The Complexity Of Boolean Networks

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

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.

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.

This thesis focuses on the dynamics of autonomous Boolean networks, on the basis of Boolean logic functions in continuous time without external clocking. These networks are realized with integrated circuits on an electronic chip as a field programmable gate array (FPGA) with roughly 100,000 logic gates, offering an extremely flexible model system. It allows fast and cheap design cycles and large networks with arbitrary topologies and coupling delays. The author presents pioneering results on theoretical modeling, experimental realization, and selected applications. In this regard, three classes of novel dynamic behavior are investigated: (i) Chaotic Boolean networks are proposed as high-speed physical random number generators with high bit rates. (ii) Networks of periodic Boolean oscillators are home to long-living transient chimera states, i.e., novel patterns of coexisting domains of spatially coherent (synchronized) and incoherent (desynchronized) dynamics. (iii) Excitable networks exhibit cluster synchronization and can be used as fast artificial Boolean neurons whose spiking patterns can be controlled. This work presents the first experimental platform for large complex networks, which will facilitate exciting future developments.

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.

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.