Structures algébriques, systèmes superintégrables et polynômes orthogonaux

Cette thèse est divisée en cinq parties portant sur les thèmes suivants: l’interprétation physique et algébrique de familles de fonctions orthogonales multivariées et leurs applications, les systèmes quantiques superintégrables en deux et trois dimensions faisant intervenir des opérateurs de réflexion, la caractérisation de familles de polynômes orthogonaux appartenant au tableau de Bannai-Ito et l’examen des structures algébriques qui leurs sont associées, l’étude de la relation entre le recouplage de représentations irréductibles d’algèbres et de superalgèbres et les systèmes superintégrables, ainsi que l’interprétation algébrique de familles de polynômes multi-orthogonaux matriciels. Dans la première partie, on développe l’interprétation physico-algébrique des familles de polynômes orthogonaux multivariés de Krawtchouk, de Meixner et de Charlier en tant qu’éléments de matrice des représentations unitaires des groupes SO(d+1), SO(d,1) et E(d) sur les états d’oscillateurs. On détermine les amplitudes de transition entre les états de l’oscillateur singulier associés aux bases cartésienne et polysphérique en termes des polynômes multivariés de Hahn. On examine les coefficients 9j de su(1,1) par le biais du système superintégrable générique sur la 3-sphère. On caractérise les polynômes de q-Krawtchouk comme éléments de matrices des «q-rotations» de U_q(sl_2). On conçoit un réseau de spin bidimensionnel qui permet le transfert parfait d’états quantiques à l’aide des polynômes de Krawtchouk à deux variables et on construit un modèle discret de l’oscillateur quantique dans le plan à l’aide des polynômes de Meixner bivariés. Dans la seconde partie, on étudie les systèmes superintégrables de type Dunkl, qui font intervenir des opérateurs de réflexion. On examine l’oscillateur de Dunkl en deux et trois dimensions, l’oscillateur singulier de Dunkl dans le plan et le système générique sur la 2-sphère avec réflexions. On démontre la superintégrabilité de chacun de ces systèmes. On obtient leurs constantes du mouvement, on détermine leurs algèbres de symétrie et leurs représentations, on donne leurs solutions exactes et on détaille leurs liens avec les polynômes orthogonaux du tableau de Bannai-Ito. Dans la troisième partie, on caractérise deux familles de polynômes du tableau de Bannai-Ito: les polynômes de Bannai-Ito complémentaires et les polynômes de Chihara. On montre également que les polynômes de Bannai-Ito sont les coefficients de Racah de la superalgèbre osp(1,2). On détermine l’algèbre de symétrie des polynômes duaux -1 de Hahn dans le cadre du problème de Clebsch-Gordan de osp(1,2). On propose une q - généralisation des polynômes de Bannai-Ito en examinant le problème de Racah pour la superalgèbre quantique osp_q(1,2). Finalement, on montre que la q -algèbre de Bannai-Ito sert d’algèbre de covariance à osp_q(1,2). Dans la quatrième partie, on détermine le lien entre le recouplage de représentations des algèbres su(1,1) et osp(1,2) et les systèmes superintégrables du deuxième ordre avec ou sans réflexions. On étudie également les représentations des algèbres de Racah-Wilson et de Bannai-Ito. On montre aussi que l’algèbre de Racah-Wilson sert d’algèbre de covariance quadratique à l’algèbre de Lie sl(2). Dans la cinquième partie, on construit deux familles explicites de polynômes d-orthogonaux basées sur su(2). On étudie les états cohérents et comprimés de l’oscillateur fini et on caractérise une famille de polynômes multi-orthogonaux matriciels.

Se convertir à l'épicurisme : ou comment devenir pieux.

