Dissertations / Theses on the topic 'Entropy'
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Bernier, Jobe Paul. "Entropy and Architecture entropic phenomena actuating dynamic space /." Thesis, Montana State University, 2008. http://etd.lib.montana.edu/etd/2008/bernier/BernierJ0508.pdf.
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Sognnæs, Ida Andrea Braathen. "Maximum Entropy and Maximum Entropy Production in Macroecology." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for fysikk, 2011. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-12651.
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The Maximum Entropy Theory of Ecology (METE), developed by John Harte, presents an entirely new method of making inferences in ecology. The method is based on the established mathematical procedure of Maximum Information Entropy (MaxEnt), developed by Edwin T. Jaynes, and is used to derive a range of important relationships in macroecology. The Maximum Entropy Production (MEP) principle is a more recent theory. This principle was used by Paltridge to successfully predict the climate on Earth in 1975. It has been suggested that this principle can be used for predicting the evolution of ecosystems over time in the framework of METE. This idea is at the very frontier of Harte's theory. This thesis investigates the hypothesis that the information entropy defined in METE is described by the MEP principle.I show that the application of the MEP principle to the information entropy in METE leads to a range of conceptual and mathematical difficulties. I show that the initial hypothesis alone cannot predict the time rate of change, but that it does predict that the number of individual organisms and the total metabolic rate of an ecosystem will continue to grow indefinitely, whereas the number of species will approach one.I also conduct a thorough review of the MEP literature and discuss the possibility of an application of the MEP principle to METE based on analogies. I also study a proof of the MEP principle published by Dewar in 2003 and 2005 in order to investigate the possibility of an application based on first principles. I conclude that the MEP principle has a low probability of success if applied directly to the information entropy in METE.One of the most central relationships derived in METE is the expected number of species in a plot of area $A$. I conduct a numerical simulation in order to study the variance of the actual number of species in a collection of plots. I then suggest two methods to be used for comparison between predictions and observations in METE.I also conduct a numerical study of selectied stability properties of Paltridge's climate model and conclude that none of these can explain the observed MEP state in nature.
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Asaad-Sultan, Asaad M. Abu. "Entropic vector optimization and simulated entropy : theory and applications." Thesis, University of Liverpool, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.293838.
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Cullen, Carley Nicole. "Empathy + entropy." Thesis, University of Iowa, 2019. https://ir.uiowa.edu/etd/6721.
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Šelinga, Martin. "Software pro hodnocení zdrojů entropie." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2019. http://www.nusl.cz/ntk/nusl-401953.
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This thesis is focused on exploring the sources of entropy. It includes a description of random number generators and tests used to evaluate entropy quality. Random number generator for Windows and Linux OS was created together with software for entropy evaluation. Subsequently, measurement of entropy was performed on physical workstations and Cloud environments.
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Mendes, Ronã Rinston Amaury [UNESP]. "Uma contribuição para a otimização de portfólios de séries heteroscedásticas usando projeto de experimento de misturas: uma abordagem do desirability aplicada a modelos." Universidade Estadual Paulista (UNESP), 2012. http://hdl.handle.net/11449/103053.
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Esta tese apresenta uma proposta inovadora com base no DOE (Design of Experiments) para tratar a otimização de portfólios multiobjetivos utilizando uma abordagem híbrida que combina arranjos de experimentos do tipo Misturas (Mixture Design of Experiments – MDE) e funções Desirability para se encontrar um portfólio ótimo modelado pelo algoritmo ARMA–GARCH. Neste tipo de estratégia experimental, as proporções investidas em cada ativo do portfólio são tratadas como fatores de um arranjo de misturas adequado para o tratamento de portfólios em geral. Ao invés de utilizar a tradicional programação matemática de portfólios de média variância (MVP), o conceito da função desirability é aqui utilizado para resolver problemas de otimização não linear multiobjetiva para a predição de valores condicionais de retorno (média), risco (variância) e entropia com suas respectivas superfícies de resposta estimadas pelo MDE. Para evitar a falta de diversificação dos portfólios, o princípio da Máxima Entropia de Shannon é incorporado ao modelo de otimização. O método fatorial de ajuste da função desirability proposto nesta tese aperfeiçoa o desempenho do algoritmo desirability conduzindo a uma eficiente alocação dos ativos no portfólio. Esta abordagem também permite a inclusão da aversão ao risco na rotina de otimização e engloba as interações (efeitos não lineares) dos efeitos entre diversos ativos enquanto reduz o esforço computacional requerido para resolver o problema de otimização não linear restrito. Para avaliar a viabilidade proposta, o método foi testado com dados reais de séries semanais do mercado mundial de preços spot de petróleo bruto. Os resultados numéricos demonstram a adequação da proposta
This thesis presents a new Design of Experiments (DOE)–based approach to treat multi– objective portfolio optimization combining Mixture Design of Experiments (MDE) and Desirability functions to find an optimal portfolio modeled by ARMA–GARCH algorithm. In this kind of experimental strategy, the design factors are treated as proportions in a mixture system considered quite adequate for treating portfolios in general. Instead of using traditional MVP mathematical programming, the concept of desirability function is here used to solve multiobjective nonlinear objective optimization problem for the predicted conditional values of return (mean), risk (variance) and entropy with their respective response surfaces estimated by MDE. To avoid the portfolio’s lack of diversity, the principle of Shannon’s maximum entropy is embodied in the optimization model. The computer–aided desirability tuning method proposed in this paper improves the desirability algorithm performance leading to an efficient assets allocation. This approach also allows the inclusion of risk aversion in the optimization routine and encompasses the interaction (nonlinear) effects among the several assets while reduces the computational effort required to solve the constrained nonlinear optimization problem. To assess the proposal feasibility, the method is tested with a real data set formed by weekly world crude oil spot prices. The numerical results verify the proposal’s adequacy
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Mendes, Ronã Rinston Amaury. "Uma contribuição para a otimização de portfólios de séries heteroscedásticas usando projeto de experimento de misturas: uma abordagem do desirability aplicada a modelos /." Guaratinguetá : [s.n.], 2012. http://hdl.handle.net/11449/103053.
