Consider a dynamical system which is positively expansive and satisfies the condition of specification. We further study the topological entropy of the level sets for local Poincare recurrence, i.e. the recurrence spectrum. It turns out that the spectrum is quite irrational as any level set has the same (topological) entropy as the whole system. The erratic recurrence behavior of the orbits brings chaos. For the system concerned, we show that it contains a Xiong chaotic set C which is large in the sense that the intersection of any non-empty open set with C has the same topological entropy as the whole system. The ergodic average can be regarded as a certain recurrence average. We give multifractal analysis of the generalized spectrum for ergodic average, which incorporates the information of the set of divergence points. Note that the set of divergence points for Poincare recurrence or ergodic average has measure zero with respect to any invariant measure. (A Xiong chaotic set may has measure zero with respect to some invariant measures with full support.) The above results support the point of view that small set unobservable in measure may account for the anomalous chaotic behavior of the whole system. / The thesis is on the recurrence and chaotic behavior of a dynamical system. Let the local Poincare recurrence rate at a point be defined as the exponential rate of the first return time of the orbit into its neighborhoods defined by the Bowen metric. Given any reference invariant probability measure mu, we show that the rate equals to the local entropy of mu a.e. Hence, the integration of the rate is exactly the (measure theoretic) entropy of the measure mu. / Shu, Lin. / "January 2007." / Adviser: Ka-Sing Lau. / Source: Dissertation Abstracts International, Volume: 68-08, Section: B, page: 5286. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 83-91). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

The master thesis studies the impact of the entropy gradient on the vorticity of ve- locity field, particularly by applying the linear momentum balances. These balances are formulated for Thermo-viscous fluids (later fluids) and Thermo-viscous-elastic ma- terial (later solids) with the other balances (energy, mass, etc.). In order to derive these balances, the Classical continuum mechanics approach is used along with the respec- tive Variational principles. The thesis emphasizes the Variational principles applica- tion representing the modification of the Bateman principle [Bat29] and its comparison with the Classical approach, linked to the L. Crocco work [Cro37], particularly in the case of vorticity generation. It is pointed that by the definition of the dissipative en- tropy sdis a harmony of both approaches can be achieved and that, in the case of an appropriate limit, the direct effect of the entropy gradient on the vorticity of velocity field can be demonstrated. By applying this conclusion the relationship between the change of circulation among a closed curve and released heat on the given geometry is indicated.

Made available in DSpace on 2015-04-22T22:07:21Z (GMT). No. of bitstreams: 1 carlos velas.pdf: 1180958 bytes, checksum: 61ddfdc0eddd3a6683e3d7b9d8715e0b (MD5) Previous issue date: 2013-04-22 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In this dissertation we present a detailed and analytical study of the information entropy using two formalisms. These formalisms are: Shannon entropy and Tsallis entropy. Shannon entropy obeys the principle of additivity, however the Tsallis entropy is nonadditive. These entropies are applied to atomic models of Mochinsky and positronium, which are two-body systems. To determine the entropy, we utilize the wave functions and probability densities for both the atomic models. The Shannon entropy has a logarithmic dependence, while the Tsallis entropy has a dependency on the entropic factor q , known as the Tsallis entropic factor. In our work, entropies were calculated in the position space and also in the momentum space and also using the concept of the principle of Heisenberg inequality adapted for the information entropy. For the Shannon entropy, we have the Bialynici, Birula, and Mycielski uncertainty principle, and Tsallis entropy we use pseudo-uncertainty. Finally we demonstrate graphically the behavior of the entropies of both the formalisms. / Nesta dissertação apresentamos um estudo detalhado e analítico da entropia da informação usando dois formalismos. Estes formalismos são: entropia de Shannon e a entropia de Tsallis, a entropia de Shannon obedece o principio da aditividade, já a entropia de Tsallis é conhecida como entropia não-aditiva. Essas entropias serão aplicadas nos modelos atômicos de Mochinsky e Positrônio, que são sistemas de dois corpos. Para determinar a densidade das entropias, nos utilizamos a função de onda e a densidade de probabilidade para ambos os modelos atômicos. A entropia de Shannon tem uma dependência logarítmica, enquanto a entropia de Tsallis tem uma dependência do fator entrópico q , conhecido como fator entrópico de Tsallis. Em nosso trabalho, as entropias foram calculadas nos espaços das posições e também no espaço dos momentos, com isso utilizamos o conceito do principio da desigualdade de Heisenberg, adaptando para a entropia da informação. Para a entropia de Shannon, temos o principio de incerteza de Bialynici, Birula, and Mycielski, para a entropia de Tsallis chamamos de pseudo-incerteza. Por fim demonstramos graficamente o comportamento das entropias de ambos os formalismos.