Les épicuriens étaient-ils pieux? Des témoins du moyen et du dernier épicurisme, tels Cicéron et Plutarque, ont eu beaucoup de peine à le croire : selon eux, les épicuriens ne voyaient dans les prêtres que des bouchers, et ne participaient au culte populaire que pour éviter les accusations d’athéisme. Les épicuriens, quant à eux, se sont toujours qualifiés de pieux. L’archéologie nous confirme que les épicuriens ont activement participé au culte populaire, et ce tout au long de l’histoire de l’école. Malgré ces preuves archéologiques, la théologie épicurienne reste problématique : bien que leur éthique fasse des dieux des modèles, il ne semble pas y avoir de place pour les dieux dans leur physique. Que faire, donc, des pratiques rituelles où les dieux sont invoqués, voire où ils sont montrés au moyen d’un support matériel? Pourrait-on réduire la piété épicurienne à un exercice rationnel, froid et distant, au cœur même des temples? Mais cette distance avec le culte ne supposerait-elle pas une certaine hypocrisie, celle-là même qui fut décriée par Cicéron ou par Plutarque? Notre travail entend montrer de quelle manière les épicuriens purent être pieux, de façon non distante, tout en restant cohérents avec le problème philosophique de la représentation des dieux. Cette cohérence ne sera possible qu’au prix d’une « conversion » à l’épicurisme (et à son épistémologie) grâce à laquelle nous pourrons voir les dieux et nous reconnaître nous-mêmes comme des dieux.

Coefficients de Clebsch-Gordan de la super-algèbre osp(1|2)

Les fonctions génératrices des coefficients de Clebsch Gordan pour la superalgèbre de Lie osp(1|2) sont dérivées en utilisant deux approches. Une première approche généralise une méthode proposée par Granovskii et Zhedanov pour l'appliquer dans le cas de osp(1|2), une algèbre dont le coproduit est torsadé. Une seconde approche repose sur la réalisation de osp(1|2) en tant qu'algèbre dynamique d'un oscillateur parabosonique et utilise une équivalence dans cette réalisation entre le changements de coordonnées polaires à cartésiennes et le problème de Clebsch-Gordan. Un chapitre moins formel précède ces dérivations et présente comment le problème de Clebsch-Gordan s'interprète en tant que réalisation d'une algèbre de fusion. La notion abstraite de fusion est introduite, soulignant son importance en physique, pour en venir au cas particulier du problème de Clebsch-Gordan. Un survol du cas de l'algèbre osp(1|2) et de ses utilisations en physique mathématique conclut ce chapitre.

Les substrats neuronaux sous-tendant le binding automatique et contrôlé en mémoire de travail dans la schizophrénie : une étude en IRMf.

Le déficit de mémoire de travail est une des caractéristiques centrales de la schizophrénie et est associé aux problèmes de fonctionnement quotidien des patients. Parmi les différents processus sous-tendus par la mémoire de travail, nous nous intéressons au binding. Le binding est un processus qui permet d’associer plusieurs informations (par exemple, associer le nom d’une personne avec son adresse). En mémoire de travail, les patients schizophrènes ne présentent pas de déficit de binding lorsque les informations sont associées involontairement. Ce type de binding est appelé binding automatique. Cependant, les informations peuvent aussi être associées sous le contrôle volontaire et attentionnel des participants, nous parlons alors de binding contrôlé. À l’heure actuelle, aucune étude n’a été effectuée sur le binding contrôlé en schizophrénie. Notre objectif est de déterminer s'il existe un déficit spécifique de binding contrôlé dans la schizophrénie, et de décrire les substrats neuronaux qui le sous-tendent. Dix-neuf patients schizophrènes et 18 sujets témoins ont effectué une tâche de binding en mémoire de travail dans un scanner IRM. Celle-ci consistait à mémoriser des mots et des positions spatiales dont l’association variait selon deux conditions. Dans la condition de binding contrôlé, les mots et les positions spatiales étaient présentés séparément et les participants devaient faire l’association entre les deux informations eux-mêmes. Dans la condition de binding automatique, les mots étaient d’emblée associés aux positions spatiales. Nos résultats suggèrent que les patients schizophrènes n’auraient pas de déficit de binding automatique alors qu’ils auraient un déficit de binding contrôlé par rapport aux sujets témoins. Le déficit de binding contrôlé serait sous-tendu par des niveaux d’activation plus faibles du cortex préfrontal dorsolatéral. Les processus contrôlés seraient altérés alors que les processus automatiques seraient préservés dans la schizophrénie.