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Orientador: Anderson Paulo de PaivaCoorientador: Pedro Paulo Balestrassi
Banca: Marcela Aparecida Guerreira Machado de Freitas
Banca: Antonio Fernando Branco Costa
Banca: Rafael Coradi Leme
Banca: João Roberto Ferreira
Resumo: Esta tese apresenta uma proposta inovadora com base no DOE (Design of Experiments) para tratar a otimização de portfólios multiobjetivos utilizando uma abordagem híbrida que combina arranjos de experimentos do tipo Misturas (Mixture Design of Experiments - MDE) e funções Desirability para se encontrar um portfólio ótimo modelado pelo algoritmo ARMA-GARCH. Neste tipo de estratégia experimental, as proporções investidas em cada ativo do portfólio são tratadas como fatores de um arranjo de misturas adequado para o tratamento de portfólios em geral. Ao invés de utilizar a tradicional programação matemática de portfólios de média variância (MVP), o conceito da função desirability é aqui utilizado para resolver problemas de otimização não linear multiobjetiva para a predição de valores condicionais de retorno (média), risco (variância) e entropia com suas respectivas superfícies de resposta estimadas pelo MDE. Para evitar a falta de diversificação dos portfólios, o princípio da Máxima Entropia de Shannon é incorporado ao modelo de otimização. O método fatorial de ajuste da função desirability proposto nesta tese aperfeiçoa o desempenho do algoritmo desirability conduzindo a uma eficiente alocação dos ativos no portfólio. Esta abordagem também permite a inclusão da aversão ao risco na rotina de otimização e engloba as interações (efeitos não lineares) dos efeitos entre diversos ativos enquanto reduz o esforço computacional requerido para resolver o problema de otimização não linear restrito. Para avaliar a viabilidade proposta, o método foi testado com dados reais de séries semanais do mercado mundial de preços spot de petróleo bruto. Os resultados numéricos demonstram a adequação da proposta
Abstract: This thesis presents a new Design of Experiments (DOE)-based approach to treat multi- objective portfolio optimization combining Mixture Design of Experiments (MDE) and Desirability functions to find an optimal portfolio modeled by ARMA-GARCH algorithm. In this kind of experimental strategy, the design factors are treated as proportions in a mixture system considered quite adequate for treating portfolios in general. Instead of using traditional MVP mathematical programming, the concept of desirability function is here used to solve multiobjective nonlinear objective optimization problem for the predicted conditional values of return (mean), risk (variance) and entropy with their respective response surfaces estimated by MDE. To avoid the portfolio's lack of diversity, the principle of Shannon's maximum entropy is embodied in the optimization model. The computer-aided desirability tuning method proposed in this paper improves the desirability algorithm performance leading to an efficient assets allocation. This approach also allows the inclusion of risk aversion in the optimization routine and encompasses the interaction (nonlinear) effects among the several assets while reduces the computational effort required to solve the constrained nonlinear optimization problem. To assess the proposal feasibility, the method is tested with a real data set formed by weekly world crude oil spot prices. The numerical results verify the proposal's adequacy
Doutor
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Pougaza, Doriano-Boris. "Utilisation de la notion de copule en tomographie." Phd thesis, Université Paris Sud - Paris XI, 2011. http://tel.archives-ouvertes.fr/tel-00684637.
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Cette thèse porte sur le lien entre la tomographie et la notion de copule. La tomographie à rayons X consiste à (re)construire la structure cachée d'un objet (une densité de matière, la distribution d'une quantité physique, ou une densité de loi conjointe) à partir de certaines données obtenues ou mesurées de l'objet (les projections, les radiographies, les densités marginales). Le lien entre les mesures et l'objet se modélise mathématiquement par la Transformée à Rayons X ou la Transformée de Radon. Par exemple, dans les problèmes d'imagerie en géométrie parallèle, lorsqu'on a seulement deux projections à deux angles de 0 et pi/2 (horizontale et verticale), le problème peut être identifié comme un autre problème très important en mathématique qui est la détermination d'une densité conjointe à partir de ses marginales. En se limitant à deux projections, les deux problèmes sont des problèmes mal posés au sens de Hadamard. Il faut alors ajouter de l'information a priori, ou bien des contraintes supplémentaires. L'apport principal de cette thèse est l'utilisation des critères de plusieurs entropies (Rényi, Tsallis, Burg, Shannon) permettant d'aboutir à une solution régularisée. Ce travail couvre alors différents domaines. Les aspects mathématiques de la tomographie via l'élément fondamental qui est la transformée de Radon. En probabilité sur la recherche d'une loi conjointe connaissant ses lois marginales d'où la notion de ''copule'' via le théorème de Sklar. Avec seulement deux projections, ce problème est extrêmement difficile. Mais en assimilant les deux projections (normalisées) aux densités marginales et l'image à reconstruire à une densité de probabilité, le lien se fait et les deux problèmes sont équivalents et peuvent se transposer dans le cadre statistique. Pour caractériser toutes les images possibles à reconstruire on a choisi alors l'outil de la théorie de probabilité, c'est-à-dire les copules. Et pour faire notre choix parmi les copules ou les images nous avons imposé le critère d'information a priori qui se base sur différentes entropies. L'entropie est une quantité scientifique importante car elle est utilisée dans divers domaines (en Thermodynamique, en théorie de l'information, etc). Ainsi, en utilisant par exemple l'entropie de Rényi nous avons découvert de nouvelles classes de copules. Cette thèse apporte de nouvelles contributions à l'imagerie, par l'interaction entre les domaines qui sont la tomographie et la théorie des probabilités et statistiques.
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Nilsson, Mattias. "Entropy and Speech." Doctoral thesis, Stockholm : Sound and Image Processing Laboratory, School of Electrical Engineering, Royal Institute of Technology, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3990.
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Charter, Mark Keith. "Maximum entropy pharmacokinetics." Thesis, University of Cambridge, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.316691.
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Casper, James Kyle. "Entropy and surfaceness." Thesis, Massachusetts Institute of Technology, 1997. http://hdl.handle.net/1721.1/65050.
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Thesis (M. Arch.)--Massachusetts Institute of Technology, Dept. of Architecture, 1997.Includes bibliographical references (leaves 103-113).
The layer of the Earth's atmosphere which contains clouds and weather systems is a thin thermoregulatory surface. It maintains an exact energy budget between the Earth and the Sun. Recent work in theoretical physics is aimed at these types of dynamic systems. Key to a system such as the atmosphere is the constant yet fluctuating input of energy which forces the system into a state distant from its thermodynamic equilibrium. Certain physical systems, when past this point begin to organize themselves into dynamic structures which work to dissipate the incoming flux. As a result, they are decreasing system entropy, a characteristic previously only assigned to life or living matter. The line between living and inert systems has expanded to a field wide enough to work within. Concurrently, developments in the engineering of so-called intelligent materials seek to invest material or inert matter with characteristics or behaviors of life. Scientists intend the materials to sense, process and respond to environmental forces in a dynamic bio-mimetic manner through engineering at the molecular scale. This paper will examine these two fields, beginning a discourse and correlation between them, in the context of a built application. Specifically, Nitinol, a shape memory alloy, will be considered as 'dissipative media' in a dynamic building system. The proposed built system will then become a metallic alloy atmosphere on the thin surface boundary of a structure. Working also to dissipate an influx of solar energy, the building's surface will develop 'weather systems', dynamic and cyclonic, moving across and around the metallic skin. Perturbations from the imprints of the clouds and shadows will seed the system throwing it into flux as it seeks to feather out the disturbance s and settle back into pulsing rhythms and patterns. Space, scale, and time and orientation will b e re-introduced.
James Kyle Casper.
M.Arch.
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Li, Xing-Si. "Entropy and optimization." Thesis, University of Liverpool, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.235500.
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Taghavianfar, Mohsen. "An Investigation on Network Entropy-Gossiping Protocol and Anti-entropy Evaluation." Thesis, Blekinge Tekniska Högskola, Sektionen för ingenjörsvetenskap, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:bth-2684.
