From Classical to Quantum Secret Sharing

Dans ce m��moire, nous nous pencherons tout particuli��rement sur une primitive cryptographique connue sous le nom de partage de secret. Nous explorerons autant le domaine classique que le domaine quantique de ces primitives, couronnant notre ��tude par la pr��sentation d���un nouveau protocole de partage de secret quantique n��cessitant un nombre minimal de parts quantiques c.-��-d. une seule part quantique par participant. L���ouverture de notre ��tude se fera par la pr��sentation dans le chapitre pr��liminaire d���un survol des notions math��matiques sous-jacentes �� la th��orie de l���information quantique ayant pour but primaire d�����tablir la notation utilis��e dans ce manuscrit, ainsi que la pr��sentation d���un pr��cis des propri��t��s math��matique de l�����tat de Greenberger-Horne-Zeilinger (GHZ) fr��quemment utilis�� dans les domaines quantiques de la cryptographie et des jeux de la communication. Mais, comme nous l���avons mentionn�� plus haut, c���est le domaine cryptographique qui restera le point focal de cette ��tude. Dans le second chapitre, nous nous int��resserons �� la th��orie des codes correcteurs d���erreurs classiques et quantiques qui seront �� leur tour d���extr��me importances lors de l���introduction de la th��orie quantique du partage de secret dans le chapitre suivant. Dans la premi��re partie du troisi��me chapitre, nous nous concentrerons sur le domaine classique du partage de secret en pr��sentant un cadre th��orique g��n��ral portant sur la construction de ces primitives illustrant tout au long les concepts introduits par des exemples pr��sent��s pour leurs int��r��ts autant historiques que p��dagogiques. Ceci pr��parera le chemin pour notre expos�� sur la th��orie quantique du partage de secret qui sera le focus de la seconde partie de ce m��me chapitre. Nous pr��senterons alors les th��or��mes et d��finitions les plus g��n��raux connus �� date portant sur la construction de ces primitives en portant un int��r��t particulier au partage quantique �� seuil. Nous montrerons le lien ��troit entre la th��orie quantique des codes correcteurs d���erreurs et celle du partage de secret. Ce lien est si ��troit que l���on consid��re les codes correcteurs d���erreurs quantiques ��taient de plus proches analogues aux partages de secrets quantiques que ne leur ��taient les codes de partage de secrets classiques. Finalement, nous pr��senterons un de nos trois r��sultats parus dans A. Broadbent, P.-R. Chouha, A. Tapp (2009); un protocole s��curitaire et minimal de partage de secret quantique a seuil (les deux autres r��sultats dont nous traiterons pas ici portent sur la complexit�� de la communication et sur la simulation classique de l�����tat de GHZ).

Studies On Classical And Retrial Inventory With Positive Service Time

Department of Mathematics, Cochin University of Science and Technology

DEVELOPMENT OF GRAMMAR IN HINDI AND MALAYALAM BASED ON CLASSICAL TEXTS

HINDI

Novel esterases from microbes through classical and metagenomics approach: Studies on the enzymes and their applications

Cochin University of Science And Technology

A generic formula for the values at the boundary points of monic classical orthogonal polynomials

In a previous paper we have determined a generic formula for the polynomial solution families of the well-known differential equation of hypergeometric type ��(x)y"n(x)+��(x)y'n(x)-��nyn(x)=0. In this paper, we give another such formula which enables us to present a generic formula for the values of monic classical orthogonal polynomials at their boundary points of definition.

Characterization theorem for classical orthogonal polynomials on non-uniform lattices: The functional approach

Using the functional approach, we state and prove a characterization theorem for classical orthogonal polynomials on non-uniform lattices (quadratic lattices of a discrete or a q-discrete variable) including the Askey-Wilson polynomials. This theorem proves the equivalence between seven characterization properties, namely the Pearson equation for the linear functional, the second-order divided-difference equation, the orthogonality of the derivatives, the Rodrigues formula, two types of structure relations,and the Riccati equation for the formal Stieltjes function.

Moments of classical orthogonal polynomials

The aim of this work is to find simple formulas for the moments mu_n for all families of classical orthogonal polynomials listed in the book by Koekoek, Lesky and Swarttouw. The generating functions or exponential generating functions for those moments are given.

