(t,x),\,\, \text{for}\,\, x\in\R^d,\,t>0,\,\alpha\in(1,2),$ where $\dot{F}$ denotes the Gaussian coloured noise. Under suitable assumptions, we show that the second moment $\E|u(t,x)|^2$ of the solution grows exponentially with time. In particular we give an affirmative answer to the open problem posed in \cite{Conus3}: given $u_0$ a positive function on a set of positive measure, does $\sup_{x\in\R^d}\E|u(t,x)|^2$ grow exponentially with time? Consequently we give the precise growth rate with respect to the parameter $\lambda$.