Backscattering of Laser Light from Colloidal Silica

Light-scattering experiments gained prominence as potential applications of quantum optics, nonlinear optics, and photon localization. The possibility of the realization of lasing action in random media has created much interest in the study of the coherent structure of the backscattered light from disordered media. Backscattering (BS) studies are carried out to analyze the possibilities of photon localization in colloidal silica. The scattering enhancement is best associated with the density of the scatterers. The width of the BS cone and, hence, the mean-free path is related to the concentration of the medium. The dependence of the photon wavelength on the possible characteristics of the scattering is presented.

Laser Induced Photothermal Investigations on Thermal and Transport Properties of Certain Selected Photonic Materials

Discovery of coherent optical sources four decades ago has revolutionized all fields of scientific development. One of the path breaking applications of lasers is the emergence of various thermo optic techniques to unravel some of the mysteries of light matter interactions.Thermo optic technique is a valuable tool to evaluate optical and thermal properties of materials in solid,liquid and gaseous states .This technique can also be employed effectively in nondestructive quality evaluation. In this doctoral thesis , the use of photothermal techniques based on photoacoustic and photothermal deflection phenomena for the study of certain class of photonics materials such as semiconductors, nano metal dispersed ceramics, composites of conducting polymers and liquid crystals is elaborated.

Screen printed nanosized ZnO thick film

Nanosized ZnO was prepared by polyol synthesis. Fluorescence spectrum of the ZnO colloid at varying pump intensities was studied. The powder was extracted and characterized by XRD and BET. The extracted powder was screen printed on glass substrates using ethyl cellulose as binder and turpinol as solvent. Coherent back scattering studies were performed on the screen printed sample which showed evidence of weak localization. The screen printed pattern showed strong UV emission.

Mean Squared Residue Based Biclustering Algorithms for the Analysis of Gene Expression Data

Computational Biology is the research are that contributes to the analysis of biological data through the development of algorithms which will address significant research problems.The data from molecular biology includes DNA,RNA ,Protein and Gene expression data.Gene Expression Data provides the expression level of genes under different conditions.Gene expression is the process of transcribing the DNA sequence of a gene into mRNA sequences which in turn are later translated into proteins.The number of copies of mRNA produced is called the expression level of a gene.Gene expression data is organized in the form of a matrix. Rows in the matrix represent genes and columns in the matrix represent experimental conditions.Experimental conditions can be different tissue types or time points.Entries in the gene expression matrix are real values.Through the analysis of gene expression data it is possible to determine the behavioral patterns of genes such as similarity of their behavior,nature of their interaction,their respective contribution to the same pathways and so on. Similar expression patterns are exhibited by the genes participating in the same biological process.These patterns have immense relevance and application in bioinformatics and clinical research.Theses patterns are used in the medical domain for aid in more accurate diagnosis,prognosis,treatment planning.drug discovery and protein network analysis.To identify various patterns from gene expression data,data mining techniques are essential.Clustering is an important data mining technique for the analysis of gene expression data.To overcome the problems associated with clustering,biclustering is introduced.Biclustering refers to simultaneous clustering of both rows and columns of a data matrix. Clustering is a global whereas biclustering is a local model.Discovering local expression patterns is essential for identfying many genetic pathways that are not apparent otherwise.It is therefore necessary to move beyond the clustering paradigm towards developing approaches which are capable of discovering local patterns in gene expression data.A biclusters is a submatrix of the gene expression data matrix.The rows and columns in the submatrix need not be contiguous as in the gene expression data matrix.Biclusters are not disjoint.Computation of biclusters is costly because one will have to consider all the combinations of columans and rows in order to find out all the biclusters.The search space for the biclustering problem is 2 m+n where m and n are the number of genes and conditions respectively.Usually m+n is more than 3000.The biclustering problem is NP-hard.Biclustering is a powerful analytical tool for the biologist.The research reported in this thesis addresses the problem of biclustering.Ten algorithms are developed for the identification of coherent biclusters from gene expression data.All these algorithms are making use of a measure called mean squared residue to search for biclusters.The objective here is to identify the biclusters of maximum size with the mean squared residue lower than a given threshold. All these algorithms begin the search from tightly coregulated submatrices called the seeds.These seeds are generated by K-Means clustering algorithm.The algorithms developed can be classified as constraint based,greedy and metaheuristic.Constarint based algorithms uses one or more of the various constaints namely the MSR threshold and the MSR difference threshold.The greedy approach makes a locally optimal choice at each stage with the objective of finding the global optimum.In metaheuristic approaches particle Swarm Optimization(PSO) and variants of Greedy Randomized Adaptive Search Procedure(GRASP) are used for the identification of biclusters.These algorithms are implemented on the Yeast and Lymphoma datasets.Biologically relevant and statistically significant biclusters are identified by all these algorithms which are validated by Gene Ontology database.All these algorithms are compared with some other biclustering algorithms.Algorithms developed in this work overcome some of the problems associated with the already existing algorithms.With the help of some of the algorithms which are developed in this work biclusters with very high row variance,which is higher than the row variance of any other algorithm using mean squared residue, are identified from both Yeast and Lymphoma data sets.Such biclusters which make significant change in the expression level are highly relevant biologically.

