In view of the fact that a same complex phenomenon can be approached by different conceptual frameworks, it is natural to inquire on the possibility to find connections between different types of quantities, such as topological, dynamical, statistical or thermodynamical, characterizing the same system. The present work is built on the idea that this line of approach can provide interesting insights on possible universal principles governing complex phenomena. In Chapter I we introduce concepts and tools of dynamical systems and thermodynamics as applied in macroscopic scale description as well as, for a later use, a number of selected representative models. In Chapter II we briefly present the elements of the theory of Markov processes describing a large class of stochastic process and also introduce some important concepts on the probabilistic description of deterministic systems. This chapter ends with a thermodynamic formulation accounting for the evolution of the entropy under the effect of stochastic fluctuations. In Chapter III, after introducing the main concepts and recent advances in network theory, we provide a connection between dynamical systems and network theory, which shows how universal structural properties of evolving networks can arise from deterministic dynamics. More specifically, we show explicitly the relation between the connectivity patterns of these networks and the indicators of the underlying dynamics, such as the local Lyapunov exponents. Our analysis is applied to representative models of chaotic maps, chaotic flows and is finally extended to stochastic processes. In Chapter IV we address the inverse problem, namely, processes whose dynamics is determined, in part, by the structure of the network in which they are embedded. In particular, we focus on systems of particles diffusing on a lattice and reacting instantaneously upon encountering each other. We study the role of the topology, the degree of synchronicity of motion and the reaction mechanism on the efficiency of the process. This lead us to identify a common generic mechanism responsible for the behavior of the efficiency, as a function of the control parameters. Finally, in Chapter V we study the connection between the topology and the thermodynamic properties of reaction networks, with focus on the entropy production and the system’s efficiency at nonequilibrium steady states. We also explore the connection between dynamic and thermodynamic properties of nonlinear feedbacks, as well as the response properties of reaction networks against both deterministic and stochastic external perturbations. We address networks of varying topologies, from regular lattices to complex structures./Le présent travail s’inscrit dans le domaine de recherche sur les systèmes complexes. Différentes approches, basées des systèmes dynamiques, de la thermodynamique des systèmes hors d’équilibre, de la physique statistique et, plus récemment, de la théorie des réseaux, sont combinés afin d’explorer des liens entre différentes types de grandeurs qui caractérisent certaines classes de comportements complexes. Dans le Chapitre I nous introduisons les principaux concepts et outils de systèmes dynamiques et de thermodynamique. Dans le Chapitre II nous présentons premièrement des éléments de la théorie de processus de Markov, ainsi que les concepts à la base de la description probabiliste des systèmes déterministes. Nous finissons le chapitre en proposant une formulation thermodynamique qui décrit l’évolution de l’entropie hors d’équilibre, soumis à l’influence de fluctuations stochastiques. Dans le Chapitre III nous introduisons les concepts de base en théorie des réseaux, ainsi qu’un résumé générale des progrès récents dans le domaine. Nous établissons ensuite une connexion entre la théorie des systèmes dynamiques et la théorie de réseaux. Celle-ci permet d’approfondir la compréhension des mécanismes responsables de l’émergence des propriétés structurelles dans des réseaux crées par des lois dynamiques déterministes. En particulier, nous mettons en évidence la relation entre des motifs de connectivité de ce type de réseaux et des indicateurs de la dynamique sous-jacente, tel que des exposant de Lyapounov locaux. Notre analyse est illustrée par des applications et des flots chaotiques et étendue à des processus stochastiques. Dans le Chapitre IV nous étudions le problème complémentaire, à savoir, celui de processus dont la dynamique est déterminée, en partie, par la structure du réseau dans lequel elle se déroule. Plus précisément, nous nous concentrons sur le cas de systèmes de particules réactives, diffusent au travers d’un réseau et réagissant instantanément lorsqu’un rencontre se produit entre elles. Nous étudions le rôle de la topologie, du degré de synchronicité des mouvements et aussi celui du mécanisme de réaction sur l’efficacité du processus. Dans les différents modèles étudiés, nous identifions un mécanisme générique commun, responsable du comportement de l’efficacité comme fonction des paramètres de contrôle. Enfin, dans le Chapitre V nous abordons la connexion entre la topologie et les propriétés thermodynamiques des réseaux de réactions, en analysant le comportement local et global de la production d’entropie et l’efficacité du système dans des état stationnaires de non-équilibre. Nous explorons aussi la connexion entre la dynamique et les propriétés de boucles de rétroaction non linéaires, ainsi que les propriétés de réponse des réseaux de réaction à des perturbations stochastiques et déterministes externes. Nous considérons le cas de réseaux à caractère régulier aussi bien que celui de réseaux complexes.