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This thesis is concerned with studying the behavior of a gossiping protocol in the specific sense meant by Ericsson; in the following pages I’ll introduce a Markov process which models the spread of information in such systems. The results will be verified by means of a discreet-event simulation.Gossiping Protocols, are inherently random in behavior.Nonetheless, they are not structure-less. Their asymptotic behavior when implemented in large scales is the matter of focus in this thesis.
Tel: +46709700505 Address: Pinnharvsgatan 3 E lgh 1202 43147 Mölndal Sweden
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Lokaj, Jiří. "Hodnocení vztahu mezi kardiovaskulárními signály pomocí nelineárních metod." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2019. http://www.nusl.cz/ntk/nusl-378149.
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The short-term regulation of blood pressure is influenced by many influences, some being represented by cardiovascular signals and their changes. Because of the complexity of this system, the linear methods for its analysis are not sufficient. Non-linear methods for time series analysis have been devised quite a lot. In the course of this work, the analysis of the relations of several signals was evaluated as the most suitable conditional entropy and the resulting indexes of affinity and directionality. This method was applied to a set of heart-rate signals and systolic and diastolic pressure signals measured on eight adults and nine children. Relationships were analyzed but unfortunately after the statistical test was held the expected information links between the individual signals were not established. The indices were very small - in the hundredths of bits. Finally, optimization of the algorithm of the whole method has been performed and the newly modified function already shows significantly better results, for example strong information binding from the time-series of systolic pressure to a series of diastolic pressures.
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Krempa, Peter. "Analysis of Entropy Levels in the Entropy Pool of Random Number Generator." Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2013. http://www.nusl.cz/ntk/nusl-236179.
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V informatice je pojem entropie obvykle znám jako nahodný proud dat. Tato práce krátce shrnuje metody generovaní nahodných dat a popisuje generátor náhodnych čísel, jež je obsažen v jádře operačního systému Linux. Dále se práce zabývá určením bitové rychlosti generování nahodných dat tímto generátorem ve virtualizovaném prosředí, které poskytují různé hypervizory. Práce popíše problémy nízkého výkonu generátory nahodných dat ve virtualním prostředí a navrhne postup pro jejich řešení. Poté je nastíňena implementace navržených postupů, které je podrobena testům a její vysledky jsou porovnány s původním systémem. Systém pro distribuci entropie může dále vylepšit množství entropie v sytémovém jádře o několik řádu, pokud je připojen k vykonému generátoru nahodných dat.
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Uthushagen, Kristian Siegel. "Entropy in Dynamical Networks." Thesis, Norges Teknisk-Naturvitenskaplige Universitet, 2013. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-20918.
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This thesis presents a new type of dynamical entropy, defined by the movement of particles beetween the nodes in a network. The entropy is intended to have similar properties as the well-known thermodynamic entropy. Simulations are run on different versions of known networks, and exhibits expected behaviour. A few applications of the variable have also been suggested, in which topographical properties, centrality and node distance is decided in relative terms for spesific networks. In addition, a historical recap is the science of thermodynamics and networks is given, and also an explanation to how these fields have come together over the recent years, culminating in this effort to further connect them.
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Patterson, Brett Alexander. "Maximum entropy data analysis." Thesis, University of Cambridge, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.240969.
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Ibinson, Ben. "Quantum information and entropy." Thesis, University of Bristol, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.492602.
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Johnson, O. "Entropy and limit theorems." Thesis, University of Cambridge, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.605633.
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This thesis uses techniques based on Shannon entropy to prove probabilistic limit theorems. Chapter 1 defines entropy and Fisher information, and reviews previous work. We reformulate the Central Limit Theorem to state that the entropy of sums of independent identically distribution real-value random variables converges to its unique maximum, the normal distribution. This is called convergence in relative entropy, and is proved by Barron. Chapter 2 extends Barron's results to non-identically distributed random variables, extending the Lindeberg-Feller Theorem, under similar conditions. Next, in Chapter 3, we provide a proof for random vectors. In Chapter 4, we discuss convergence to other non-Gaussian stable distributions. Whilst not giving a complete solution to this problem, we provide some suggestions as to how the entropy theoretic method may apply in this case. The next two chapters concern random variables with values on compact groups. Although the situation is different, in that the limit distribution is uniform, again this is a maximum entropy distribution, so some of the same ideas will apply. In Chapter 7 we discuss conditional limit theorems, which relate to the problem in Statistical Physics of 'equivalence of ensembles'. We consider random variables equidistributed on the surface of certain types of manifolds, and show their projections are close to Gibbs densities. Once again, the proof involves convergence in relative entropy, establishing continuity of the projection map with respect to the Kullback-Leibler topology. The bound is sharp and provides a necessary and sufficient condition for convergence in relative entropy. If we consider the manifold as a surface of equal energy for a particular Hamiltonian, this implies that the microcanonical and canonical ensembles are close to one another.
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Xie, Yong. "Maximum entropy in crystallography." Thesis, De Montfort University, 2003. http://hdl.handle.net/2086/4220.
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Purahoo, K. "Maximum entropy data analysis." Thesis, Cranfield University, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.260038.
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Pathak, Akhilesh. "Entropy Optimal Orthogonal Matrices." Wright State University / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=wright1369696712.
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Gamundi, Michel. ""Two faces of entropy"." The Ohio State University, 1985. http://rave.ohiolink.edu/etdc/view?acc_num=osu1300130144.
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Cioe, Anthony. "Objects: Entropy and Temporality." VCU Scholars Compass, 2008. http://scholarscompass.vcu.edu/etd/1602.
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The transparent qualities of glass lend to the creation of elements that suggest presence and absence. I often use glass as a surrogate for lost time or space in an object, comparable to the human prosthetic and the notion of a phantom limb. Recent objects of exploration have included broken bottles, fallen tree limbs, and a human skull. The practical knowledge I gained while working in a conservation lab has directly influenced the methodology for treating these objects of disrepair. My primary impetus is a desire to construct what has been lost during an objects existence and reveal sublime qualities. Looking for the spaces in-between things, I create sculpture and installations that transcend static objects beyond their corporeal existence, engage in the process of entropy, and negate it.
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Stellato, Marco. "Horizon entropy from scratch." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2014. http://amslaurea.unibo.it/6693/.
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Scopo di questo lavoro di tesi è lo studio di alcune proprietà delle teorie generali della gravità in relazione alla meccanica e la termodinamica dei buchi neri. In particolare, la trattazione che seguirà ha lo scopo di fornire un percorso autoconsistente che conduca alla nozione di entropia di un orizzonte descritta in termini delle carica di Noether associata all'invarianza del funzionale d'azione, che descrive la teoria gravitazionale in considerazione, per trasformazioni di coordinate generali. Si presterà particolare attenzione ad alcune proprietà geometriche della Lagrangiana, proprietà che sono indipendenti dalla particolare forma della teoria che si sta prendendo in considerazione; trattasi cioè non di proprietà dinamiche, legate cioè alla forma delle equazioni del moto del campo gravitazionale, ma piuttosto caratteristiche proprie di qualunque varietà rappresentante uno spaziotempo curvo. Queste caratteristiche fanno sì che ogni teoria generale della gravità possieda alcune grandezze definite localmente sullo spaziotempo, in particolare una corrente di Noether e la carica ad essa associata. La forma esplicita della corrente e della carica dipende invece dalla Lagrangiana che si sceglie di adottare per descrivere il campo gravitazionale. Il lavoro di tesi sarà orientato prima a descrivere come questa corrente di Noether emerge in qualunque teoria della gravità invariante per trasformazioni generali e come essa viene esplicitata nel caso di Lagrangiane particolari, per poi identificare la carica ad essa associata come una grandezza connessa all' entropia di un orizzonte in qualunque teoria generale della gravità.