<p>Objectives: Self-monitoring in health applications has already been recognized as a part of the mobile crowdsensing concept, where subjects, equipped with adequate sensors, share and extract information for personal or common benefit. Limited data transmission resources force a local analysis at wearable devices, but it is incompatible with analytical tools that require stationary and artifact-free data. The key objective of this thesis is to explain a computationally efficient binarized cross-approximate entropy, (X)BinEn, for blind cardiovascular signal processing in environments where energy and processor resources are limited.<br />Methods: The proposed method is a descendant of cross-approximate entropy ((X)ApEn). It operates over binary differentially encoded data series, split into m-sized binary vectors. Hamming distance is used as a distance measure, while a search for similarities is performed over the vector sets, instead of over the individual vectors. The procedure is tested in laboratory rats exposed to shaker and restraint stress and compared to the existing (X)ApEn results.</p><p>Results: The number of processor operations is reduced. (X)BinEn captures entropy changes similarly to (X)ApEn. The coding coarseness has an adverse effect of reduced sensitivity, but it attenuates parameter inconsistency and binary bias. A special case of (X)BinEn is equivalent to Shannon entropy. A binary conditional m=1 entropy is embedded into the procedure and can serve as a complementary dynamic measure.<br />Conclusion: (X)BinEn can be applied to a single time series as auto-entropy or, more generally, to a pair of time series, as cross-entropy. It is intended for mobile, battery operated self-attached sensing devices with limited power and processor resources.</p> / <p>Cilj: Snimanje sopstvenih zdravstveih prametara je postalo deo koncepta mobilnog &lsquo;crowdsensing-a&rsquo; prema kojem učesnici sa nakačenim senzorima skupljaju i dele informacije, na ličnu ili op&scaron;tu dobrobit. Međutim, ograničenja u prenosu podataka dovela su do koncepta lokalne obrade (na licu mesta). To je pak nespojivo sa uobičajenim metodama za koje je potrebno da podaci koji se obrađuju budu stacionarni i bez artefakata. Ključni deo ove teze je opis procesorski nezahtevne binarizovane unakrsne aproksimativne entropije (X)BinEn koja omogućava analizu kardiovaskularnih podataka bez prethodne predobrade, u uslovima ograničenog napajanja i procesorskih resursa.<br />Metoda: (X)BinEn je nastao razradom postojećeg postupka unakrsne entropije ((X)ApEn). Definisan je nad binarnim diferencijalno kodovanim vremenskim nizovima, razdeljenim u binarne vektore dužine m. Za procenu razmaka između vektora koristi se Hemingovo rastojanje, a sličnost vektora se ne procenjuje između svakog vektora pojedinačno, već između skupova vektora. Procedura je testirana nad laboratorijskim pacovima izloženim različitim vrstova stresova i upoređena sa postojećim rezultatima.</p><p>Rezultati: Broj potrebnih procesorskih operacija je značajno smanjen. (X)BinEn registruje promene entropije slično (X)ApEn. Beskonačno klipovanje je gruba kvantizacija i za posledicu ima smanjenu osetljivost na promene, ali, sa druge strane, prigu&scaron;uje binarnu asimetriju i nekonzistentnan uticaj parametara. Za određeni skup parametara (X)BinEn je ekvivalentna &Scaron;enonovoj entropiji. Uslovna binarna m=1 entropija automatski se dobija kao uzgredni product binarizovane entropije, i može da se iskoristi kao komplementarna dinamička mera.<br />Zaključak: (X)BinEn može da se koristi za jedan vremenski niz, kao auto-entropija, ili, u op&scaron;tem slučaju, za dva vremenska niza kao unakrsna entropija. Namenjena je mobilnim uređajima sa baterijskim napajanjem za individualne korisnike, to jest za korisnike sa ograničenim napajanjem i procesorskim resursima.</p>