More and more effort is being spent on security improvements in today's computer environments, with the aim to achieve an appropriate level of security. However, for small computing devices it might be necessary to reduce the computational cost imposed by security in order to gain reasonable performance and/or energy consumption. To accomplish this selective encryption can be used, which provides confidentiality by only encrypting chosen parts of the information. Previous work on selective encryption has chiefly focused on how to reduce the computational cost while still making the information perceptually secure, but not on how computationally secure the selectively encrypted information is.  Despite the efforts made and due to the harsh nature of computer security, good quantitative assessment methods for computer security are still lacking. Inventing new ways of measuring security are therefore needed in order to better understand, assess, and improve the security of computer environments. Two proposed probabilistic quantitative security measures are entropy and guesswork. Entropy gives the average number of guesses in an optimal binary search attack, and guesswork gives the average number of guesses in an optimal linear search attack. In information theory, a considerable amount of research has been carried out on entropy and on entropy-based metrics. However, the same does not hold for guesswork. In this thesis, we evaluate the performance improvement when using the proposed generic selective encryption scheme. We also examine the confidentiality strength of selectively encrypted information by using and adopting entropy and guesswork. Moreover, since guesswork has been less theoretical investigated compared to entropy, we extend guesswork in several ways and investigate some of its behaviors.

In this thesis, we study the representation of speech signals and the estimation of information-theoretical measures from observations containing features of the speech signal. The main body of the thesis consists of four research papers. Paper A presents a compact representation of the speech signal that facilitates perfect reconstruction. The representation is constituted of models, model parameters, and signal coefficients. A difference compared to existing speech representations is that we seek a compact representation by adapting the models to maximally concentrate the energy of the signal coefficients according to a selected energy concentration criterion. The individual parts of the representation are closely related to speech signal properties such as spectral envelope, pitch, and voiced/unvoiced signal coefficients, bene cial for both speech coding and modi cation. From the information-theoretical measure of entropy, performance limits in coding and classi cation can be derived. Papers B and C discuss the estimation of di erential entropy. Paper B describes a method for estimation of the di erential entropies in the case when the set of vector observations (from the representation) lie on a lower-dimensional surface (manifold) in the embedding space. In contrast to the method presented in Paper B, Paper C introduces a method where the manifold structures are destroyed by constraining the resolution of the observation space. This facilitates the estimation of bounds on classi cation error rates even when the manifolds are of varying dimensionality within the embedding space. Finally, Paper D investigates the amount of shared information between spectral features of narrow-band (0.3-3.4 kHz) and high-band (3.4-8 kHz) speech. The results in Paper D indicate that the information shared between the high-band and the narrow-band is insufficient for high-quality wideband speech coding (0.3-8 kHz) without transmission of extra information describing the high-band. / QC 20100914

We consider transmission over a binary erasure wiretap channel using the code construction method introduced by Rathi et al. based on two edge type Low-Density Parity-Check (LDPC) codes and the coset encoding scheme. By generalizing the method of computing conditional entropy for standard LDPC ensembles introduced by Méasson, Montanari, and Urbanke to two edge type LDPC ensembles, we show how the equivocation for the wiretapper can be computed. We find that relatively simple constructions give very good secrecy performance and are close to the secrecy capacity. / <p>Copyright 2010 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. QC 20120110</p>

