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Probabilistic Boolean Networks
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Book Synopsis Probabilistic Boolean Networks by : Ilya Shmulevich
Download or read book Probabilistic Boolean Networks written by Ilya Shmulevich and published by SIAM. This book was released on 2010-01-21 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first comprehensive treatment of probabilistic Boolean networks, unifying different strands of current research and addressing emerging issues.
Book Synopsis Probabilistic Boolean Networks by : Ilya Shmulevich
Download or read book Probabilistic Boolean Networks written by Ilya Shmulevich and published by SIAM. This book was released on 2010-01-01 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first comprehensive treatment of probabilistic Boolean networks (PBNs), an important model class for studying genetic regulatory networks. This book covers basic model properties, including the relationships between network structure and dynamics, steady-state analysis, and relationships to other model classes." "Researchers in mathematics, computer science, and engineering are exposed to important applications in systems biology and presented with ample opportunities for developing new approaches and methods. The book is also appropriate for advanced undergraduates, graduate students, and scientists working in the fields of computational biology, genomic signal processing, control and systems theory, and computer science.
Book Synopsis Algorithms For Analysis, Inference, And Control Of Boolean Networks by : Akutsu Tatsuya
Download or read book Algorithms For Analysis, Inference, And Control Of Boolean Networks written by Akutsu Tatsuya and published by World Scientific. This book was released on 2018-02-13 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Boolean network (BN) is a mathematical model of genetic networks and other biological networks. Although extensive studies have been done on BNs from a viewpoint of complex systems, not so many studies have been undertaken from a computational viewpoint. This book presents rigorous algorithmic results on important computational problems on BNs, which include inference of a BN, detection of singleton and periodic attractors in a BN, and control of a BN. This book also presents algorithmic results on fundamental computational problems on probabilistic Boolean networks and a Boolean model of metabolic networks. Although most contents of the book are based on the work by the author and collaborators, other important computational results and techniques are also reviewed or explained. Contents: Preliminaries Boolean Networks Detection of Attractors Detection of Singleton Attractors Detection of Periodic Attractors Identification of Boolean Networks Control of Boolean Networks Predecessor and Observability Problems Semi-Tensor Product Approach Analysis of Metabolic Networks Probabilistic Boolean Networks Identification of Probabilistic Boolean Networks Control of Probabilistic Boolean Networks Readership: Graduate students and researchers working on string theory and related topics. Keywords: Boolean Networks;Bioinformatics;Systems Biology;Combinatorial Algorithms;AttractorsReview: Key Features: Unique book focusing on computational aspects of Boolean networks Provide computational foundations on Boolean networks Contain recent and up-to-date results on algorithms for Boolean networks
Book Synopsis An Introduction to Semi-tensor Product of Matrices and Its Applications by : Dai-Zhan Cheng
Download or read book An Introduction to Semi-tensor Product of Matrices and Its Applications written by Dai-Zhan Cheng and published by World Scientific. This book was released on 2012 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: A generalization of Conventional Matrix Product (CMP), called the Semi-Tensor Product (STP), is proposed. It extends the CMP to two arbitrary matrices and maintains all fundamental properties of CMP. In addition, it has a pseudo-commutative property, which makes it more superior to CMP. The STP was proposed by the authors to deal with higher-dimensional data as well as multilinear mappings. After over a decade of development, STP has been proven to be a powerful tool in dealing with nonlinear and logical calculations.This book is a comprehensive introduction to the theory of STP and its various applications, including logical function, fuzzy control, Boolean networks, analysis and control of nonlinear systems, amongst others.