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Sampaio, Claudio Luis Marques. "Busca de um tamanho otimo de gene e proteina para maximização da qualidade da filogenia resultante." [s.n.], 2010. http://repositorio.unicamp.br/jspui/handle/REPOSIP/317448.
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Orientador: Gonçalo Amarante Guimarães PereiraDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Biologia
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Resumo: Um problema recorrente em Filogenética é saber de antemão que melhores tamanhos de genes ou proteínas se deve ter para a construção de dendrogramas mais precisos. Neste trabalho, examinamos quais os efeitos de variados tamanhos de um alinhamento conhecido na qualidade da inferência de filogenia, em particular a filogenia dos fungos, utilizando 198 táxons fungais e 16 de grupo externo. Adicionalmente, calculamos a entropia de Shannon de cada ponto do alinhamento e fizemos iterações semelhantes por seus limiares. Para isto construímos um programa open-source baseado no toolkit bioperl que calcula estes dados. Concluímos que tanto para as iterações por tamanho quanto os para entropia, os limiares ideais são aquém do tamanho total do gene, podendo justificar uso de drafts de seqüenciamentos em inferências filogenéticas usando um pequeno número de regras
Abstract: A recurring issue in phylogenetics is knowing beforehand which best sizes for genes or proteins one should have for building more accurate cladograms. Herein we examine the effects or varying sizes of a known aligment on the quality of its inferred phylogeny, specifically considering the fungi phylogeny by using 198 fungal taxa plus 16 outgroup taxa. Additionally, we calculate the Shannon entropy of each point of the alignment and iterate similarly by its thresholds. To that end, we developed an open-source software based on the bioperl toolkit to calculate this data. Finally, we concluded that either for the size iterations or for the entropy iterations, the ideal thresholds are below the gene full size, justifying the use of sequencing drafts in phylogenetic inferrences using a handful of rules
Mestrado
Bioinformatica
Mestre em Genética e Biologia Molecular
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JAIN, PARUL. "Aspects of the relation between the black hole entropy and the entanglement entropy." Doctoral thesis, Università degli Studi di Cagliari, 2019. http://hdl.handle.net/11584/259889.
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The relationship between Bekenstein-Hawking and entanglement entropy is one
of the most intriguing problems of black hole and theoretical physics. Although both entropies have the same geometric characterization (they scale as an area), they have a different origin. The Bekenstein-Hawking entropy has it’s roots in the thermal correlations whereas the entanglement entropy describes the quantum correlations. In this thesis we address this problem from a holographic
perspective, making large use of the AdS/CFT correspondence.
We first look at the BTZ black hole in which case the black hole horizon and
the conical singularity are related to each other. Using the modular transformations of the dual 2D CFT, we first obtain an expression of the holographicentanglement entropy for the Euclidean BTZ black hole, AdS3 vacua and conical singularity and then analyse the behaviour of the leading terms in the expansions of the holographic entanglement entropy for the BTZ black hole and the
conical singularity. From these calculations, we have extracted the “signatures” through which entanglement entropy differentiates between the horizon and the conical singularity. When we deal with CFT at a finite temperature then it is well known that, entanglement entropy fails as a measure and hence it is replaced by entanglement negativity which is able to separate the thermal/classical
correlations from the quantum correlations thereby capturing “distillable” entanglement. We address the problem of finding a suitable holographic prescription
to calculate the entanglement negativity for two adjacent intervals when the CFT is at a finite temperature and in turn dual to a black hole in the bulk. We first propose a conjecture for the holographic entanglement negativity for two adjacent intervals in the
AdS3/CFT2 setup and perform calculations in the
various cases to support this conjecture. We further push forward the validity of this conjecture by calculating the holographic entanglement negativity for two
adjacent subsystems when we have RN-AdS black holes in the bulk which in
turn are dual to CFT with a conserved charge.
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Ribeiro, Patrick. "Analyse entropique et multi-échelle pour la fatigue et la rupture thermomécanique." Thesis, Paris 10, 2017. http://www.theses.fr/2017PA100108/document.
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Ce travail de thèse apporte une contribution à l’utilisation de grandeurs thermodynamiques ainsi que géométriques en mécanique. La première partie de ce manuscrit est consacrée à l’étude de la fatigue oligocyclique, et de l’entropie de rupture en fatigue. Des entropies de rupture en fatigue sont estimées expérimentalement par diverses relations et sont comparées aux modèles empiriques utilisés dans la littérature. Il apparait que ces diverses entropies de rupture sont très proches ce qui permet de conclure qu'il existe une entropie de rupture constante liée uniquement au matériau. Pour les modèles empiriques, une extension du modèle de Ramberg-Osgood cyclique prenant en compte la variation temporelle de la contrainte est proposée et une étude sur l'imprécision du modèle de Park et Nelson est réalisée. Puis, une étude des différentes phases durant le test de fatigue est effectuée à travers l’étude de l’endommagement lié à l’entropie accumulée par le matériau. Une extension par l’utilisation du concept d’exergie permet la mise en évidence d’une nouvelle quantité, une exergie associée au travail de déformation plastique faisant intervenir une notion de qualité de la déformation plastique. Dans une deuxième partie, la diffusion de l’entropie d’échelle est étudiée et permet de créer divers comportements dépendants d’échelle. Elle permet d’étudier la log-périodicité d’un fractal déterministe fini (ou préfractal) ou de vérifier la construction de géométries déterministes finies dépendantes d’échelle. Une application de ces modèles dépendants d’échelle est effectuée dans le cadre de la détermination de propriétés mécaniques, pour l’analyse de faciès de rupture et pour la fragmentation. Finalement un lien possible entre comportement mécanique, géométrie et théorie constructale est présentéThis Phd thesis is a contribution to the use of thermodynamics and geometry in mechanics. The first part of this manuscript is devoted to the study of low cycle fatigue and the notion of fracture fatigue entropy. Fracture fatigue entropies are experimentally estimated by various equations and compared to empirical models used in the litterature. It appears that these diverse fracture fatigue entropies are very close and allows to conclude that a constant fracture fatigue entropy exists only depending on the material. For the empirical models, an extension of the Ramberg-Osgood model is proposed taking into account the temporal variation of the loading, and, a study on the inaccuracy of the Park and Nelson model is realized. Then, a study on the different phases occurring in a fatigue test is done through the study of a damage parameter based on the entropy accumulated by the material. An extension using the concept of exergy allows the highlight of a new quantity, an exergy associated with plastic strain involving a quality factor. In a second part, the diffusion of scale-entropy is studied and permits to create various scale-dependent behaviors. It allows the study of log-periodicity of a finite deterministic fractal (or prefractal), or the verification of finite deterministic scale-dependent geometries. An application of these scale-dependent models is performed within the framework of the determination of mechanical properties, for the analysis of fractured surfaces and for fragmentation. Finally, a possible link between mechanical behavior, geometry and constructal theory is presented
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Sagarra, Pascual Oleguer Josep. "Non-binary maximum entropy network ensembles and their application to the study of urban mobility." Doctoral thesis, Universitat de Barcelona, 2016. http://hdl.handle.net/10803/400560.