Studies on gaussian effective potentials in some models

In classical field theory, the ordinary potential V is an energy density for that state in which the field assumes the value ¢. In quantum field theory, the effective potential is the expectation value of the energy density for which the expectation value of the field is ¢o. As a result, if V has several local minima, it is only the absolute minimum that corresponds to the true ground state of the theory. Perturbation theory remains to this day the main analytical tool in the study of Quantum Field Theory. However, since perturbation theory is unable to uncover the whole rich structure of Quantum Field Theory, it is desirable to have some method which, on one hand, must go beyond both perturbation theory and classical approximation in the points where these fail, and at that time, be sufficiently simple that analytical calculations could be performed in its framework During the last decade a nonperturbative variational method called Gaussian effective potential, has been discussed widely together with several applications. This concept was described as a means of formalizing our intuitive understanding of zero-point fluctuation effects in quantum mechanics in a way that carries over directly to field theory.

Quantum dynamics of crystals of molecular nanomagnets inside a resonant cavity

It is found that crystals of molecular nanomagnets exhibit enhanced magnetic relaxation when placed inside a resonant cavity. A strong dependence of the magnetization curve on the geometry of the cavity has been observed, providing indirect evidence of the coherent microwave radiation by the crystals. A similar dependence has been found for a crystal placed between the Fabry-Perot superconducting mirrors.

“Income, Livelihood and Education of Tribal Communities in Kerala – Exploring Inter Community Disparities

The overall objective of the study is to examine whether the tribal communities in Kerala can be considered a coherent group in terms of select indicators of development by focusing on nine major tribal communities. The study also aims to bring out the intercommunity differences if any in aspects of livelihood options and education level of the tribal communities in Kerala

Growth of metal and semiconductor nanostructures for nonlinear optical applications

Nonlinear optics has been a rapidly growing field in recent decades since the invention of lasers. The systematic progress in the laser technology increases our efficiency in the generation and control of coherent optical radiations. Nonlinear optics is based on the study ofeffects and phenomena related to the interaction of intense coherent light radiation with matter. Compared to other light sources laser radiation can provide high directionality, high monochromaticiry, high brightness and high photon degeneracy. At such a very intense incident beam, the matter responds in a nonlinear manner to the incident radiation fields, which endows the media :1 characteristic to change the refractive index or absorption coe fflcient of the media or the wavelength, or the frequency of the incident electromagnetic waves. This thesis encompasses the fabrication of nonlinear optical devices based on semiconductor and metal nanostructures. The presented work focus on the experimental and theoretical discussions on nonlinear optical effects especially nonlinear absorption and refraction exhibitted by metal and semiconductor nanostructures

Ultrasound Image Despeckling using Local Binary Pattern Weighted Linear Filtering

Speckle noise formed as a result of the coherent nature of ultrasound imaging affects the lesion detectability. We have proposed a new weighted linear filtering approach using Local Binary Patterns (LBP) for reducing the speckle noise in ultrasound images. The new filter achieves good results in reducing the noise without affecting the image content. The performance of the proposed filter has been compared with some of the commonly used denoising filters. The proposed filter outperforms the existing filters in terms of quantitative analysis and in edge preservation. The experimental analysis is done using various ultrasound images

Studies on the interaction of two level atoms with quantized electromagnetic field

