A central problem in the bioinformatics is to find the binding sites for regulatory motifs. This is a challenging problem that leads us to a platform to apply a variety of data mining methods. In the efforts described here, a combined motif discovery method that uses mutual information and Gibbs sampling was developed. A new scoring schema was introduced with mutual information and joint information content involved. Simulated tempering was embedded into classic Gibbs sampling to avoid local optima. This method was applied to the 18 pieces DNA sequences containing CRP binding sites validated by Stormo and the results were compared with Bioprospector. Based on the results, the new scoring schema can get over the defect that the basic model PWM only contains single positioin information. Simulated tempering proved to be an adaptive adjustment of the search strategy and showed a much increased resistance to local optima.

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A integração de diferentes modalidades de imagens médicas possibilita uma análise mais detalhada de seu conteúdo, visando-se um diagnóstico mais preciso da patologia presente. Este processo, conhecido como corregistro, busca o alinhamento das imagens através da transformação rígida (ou não rígida) das mesmas, por algoritmos matemáticos de distorção, translação, rotação e ajuste de escala. A amplitude de cada transformação é determinada por uma medida de similaridade das imagens. Quanto menor a similaridade, maior será a transformação aplicada. Neste sentido, a métrica de similaridade é uma peça chave do processo de corregistro. No presente trabalho, inicialmente são propostas novas definições para o cálculo dos erros de alinhamento nas transformações de translação, rotação e escala, com o objetivo de se avaliar o desempenho do corregistro. Em seguida, cinco experimentos são realizados. No primeiro, a Informação Mútua Generalizada é avaliada como medida de similaridade para corregistro em imagens fractais e cerebrais. Neste caso, os resultados sugerem a viabilidade do emprego desta métrica, pois em geral conduz a erros de alinhamento muito pequenos, mas sem vantagens aparentes em relação à formulação de Shannon. No segundo experimento, um estudo comparativo entre a Informação Mútua e as métricas clássicas (Coeficiente de Correlação, Média dos Quadrados, Diferença de Gradiente e Cardinalidade) é então realizado. Para as imagens binárias analisadas, as métricas com menores valores de erro de alinhamento para os corregistros de translação e rotação foram a Informação Mútua e a Diferença de Gradiente. Para o corregistro de escala, todas as métricas conduziram a erros de alinhamento próximos de zero. No terceiro experimento, o processo de alinhamento é investigado em termos do número de iterações do algoritmo de corregistro. Considerando-se ambas as variáveis erro de alinhamento e número de iterações, conclui-se que o uso da Informação Mútua Generalizada com q = 1.0 é adequado ao corregistro. No quarto experimento, a influência da dimensão fractal no corregistro de imagens fractais binárias foi estudada. Para algumas métricas, a tendência geral observada é a de uma diminuição do erro de alinhamento em resposta ao aumento da dimensão fractal. Finalmente, no quinto experimento, constatou-se a existência de correlação linear entre os erros de alinhamento de imagens em tons de cinza do córtex cerebral e de fractais do conjunto Julia. / The integration of different modalities of medical images provides a detailed analysis of its contents, aiming at a more accurate diagnosis of the pathology. This process, known as coregistration, seeks to align the images through rigid (or non-rigid) transformations, by mathematical algorithms of distortion, translation, rotation and scaling. The amplitude of each transformation is determined by a similarity measure of the images. The lower the similarity, the greater the transformation applied. In this sense, the similarity metric is the key for the coregistration process. In this work, new definitions are proposed for the calculation of alignment errors in the transformations of translation, rotation and scale, with the objective of evaluating the performance of coregistration. Then, five experiments are performed. In the first one, the Generalized Mutual Information is evaluated as a similarity measure for coregistration of brain images and fractals. In this case, the results suggest the feasibility of using this measure, since it leads to very small alignment errors, although no advantages in relation to Shannon formulation are evident. In the second experiment, a comparative study between Mutual Information and the classical metrics (Correlation Coefficient, Mean Squares, Gradient Difference and Cardinality) is performed. For the binary images analyzed, the metrics with lower alignment errors for translation and rotation are the Mutual Information and Gradient Difference. For scaling transformation, all the metrics lead to alignment errors close to zero. In the third experiment, the alignment process is investigated in terms of number of iterations of the coregistration algorithm. Considering both variables alignment error and number of iterations, it is concluded that the use of Generalized Mutual Information with q =1 is appropriate for coregistration. In the fourth experiment, it is studied the influence of fractal dimension in coregistration of binary fractal images. For some metrics, as a general trend, one observes the decay of the alignment error in response to the increase of the fractal dimension. Finally, in the fifth experiment, the results indicate the existence of a linear correlation between the alignment errors of grayscale images of the cerebral cortex and Julia set fractals.

