Thesis (MSc.(Physics)--University of Pretoria, 2007. / Includes bibliographical references.

Thesis (M.S.)--Rochester Institute of Technology, 2008. / Typescript. Includes bibliographical references (leaves 83-85).

O câncer é uma doença originada a partir de mutações no genoma. Um dos principais tipos de mutação são as variações do número de cópias gênicas, que ocorre quando o número de cópias de uma determinada região genômica difere de dois. Esta variação pode alterar a expressão gênica e contribuir para a progressão tumoral. Recentes plataformas experimentais permitem medir o número de cópias gênicas para todo o genoma. Entretanto, aberrações que contém oncogenes e surpessores tumorais normalmente também possuem genes que não estão relacionado com o câncer. O uso combinado de diversos pacientes têm sido uma estratégia utilizada para solucionar este problema, entretanto, esta aboradagem carece de métodos matemáticos adequados. Nesta dissertação, um novo método para identificar regiões aberrantes em um conjunto de experimentos de medição de número de cópias gênicas é apresentado, utilizando a entropia como medida de aberração biológica. Seu desenpenho superou os outros dois métodos disponíveis para o memso tipo de análise. Adicionalmente, foi desenvolvida uma ferramenta gráfica para a visualização e análise dos dados. A nova metodologia foi aplicada a estimativas de número de cópias gênicas de 167 amostras de glioblastoma multiforme geradas pelo projeto The Cancer Genome Atlas, um dos maiores projetos de câncer da atualidade. Ao total, 31 regiões de interesse foram econtradas, sendo que 8 destas regiões são mutações já descritas em GBM, contendo os genes: EGFR , MDM2, MDM4, CDK4, PTEN, PDGFRA, CDKN2A e CHD5. Oncogenes e supressores tumorais que atuam em outros cânceres também foram encontrados nos resultados, assim como alguns genes sem prévia relação com câncer. / Cancer is a disease originated from mutations in the genome. One of the main types of mutations is the copy number variation, which is defined when a certain region of the genome has a copy number different than two. This variation may alter gene expression and modulate tumor progression. Recent experimental platforms allow the measure of copy number in a genomic scale, however, these aberrations encompass oncogenes and tumor suppressor together with genes that are not related to cancer. The use of set of experiments from several patients is normally used as a solution for this problem, however, this approach lacks adequate mathematical methods for indentifying biologically important regions. In this dissertation, a new method for finding aberrant regions in a set of copy number experiments is presented, using the entropy as a measure for biological aberration, and outperforming other methods with similar propose. Moreover, a graphical tool was developed to visualization and analysis of the data. The new methodology was applied in 167 copy number experiments from glioblastoma multiforme samples generated by The Cancer Genome Atlas project, one of the biggest projects on cancer research. As a result, 31 aberrant regions were found, being 8 of these regions previously known in glioblastoma multiforme, carrying the genes: EGFR , MDM2, MDM4, CDK4, PTEN, PDGFRA, CDKN2A and CHD5. Other oncogenes and tumor suppressors that are important in other types of cancer were also found as well as genes without previously described relation with cancer.

This study explores the use of the information theory entropy equation in representations of videos for children. The calculated rates of information in the videos are calibrated to the corresponding perceived rates of information as elicited from the twelve 7 to 10 year old girls who were shown video documents. Entropy measures are calculated for several video elements: set time, set incidence, verbal time, verbal incidence, set constraint, nonverbal dependence, and character appearance. As hypothesized, mechanically calculated entropy measure (CEM) was found to be sufficiently similar to perceived entropy measure (PEM) made by children so that they can be used as useful and predictive elements of representations of children’s videos. The relationships between the CEM and the PEM show that CEM could stand for PEM in order to enrich representations for video documents for this age group. Speculations on transferring the CEM to PEM calibration to different age groups and different document types are made, as well as further implications for the field of information science.