Book Synopsis On Construction and Identification Problems in Probabilistic Boolean Networks by : Xiaoqing Cheng
Download or read book On Construction and Identification Problems in Probabilistic Boolean Networks written by Xiaoqing Cheng and published by . This book was released on 2017-01-26 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation, "On Construction and Identification Problems in Probabilistic Boolean Networks" by Xiaoqing, Cheng, 程晓青, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: In recent decades, rapidly evolving genomic technologies provide a platform for exploring the massive amount of genomic data. At the same time, it also triggers dramatic development in systems biology. A number of mathematical models have been proposed to understand the dynamical behavior of the biological systems. Among them, Boolean Network (BN) and its stochastic extension Probabilistic Boolean Network (PBN) have attracted much attention. Identification and construction problems are two kinds of vital problems in studying the behavior of a PBN. A novel problem of observability of singleton attractors was firstly proposed, which was defined as identifying the minimum number of consecutive nodes to discriminate different singleton attractors. It may help in finding biomarkers for different disease types, thus it plays a vital role in the study of signaling networks. The observability of singleton attractor problem can be solved in O(n) time, where n is the number of genes in a BN. Later, the problem was extended to discriminating periodical attractors. For the periodical case, one has to consider multiple time steps and a new algorithm was proposed. Moreover, one may also curious about identifying the minimum set of nodes that can determine uniquely the attractor cycles from the others in the network, this problem was also addressed. In order to study realistic PBNs, inference on the structure of PBNs from gene expression time series data was investigated. The number of samples required to uniquely determine the structure of a PBN was studied. Two models were proposed to study different classes of PBNs. Using theoretical analysis and computational experiments the structure of a PBN can be exactly identified with high probability from a relatively small number of samples for some classes of PBNs having bounded indegree. Furthermore, it is shown that there exist classes of PBNs for which it is impossible to uniquely determine their structure from samples under these two models. Constructing the structure of a PBN from a given probability transition matrix is another key problem. A projection-based gradient descent method was proposed for solving huge size constrained least square problems. It is a matrixfree iterative scheme for solving the minimizer of the captured problem. A convergence analysis of the scheme is given, and the algorithm is then applied to the construction of a PBN given its probability transition matrix. Efficiency and effectiveness of the proposed method are verified through numerical experiments. Semi-tensor product approach is another powerful tool in constructing of BNs. However, to our best knowledge, there is no result on the relationship of the structure matrix and transition matrix of a BN. It is shown that the probability structure matrix and probability transition matrix are similar matrices. Three main problems in PBN were discussed afterward: dynamics, steady-state distribution and the inverse problem. Numerical examples are provided to show the validity of our proposed theory. Subjects: Algebra, Boolean Genetic regulation - Mathematical models
Book Synopsis Modeling and Reasoning with Bayesian Networks by : Adnan Darwiche
Download or read book Modeling and Reasoning with Bayesian Networks written by Adnan Darwiche and published by Cambridge University Press. This book was released on 2009-04-06 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a thorough introduction to the formal foundations and practical applications of Bayesian networks. It provides an extensive discussion of techniques for building Bayesian networks that model real-world situations, including techniques for synthesizing models from design, learning models from data, and debugging models using sensitivity analysis. It also treats exact and approximate inference algorithms at both theoretical and practical levels. The author assumes very little background on the covered subjects, supplying in-depth discussions for theoretically inclined readers and enough practical details to provide an algorithmic cookbook for the system developer.
Book Synopsis Analysis and Control of Boolean Networks by : Daizhan Cheng
Download or read book Analysis and Control of Boolean Networks written by Daizhan Cheng and published by Springer Science & Business Media. This book was released on 2010-11-23 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analysis and Control of Boolean Networks presents a systematic new approach to the investigation of Boolean control networks. The fundamental tool in this approach is a novel matrix product called the semi-tensor product (STP). Using the STP, a logical function can be expressed as a conventional discrete-time linear system. In the light of this linear expression, certain major issues concerning Boolean network topology – fixed points, cycles, transient times and basins of attractors – can be easily revealed by a set of formulae. This framework renders the state-space approach to dynamic control systems applicable to Boolean control networks. The bilinear-systemic representation of a Boolean control network makes it possible to investigate basic control problems including controllability, observability, stabilization, disturbance decoupling etc.
Book Synopsis Analysis of Microarray Data by : Matthias Dehmer
Download or read book Analysis of Microarray Data written by Matthias Dehmer and published by John Wiley & Sons. This book was released on 2008-03-17 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first to focus on the application of mathematical networks for analyzing microarray data. This method goes well beyond the standard clustering methods traditionally used. From the contents: * Understanding and Preprocessing Microarray Data * Clustering of Microarray Data * Reconstruction of the Yeast Cell Cycle by Partial Correlations of Higher Order * Bilayer Verification Algorithm * Probabilistic Boolean Networks as Models for Gene Regulation * Estimating Transcriptional Regulatory Networks by a Bayesian Network * Analysis of Therapeutic Compound Effects * Statistical Methods for Inference of Genetic Networks and Regulatory Modules * Identification of Genetic Networks by Structural Equations * Predicting Functional Modules Using Microarray and Protein Interaction Data * Integrating Results from Literature Mining and Microarray Experiments to Infer Gene Networks The book is for both, scientists using the technique as well as those developing new analysis techniques.