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Complex networks grow subject to structural constraints which affect their measurable properties. Assessing the effect that such constraints impose on their observables is thus a crucial aspect to be taken into account in their analysis, if one wants to quantify the effect a given topological property has on other observed network quantities observed in empirical datasets.
Null models are needed for this end. A well understood analytical approach to face the generation and development of flexible models for binary networks is based on considering ensembles of networks obtained using an entropy maximization principle. In this work, we explore the generalization of maximum entropy ensembles to networks where multiple or non-dihcotomic connections among nodes are allowed. We develop a statistical mechanics framework where it is possible to get information about the most relevant observables given a large spectrum of linear and non-linear constraints including those depending both on the weight per link and their binary projection. We furthermore identify three different relevant cases that lead to distinctively different edge statistics, depending on the distinguishable nature of the events allocated to each link. For each case, we perform an extensive study considering microcanonical or hard constrained ensembles as well as grand canonical or soft constrained ones. We provide tools for the generation an analysis of network instances belonging to each model which are implemented and available in the form of open-source software packages, and we provide also analytical tools to obtain null model expectations to later compare to real data.
Developing the theory developed, we apply the obtained insights to the analysis of urban mobility considering four large datasets of taxi displacements in the cities of New York, Singapore, San Francisco and Vienna. We show that, once they are appropriately transformed, mobility patterns are highly stable over long time scales and display common features across the studied datasets which are very conveniently represented using one of the cases earlier studied maximum entropy ensembles. We furthermore perform a critical review on existing mobility demand forecasting models and discuss their strengths and weaknesses when adapted to the urban environment, while showing how entropy maximizing models display the best descriptive power of the datasets using a number of network-based, information and matrix similarity metrics to assess the accuracy of the predicted vehicle flows.
Based on our observations, we develop two practical applications based on our theoretical work. On the hand, we envisage a supersampling methodology to reliably extrapolate mobility records from a reduced sample which opens the possibility to scale up data from limited records when information on the full system is required. On the other hand, we adapt previous work on graph filtering to our proposed models that allows to extract random contributions from the observed empirical data. This allows to obtain simplified network backbones which contain the most relevant features of mobility datasets not explained by the considered constraints imposed in the maximum entropic models considered. Such a filter is useful for easing the analysis, computational handling and visualization of dense datasets, as well as assessing the degree of proximity between a model and empirical data
using suitable hypothesis testing arguments.Les xarxes complexes tenen una estructura complicada, on sovint es fa difícil establir les relacions de causalitat entre les seves propietats macroscòpiques (mesurables). Per tal de fer-ho es necessiten models nuls amb propietats flexibles que es puguin fixar. Per a xarxes amb connexions binàries (que tenen valor dicotòmic u o zero), s'han proposat col·lectivitats de xarxes que compleixen un principi de màxima entropia per a resoldre el problema de generació d'aquest tipus de models. En aquest treball explorem la seva generalització per a xarxes no-binàries, on les connexions entre elements estan graduades. Desenvolupem un tractament matemàtic que ens permet obtenir prediccions sobre els observables més rellevants d'una xarxa que tingui certes propietats prefixades, a triar en un rang ampli de funcions lineals i no-lineals pertanyent a col·lectivitats micro-canòniques (propietats fixades de manera estricta) i gran canòniques (propietats fixades sols en promig sobre la col·lectivitat). Detectem tres possibles varietats que duen a estadístiques d'ocupació d'enllaços diferents, depenent de la distingibilitat dels elements a partir del qual s'ha generat la xarxa. Per cada cas, desenvolupem eines per a la generació computacional i l'anàlisi de mostres de xarxes pertanyents a cada col·lectivitat. Tot seguit apliquem la teoria desenvolupada a l'anàlisi de mobilitat humana emprant sets de dades de desplaçaments de taxis a Nova York, Singapur, San Francisco i Viena. Mostrem l'estabilitat espaciotemporal de les dades estudiades i l'aparició de propietats comunes. Tot seguit realitzem un anàlisi crític de models de predicció de mobilitat existents i la seva possible adaptació als entorns urbans, mostrant com els models de màxima entropia tenen el major poder predictiu per descriure les dades. Finalment presentem dues aplicacions de la teoria desenvolupada que exploten les propietats comunes detectades a les dades estudiades. D'una banda, derivem un model que permet extrapolar dades de mobilitat sobre sets de dades reduïts. De l'altra, proposem un mètode de filtratge per extreure les contribucions de les dades reals dels trajectes esperats d'acord a qualssevol dels nostres models de màxima entropia. Aquest procediment permet obtenir versions simplificades de les xarxes originals que continguin les seves propietats més rellevants.
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Kobayashi, Jorge Mamoru. "Entropy: algoritmo de substituição de linhas de cache inspirado na entropia da informação." Universidade de São Paulo, 2010. http://www.teses.usp.br/teses/disponiveis/3/3141/tde-29112016-102603/.
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Este trabalho apresenta um estudo sobre o problema de substituição de linhas de cache em microprocessadores. Inspirado no conceito de Entropia da Informação proposto em 1948 por Claude E. Shannon, este trabalho propõe uma nova heurística de substituição de linhas de cache. Seu objetivo é capturar e explorar melhor a localidade de referência dos programas e diminuir a taxa de miss rate durante a execução dos programas. O algoritmo proposto, Entropy, utiliza a heurística de entropia da informação para estimar as chances de uma linha ou bloco de cache ser referenciado após ter sido carregado na cache. Uma nova função de decaimento de entropia foi introduzida no algoritmo, otimizando seu funcionamento. Dentre os resultados obtidos, o Entropy conseguiu reduzir em até 50,41% o miss rate em relação ao algoritmo LRU. O trabalho propõe, ainda, uma implementação em hardware com complexidade e custo computacional comparáveis aos do algoritmo LRU. Para uma memória cache de segundo nível com 2-Mbytes e 8-way associative, a área adicional requerida é da ordem de 0,61% de bits adicionais. O algoritmo proposto foi simulado no SimpleScalar e comparado com o algoritmo LRU utilizando-se os benchmarks SPEC CPU2000.This work presents a study about cache line replacement problem for microprocessors. Inspired in the Information Entropy concept stated by Claude E. Shannon in 1948, this work proposes a novel heuristic to replace cache lines in microprocessors. The major goal is to capture the referential locality of programs and to reduce the miss rate for cache access during programs execution. The proposed algorithm, Entropy, employs that new entropy heuristic to estimate the chances of a cache line to be referenced after it has been loaded into cache. A novel decay function has been introduced to optimize its operation. Results show that Entropy could reduce miss rate up to 50.41% in comparison to LRU. This work also proposes a hardware implementation which keeps computation and complexity costs comparable to the most employed algorithm, LRU. To a 2-Mbytes and 8-way associative cache memory, the required storage area is 0.61% of the cache size. The Entropy algorithm was simulated using SimpleScalar ISA simulator and compared to LRU using SPEC CPU2000 benchmark programs.