Orientador: Luiz Antonio Barrera San Martin / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-24T06:41:54Z (GMT). No. of bitstreams: 1 Silva_AdrianoJoaoda_D.pdf: 1386475 bytes, checksum: 4df53d915a2079ada6c7136f20e5fe16 (MD5) Previous issue date: 2014 / Resumo: Na presente tese iremos analisar a entropia invariante de pares admissíveis para sistemas de controle sobre grupos de Lie e espaços homogêneos. O objetivo é melhorar os limitantes superiores e inferiores já conhecidos para tal entropia e ver quando é possível mostrar que tais limitantes coincidem, nos dando então uma expressão para ela. Mostraremos que para sistemas afins induzidos em variedades flag os limitantes, tanto superior como inferior, são dados com ínfimo do determinante da parte instável do sistema e diferem apenas em qual conjunto tal ínfimo é considerado. Para sistemas Lineares sobre grupos abelianos, nilpotentes e compactos temos uma expressão para a entropia e no caso semi-simples, a igualdade dos limitantes depende do crescimento exponencial de um sistema de controle afim sem drift associado. No fim da tese é ainda introduzido um conceito de entropia invariante para sistemas aleatórios e limitantes gerais para este são derivados / Abstract: In this Thesis we will analyse the invariance entropy of admissible pairs for control systems on Lie groups and homogeneous spaces. The main goal is to improve the known upper and lower bounds for such entropy and see when it is possible to prove that these bounds coincide, which give us an expression for the entropy. We will show that for induced control-affine systems on the flag manifolds both, the upper and lower bounds are given by the determinant of the unstable part of the system and they differ just on the set where we consider the infimum. For Linear systems on abelian, nilpotents and compact Lie groups we have an expression for the invariance entropy and in the semi-simple case, the upper and lower bounds equality depend on the exponential growth of an associated driftless control-affine system. At the end of the Thesis we introduce a concept of entropy for random control systems and derive general bounds for it / Doutorado / Matematica / Doutor em Matemática

Many image encoders exist that reduce the amount of information that needs to be transmitted or stored on disk. Reduction of information reduces the transmission rate but compromises i~age quality. The encoders that have the best compression ratios often lose image quality by distorting the high frequency portions of the image. Other encoders have slow algorithms that will not work in real time. Encoders that use quantizers often exhibit a gray scale contouring effect due to insufficient quantizer levels. This paper presents a fast encoding algorithm that reduces the number of quantizer levels without introducing an error large enough to cause gray scale contouring. The new algorithm uses entropy to determine the most advantageous difference mapping technique and the number of bits per pixel used to encode the image. The double Difference values are reduced in magnitude such that an eight level power series quantizer can be used without introducing an error large enough to cause gray scale contouring. The one dimensional application of the algorithm results in 3.0 bits per pixel with a RMS error of 4.2 gray scale values. Applied two dimensionally, the algorithm reduces the image to 1.5 bits per pixel with a RMS error of 6.7 gray scale values.

Made available in DSpace on 2015-03-04T18:51:01Z (GMT). No. of bitstreams: 1 DissertacaoPabloRFreire-Maio2008.pdf: 2235648 bytes, checksum: 9e7612e91a013d00bada5d3d53f0145d (MD5) Previous issue date: 2008-05-29 / Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior / Cancer is a disease originated from mutations in the genome. One of the main types of mutations is the copy number variation, which is defined when a certain region of the genome has a copy number different than two. This variation may alter gene expression and modulate tumor progression. Recent experimental platforms allow the measure of copy number in a genomic scale, however, these aberrations encompass oncogenes and tumor suppressor together with genes that are not related to cancer. The use of set of experiments from several patients is normally used as a solution for this problem, however, this approach lacks adequate mathematical methods for indentifying biologically important regions. In this dissertation, a new method for finding aberrant regions in a set of copy number experiments is presented, using the entropy as a measure for biological aberration, and outperforming other methods with similar propose. Moreover, a graphical tool was developed to visualization and analysis of the data. The new methodology was applied in 167 copy number experiments from glioblastoma multiforme samples generated by The Cancer Genome Atlas project, one of the biggest projects on cancer research. As a result, 31 aberrant regions were found, being 8 of these regions previously known in glioblastoma multiforme, carrying the genes: EGFR , MDM2, MDM4, CDK4, PTEN, PDGFRA, CDKN2A and CHD5. Other oncogenes and tumor suppressors that are important in other types of cancer were also found as well as genes without previously described relation with cancer. / O câncer é uma doença originada a partir de mutações no genoma. Um dos principais tipos de mutação são as variações do número de cópias gênicas, que ocorre quando o número de cópias de uma determinada região genômica difere de dois. Esta variação pode alterar a expressão gênica e contribuir para a progressão tumoral. Recentes plataformas experimentais permitem medir o número de cópias gênicas para todo o genoma. Entretanto, aberrações que contém oncogenes e surpessores tumorais normalmente também possuem genes que não estão relacionado com o câncer. O uso combinado de diversos pacientes têm sido uma estratégia utilizada para solucionar este problema, entretanto, esta aboradagem carece de métodos matemáticos adequados. Nesta dissertação, um novo método para identificar regiões aberrantes em um conjunto de experimentos de medição de número de cópias gênicas é apresentado, utilizando a entropia como medida de aberração biológica. Seu desenpenho superou os outros dois métodos disponíveis para o memso tipo de análise. Adicionalmente, foi desenvolvida uma ferramenta gráfica para a visualização e análise dos dados. A nova metodologia foi aplicada a estimativas de número de cópias gênicas de 167 amostras de glioblastoma multiforme geradas pelo projeto The Cancer Genome Atlas, um dos maiores projetos de câncer da atualidade. Ao total, 31 regiões de interesse foram econtradas, sendo que 8 destas regiões são mutações já descritas em GBM, contendo os genes: EGFR , MDM2, MDM4, CDK4, PTEN, PDGFRA, CDKN2A e CHD5. Oncogenes e supressores tumorais que atuam em outros cânceres também foram encontrados nos resultados, assim como alguns genes sem prévia relação com câncer.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1982. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Vita. / Includes bibliographical references. / by Bruce R. Musicus. / Ph.D.

