Dynamics Of Complex Autonomous Boolean Networks

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 research aims to achieve a fundamental understanding of synchronization and its interplay with the topology of complex networks. Synchronization is a ubiquitous phenomenon observed in different contexts in physics, chemistry, biology, medicine and engineering. Most prominently, synchronization takes place in the brain, where it is associated with several cognitive capacities but is - in abundance - a characteristic of neurological diseases. Besides zero-lag synchrony, group and cluster states are considered, enabling a description and study of complex synchronization patterns within the presented theory. Adaptive control methods are developed, which allow the control of synchronization in scenarios where parameters drift or are unknown. These methods are, therefore, of particular interest for experimental setups or technological applications. The theoretical framework is demonstrated on generic models, coupled chemical oscillators and several detailed examples of neural networks.

Discrete-Time and Discrete-Space Dynamical Systems provides a systematic characterization of the similarities and differences of several types of discrete-time and discrete-space dynamical systems, including: Boolean control networks; nondeterministic finite-transition systems; finite automata; labelled Petri nets; and cellular automata. The book's perspective is primarily based on topological properties though it also employs semitensor-product and graph-theoretic methods where appropriate. It presents a series of fundamental results: invertibility, observability, detectability, reversiblity, etc., with applications to systems biology. Academic researchers with backgrounds in applied mathematics, engineering or computer science and practising engineers working with discrete-time and discrete-space systems will find this book a helpful source of new understanding for this increasingly important class of systems. The basic results to be found within are of fundamental importance for further study of related problems such as automated synthesis and safety control in cyber-physical systems using formal methods.

This book presents collaborative research presented by experts in the field of nonlinear science provides the reader with contemporary, cutting-edge, research works that bridge the gap between theory and device realizations of nonlinear phenomena. The conference provides a unique forum for applications of nonlinear systems while solving practical problems in science and engineering. Topics include: chaos gates, social networks, communication, sensors, lasers, molecular motors, biomedical anomalies, and stochastic resonance. This book provides a comprehensive report of the various research projects presented at the International Conference on Applications in Nonlinear Dynamics (ICAND 2018) held in Maui, Hawaii, 2018. It can be a valuable tool for scientists and engineering interested in connecting ideas and methods in nonlinear dynamics with actual design, fabrication and implementation of engineering applications or devices.

This book is the first comprehensive book about reservoir computing (RC). RC is a powerful and broadly applicable computational framework based on recurrent neural networks. Its advantages lie in small training data set requirements, fast training, inherent memory and high flexibility for various hardware implementations. It originated from computational neuroscience and machine learning but has, in recent years, spread dramatically, and has been introduced into a wide variety of fields, including complex systems science, physics, material science, biological science, quantum machine learning, optical communication systems, and robotics. Reviewing the current state of the art and providing a concise guide to the field, this book introduces readers to its basic concepts, theory, techniques, physical implementations and applications. The book is sub-structured into two major parts: theory and physical implementations. Both parts consist of a compilation of chapters, authored by leading experts in their respective fields. The first part is devoted to theoretical developments of RC, extending the framework from the conventional recurrent neural network context to a more general dynamical systems context. With this broadened perspective, RC is not restricted to the area of machine learning but is being connected to a much wider class of systems. The second part of the book focuses on the utilization of physical dynamical systems as reservoirs, a framework referred to as physical reservoir computing. A variety of physical systems and substrates have already been suggested and used for the implementation of reservoir computing. Among these physical systems which cover a wide range of spatial and temporal scales, are mechanical and optical systems, nanomaterials, spintronics, and quantum many body systems. This book offers a valuable resource for researchers (Ph.D. students and experts alike) and practitioners working in the field of machine learning, artificial intelligence, robotics, neuromorphic computing, complex systems, and physics.

This current volume contains 12 new papers on the subject of chaos in the physical sciences, which was initiated with the publication of the book Research Advances in Chaos Theory. It is clear the subject continues to attract a great deal of attention among scientists in the scientific community. This volume looks at such problems as chaos in nonlinear systems, in dynamical systems, quantum chaos, biological applications, and a few new emerging areas as well.

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.

Performing Math tells the history of expectations for math communication—and the conversations about math hatred and math anxiety that occurred in response. Focusing on nineteenth-century American colleges, this book analyzes foundational tools and techniques of math communication: the textbooks that supported reading aloud, the burnings that mimicked pedagogical speech, the blackboards that accompanied oral presentations, the plays that proclaimed performers’ identities as math students, and the written tests that redefined “student performance.” Math communication and math anxiety went hand in hand as new rules for oral communication at the blackboard inspired student revolt and as frameworks for testing student performance inspired performance anxiety. With unusual primary sources from over a dozen educational archives, Performing Math argues for a new, performance-oriented history of American math education, one that can explain contemporary math attitudes and provide a way forward to reframing the problem of math anxiety.