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Percca, Edwin Marcos Maraví. "Resolução do problema de Riemann através de um método variacional." Universidade Federal de Juiz de Fora (UFJF), 2017. https://repositorio.ufjf.br/jspui/handle/ufjf/4037.
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As leis de balanço expressam de uma maneira mais geral as leis de conservação e, portanto, é natural que coincidam em algumas definições ou resultados que vamos mostrar aqui. Um sistema de leis de conservação estritamente hiperbólico numa dimensão espacial sob certas condições é um sistema simetrizável, portanto, possui uma entropia convexa. Isto induz a definiroparentropia-fluxodeentropiaeaproduçãodeentropia,ingredientesmínimospara usar o critério de admissibilidade da taxa de entropia e conferir se a solução do problema de Riemann respectivo é ótimo. A taxa de entropia definida aqui em termos da entropia é um funcional que pode ser minimizada nos leques de ondas com estados constantes do problema de Riemann, usando as equações de Euler-Lagrange. Primeiramente, mostramos que as soluções do problema de Riemann são funções de variação limitada, resultando num método variacional para resolver o problema. Neste trabalho será mostrado que a solução obtida pelo método variacional, coincide com a solução obtida pelo método das curvas caraterísticas.
The balance laws express in a more general way the conservation laws and therefore it is naturalthattheycoincideinsomedefinitionsorresultsthatwewillshowhere. Thestrictly hyperbolic systems of conservation laws in a spatial dimension under certain conditions is a symmetrizable system, therefore it has a convex entropy. This induces to define the entropy-entropy flux pair and the entropy production, minimum ingredients to use the Entropy rate admissibility criterion and check whether the solution of the respective Riemann problem is optimal. The entropy rate defined here in terms of entropy is a functional that can be minimized in the wave fans with constant states of the Riemann problem using the Euler-Lagrange equations, we show that the solutions of the Riemann problem are functions of bounded variation, resulting in a variational method to solve the respective problem. In this work it will be shown that the solution obtained by the variational method, coincides with the solution obtained by the method of characteristics.
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De, Fazio Cecilia. "Entanglement Entropy In Excited States." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amslaurea.unibo.it/15833/.
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Negli ultimi anni l’entropia di entaglement è stata ampiamente studiata nel campo dell‘integrabilità. Con l‘introduzione del modello a replica è stato possibile portare alla luce le proprietà universali dell’ entropia di entanglement di un sistema bipartito nello stato di vuoto.
In questa tesi si è investigato il problema dell’entropia di entanglement di un sistema bipartito in uno stato eccitato di singola particella. In particolare, si è considerata una teoria bosonica libera in un volume finito, in modo da sfruttare al meglio le tecniche dell‘integrabilità. Nel corso di questa analisi, è stato possibile rielaborare il modello a replica in un volume finito grazie ad un raddoppiamento della teoria bosonica che ha indotto una simmetria U(1) su ogni copia del modello. Tale tecnica, nota in letter- atura come doubling trick ha permesso di ricondurre il calcolo dell’entropia di Renyi a un’opportuna espansione in form factors dei campi U(1) implementanti tale simmetria e valutarne il contributo dominante nel limite in cui il volume è grande.
I risultati ottenuti per la Second Rènyi entropy mostrano che in tale limite, l’eccesso di entanglement dovuto allo stato eccitato rispetto a quello di vuoto è indipendente dall’energia dello stato stesso e può essere interpretato come quantità che misura l’incertezza sulla localizzazione dell’eccitazione nelle due parti di cui è composto il sistema.
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Paavola, M. (Marko). "An efficient entropy estimation approach." Doctoral thesis, Oulun yliopisto, 2011. http://urn.fi/urn:isbn:9789514295935.
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Abstract Advances in miniaturisation have led to the development of new wireless measurement technologies such as wireless sensor networks (WSNs). A WSN consists of low cost nodes, which are battery-operated devices, capable of sensing the environment, transmitting and receiving, and computing. While a WSN has several advantages, including cost-effectiveness and easy installation, the nodes suffer from small memory, low computing power, small bandwidth and limited energy supply. In order to cope with restrictions on resources, data processing methods should be as efficient as possible. As a result, high quality approximates are preferred instead of accurate answers. The aim of this thesis was to propose an efficient entropy approximation method for resource-constrained environments. Specifically, the algorithm should use a small, constant amount of memory, and have certain accuracy and low computational demand. The performance of the proposed algorithm was evaluated experimentally with three case studies. The first study focused on the online monitoring of WSN communications performance in an industrial environment. The monitoring approach was based on the observation that entropy could be applied to assess the impact of interferences on time-delay variation of periodic tasks. The main purpose of the additional two cases, depth of anaesthesia (DOA) –monitoring and benchmarking with simulated data sets was to provide additional evidence on the general applicability of the proposed method. Moreover, in case of DOA-monitoring, an efficient entropy approximation could assist in the development of handheld devices or processing large amount of online data from different channels simultaneously. The initial results from the communication and DOA monitoring applications as well as from simulations were encouraging. Therefore, based on the case studies, the proposed method was able to meet the stated requirements. Since entropy is a widely used quantity, the method is also expected to have a variety of applications in measurement systems with similar requirementsTiivistelmä Mekaanisten- ja puolijohdekomponenttien pienentyminen on mahdollistanut uusien mittaustekniikoiden, kuten langattomien anturiverkkojen kehittämisen. Anturiverkot koostuvat halvoista, paristokäyttöisistä solmuista, jotka pystyvät mittaamaan ympäristöään sekä käsittelemään, lähettämään ja vastaanottamaan tietoja. Anturiverkkojen etuja ovat kustannustehokkuus ja helppo käyttöönotto, rajoitteina puolestaan vähäinen muisti- ja tiedonsiirtokapasiteetti, alhainen laskentateho ja rajoitettu energiavarasto. Näiden rajoitteiden vuoksi solmuissa käytettävien laskentamenetelmien tulee olla mahdollisimman tehokkaita. Tämän työn tavoitteena oli esittää tehokas entropian laskentamenetelmä resursseiltaan rajoitettuihin ympäristöihin. Algoritmin vaadittiin olevan riittävän tarkka, muistinkulutukseltaan pieni ja vakiosuuruinen sekä laskennallisesti tehokas. Työssä kehitetyn menetelmän suorituskykyä tutkittiin sovellusesimerkkien avulla. Ensimmäisessä tapauksessa perehdyttiin anturiverkon viestiyhteyksien reaaliaikaiseen valvontaan. Lähestymistavan taustalla oli aiempi tutkimus, jonka perusteella entropian avulla voidaan havainnoida häiriöiden vaikutusta viestien viiveiden vaihteluun. Muiden sovellusesimerkkien, anestesian syvyysindikaattorin ja simulaatiokokeiden, päätavoite oli tutkia menetelmän yleistettävyyttä. Erityisesti anestesian syvyyden seurannassa menetelmän arvioitiin voivan olla lisäksi hyödyksi langattomien, käsikäyttöisten syvyysmittareiden kehittämisessä ja suurten mittausmäärien reaaliaikaisessa käsittelyssä. Alustavat tulokset langattoman verkon yhteyksien ja anestesian syvyyden valvonnasta sekä simuloinneista olivat lupaavia. Sovellusesimerkkien perusteella esitetty algoritmi kykeni vastaamaan asetettuihin vaatimuksiin. Koska entropia on laajalti käytetty suure, menetelmä saattaa soveltua useisiin mittausympäristöihin, joissa on samankaltaisia vaatimuksia
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Nickerson, William Alexander. "Developments in minimum entropy deconvolution." Thesis, University of British Columbia, 1986. http://hdl.handle.net/2429/26015.