An important application of term structure models is to measure the difference between the evolutions of two yield curves starting from the same initial point. Such a geometric problem can be tackled by use of the notion of information geometry after the mapping of yield curves to density functions on a Hilbert space. We prove that a pair of yield curves with large initial Bhattacharyya spherical distance would diverge from each other with a significant probability. / Finally, we implement the proposed model with initial data in the US swap market for 15 Feb, 2007. To test our model improvements over the traditional models, we also run the simulation with the Hull-White model and compare these two no-arbitrage models in various major characteristics. It shows that the proposed model forms a bridge linking interest rates and discount bonds, namely, given the initial term structure density and the volatility structure, we are able to reconstruct the short rate process and the bond price process. Our term structure density model is thus a unification of traditional models each having its own advantage. / Following the initial study of Brody and Hughston on applying information geometry to interest rate modeling, we propose a novel term structure model and investigate its application in the US swap market. Different from the traditional term structure models that impose assumptions on either bonds or rates, the newly proposed model is characterized by the evolution of a density function which is obtained from the derivative of the discount function with respect to the time left till maturity. We prove that such a density function can be interpreted as interest return on the discount bond. / The introduction of the term structure density turns the problem of yield curve dynamics into a problem of the evolution of a density distribution. There are at least three steps to model the dynamics of the density function: calibrate the initial term structure density, specify the market risk premium, and choose a proper volatility structure. First, we introduce two initial calibration methods, one by maximizing the Tsallis entropy and the other by the notion of superstatistics. By use of either method, we deduce a power-law distribution for the initial term structure density function. The entropy index q in this function, which is a well-known physics quantity, now finds its financial interpretation as the measure of departure of the current term structure from flatness on a continuously compounded basis. Our empirical experiments in the US swap market fully demonstrate this observation. Next, given the calibrated initial density, we develop the term structure dynamics in the risk-neutral world and prove that the market risk premium is immaterial. To deduce a concise martingale representation for the bond pricing formula, we choose a density volatility that possesses zero mean. Finally, as an illustration of the importance of volatility structure, the HJM volatilities are redesigned for interest rate positivity under the framework of the current model. / Yang, Yiping. / Adviser: Kwong Chung Ping. / Source: Dissertation Abstracts International, Volume: 73-03, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 187-192). / 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, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

Bruce Ronald Musicus. / Originally published as thesis (Dept. of Electrical Engineering and Computer Science, Ph.D., 1982). / Includes bibliographies. / Supported in part by the Advanced Research Projects Agency monitored by ONR under Contract N00014-81-K-0742 NR-049-506 Supported in part by the National Science Foundation under Grant ECS80-07102