As hybrid and electric vehicles continue to evolve there is a need for better battery thermal management systems (BTMS), which maintain uniformity of operating temperature of the batteries in the vehicles. This thesis investigates the use of an indirect liquid cooled system, which can be applied to hybrid and electric vehicles. The design is modeled as part of the UOIT EcoCAR. The predominant focus of this indirect liquid cooled system is the entropy generation in each of the components within the system, as well as a total system analysis. Four main components of the system are the battery module, heat exchanger, pump, and throttle. The battery module coolant tubes and the entire heat exchanger model are developed. Various parameters are changed in each component, leading to a decrease in entropy generation depending on the variable changed. Of the four components identified, the heat exchanger produced the majority of entropy generation, which leads to an overall increase in system entropy generation. There are many factors to consider when designing a liquid cooled BTMS. The new model shows a unique ability to improve system performance by reducing the entropy generation in the BTMS. / UOIT

A concentric pneumatic nebulizer (CPN) and a custom designed flow focusing nebulizer (FFN) are characterized. As will be shown, the classical Nukiyama-Tanasawa and Rizk-Lefebvre models lead to erroneous size prediction for the concentric nebulizer under typical operating conditions due to its specific design, geometry, dimension and different flow regimes. The models are then modified to improve the agreement with the experimental results. The size prediction of the modified models together with the spray velocity characterization are used to determine the overall nebulizer efficiency and also employed as input to a new Maximum Entropy Principle (MEP) based model to predict joint size-velocity distribution analytically. The new MEP model is exploited to study the local variation of size-velocity distribution in contrast to the classical models where MEP is applied globally to the entire spray cross section. As will be demonstrated, the velocity distribution of the classical MEP models shows poor agreement with experiments for the cases under study. Modifications to the original MEP modeling are proposed to overcome this deficiency. In addition, the new joint size-velocity distribution agrees better with our general understanding of the drag law and yields realistic results. / PhD