A comunicação entre indivíduos da mesma espécie está presente em todos os táxons conhecidos. Tendo por foco organismos que possuem sistemas nervosos, dado que uma capacidade limitada para processar todos os sinais vindos do ambiente, é interessante supor que, ao longo da evolução, exista uma tendência à minimização do processamento associado com a comunicação de modo a liberar atenção para outros eventos. Como tal minimização pode ser associada a uma diminuição da energia gasta com o processo, podemos levantar a hipótese de que existe, também, uma tendência à minimização de geração de entropia &#963;, já que esta está diretamente associada com a potência dissipada durante potenciais de ação. O objetivo do presente estudo é testar a hipótese descrita acima. Para tanto, consideramos os organismos envolvidos na comunicação como osciladores descritos por equações diferenciais, e comunicação foi definida pelo acoplamento de tais osciladores. Em um modelo inicial, a freqüência e a fase foram as variáveis de estado, enquanto que, num segundo modelo, foram acrescentadas mais duas variáveis associadas à volição de emitir sinais. A geração de entropia é dada pelo produto do fluxo (i.e., freqüência) pela diferença de potencial (parâmetro de forçamento do oscilador). O cálculo de &#963; foi realizado para os dois modelos, comparando as situações de osciladores de parâmetros idênticos com aquelas de parâmetros diferentes. Para ambos os modelos, os resultados obtidos indicam que osciladores idênticos minimizam a geração de entropia em relação a sistemas de osciladores com diferentes parâmetros. Tratando, então, os sistemas de osciladores idênticos, analisamos as regiões dos valores de parâmetros que permitem uma maior minimização de &#963;. Isto ocorre, no modelo inicial, quando o parâmetro de acoplamento de freqüência tende a zero ou ao infinito. Já no modelo final, é minimizada quando os parâmetros associados com a referência interna dos osciladores são bem maiores que as constantes de acoplamento de freqüência. Podemos concluir que a melhor estratégia, em termos evolutivos, para minimizar a geração de entropia numa troca continuada de sinais é manter uma alta semelhança (intraespecífica) entre os animais que se comunicam num dado ambiente. / Communication between individuals of the same species is present in all known taxa. Focusing in organisms that have nervous system, since there is a limited capacity to process all the environmental input, it is interesting to assume an evolutionary trend to minimize the information processing associated with communication in order to redirect attention to other events. As such a minimization may be associated with a reduction in the amount of energy spent in the process, we may put forward the hypothesis that there is, also, a trend to minimize entropy generation (&#963;), since this is directly associated with power dissipation during action potentials. The objective of this study is to test the above described hypothesis. To this end, we considered the organisms involved in the communication as oscillators described by differential equations, and communication was defined as the coupling between oscillators. In an initial model, the frequency and the phase were the state variables, whereas in a second model we added two more variables associated with the volition to emit signals. Entropy generation is calculated through the product of the flux (i.e., frequency) by a potential difference (a forcing parameter). Computations of &#963; were performed for both models, and we compared the conditions of identical with those of non-identical parameters of the oscillators. In both models, the results obtained indicate that identical oscillators are those that minimize entropy generation in relation to systems of non-identical oscillators. Within the context of systems of identical oscillators, we analyzed the regions of the parameters that allow for a further minimization of &#963;. In the first model, such a minimization occurs when the parameter of frequency coupling tends either to zero or to infinite. In the second model, &#963; attains minimal values when the parameters associated with internal references of the oscillators are significantly higher than those associated with frequency coupling. We are lead to the conclusion that the best strategy, in evolutionary terms, to minimize the entropy generation in a long-lasting exchange of signals is to keep a high similarity (intra-specific) between the animals that communicate in a given environment.