Book Synopsis The Probabilistic Method by : Noga Alon
Download or read book The Probabilistic Method written by Noga Alon and published by John Wiley & Sons. This book was released on 2015-11-02 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the Third Edition “Researchers of any kind of extremal combinatorics or theoretical computer science will welcome the new edition of this book.” - MAA Reviews Maintaining a standard of excellence that establishes The Probabilistic Method as the leading reference on probabilistic methods in combinatorics, the Fourth Edition continues to feature a clear writing style, illustrative examples, and illuminating exercises. The new edition includes numerous updates to reflect the most recent developments and advances in discrete mathematics and the connections to other areas in mathematics, theoretical computer science, and statistical physics. Emphasizing the methodology and techniques that enable problem-solving, The Probabilistic Method, Fourth Edition begins with a description of tools applied to probabilistic arguments, including basic techniques that use expectation and variance as well as the more advanced applications of martingales and correlation inequalities. The authors explore where probabilistic techniques have been applied successfully and also examine topical coverage such as discrepancy and random graphs, circuit complexity, computational geometry, and derandomization of randomized algorithms. Written by two well-known authorities in the field, the Fourth Edition features: Additional exercises throughout with hints and solutions to select problems in an appendix to help readers obtain a deeper understanding of the best methods and techniques New coverage on topics such as the Local Lemma, Six Standard Deviations result in Discrepancy Theory, Property B, and graph limits Updated sections to reflect major developments on the newest topics, discussions of the hypergraph container method, and many new references and improved results The Probabilistic Method, Fourth Edition is an ideal textbook for upper-undergraduate and graduate-level students majoring in mathematics, computer science, operations research, and statistics. The Fourth Edition is also an excellent reference for researchers and combinatorists who use probabilistic methods, discrete mathematics, and number theory. Noga Alon, PhD, is Baumritter Professor of Mathematics and Computer Science at Tel Aviv University. He is a member of the Israel National Academy of Sciences and Academia Europaea. A coeditor of the journal Random Structures and Algorithms, Dr. Alon is the recipient of the Polya Prize, The Gödel Prize, The Israel Prize, and the EMET Prize. Joel H. Spencer, PhD, is Professor of Mathematics and Computer Science at the Courant Institute of New York University. He is the cofounder and coeditor of the journal Random Structures and Algorithms and is a Sloane Foundation Fellow. Dr. Spencer has written more than 200 published articles and is the coauthor of Ramsey Theory, Second Edition, also published by Wiley.
Book Synopsis Boolean Models and Methods in Mathematics, Computer Science, and Engineering by : Yves Crama
Download or read book Boolean Models and Methods in Mathematics, Computer Science, and Engineering written by Yves Crama and published by Cambridge University Press. This book was released on 2010-06-28 with total page 781 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of papers written by prominent experts that examine a variety of advanced topics related to Boolean functions and expressions.
Book Synopsis Genomic Signal Processing by : Ilya Shmulevich
Download or read book Genomic Signal Processing written by Ilya Shmulevich and published by Princeton University Press. This book was released on 2014-09-08 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Genomic signal processing (GSP) can be defined as the analysis, processing, and use of genomic signals to gain biological knowledge, and the translation of that knowledge into systems-based applications that can be used to diagnose and treat genetic diseases. Situated at the crossroads of engineering, biology, mathematics, statistics, and computer science, GSP requires the development of both nonlinear dynamical models that adequately represent genomic regulation, and diagnostic and therapeutic tools based on these models. This book facilitates these developments by providing rigorous mathematical definitions and propositions for the main elements of GSP and by paying attention to the validity of models relative to the data. Ilya Shmulevich and Edward Dougherty cover real-world situations and explain their mathematical modeling in relation to systems biology and systems medicine. Genomic Signal Processing makes a major contribution to computational biology, systems biology, and translational genomics by providing a self-contained explanation of the fundamental mathematical issues facing researchers in four areas: classification, clustering, network modeling, and network intervention.
Book Synopsis Bayesian Networks by : Marco Scutari
Download or read book Bayesian Networks written by Marco Scutari and published by CRC Press. This book was released on 2021-07-28 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explains the material step-by-step starting from meaningful examples Steps detailed with R code in the spirit of reproducible research Real world data analyses from a Science paper reproduced and explained in detail Examples span a variety of fields across social and life sciences Overview of available software in and outside R
Book Synopsis High-Dimensional Probability by : Roman Vershynin
Download or read book High-Dimensional Probability written by Roman Vershynin and published by Cambridge University Press. This book was released on 2018-09-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
Book Synopsis Foundations of Probabilistic Programming by : Gilles Barthe
Download or read book Foundations of Probabilistic Programming written by Gilles Barthe and published by Cambridge University Press. This book was released on 2020-12-03 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of the theoretical underpinnings of modern probabilistic programming and presents applications in e.g., machine learning, security, and approximate computing. Comprehensive survey chapters make the material accessible to graduate students and non-experts. This title is also available as Open Access on Cambridge Core.
Book Synopsis Complex Networks & Their Applications IX by : Rosa M. Benito
Download or read book Complex Networks & Their Applications IX written by Rosa M. Benito and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book highlights cutting-edge research in the field of network science, offering scientists, researchers, students and practitioners a unique update on the latest advances in theory and a multitude of applications. It presents the peer-reviewed proceedings of the IX International Conference on Complex Networks and their Applications (COMPLEX NETWORKS 2020). The carefully selected papers cover a wide range of theoretical topics such as network models and measures; community structure, network dynamics; diffusion, epidemics and spreading processes; resilience and control as well as all the main network applications, including social and political networks; networks in finance and economics; biological and neuroscience networks and technological networks. .
