From Classical to Quantum Secret Sharing

Dans ce mémoire, nous nous pencherons tout particulièrement 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 étude par la présentation d’un nouveau protocole de partage de secret quantique nécessitant un nombre minimal de parts quantiques c.-à-d. une seule part quantique par participant. L’ouverture de notre étude se fera par la présentation dans le chapitre préliminaire d’un survol des notions mathématiques sous-jacentes à la théorie de l’information quantique ayant pour but primaire d’établir la notation utilisée dans ce manuscrit, ainsi que la présentation d’un précis des propriétés mathématique de l’état de Greenberger-Horne-Zeilinger (GHZ) fréquemment utilisé dans les domaines quantiques de la cryptographie et des jeux de la communication. Mais, comme nous l’avons mentionné plus haut, c’est le domaine cryptographique qui restera le point focal de cette étude. Dans le second chapitre, nous nous intéresserons à la théorie des codes correcteurs d’erreurs classiques et quantiques qui seront à leur tour d’extrême importances lors de l’introduction de la théorie quantique du partage de secret dans le chapitre suivant. Dans la première partie du troisième chapitre, nous nous concentrerons sur le domaine classique du partage de secret en présentant un cadre théorique général portant sur la construction de ces primitives illustrant tout au long les concepts introduits par des exemples présentés pour leurs intérêts autant historiques que pédagogiques. Ceci préparera le chemin pour notre exposé sur la théorie quantique du partage de secret qui sera le focus de la seconde partie de ce même chapitre. Nous présenterons alors les théorèmes et définitions les plus généraux connus à date portant sur la construction de ces primitives en portant un intérêt particulier au partage quantique à seuil. Nous montrerons le lien étroit entre la théorie quantique des codes correcteurs d’erreurs et celle du partage de secret. Ce lien est si étroit que l’on considère les codes correcteurs d’erreurs quantiques étaient de plus proches analogues aux partages de secrets quantiques que ne leur étaient les codes de partage de secrets classiques. Finalement, nous présenterons un de nos trois résultats parus dans A. Broadbent, P.-R. Chouha, A. Tapp (2009); un protocole sécuritaire et minimal de partage de secret quantique a seuil (les deux autres résultats dont nous traiterons pas ici portent sur la complexité de la communication et sur la simulation classique de l’état de GHZ).

Intention-based economic theories of reciprocity

In recent years, several experiments have shown individuals exhibit authentic reciprocal behaviour in anonymous one-shot interactions. As reciprocity has been shown to be relevant in several economic fields, there have also been several attempts to model reciprocal bahaviour. I review the intention-based models of reciprocity and present an example of teacher management in the public sector in which the government offers an incentive scheme to implement a program. The incentive scheme has a prisoner´s dilemma structure. In both simultaneous and sequential games, equilibrium results may differ from those predicted by standard theory.

Modelos de presupuestación de capital en finanzas corporativas y utilidad de los mismos

La siguiente investigación describe una aproximación teórica al tema de los modelos de presupuestación de capital, el objetivo fundamental se basa en comprender su enfoque e importancia al momento de tomar decisiones de inversión por parte de los directores de una empresa, así como de prever los efectos de esta en un futuro. Al respecto, y sobre la base de que los modelos de presupuestación de capital son herramientas para analizar posibles erogaciones de capital por parte de una empresa, es necesario para efectos del presente proyecto de investigación, definir sus diferentes modelos desde lo teórico y metodológico, explicando los diferentes conceptos relacionados con el tema. Así mismo, se explican algunos de los indicadores financieros utilizados en las compañías para medir y estimar la “salud financiera” de la empresa, además de puntualizar su impacto en la perdurabilidad de las entidades, lo cual permite dar una visión más general sobre la importancia que trasciende de los indicadores financieros, generando un impacto positivo en la evolución o crecimiento de la organización. En complemento, la investigación aborda la presupuestación de capital de manera particular aplicado en la gestión empresarial, sean estas privadas o públicas (estatal y gubernamental). En este sentido, se abordan conceptos elaborados por diferentes académicos en los que se exponen algunas aproximaciones respecto al posible mejoramiento de la presupuestación para los sectores a los que pertenecen determinadas entidades. Finalmente, se presenta de manera explícita las conclusiones que surgieron a lo largo de la construcción del documento de investigación, con el fin de dar cumplimiento concreto al objetivo general del trabajo, el cual constituye una respuesta a la pregunta de investigación que se enunciará en el desarrollo del documento.