La tesi versa sobre sistemes dinàmics discrets 1-dimensionals, des d'un punt de vista combinatori i topològic. Estem interessats en les òrbites periòdiques i l'entropia topològica de les aplicacions contínues definides en arbres i grafs.El problema central és la caracterització del conjunt de períodes de totes les òrbites periòdiques d'una aplicació contínua d'un arbre en ell mateix. El teorema de Sharkovskii (1964) fou el primer resultat remarcable en aquest sentit. Aquest bonic teorema estableix que el conjunt de períodes d'una aplicació de l'interval és un segment inicial d'un ordre lineal (ordre de Sharkovskii). Recíprocament, donat qualsevol segment inicial d'aquest ordre, existeix una aplicació de l'interval que el té com a conjunt de períodes. Durant les darreres dècades hi ha hagut diversos intents de trobar resultats similars al de Sharkovskii per a altres espais 1-dimensionals. Recentment, el cas d'arbres ha estat tractat especialment. El Teorema de Baldwin (1991) resol el problema en el cas de les n-estrelles i ha estat un dels avenços més significatius en aquesta direcció. Aquest resultat estableix que el conjunt de períodes per a una aplicació de la n-estrella és unió finita de segments inicials de n ordres parcials (ordres de Baldwin), i recíprocament.El nostre objectiu principal és descriure l'estructura del conjunt de períodes de qualsevol aplicació contínua d'un arbre T en termes de les propietats combinatòries i topològiques de T: quantitat i disposició d'extrems, vèrtexs i arestes. En el capítol 1 discutim detalladament la manera més natural d'atacar el problema, i proposem una estratègia consistent en tres etapes consecutives. L'eina principal d'aquesta estratègia són els models minimals de patrons. Aquestes nocions es van desenvolupar i utilitzar durant les darreres dècades en el context de l'interval. En canvi, no es disposava de definicions operatives equivalents per a arbres, fins que al 1997 Alseda, Guaschi, Los, Manyosas i Mumbru proposaren de definir el patró d'un conjunt finit invariant P essencialment com una classe d'homotopia d'aplicacions relativa a P, i provaren (constructivament) que sempre existeix un model P-canònic amb propietats de minimalitat dinàmica. L'objectiu del capítol 2 és implementar completament el programa proposat, duent a terme les etapes 2 i 3. El resultat principal d'aquest capítol diu que, donada una aplicació g definida en un arbre T, existeix un conjunt S de successions finites d'enters positius tal que el conjunt de períodes de g és (excepte un conjunt finit explícitament acotat) una unió finita de segments inicials d'ordres de Baldwin donats en termes del conjunt S, que depèn de les propietats combinatòries de l'arbre T. També provem el recíproc. En el capítol 3 duem a terme experiments informàtics sobre la minimalitat dinàmica dels models canònics. En un esperit de programació modular, hem dissenyat moltes funcions autocontingudes que poden ser usades per implementar una gran varietat d'aplicacions d'ús divers. Entre altres, tenim funcions que calculen el model canònic d'un patró donat per l'usuari, calculen la matriu de Markov associada a un model monòton a trossos i extreuen tots els llaços simples d'una matriu de transició de Markov. Finalment, en el capítol 4 generalitzem alguns resultats de Block i Coven, Misiurewicz i Nitecki i Takahashi, en els quals l'entropia topològica d'una aplicació de l'interval s'aproxima per les entropies de les seves òrbites periòdiques. Hem provat relacions anàlogues en el context de les aplicacions de grafs. / This memoir deals with one-dimensional discrete dynamical systems, from both a topological and a combinatorial point of view. We are interested in the periodic orbits and topological entropy of continuous self-maps defined on trees and graphs.The central problem is the characterisation of the set of periods of all periodic orbits exhibited by any continuous map from a tree into itself. The Sharkovskii's Theorem (1964) was the first remarkable result in this setting. This theorem states that the set of periods of any interval map is an initial segment of a linear ordering (the so-called Sharkovskii ordering). Conversely, given any initial segment of the Sharkovskii ordering, there exists an interval map whose set of periods coincides with it.During the last decades there have been several attempts to find results similar to that of Sharkovskii for other one-dimensional spaces. Recently, the case of maps defined on general trees has been specially treated. Baldwin's Theorem (1991), which solves the problem in the case of n-stars for any n, has been one of the most significant advances in this direction. This result states that the set of periods of any n-star map is a finite union of initial segments of n-many partial orderings (the Baldwin orderings). The converse is also true.Our main purpose is to describe the generic structure of the set of periods of any continuous self-map defined on a tree T in terms of the combinatorial and topological properties of T: amount and arrangement of endpoints, vertices and edges. In Chapter 1 we make a detailed discussion about which is the more natural approach to this problem, and we propose a strategy consisting on three consecutive stages and using minimal models of patterns as the main tool. These notions were developed in the context of interval maps and widely used in a number of papers during the last two decades. However, equivalent operative definitions for tree maps were not available until 1997, when Alseda, Guaschi, Los, Manosas and Mumbru proposed to define the pattern of a finite invariant set P essentially as a homotopy class of maps relative to the points of P, and proved (constructively) that there always exists a P-canonical model displaying dynamic minimality properties.The goal of Chapter 2 is to implement in full the above programme by completing stages 2 and 3. The main result of Chapter 2 tells us that for each tree map g defined on a tree T there exists a finite set S of sequences of positive integers such that the set of periods of g is (up to an explicitly bounded finite set) a finite union of initial segments of Baldwin orderings, given in terms of the set S, which depends on the combinatorial properties of the tree T. We also prove the converse result.In Chapter 3 we report some computer experiments on the minimality of the dynamics of canonical models. In a spirit of modular programming, we have designed lots of self-contained functions which can be used to implement a wide variety of several-purpose software. Among other, we have functions that: compute the canonical model of a pattern provided by the user, calculate the Markov transition matrix associated to a piecewise monotone tree map and extract all the simple loops of a given length from a Markov transition matrix.Finally, in Chapter 4 we generalize some results of Block & Coven, Misiurewicz & Nitecki and Takahashi, where the topological entropy of an interval map was approximated by the entropies of its periodic orbits. We prove analogous relations in the setting of graph maps.

