The development of cDNA microarray technology has made it possible to simultaneously monitor the expression status of thousands of genes. A natural use for this vast amount of information would be to try and figure out inter-gene relationships by studying the gene expression patterns across different experimental conditions and to build Gene Regulatory Networks from these data. In this thesis, we study some of the issues involved in Genetic Regulatory Networks. One of them is to discover and elucidate multivariate logical predictive relations among gene expressions and to demonstrate how these logical relations based on coarse quantization closely reflect corresponding relations in the continuous data. The other issue involves construction of synthetic Probabilistic Boolean Networks with particular attractor structures. These synthetic networks help in testing of various algorithms like Bayesian Connectivity based approach for design of Probabilistic Boolean Networks.

With the growing complexity of modern VLSI designs, design errors become increasingly common. Design debugging today emerges as a bottleneck in the design flow, consuming up to 30% of the overall design effort. Unfortunately, design debugging is still a predominantly manual process in the industry. To tackle this problem, we enhance existing automated debugging tools and extend their applications to different design domains. The first contribution improves the performance of automated design debugging tools by using structural circuit properties, namely dominance relationships and non-solution implications. Overall, a 42% average reduction in solving run-time demonstrates the efficacy of this approach. The second contribution presents an automated debugging methodology for clock-gating design. Using clock-gating properties, we optimize existing debugging techniques to localizes and rectifies the design errors introduced by clock-gating implementations. Experiments show a 6% average reduction in debugging time and 80% of the power-savings retained.

With the growing complexity of modern VLSI designs, design errors become increasingly common. Design debugging today emerges as a bottleneck in the design flow, consuming up to 30% of the overall design effort. Unfortunately, design debugging is still a predominantly manual process in the industry. To tackle this problem, we enhance existing automated debugging tools and extend their applications to different design domains. The first contribution improves the performance of automated design debugging tools by using structural circuit properties, namely dominance relationships and non-solution implications. Overall, a 42% average reduction in solving run-time demonstrates the efficacy of this approach. The second contribution presents an automated debugging methodology for clock-gating design. Using clock-gating properties, we optimize existing debugging techniques to localizes and rectifies the design errors introduced by clock-gating implementations. Experiments show a 6% average reduction in debugging time and 80% of the power-savings retained.

<p>Switching networks are a common model for biological systems, especially</p><p>for genetic transcription networks. Stuart Kaufman originally proposed</p><p>the usefulness of the Boolean framework, but much of the dynamical </p><p>features there are not realizable in a continuous analogue. We introduce the notion</p><p>of braid-like dynamics as a bridge between Boolean and continuous dynamics and</p><p>study its importance in the local dynamics of ring and ring-like networks. We discuss</p><p>a near-theorem on the global dynamics of general feedback networks, and in the final</p><p>chapter study the main ideas of this thesis in models of a yeast cell transcription network.</p> / Dissertation

MPEG is a primary standards for dynamic image compression. The error can be introduced in the quantization process of the block DCT transformation . In this sense, the shape compensation by Boolean filter is proposed by us to adjust the intensity distribution of the motion compensated image. That is, our dynamic images are coded by the kinds of Boolean filter in addition to motion vectors after DCT coding. Boolean operation is usually applied to the binary images. The minterms of Boolean operations can be reprensented by masks. For the gray level images the mask operation is changed to be the more complex window operations. More clearly, there are two masks for a miniterm. One is a complement mask. The other is a maximum or minium window. For coding efficiency, in this paper a common complemented mask is used for two miniterms. In this sense, our Boolean filters are limited in a category of two miniterms with a same complemented structure. Experiment results have demonstrated that images going through the extra Boolean filtering have better visual quality than images processed by motion compensation only. The price is paid by the coding complexity and a relatively simple decoding structure. However, it is the decoding process which is more crucial in real time play. Therefore, we successfully integrated the Boolean filtering into MPEG-1 system in software implementation.

The development of cDNA microarray technology has made it possible to simultaneously monitor the expression status of thousands of genes. A natural use for this vast amount of information would be to try and &#64257;gure out inter-gene relationships by studying the gene expression patterns across different experimental conditions and to build Gene Regulatory Networks from these data. In this thesis, we study some of the issues involved in Genetic Regulatory Networks. One of them is to discover and elucidate multivariate logical predictive relations among gene expressions and to demonstrate how these logical relations based on coarse quantization closely re&#64258;ect corresponding relations in the continuous data. The other issue involves construction of synthetic Probabilistic Boolean Networks with particular attractor structures. These synthetic networks help in testing of various algorithms like Bayesian Connectivity based approach for design of Probabilistic Boolean Networks.

Thesis (Ph. D.)--Ohio State University, 2008. / Title from first page of PDF file. Includes bibliographical references (p. 88-89).

Sign pattern theory examines what can be said about a matrix if one knows the signs of all or some of its entries but not the exact values. Since all we know is the sign of each entry, we can write these sign patterns as matrices whose entries come from the set {+1, -1, 0, #}, where # is used for an unknown sign. Semirings satisfy all properties of rings with unity except the existence of additive inverses. The set {+1, -1, 0, #} can be viewed as a commutative semiring in natural way. In the thesis, we give a semiring version of the Cayley-Dickson construction which allows one to construct the sign pattern semiring from the Boolean semiring. We use tools from Boolean matrices to study sign nonsingular (SNS) matrices. We also investigate different notions of rank of matrices over semirings. For these rank functions we simplify proofs of classical inequalities for the sum and the product of matrices using the semiring versions of the Cauchy-Binet and Laplace theorems. For matrices over the sign pattern semiring, the minimum rank of the sign pattern is compared with the other versions of the rank. We also characterize irreducible powerful sign pattern matrices and investigate the period and base of an SNS matrix.

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