Does uncertainty cause inertia in decision making? An experimental study of the role of regret aversion and indecisiveness

Previous research has shown that often there is clear inertia in individual decision making---that is, a tendency for decision makers to choose a status quo option. I conduct a laboratory experiment to investigate two potential determinants of inertia in uncertain environments: (i) regret aversion and (ii) ambiguity-driven indecisiveness. I use a between-subjects design with varying conditions to identify the effects of these two mechanisms on choice behavior. In each condition, participants choose between two simple real gambles, one of which is the status quo option. I find that inertia is quite large and that both mechanisms are equally important.

Compression-based Image Registration

Image registration is an important component of image analysis used to align two or more images. In this paper, we present a new framework for image registration based on compression. The basic idea underlying our approach is the conjecture that two images are correctly registered when we can maximally compress one image given the information in the other. The contribution of this paper is twofold. First, we show that the image registration process can be dealt with from the perspective of a compression problem. Second, we demonstrate that the similarity metric, introduced by Li et al., performs well in image registration. Two different versions of the similarity metric have been used: the Kolmogorov version, computed using standard real-world compressors, and the Shannon version, calculated from an estimation of the entropy rate of the images

Shape complexity based on mutual information

Shape complexity has recently received attention from different fields, such as computer vision and psychology. In this paper, integral geometry and information theory tools are applied to quantify the shape complexity from two different perspectives: from the inside of the object, we evaluate its degree of structure or correlation between its surfaces (inner complexity), and from the outside, we compute its degree of interaction with the circumscribing sphere (outer complexity). Our shape complexity measures are based on the following two facts: uniformly distributed global lines crossing an object define a continuous information channel and the continuous mutual information of this channel is independent of the object discretisation and invariant to translations, rotations, and changes of scale. The measures introduced in this paper can be potentially used as shape descriptors for object recognition, image retrieval, object localisation, tumour analysis, and protein docking, among others

New medical registration and segmentation techniques using information-theoretic tools

El processament d'imatges mèdiques és una important àrea de recerca. El desenvolupament de noves tècniques que assisteixin i millorin la interpretació visual de les imatges de manera ràpida i precisa és fonamental en entorns clínics reals. La majoria de contribucions d'aquesta tesi són basades en Teoria de la Informació. Aquesta teoria tracta de la transmissió, l'emmagatzemament i el processament d'informació i és usada en camps tals com física, informàtica, matemàtica, estadística, biologia, gràfics per computador, etc. En aquesta tesi, es presenten nombroses eines basades en la Teoria de la Informació que milloren els mètodes existents en l'àrea del processament d'imatges, en particular en els camps del registre i la segmentació d'imatges. Finalment es presenten dues aplicacions especialitzades per l'assessorament mèdic que han estat desenvolupades en el marc d'aquesta tesi.

Opportunistic cooperative diversity protocols for wireless networks

In this paper we consider a cooperative communication system where some a priori information of wireless channels is available at the transmitter. Several opportunistic relaying strategies are developed to fully utilize the available channel information. Then an explicit expression of the outage probability is developed for each proposed cooperative scheme as well as the diversity-multiplexing tradeoff by using order statistics. Our analytical results show that the more channel information available at the transmitter, the better performance a cooperative system can achieve. When the exact values of the source-relay channels are available, the performance loss at low SNR can be effectively suppressed. When the source node has the access to the source-relay and relay-destination channels, the full diversity can be achieved by costing only one extra channel used for relaying transmission, and an optimal diversity-multiplexing tradeoff can be achieved d(r) = (N + 1)(1 - 2r), where N is the number of all possible relaying nodes.

The Mathematics of Control Theory

This text contains papers presented at the Institute of Mathematics and its Applications Conference on Control Theory, held at the University of Strathclyde in Glasgow. The contributions cover a wide range of topics of current interest to theoreticians and practitioners including algebraic systems theory, nonlinear control systems, adaptive control, robustness issues, infinite dimensional systems, applications studies and connections to mathematical aspects of information theory and data-fusion.