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Minimum entropy deconvolution (MED) is investigated in light of recent work, and reports of poor performance in the deconvolution of real reflection seismograms. The problems with MED fall into two catagories. The first contains problems related to operator design such as avoiding local extrema in the simplicity criterion, problems with bandwidth, and the selection of filter length and preprocessing parameters. The second is the determination of model validity for the data at hand.
MED is based on the iterative maximization of a data simplicity criterion which exhibits multiple extrema. A geometrical interpretation of this algorithm leads to an intuitive alternative algorithm, the projection method, and to the conclusion that iteration starting filter governs which extremum is reached and hence output wavelet delay. Choice of starting filter is therefore tantamount to a wavelet phase assumption and there is no basis for choosing the standard, centred impulse, starting filter if the global extremum is desired. An optimum lag MED algorithm is proposed to achieve the global maximum. Bandlimiting, data tapering and other aspects of MED operator design are discussed.
No criterion exists for assessing MED model validity. Studies with various synthetic reflectivity statistics reveal that "sparseness" and "simplicity" are poor descriptors of the minimum entropy assumption. Preliminary attempts to quantify MED applicability are made but fail and indicate that any successful measure must include both underlying reflectivity and wavelet characteristics.
Examples using synthetic data show the advantages of the bandlimited optimum lag MED algorithm over a conventional starting filter method.Science, Faculty of
Earth, Ocean and Atmospheric Sciences, Department of
Graduate
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Joret, Gwenaël. "Entropy and stability in graphs." Doctoral thesis, Universite Libre de Bruxelles, 2007. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210605.
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Un stable (ou ensemble indépendant) est un ensemble de sommets qui sont deux à deux non adjacents. De nombreux résultats classiques en optimisation combinatoire portent sur le nombre de stabilité (défini comme la plus grande taille d'un stable), et les stables se classent certainement parmi les structures les plus simples et fondamentales en théorie des graphes.La thèse est divisée en deux parties, toutes deux liées à la notion de stables dans un graphe. Dans la première partie, nous étudions un problème de coloration de graphes, c'est à dire de partition en stables, où le but est de minimiser l'entropie de la partition. C'est une variante du problème classique de minimiser le nombre de couleurs utilisées. Nous considérons aussi une généralisation du problème aux couvertures d'ensembles. Ces deux problèmes sont appelés respectivement minimum entropy coloring et minimum entropy set cover, et sont motivés par diverses applications en théorie de l'information et en bioinformatique. Nous obtenons entre autres une caractérisation précise de la complexité de minimum entropy set cover :le problème peut être approximé à une constante lg e (environ 1.44) près, et il est NP-difficile de faire strictement mieux. Des résultats analogues sont prouvés concernant la complexité de minimum entropy coloring.
Dans la deuxième partie de la thèse, nous considérons les graphes dont le nombre de stabilité augmente dès qu'une arête est enlevée. Ces graphes sont dit être "alpha-critiques", et jouent un rôle important dans de nombreux domaines, comme la théorie extrémale des graphes ou la combinatoire polyédrique. Nous revisitons d'une part la théorie des graphes alpha-critiques, donnant à cette occasion de nouvelles démonstrations plus simples pour certains théorèmes centraux. D'autre part, nous étudions certaines facettes du polytope des ordres totaux qui peuvent être vues comme une généralisation de la notion de graphe alpha-critique. Nous étendons de nombreux résultats de la théorie des graphes alpha-critiques à cette famille de facettes.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished
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Karamanos, Konstantinos. "Entropy analysis of nonequilibrium systems." Doctoral thesis, Universite Libre de Bruxelles, 2002. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/211390.
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Moher, Michael L. "Cross-entropy and iterative detection." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq22171.pdf.
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Foltin, Christian. "Billiards with positive topological entropy /." Bonn : Univ, 2000. http://www.gbv.de/dms/goettingen/331681293.pdf.
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Mustafa, Denis. "Minimum entropy H#infinity# control." Thesis, University of Cambridge, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.306487.
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Sun, Yun. "Network coding and graph entropy." Thesis, Queen Mary, University of London, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.509608.
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Sung, Shih-Ta. "Black hole entropy and models." Thesis, Durham University, 1997. http://etheses.dur.ac.uk/4677/.
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No universally accepted statistical explanation of black hole entropy exists up to now, therefore, it is worth another try. Admittedly, black hole entropy does not have to have a statistical origin. If the "black hole entropy" is called "black hole index" instead, someone might be lured to give it an economic explanation. Nonetheless, the only way to justify one's claim about the statistical origin of black hole entropy is to compute it statistically. This is the motivation for the construction of black hole models. In chapter 1, I first review the four laws of classical black hole mechanics which form the basis for the introduction of black hole thermodynamics. After observing the formal analogy between the four laws of the black hole mechanics and that of the ordinary thermodynamics, I further explore the thermodynamic properties of black holes in chapter 2 by reviewing the phenomenon of Hawking radiation and introducing the idea of black hole entropy. Three statistical explanations of black hole entropy are introduced in chapter 3. I will start with’t Hooft's brick wall model. Then, á la Brown and York, I review the approach based on the gravitational degrees of freedom via path integral. In the final part of this chapter, I present my own version of a quantum statistical explanation of black hole entropy by regarding a black hole as a cavity with thermal states inside. The final chapter will be devoted to the construction of black hole models to materialise the idea that a black hole, in some sense, can be regarded as a cavity where thermalised quantum states reside with quantised spectrum. These quantum states and the corresponding spectrum will then justify the statistical explanation of black hole entropy presented in the final section of chapter 3.
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Anand, Gautam. "Simulation of high-entropy materials." Thesis, University of Sheffield, 2018. http://etheses.whiterose.ac.uk/20063/.