Book Synopsis ON CONSTRUCTION & IDENTIFICATI by : Xiaoqing Cheng
Download or read book ON CONSTRUCTION & IDENTIFICATI written by Xiaoqing Cheng and published by Open Dissertation Press. This book was released on 2017-01-26 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation, "On Construction and Identification Problems in Probabilistic Boolean Networks" by Xiaoqing, Cheng, 程晓青, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: In recent decades, rapidly evolving genomic technologies provide a platform for exploring the massive amount of genomic data. At the same time, it also triggers dramatic development in systems biology. A number of mathematical models have been proposed to understand the dynamical behavior of the biological systems. Among them, Boolean Network (BN) and its stochastic extension Probabilistic Boolean Network (PBN) have attracted much attention. Identification and construction problems are two kinds of vital problems in studying the behavior of a PBN. A novel problem of observability of singleton attractors was firstly proposed, which was defined as identifying the minimum number of consecutive nodes to discriminate different singleton attractors. It may help in finding biomarkers for different disease types, thus it plays a vital role in the study of signaling networks. The observability of singleton attractor problem can be solved in O(n) time, where n is the number of genes in a BN. Later, the problem was extended to discriminating periodical attractors. For the periodical case, one has to consider multiple time steps and a new algorithm was proposed. Moreover, one may also curious about identifying the minimum set of nodes that can determine uniquely the attractor cycles from the others in the network, this problem was also addressed. In order to study realistic PBNs, inference on the structure of PBNs from gene expression time series data was investigated. The number of samples required to uniquely determine the structure of a PBN was studied. Two models were proposed to study different classes of PBNs. Using theoretical analysis and computational experiments the structure of a PBN can be exactly identified with high probability from a relatively small number of samples for some classes of PBNs having bounded indegree. Furthermore, it is shown that there exist classes of PBNs for which it is impossible to uniquely determine their structure from samples under these two models. Constructing the structure of a PBN from a given probability transition matrix is another key problem. A projection-based gradient descent method was proposed for solving huge size constrained least square problems. It is a matrixfree iterative scheme for solving the minimizer of the captured problem. A convergence analysis of the scheme is given, and the algorithm is then applied to the construction of a PBN given its probability transition matrix. Efficiency and effectiveness of the proposed method are verified through numerical experiments. Semi-tensor product approach is another powerful tool in constructing of BNs. However, to our best knowledge, there is no result on the relationship of the structure matrix and transition matrix of a BN. It is shown that the probability structure matrix and probability transition matrix are similar matrices. Three main problems in PBN were discussed afterward: dynamics, steady-state distribution and the inverse problem. Numerical examples are provided to show the validity of our proposed theory. Subjects: Algebra, Boolean Genetic regulation - Mathematical models
Book Synopsis Genomic Signal Processing and Statistics by : Edward R. Dougherty
Download or read book Genomic Signal Processing and Statistics written by Edward R. Dougherty and published by Hindawi Publishing Corporation. This book was released on 2005 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent advances in genomic studies have stimulated synergetic research and development in many cross-disciplinary areas. Processing the vast genomic data, especially the recent large-scale microarray gene expression data, to reveal the complex biological functionality, represents enormous challenges to signal processing and statistics. This perspective naturally leads to a new field, genomic signal processing (GSP), which studies the processing of genomic signals by integrating the theory of signal processing and statistics. Written by an international, interdisciplinary team of authors, this invaluable edited volume is accessible to students just entering this emergent field, and to researchers, both in academia and in industry, in the fields of molecular biology, engineering, statistics, and signal processing. The book provides tutorial-level overviews and addresses the specific needs of genomic signal processing students and researchers as a reference book. The book aims to address current genomic challenges by exploiting potential synergies between genomics, signal processing, and statistics, with special emphasis on signal processing and statistical tools for structural and functional understanding of genomic data. The first part of this book provides a brief history of genomic research and a background introduction from both biological and signal-processing/statistical perspectives, so that readers can easily follow the material presented in the rest of the book. In what follows, overviews of state-of-the-art techniques are provided. We start with a chapter on sequence analysis, and follow with chapters on feature selection, classification, and clustering of microarray data. We then discuss the modeling, analysis, and simulation of biological regulatory networks, especially gene regulatory networks based on Boolean and Bayesian approaches. Visualization and compression of gene data, and supercomputer implementation of genomic signal processing systems are also treated. Finally, we discuss systems biology and medical applications of genomic research as well as the future trends in genomic signal processing and statistics research.