An investigation into feature construction to assist word sense disambiguation

Identifying the correct sense of a word in context is crucial for many tasks in natural language processing (machine translation is an example). State-of-the art methods for Word Sense Disambiguation (WSD) build models using hand-crafted features that usually capturing shallow linguistic information. Complex background knowledge, such as semantic relationships, are typically either not used, or used in specialised manner, due to the limitations of the feature-based modelling techniques used. On the other hand, empirical results from the use of Inductive Logic Programming (ILP) systems have repeatedly shown that they can use diverse sources of background knowledge when constructing models. In this paper, we investigate whether this ability of ILP systems could be used to improve the predictive accuracy of models for WSD. Specifically, we examine the use of a general-purpose ILP system as a method to construct a set of features using semantic, syntactic and lexical information. This feature-set is then used by a common modelling technique in the field (a support vector machine) to construct a classifier for predicting the sense of a word. In our investigation we examine one-shot and incremental approaches to feature-set construction applied to monolingual and bilingual WSD tasks. The monolingual tasks use 32 verbs and 85 verbs and nouns (in English) from the SENSEVAL-3 and SemEval-2007 benchmarks; while the bilingual WSD task consists of 7 highly ambiguous verbs in translating from English to Portuguese. The results are encouraging: the ILP-assisted models show substantial improvements over those that simply use shallow features. In addition, incremental feature-set construction appears to identify smaller and better sets of features. Taken together, the results suggest that the use of ILP with diverse sources of background knowledge provide a way for making substantial progress in the field of WSD.

Quantitative Information Flow, Relations and Polymorphic Types

This paper uses Shannon's information theory to give a quantitative definition of information flow in systems that transform inputs to outputs. For deterministic systems, the definition is shown to specialise to a simpler form when the information source and the known inputs jointly determine the inputs. For this special case, the definition is related to the classical security condition of non-interference and an equivalence is established between non-interference and independence of random variables. Quantitative information flow for deterministic systems is then presented in relational form. With this presentation, it is shown how relational parametricity can be used to derive upper and lower bounds on information flows through families of functions defined in the second order lambda calculus.

A notion of subgame perfect Nash equilibrium under knightian uncertainty

We define a subgame perfect Nash equilibrium under Knightian uncertainty for two players, by means of a recursive backward induction procedure. We prove an extension of the Zermelo-von Neumann-Kuhn Theorem for games of perfect information, i. e., that the recursive procedure generates a Nash equilibrium under uncertainty (Dow and Werlang(1994)) of the whole game. We apply the notion for two well known games: the chain store and the centipede. On the one hand, we show that subgame perfection under Knightian uncertainty explains the chain store paradox in a one shot version. On the other hand, we show that subgame perfection under uncertainty does not account for the leaving behavior observed in the centipede game. This is in contrast to Dow, Orioli and Werlang(1996) where we explain by means of Nash equilibria under uncertainty (but not subgame perfect) the experiments of McKelvey and Palfrey(1992). Finally, we show that there may be nontrivial subgame perfect equilibria under uncertainty in more complex extensive form games, as in the case of the finitely repeated prisoner's dilemma, which accounts for cooperation in early stages of the game.

Teste Illinois de Habilidades Psicolinguísticas: analise critica do modelo mediacional e de diversos aspectos da validade do instrumento