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Multicomponent materials containing a comparatively large number of different elemental components, yet exhibiting simple crystal structures have opened up a new era of materials design with the possibility of tuning properties of materials with greater degrees of freedom. This poses a formidable challenge in terms of design as the number of parameters involved in simulating such systems increase significantly with the increasing number of components. This work reports a sampling methodology based on hybrid genetic algorithm-molecular dynamics for sampling positional-disordered materials such as high-entropy systems. This investigation also demonstrates the influence of individual cationic species on the evolution of distortion in single-phase solid solution with the rock-salt structure, when oxides such as CoO, CuO, MgO, NiO and ZnO are mixed together. Additionally, the relationship between the number of atomic species and its effect on the lattice distortion has been presented. The influence of alloying elements on the evolution of lattice friction in substitutional alloys has been studied using Monte Carlo simulations with a continuum elasticity relation for dislocations. The spread in energy-range due to elastic properties and size-misfit of elements provides physical justification for friction stress being low in CoNi alloy, high in CoCrNi (medium entropy alloy), along with intermediate values in CoCrFeNi (High Entropy Alloy). A similar approach justifies strengthening due to dilute addition of Al into CoCrFeMnNi and CoCrFeNi. This approach is a computationally cheap method of screening a range of possible alloys with respect to their lattice friction stress. Spin-polarised density functional theory (DFT) calculations presented here were carried out to study the charge transfer among elements and evolution of distortion in substitutional alloys. To study the characteristics of the individual element, impurity-in- matrix type calculations were carried out. The charge transfer between impurity and matrix element is presented to determine issues with the electronegativity parameter of Miedema’s model for enthalpy calculations. The distortion in substitutional alloys, particularly due to Cr has been found to be related to interaction of electrons with complementary spins in their d-orbitals.
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Le, Floch-Yin François T. (François Thomas). "Entropy generation in fluid mixing." Thesis, Massachusetts Institute of Technology, 2006. http://hdl.handle.net/1721.1/36169.
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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2006.Includes bibliographical references (leaf 64).
This thesis describes the processes of viscous dissipation in two generic situations for mixing flows. The objective is to illustrate, with simple examples, details of the entropy generation processes that are captured in an overall manner by a control volume analysis. The two situations are parallel mixing flows in a duct and the evolution of a wake in a centrifugal compressor. Results are given for the evolution of the velocity profile and for the dissipation function and stagnation pressure fields.
by François T. Le Floch-Yin.
S.M.
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Monteiro, André Bosque. "Entropy statistics and aeronautical evolution." Instituto Tecnológico de Aeronáutica, 2006. http://www.bd.bibl.ita.br/tde_busca/arquivo.php?codArquivo=2169.
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Employing the probabilistic entropy methodology, one of the objectives of this work is to develop a robust and simple tool to be employed in the empirical analysis of airplane configuration and technology evolution. Two specific analyses were performed to validate the procedure. One is the evolution of civil aviation transportation in the jet age (1950-2006) and the other being the evolution of fighter aircraft during the period of 1914 to 2009. An extensive study was carried out in order to select the variables used to describe each aircraft. After the creation of the aircraft databank, the tool developed in the present work takes the variables as input do evaluate two important technological indexes: the convergence and the diffusion. Studies analyzing the combination of the diffusion and the convergence indexes, as well as the critical transition of the airplanes were conducted in this paper. The methodology herein developed can be highly helpful as a decision making tool to be used during the conceptual design phase of an airplane.
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Williams, Jeremy M. "Lyapunov Exponents, Entropy and Dimension." Thesis, University of North Texas, 2004. https://digital.library.unt.edu/ark:/67531/metadc4559/.
Full textAbstract:
We consider diffeomorphisms of a compact Riemann Surface. A development of Oseledec's Multiplicative Ergodic Theorem is given, along with a development of measure theoretic entropy and dimension. The main result, due to L.S. Young, is that for certain diffeomorphisms of a surface, there is a beautiful relationship between these three concepts; namely that the entropy equals dimension times expansion.
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Moher, Michael L. Carleton University Dissertation Engineering Systems and Computer. "Cross-entropy and iterative detection." Ottawa, 1997.
Find full text
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Kaewtem, Thanatkrit. "Entropy numbers in sequence spaces." Thesis, University of Bristol, 2017. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.738278.
Full text
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Meneghetti, Alessio. "Optimal Codes and Entropy Extractors." Doctoral thesis, Università degli studi di Trento, 2017. https://hdl.handle.net/11572/368164.
Full textAbstract:
In this work we deal with both Coding Theory and Entropy Extraction for Random Number Generators to be used for cryptographic purposes. We start from a thorough analysis of known bounds on code parameters and a study of the properties of Hadamard codes. We find of particular interest the Griesmer bound, which is a strong result known to be true only for linear codes. We try to extend it to all codes, and we can determine many parameters for which the Griesmer bound is true also for nonlinear codes. In case of systematic codes, a class of codes including linear codes, we can derive stronger results on the relationship between the Griesmer bound and optimal codes. We also construct a family of optimal binary systematic codes contradicting the Griesmer bound. Finally, we obtain new bounds on the size of optimal codes. Regarding the study of random number generation, we analyse linear extractors and their connection with linear codes. The main result on
this topic is a link between code parameters and the entropy rate obtained by a processed random number generator. More precisely, to any linear extractor we can associate the generator matrix of a linear code. Then, we link the total variation distance between the uniform distribution and the probability mass function of a random number generator with the weight distribution of the linear code associated to
the linear extractor. Finally, we present a collection of results derived while pursuing a way to classify optimal codes, such as a probabilistic algorithm to compute
the weight distribution of linear codes and a new bound on the size of codes.
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Meneghetti, Alessio. "Optimal Codes and Entropy Extractors." Doctoral thesis, University of Trento, 2017. http://eprints-phd.biblio.unitn.it/1893/1/AM_thesis.pdf.
Full textAbstract:
In this work we deal with both Coding Theory and Entropy Extraction for Random Number Generators to be used for cryptographic purposes. We start from a thorough analysis of known bounds on code parameters and a study of the properties of Hadamard codes. We find of particular interest the Griesmer bound, which is a strong result known to be true only for linear codes. We try to extend it to all codes, and we can determine many parameters for which the Griesmer bound is true also for nonlinear codes. In case of systematic codes, a class of codes including linear codes, we can derive stronger results on the relationship between the Griesmer bound and optimal codes. We also construct a family of optimal binary systematic codes contradicting the Griesmer bound. Finally, we obtain new bounds on the size of optimal codes. Regarding the study of random number generation, we analyse linear extractors and their connection with linear codes. The main result on
this topic is a link between code parameters and the entropy rate obtained by a processed random number generator. More precisely, to any linear extractor we can associate the generator matrix of a linear code. Then, we link the total variation distance between the uniform distribution and the probability mass function of a random number generator with the weight distribution of the linear code associated to
the linear extractor. Finally, we present a collection of results derived while pursuing a way to classify optimal codes, such as a probabilistic algorithm to compute
the weight distribution of linear codes and a new bound on the size of codes.
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Pasqualini, Andrea <1990>. "Approaching Systemic Risk with Entropy." Master's Degree Thesis, Università Ca' Foscari Venezia, 2014. http://hdl.handle.net/10579/5208.
Full textAbstract:
This Thesis focuses on the Marginal Expected Shortfall (MES) and its application in Finance as early-warning reference. I will specify a logit model that allows to link MES to the conditional probability of financial crisis.
The analysis includes a multinomial bayesian density estimation approach, and considers different crisis indicators as dependent variables.