This thesis focuses particularly on the application of chemometrics in the field of analytical chemistry. Chemometrics (or multivariate analysis) consists in finding a relationship between two groups of variables, often called dependent and independent variables. In infrared spectroscopy for instance, chemometrics consists in the prediction of a quantitative variable (the obtention of which is delicate, requiring a chemical analysis and a qualified operator), such as the concentration of a component present in the studied product from spectral data measured on various wavelengths or wavenumbers (several hundreds, even several thousands). In this research we propose a methodology in the field of chemometrics to handle the chemical data (spectrophotometric data) which are often in high dimension. To handle these data, we first propose a new incremental method (step-by-step) for the selection of spectral data using linear and non-linear regression based on the combination of three principles: linear or non-linear regression, incremental procedure for the variable selection, and use of a validation set. This procedure allows on one hand to benefit from the advantages of non-linear methods to predict chemical data (there is often a non-linear relationship between dependent and independent variables), and on the other hand to avoid the overfitting phenomenon, one of the most crucial problems encountered with non-linear models. Secondly, we propose to improve the previous method by a judicious choice of the first selected variable, which has a very important influence on the final performances of the prediction. The idea is to use a measure of the mutual information between the independent and dependent variables to select the first one; then the previous incremental method (step-by-step) is used to select the next variables. The variable selected by mutual information can have a good interpretation from the spectrochemical point of view, and does not depend on the data distribution in the training and validation sets. On the contrary, the traditional chemometric linear methods such as PCR or PLSR produce new variables which do not have any interpretation from the spectrochemical point of view. Four real-life datasets (wine, orange juice, milk powder and apples) are presented in order to show the efficiency and advantages of both proposed procedures compared to the traditional chemometric linear methods often used, such as MLR, PCR and PLSR.

Moderne Hochdurchsatzmethoden erlauben die Messung einer Vielzahl von komplementären Daten und implizieren die Existenz von regulativen Netzwerken auf einem systembiologischen Niveau. Ein üblicher Ansatz zur Rekonstruktion solcher Netzwerke stellt die Clusteranalyse dar, die auf einem Ähnlichkeitsmaß beruht.<br /> Wir verwenden das informationstheoretische Konzept der wechselseitigen Information, das ursprünglich für diskrete Daten definiert ist, als Ähnlichkeitsmaß und schlagen eine Erweiterung eines für gewöhnlich für die Anwendung auf kontinuierliche biologische Daten verwendeten Algorithmus vor. Wir vergleichen unseren Ansatz mit bereits existierenden Algorithmen. Wir entwickeln ein geschwindigkeitsoptimiertes Computerprogramm für die Anwendung der wechselseitigen Information auf große Datensätze. Weiterhin konstruieren und implementieren wir einen web-basierten Dienst fuer die Analyse von integrierten Daten, die durch unterschiedliche Messmethoden gemessen wurden. Die Anwendung auf biologische Daten zeigt biologisch relevante Gruppierungen, und rekonstruierte Signalnetzwerke zeigen Übereinstimmungen mit physiologischen Erkenntnissen. / Recent high-throughput technologies enable the acquisition of a variety of complementary data and imply regulatory networks on the systems biology level. A common approach to the reconstruction of such networks is the cluster analysis which is based on a similarity measure.<br /> We use the information theoretic concept of the mutual information, that has been originally defined for discrete data, as a measure of similarity and propose an extension to a commonly applied algorithm for its calculation from continuous biological data. We compare our approach to previously existing algorithms. We develop a performance optimised software package for the application of the mutual information to large-scale datasets. Furthermore, we design and implement a web-based service for the analysis of integrated data measured with different technologies. Application to biological data reveals biologically relevant groupings and reconstructed signalling networks show agreements with physiological findings.