Este trabalho investiga basicamente a validade do Teste Illinois de Habilidades Psicolinguísticas -ITPA -instrumento de avaliação do desenvolvimento da linguagem infantil. Seus autores, S. Kirk e J.J. McCarthy (1961), utilizam o referencial teórico proposto por C. Osgood (1957), a ele incorporando o modelo derivado da Teoria da Informação, o que permite que, na prática clínica, o ITPA possa ser incluído no processo psicodiagnóstico como instrumento de avaliação dos problemas da comunicação em crianças entre três e dez anos. Os objetivos que conduzem e orientam o trabalho apresentado podem ser definidos em três níveis: 1) O que trata dos constructos e suas interrelaç6es -análise crítica da validade teóricado ITPA; 2) O que avalia sua condição de instrumento diagnóstico do desempenho escolar -sensibilidade discriminante do rendimento acadêmico; 3) O que trata da eficácia da prática psicopedagógica proposta pelo mesmo instrumento. O estudo sobre a validade teórica foi realizado com 931 crianças entre três e dez anos de idade, em processo de escolarização, frequentando creches, jardins de infância ou classes regulares da Rede de Ensino do Primeiro Grau no Município do Rio de Janeiro. Utilizou-se a técnica da Análise Fatorial, complementada por uma abordagem lógica que comprovaram algumas das dimensões propostas pelo referencial teórico de Kirk e McCarthy. Para a validade diagnóstica foram avaliadas 71 crianças com dificuldades no desempenho acadêmico, expressas através de conceitos de insuficiência ou deficiência de rendimento e seus resultados foram comparados com os de um subgrupo, aleatoriamente constituído de crianças que participaram do estudo anterior. Utilizou-se a técnica da Análise Discriminante chegando-se à seguinte conclusão: embora a validade de constructo do IIPA não tenha sido completamente confirmada num nível diagnóstico os resultados permitem identificar, com baixa margem de erro, as crianças que pertencem a um ou outro dos grupos de contraste. Quanto ao terceiro nível, foi feita ampla-revelação bibliográfica sobre investigações efetuadas com este instrumento no Brasil e no Exterior. Visou-se avaliar a eficácia da prática psicopedagógica utilizada quando desenvolvida à luz dos recursos de intervenção que o IIPA propõe. Concluiu-se que as pesquisas, até o presente momento efetuadas, não são suficientes para formar um juízo mais seguro da praxis educativa destinada à reabilitação das crianças com problemas da comunicação - o que constitui impedimento a seu desempenho acadêmico - em função das controvérsias que tais pesquisas apresentam.

Informação e organização: um modelo de diagnostico e intervenção na administração da universidade

Este trabalho, concebido dentro de uma perspectiva humanista, propõe-se a elaborar e testar um modelo de Diagnóstico e Intervenção Organizacional. A abordagem sistêmica permitiu a aplicação de conceitos da Teoria da Informação, tendo em vista a ideia de se elaborar uma sistemática de tratamento de dados coleta dos, que possibilite uma nova forma de Descrição de Cargos e consequente Especificações de Trabalho. O objetivo de tal colocação visa minorar as principais falhas existentes na passagem ' dos requisitos de Trabalho às Especificações decorrentes, tornando este "salto" menos subjetivo, mais operacional e melhor quantificável. Por outro lado, o tratamento de dados à luz da Teoria da Informação, permite a elaboração de novas categorizações e avaliações para fins psicológicos. Além de se obter uma classificação objetiva, operacional e dinâmica em termos de análise de trabalho, são formulados novos recursos com vista s a uma seleção adequada, um tratamento útil e específico, fundamentados nos elementos discriminantes de cada cargo. Finalmente, através de uma análise da estrutura e da dinâmica de uma organização específica, fundamentada em processos de análise de trabalho e de avaliação de pessoal, baseadas na teoria da, informação é também possível planejar-se mudanças organizacionais - com perspectivas ergonômicas - na área considera da crítica, para minimizar a eficiência dos recursos humanos de uma organização, isto é, a adaptação do trabalho ao Homem.

A notion of subgame perfect nash equilibrium under knightian uncertainty

We define a subgame perfect Nash equilibrium under Knightian uncertainty for two players, by means of a recursive backward induction procedure. We prove an extension of the Zermelo-von Neumann-Kuhn Theorem for games of perfect information, i. e., that the recursive procedure generates a Nash equilibrium under uncertainty (Dow and Werlang(1994)) of the whole game. We apply the notion for two well known games: the chain store and the centipede. On the one hand, we show that subgame perfection under Knightian uncertainty explains the chain store paradox in a one shot version. On the other hand, we show that subgame perfection under uncertainty does not account for the leaving behavior observed in the centipede game. This is in contrast to Dow, Orioli and Werlang(1996) where we explain by means of Nash equilibria under uncertainty (but not subgame perfect) the experiments of McKelvey and Palfrey(1992). Finally, we show that there may be nontrivial subgame perfect equilibria under uncertainty in more complex extensive form games, as in the case of the finitely repeated prisoner's dilemma, which accounts for cooperation in early stages of the game .