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

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.

The first comprehensive treatment of probabilistic Boolean networks, unifying different strands of current research and addressing emerging issues.

This book constitutes the refereed proceedings of the Third International Conference on Algebraic Biology, AB 2008, held at the Castle of Hagenberg, Austria in July 2008 as part of the RISC Summer 2008, organized by the Research Institute for Symbolic Computation. The 14 revised full papers presented together with 3 tutorial lectures were carefully reviewed and selected from 27 submissions. The conference is the interdisciplinary forum for the presentation of research on all aspects of applications of symbolic computation (computer algebra, computational logic, and related methods) to various issues in biology and life sciences as well as other problems in biology being approached with symbolic methods.

Boolean control networks (BCNs) are a kind of parameter-free model, which can be used to approximate the qualitative behavior of biological systems. After converting into a model similar to the standard discrete-time state-space model, control-theoretic problems of BCNs can be studied. In control theory, state observers can provide state estimation for any other applications. Reconstructibility condition is necessary for the existence of state observers. In this thesis explicit and recursive methods have been developed for reconstructibility analysis. Then, an approach to design Luenberger-like observer has been proposed, which works in a two-step process (i.e. predict and update). If a BCN is reconstructible, then an accurate state estimate can be provided by the observer no later than the minimal reconstructibility index. For a wide range of applications the approach has been extended to enable design of unknown input observer, distributed observers and reduced-order observer. The performance of the observers has been evaluated thoroughly. Furthermore, methods for output tracking control and fault diagnosis of BCNs have been developed. Finally, the developed schemes are tested with numerical examples.

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.

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.