Image registration is widely used in different areas nowadays. Usually, the efficiency, accuracy, and robustness in the registration process are concerned in applications. This thesis studies these issues by presenting an efficient intensity-based mono-modality rigid 2D-3D image registration method and constructing a novel mathematical model for intensity-based multi-modality rigid image registration. For mono-modality image registration, an algorithm is developed using RapidMind Multi-core Development Platform (RapidMind) to exploit the highly parallel multi-core architecture of graphics processing units (GPUs). A parallel ray casting algorithm is used to generate the digitally reconstructed radiographs (DRRs) to efficiently reduce the complexity of DRR construction. The optimization problem in the registration process is solved by the Gauss-Newton method. To fully exploit the multi-core parallelism, almost the entire registration process is implemented in parallel by RapidMind on GPUs. The implementation of the major computation steps is discussed. Numerical results are presented to demonstrate the efficiency of the new method. For multi-modality image registration, a new model for computing mutual information functions is devised in order to remove the artifacts in the functions and in turn smooth the functions so that optimization methods can converge to the optimal solutions accurately and efficiently. With the motivation originating from the objective to harmonize the discrepancy between the image presentation and the mutual information definition in previous models, the new model computes the mutual information function using both the continuous image function representation and the mutual information definition for continuous random variables. Its implementation and complexity are discussed and compared with other models. The mutual information computed using the new model appears quite smooth compared with the functions computed by others. Numerical experiments demonstrate the accuracy and efficiency of optimization methods in the case that the new model is used. Furthermore, the robustness of the new model is also verified.

Modern medicine has become reliant on medical imaging. Multiple modalities, e. g. magnetic resonance imaging (MRI), computed tomography (CT), etc. , are used to provide as much information about the patient as possible. The problem of geometrically aligning the resulting images is called image registration. Mutual information, an information theoretic similarity measure, allows for automated intermodal image registration algorithms. <br /><br /> In applications such as cancer therapy, diagnosticians are more concerned with the alignment of images over a region of interest such as a cancerous lesion, than over an entire image set. Attempts to register only the regions of interest, defined manually by diagnosticians, fail due to inaccurate mutual information estimation over the region of overlap of these small regions. <br /><br /> This thesis examines the region of union as an alternative to the region of overlap. We demonstrate that the region of union improves the accuracy and reliability of mutual information estimation over small regions. <br /><br /> We also present two new mutual information based similarity measures which allow for localized image registration by combining local and global image information. The new similarity measures are based on convex combinations of the information contained in the regions of interest and the information contained in the global images. <br /><br /> Preliminary results indicate that the proposed similarity measures are capable of localizing image registration. Experiments using medical images from computer tomography and positron emission tomography demonstrate the initial success of these measures. <br /><br /> Finally, in other applications, auto-detection of regions of interest may prove useful and would allow for fully automated localized image registration. We examine methods to automatically detect potential regions of interest based on local activity level and present some encouraging results.