We propose a family of search directions based on primal-dual entropy in the context of interior point methods for linear programming. This new family contains previously proposed search directions in the context of primal-dual entropy. We analyze the new family of search directions by studying their primal-dual affine-scaling and constant-gap centering components. We then design primal-dual interior-point algorithms by utilizing our search directions in a homogeneous and self-dual framework. We present iteration complexity analysis of our algorithms and provide the results of computational experiments on NETLIB problems.

We study a proposed statistical explanation for the Bekenstein-Hawking entropy of a black hole in which entropy arises quantum-mechanically as a result of entanglement. Arguments for the identification of black hole entropy with entanglement entropy are reviewed in the framework of quantum field theory, emphasizing the role of renormalization and the need for a physical short-distance cutoff. Our main novel contribution is a calculation of entanglement entropy in loop quantum gravity. The kinematical Hilbert space and spin network states are introduced, and the entanglement entropy of these states is calculated using methods from quantum information theory. The entanglement entropy is compared with the density of states previously computed for isolated horizons in loop quantum gravity, and the two are found to agree up to a topological term. We investigate a conjecture due to Sorkin that the entanglement entropy must be a monotonically increasing function of time under the assumption of causality. For a system described by a finite-dimensional Hilbert space, the conjecture is found to be trivial, and for a system described by an infinite-dimensional Hilbert space a counterexample is provided. For quantum states with Euclidean symmetry, the area scaling of the entanglement entropy is shown to be equivalent to the strong additivity condition on the entropy. The strong additivity condition is naturally interpreted in information-theoretic terms as a continuous analog of the Markov property for a classical random variable. We explicitly construct states of a quantum field theory on the one-dimensional real line in which the area law is exactly satisfied.

There is now ample evidence to support the notion that a lack of oxygen (hypoxia) within the tumour adversely affects the outcome of radiotherapy and whether a patient is able to remain disease free. Thus, there is increasing interest in accurately determining oxygen concentration levels within a tumour. Hypoxic regions arise naturally in cancerous tumours because of their abnormal vasculature and it is believed that oxygen is necessary in order for radiation to be effective in killing cancer cells. One method of measuring oxygen concentration within a tumour is the Eppendorf polarographic needle electrode; a method that is favored by many clinical researchers because it is the only device that is inserted directly into the tumour, and reports its findings in terms of oxygen partial pressure (PO2). Unfortunately, there are often anomalous readings in the Eppendorf measurements (negative and extremely high values) and there is little consensus as to how best to interpret the data. In this thesis, Bayesian methods are applied to estimate two measures commonly used to quantify oxygen content within a tumour in the current literature: the median PO2, and Hypoxic Proportion (HP5), the percentage of readings less than 5mmHg. The results will show that Bayesian methods of parameter estimation are able to reproduce the standard estimate for HP5 while providing an additional piece of information, the error bar, that quantifies how uncertain we believe our estimate to be. Furthermore, using the principle of Maximum Entropy, we will estimate the true median PO2 of the distribution instead of simply relying on the sample median, a value which may or may not be an accurate indication of the actual median PO2 inside the tumour. The advantage of the Bayesian method is that it takes advantage of probability theory and presents its results in the form of probability density functions. These probability density functions provide us with more information about the desired quantity than the single number that is produced in the current literature and allows us to make more accurate and informative statements about the measure of hypoxia that we are trying to estimate.