The present study described about the interaction of a two level atom and squeezed field with time varying frequency. By applying a sinusoidal variation in the frequency of the field, the randomness in population inversion is reduced and the collapses and periodic revivals are regained. Quantum optics is an emerging field in physics which mainly deals with the interaction of atoms with quantised electromagnetic fields. Jaynes-Cummings Model (JCM) is a key model among them, which describes the interaction between a two level atom and a single mode radiation field. Here the study begins with a brief history of light, atom and their interactions. Also discussed the interaction between atoms and electromagnetic fields. The study suggest a method to manipulate the population inversion due to interaction and control the randomness in it, by applying a time dependence on the frequency of the interacting squeezed field.The change in behaviour of the population inversion due to the presence of a phase factor in the applied frequency variation is explained here.This study also describes the interaction between two level atom and electromagnetic field in nonlinear Kerr medium. It deals with atomic and field state evolution in a coupled cavity system. Our results suggest a new method to control and manipulate the population of states in two level atom radiation interaction,which is very essential for quantum information processing.We have also studied the variation of atomic population inversion with time, when a two level atom interacts with light field, where the light field has a sinusoidal frequency variation with a constant phase. In both coherent field and squeezed field cases, the population inversion variation is completely different from the phase zero frequency modulation case. It is observed that in the presence of a non zero phase φ, the population inversion oscillates sinusoidally.Also the collapses and revivals gradually disappears when φ increases from 0 to π/2. When φ = π/2 the evolution of population inversion is identical to the case when a two level atom interacts with a Fock state. Thus, by applying a phase shifted frequency modulation one can induce sinusoidal oscillations of atomic inversion in linear medium, those normally observed in Kerr medium. We noticed that the entanglement between the atom and field can be controlled by varying the period of the field frequency fluctuations. The system has been solved numerically and the behaviour of it for different initial conditions and different susceptibility values are analysed. It is observed that, for weak cavity coupling the effect of susceptibility is minimal. In cases of strong cavity coupling, susceptibility factor modifies the nature in which the probability oscillates with time. Effect of susceptibility on probability of states is closely related to the initial state of the system.

Service provider switching: a study on the switching process in retail banking

In a business environment that is characterized by intense competition, building customer loyalty has become a key area of focus for most financial institutions. The explosion of the services sector, changing customer demographics and deregulation and emergence of new technology in the financial services industry have had a critical impact on consumers’ financial services buying behaviour. The changes have forced banks to modify their service offerings to customers so as to ensure high levels of customer satisfaction and also high levels of customer retention. Banks have historically had difficulty distinguishing their products from one another because of their relative homogeneity; with increasing competition,the problem has only intensified with no coherent distinguishing theme. Rising wealth, product proliferation, regulatory changes and newer technologies are together making bank switching easier for customers. In order to remain competitive, it is important for banks to retain their customer base. The financial services sector is the foundation for any economy and plays the role of mobilization of resources and their allocation. The retail banking sector in India has emerged as one of the major drivers of the overall banking industry and has witnessed enormous growth. Switching behaviour has a negative impact on the banks’ market share and profitability as the costs of acquiring customers are much higher than the costs of retaining. When customers switch, the business loses the potential for additional profits from the customer the initial costs invested in the customer by the business get . The Objective of the thesis was to examine the relationship among triggers that customers experience, their perceptions of service quality, consumers’ commitment and behavioral intentions in the contemporary India retail banking context through the eyes of the customer. To understand customers’ perception of these aspects, data were collected from retail banking customers alone for the purpose of analysis, though the banks’ views were considered during the qualitative work carried out prior to the main study. No respondent who is an employee of a banking organization was considered for the final study to avoid the possibility of any bias that could affect the results adversely. The data for the study were collected from customers who have switched banks and from those who were non switchers. The study attempted to develop and validate a multidimensional construct of service quality for retail banking from the consumer’s perspective. A major conclusion from the empirical research was the confirmation of the multidimensional construct for perceived service quality in the banking context. Switching can be viewed as an optimization problem for customers; customers review the potential gains of switching to another service provider against the costs of leaving the service provider. As banks do not provide tangible products, their service quality is usually assessed through service provider’s relationship with customers. Thus, banks should pay attention towards their employees’ skills and knowledge; assessing customers’ needs and offering fast and efficient services.