On Connection, Linearization and Duplication Coefficients of Classical Orthogonal Polynomials

In this work, we have mainly achieved the following: 1. we provide a review of the main methods used for the computation of the connection and linearization coefficients between orthogonal polynomials of a continuous variable, moreover using a new approach, the duplication problem of these polynomial families is solved; 2. we review the main methods used for the computation of the connection and linearization coefficients of orthogonal polynomials of a discrete variable, we solve the duplication and linearization problem of all orthogonal polynomials of a discrete variable; 3. we propose a method to generate the connection, linearization and duplication coefficients for q-orthogonal polynomials; 4. we propose a unified method to obtain these coefficients in a generic way for orthogonal polynomials on quadratic and q-quadratic lattices. Our algorithmic approach to compute linearization, connection and duplication coefficients is based on the one used by Koepf and Schmersau and on the NaViMa algorithm. Our main technique is to use explicit formulas for structural identities of classical orthogonal polynomial systems. We find our results by an application of computer algebra. The major algorithmic tools for our development are Zeilberger���s algorithm, q-Zeilberger���s algorithm, the Petkov��ek-van-Hoeij algorithm, the q-Petkov��ek-van-Hoeij algorithm, and Algorithm 2.2, p. 20 of Koepf's book "Hypergeometric Summation" and it q-analogue.

Controlling the transport of an ion: classical and quantum mechanical solutions

The accurate transport of an ion over macroscopic distances represents a challenging control problem due to the different length and time scales that enter and the experimental limitations on the controls that need to be accounted for. Here, we investigate the performance of different control techniques for ion transport in state-of-the-art segmented miniaturized ion traps. We employ numerical optimization of classical trajectories and quantum wavepacket propagation as well as analytical solutions derived from invariant based inverse engineering and geometric optimal control. The applicability of each of the control methods depends on the length and time scales of the transport. Our comprehensive set of tools allows us make a number of observations. We find that accurate shuttling can be performed with operation times below the trap oscillation period. The maximum speed is limited by the maximum acceleration that can be exerted on the ion. When using controls obtained from classical dynamics for wavepacket propagation, wavepacket squeezing is the only quantum effect that comes into play for a large range of trapping parameters. We show that this can be corrected by a compensating force derived from invariant based inverse engineering, without a significant increase in the operation time.

Automated Reasoning About Classical Mechanics

In recent years, researchers in artificial intelligence have become interested in replicating human physical reasoning talents in computers. One of the most important skills in this area is predicting how physical systems will behave. This thesis discusses an implemented program that generates algebraic descriptions of how systems of rigid bodies evolve over time. Discussion about the design of this program identifies a physical reasoning paradigm and knowledge representation approach based on mathematical model construction and algebraic reasoning. This paradigm offers several advantages over methods that have become popular in the field, and seems promising for reasoning about a wide variety of classical mechanics problems.

Self-organized sociopolitical interactions as the best way to achieve organized patterns in human social systems: going beyond the top-down control of classical political regimes

La monograf��a presenta la auto-organizaci��n sociopol��tica como la mejor manera de lograr patrones organizados en los sistemas sociales humanos, dada su naturaleza compleja y la imposibilidad de las tareas computacionales de los reg��menes pol��ticos cl��sico, debido a que operan con control jer��rquico, el cual ha demostrado no ser ��ptimo en la producci��n de orden en los sistemas sociales humanos. En la monograf��a se extrapola la teor��a de la auto-organizaci��n en los sistemas biol��gicos a las din��micas sociopol��ticas humanas, buscando maneras ��ptimas de organizarlas, y se afirma que redes complejas an��rquicas son la estructura emergente de la auto-organizaci��n sociopol��tica.

Governance and change in higher education : the debate between classical political sociology, new institutionalism and critical theories

Resumen tomado de la publicaci??n

Classical and causal inference approaches to statistical mediation analysis

Resumen tomado de la publicaci??n

Quantum similarity topological indices definition, analysis and comparison with classical molecular topological indices

Es mostra que, gracies a una extensi�� en la definici�� dels ��ndexs Moleculars Topol��gics, s'arriba a la formulaci�� d'��ndexs relacionats amb la teoria de la Semblan��a Molecular Qu��ntica. Es posa de manifest la connexi�� entre les dues metodologies: es revela que un marc de treball te��ric s��lidament fonamentat sobre la teoria de la Mec��nica Qu��ntica es pot connectar amb una de les t��cniques m��s antigues relacionades amb els estudis de QSPR. Es mostren els resultats per a dos casos d'exemple d'aplicaci�� d'ambdues metodologies