Image registration is widely used in different areas nowadays. Usually, the efficiency, accuracy, and robustness in the registration process are concerned in applications. This thesis studies these issues by presenting an efficient intensity-based mono-modality rigid 2D-3D image registration method and constructing a novel mathematical model for intensity-based multi-modality rigid image registration. For mono-modality image registration, an algorithm is developed using RapidMind Multi-core Development Platform (RapidMind) to exploit the highly parallel multi-core architecture of graphics processing units (GPUs). A parallel ray casting algorithm is used to generate the digitally reconstructed radiographs (DRRs) to efficiently reduce the complexity of DRR construction. The optimization problem in the registration process is solved by the Gauss-Newton method. To fully exploit the multi-core parallelism, almost the entire registration process is implemented in parallel by RapidMind on GPUs. The implementation of the major computation steps is discussed. Numerical results are presented to demonstrate the efficiency of the new method. For multi-modality image registration, a new model for computing mutual information functions is devised in order to remove the artifacts in the functions and in turn smooth the functions so that optimization methods can converge to the optimal solutions accurately and efficiently. With the motivation originating from the objective to harmonize the discrepancy between the image presentation and the mutual information definition in previous models, the new model computes the mutual information function using both the continuous image function representation and the mutual information definition for continuous random variables. Its implementation and complexity are discussed and compared with other models. The mutual information computed using the new model appears quite smooth compared with the functions computed by others. Numerical experiments demonstrate the accuracy and efficiency of optimization methods in the case that the new model is used. Furthermore, the robustness of the new model is also verified.

<p>Breast cancer screening is currently performed by mammography, which is limited by overlying anatomy and dense breast tissue. Computer aided detection (CADe) systems can serve as a double reader to improve radiologist performance. Tomosynthesis is a limited-angle cone-beam x-ray imaging modality that is currently being investigated to overcome mammography's limitations. CADe systems will play a crucial role to enhance workflow and performance for breast tomosynthesis.</p><p>The purpose of this work was to develop unique CADe algorithms for breast tomosynthesis reconstructed volumes. Unlike traditional CADe algorithms which rely on segmentation followed by feature extraction, selection and merging, this dissertation instead adopts information theory principles which are more robust. Information theory relies entirely on the statistical properties of an image and makes no assumptions about underlying distributions and is thus advantageous for smaller datasets such those currently used for all tomosynthesis CADe studies.</p><p>The proposed algorithm has two 2 stages (1) initial candidate generation of suspicious locations (2) false positive reduction. Images were accrued from 250 human subjects. In the first stage, initial suspicious locations were first isolated in the 25 projection images per subject acquired by the tomosynthesis system. Only these suspicious locations were reconstructed to yield 3D Volumes of Interest (VOI). For the second stage of the algorithm false positive reduction was then done in three ways: (1) using only the central slice of the VOI containing the largest cross-section of the mass, (2) using the entire volume, and (3) making decisions on a per slice basis and then combining those decisions using either a linear discriminant or decision fusion. A 92% sensitivity was achieved by all three approaches with 4.4 FPs / volume for approach 1, 3.9 for the second approach and 2.5 for the slice-by-slice based algorithm using decision fusion.</p><p>We have therefore developed a novel CADe algorithm for breast tomosynthesis. The techniques uses an information theory approach to achieve very high sensitivity for cancer detection while effectively minimizing false positives.</p> / Dissertation

The observability measure based on the mutual information between the last state and the measurement sequence originally proposed by Mohler and Hwang (1988) is analyzed in detail and improved further for linear time invariant discrete-time Gaussian stochastic systems by extending the definition to the observability measure of a state sequence. By using the new observability measure it is shown that the unobservable states of the deterministic system have no effect on this measure and any observable part with no measurement uncertainty makes it infinite. Other distance measures i.e., Bhattacharyya and Hellinger distances are also investigated to be used as observability measures. The relationships between the observability measures and the covariance matrices of Kalman filter and the state sequence conditioned on the measurement sequence are derived. Steady state characteristics of the observability measure based on the last state is examined. The observability measures of a subspace of the state space, an individual state, the modes of the system are investigated. One of the results obtained in this part is that the deterministically unobservable states may have nonzero observability measures. The observability measures based on the mutual information are represented recursively and calculated for nonlinear stochastic systems. Then the measures are applied to a nonlinear stochastic system by using the particle filter methods. The arguments given for the LTI case are also observed for nonlinear stochastic systems. The second moment approximation deviates from the actual values when the nonlinearity in the system increases.