Estudos de correlação entre variações de preços de ações e variação de índices de mercado são importantes na compreensão da relação entre o retorno e o risco envolvido na alocação de recursos (investimentos). De acordo com o risco envolvido, deve haver um adequado retorno. Esta questão é abordada pelo modelo CAPM Capital Asset Pricing Model , que parte da premissa de que o risco sistemático de um ativo pode ser mensurado pela sua sensibilidade aos movimentos do mercado, e para isso se supõe que os retornos dos títulos são linearmente relacionados às flutuações de um índice de mercado amplo com um grau conhecido de sensibilidade. No entanto, pode haver relações não lineares entre os retornos dos títulos e as flutuações do índice de mercado. Sendo assim, o presente trabalho analisa uma medida de correlação global vinda da teoria da informação, que mensura qualquer tipo de relação entre duas variáveis, isto é, lineares e não lineares. O objetivo é mostrar a presença de correlações não lineares no mercado de capitais brasileiro. Demonstra-se que a correlação global é expressiva e maior ou igual à correlação linear em toda a amostra constituída de todas as ações que se mantiveram no Índice da Bolsa de Valores de São Paulo (IBOVESPA) de maio de 2001 a abril de 2008, totalizando 84 meses (7 anos). / Correlations among stock price variations and stock market indices variations are important in understanding the relationship between return and risk involved in the allocation of resources (investments). According to the risk involved there exists an appropriate return. This issue is addressed by the CAPM Capital Asset Pricing Model , based on the premise that the systematic risk of an asset can be measured by its sensitivity to market movements and it is assumed that the returns are linearly related to the fluctuations of a market index with a known degree of sensitivity. However, nonlinear relationships may occur. Thus, the present study analyzes a global measure of correlation of information coming from theory, which measures any type of relationship between two variables, i.e. linear and nonlinear. The goal here is to show the presence of nonlinear correlations in the Brazilian capital market. The overall correlation obtained is expressive and greater than the linear correlation across the sample of 33 stock assets from the theoretical portfolio of São Paulo Exchange Index (IBOVESPA), from May 2001 to April 2008, totaling 84 months (7 years).

No description available.

Image reconstruction, in common with many other inverse problems, is often mathematically ill-posed in the sense that solutions are neither stable nor unique. Ultrasonic image reconstruction is particularly notorious in this regard, with narrow transducer bandwidths and limited - sometimes sparsely sampled apertures posing formidable difficulties for conventional signal processing. To overcome these difficulties, some form of regularisation is mandatory, whereby the ill-posed problem is restated as a closely related, well-posed problem, and then solved uniquely. This thesis explores the application of maximum entropy (MaxEnt) regularisation to the problem of reconstructing complex-valued imagery from sparsely sampled coherent ultrasonic field data, with particular emphasis on three-dimensional problems in the non-destructive evaluation (NDE) of materials. MaxEnt has not previously been applied to this class of problem, and yet in comparison with many other approaches to image reconstruction, it emerges as the clear leader in terms of resolution and overall image quality. To account for this performance, it is argued that the default image model used with MaxEnt is particularly meaningful in cases of ultrasonic scattering by objects embedded in homogeneous media. To establish physical and mathematical insights into the forward problem, linear equations describing scattering from both penetrable and impenetrable objects are first derived using the Born and physical optics approximations respectively. These equations are then expressed as a shift-invariant computational model that explicitly incorporates sparse sampling. To validate this model, time-domain scattering responses are computed and compared with analytical solutions for a simple canonical test case drawn from the field of NDE. The responses computed via the numerical model are shown to accurately reproduce the analytical responses. To solve inverse scattering problems via MaxEnt, the robust Cambridge algorithm is generalised to the complex domain and extended to handle broadband (multiple-frequency) data. Two versions of the augmented algorithm are then compared with a range of other algorithms, including several linearly regularised algorithms and lastly, due to its acknowledged status as a competitor with MaxEnt in radio-astronomy, the non-linear CLEAN algorithm. These comparisons are made through simulated 3-D imaging experiments under conditions of both complete and sparse aperture sampling with low and high levels of additive Gaussian noise. As required in any investigation of inverse problems, the experimental confirmation of algorithmic performance is emphasised, and two common imaging geometries relevant to NDE are selected for this purpose. In monostatic synthetic aperture imaging experiments involving side-drilled holes in an aluminium plate and test objects immersed in H2O, MaxEnt image reconstruction is demonstrated to be robust against grating-lobe and side-lobe formation, in addition to temporal bandwidth restriction. This enables efficient reconstruction of 2-D and 3-D images from small numbers of discrete samples in the spatial and frequency domains. The thesis concludes with a description of the design and testing of a novel polyvinylidene fluoride (PVDF) bistatic array transducer that offers advantages over conventional point-sampled arrays in terms of construction simplicity and signal-to-noise ratio. This ultra-sparse orthogonal array is the only one of its kind yet demonstrated, and was made possible by MaxEnt signal processing.

Jack Capon. / "May 25, 1955." "This report is based on a thesis submitted to the Department of Electrical Engineering, M.I.T., ... for the degree of Master of Science." / Bibliography: p. 53. / Army Signal Corps Contract DA36-039 sc-42607 Project 102B Dept. of the Army Project 3-99-10-022

No description available.