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Leading experts reveal role of chaos & complexity in biological info processing

World Scientific


IMAGE: Sketch of Biological Information Processing showing the categorizing of input stimuli impinging on the processor. Part of environmental stimuli is 'captured' by the processor's nonlinear dissipative operator as initial conditions.... view more

Credit: "Chaos & Biological Information Processing " J.S. Nicolis (World Scientific Press, 1991)

Do chaos and complexity play a fundamental role in biological information processing?

The interdisciplinary approach to problems that till recently were addressed in the hermetic framework of distinct disciplines such as physics, informatics, biology or sociology constitutes today one of the most active and innovative areas of science, where fundamental issues meet problems of everyday concern.

John Nicolis, an eminent Greek scientist and thinker who passed away unexpectedly on the 20th of April 2012, brought out to the highest degree the interdisciplinary approach to key scientific problems and, at the same time, their cultural dimension. Complexity has been at the core of his interests for almost 40 years. He imprinted on it a new direction focusing on the generation and processing of information in hierarchical systems, that is to say, systems involving coexisting components evolving on different scales and coupled to each other in a nonlinear fashion through positive and negative feedback loops. He defined three basic levels of organization:

-The ``syntactical'' level where the elementary dynamical processes are taking place.

-The ``semantic'' level, where relationships between stimuli impinging on a system and the formation of "categories" related to global, collective properties e. g. the attractors that emerge from the syntactical level and follow a dynamics of their own.

-The ``pragmatic level'', where different hierarchical systems are viewed as players communicating dynamically via a set of selected strategic rules such as cooperation, competition, cheating, etc.

Based on this vision John Nicolis generated a phenomenal number of ideas and intuitions, In the present volume surveys by eminent international specialists of the mechanisms presiding in information processing and communication are provided. Physical, biological and cognitive systems are approached from different, complementary points of view using the unifying methods of nonlinear dynamics, chaos theory, probability and information theories and complexity science. Unexpected connections between these disciplines are stressed by bringing together ideas and tools that had so far been developed independently of each other. Epistemological issues in connection with incompleteness and self-reference are also addressed.

The following topics are featured in the volume.

I. Glimpses at nonlinear dynamics and chaos:

Nonlinear dynamics and chaos theory provide the general setting within which complexity and information processing can be formulated. In the opening chapter by G. Contopoulos et al the transition from quantum to classical behaviour is analysed in the paradigmatic case of the scattering problem. The connection between classical and quantum descriptions is further addressed in the chapter by M. Axenides and E. Floratos, where the classic Lorenz attractor is revisited using a formulation originally developed by Nambu in the context of quantum mechanics. G. Tsironis et al discuss in their chapter the onset of spatio-temporal complexity in nonlinear lattices. In the chapter by D. Mac Kernan a systematic probabilistic approach is outlined based on coarse-grained description and symbolic dynamics. Symbolic dynamics is taken up again in the closing chapter of this Part by A. Shilnikov et al., where fractal-hierarchical organizations of the parameter space of Lorenz-type chaotic systems induced by homoclinic and heteroclinic bifurcations are revealed using a binary representation of the solutions.

II. Chaos and information:

Information theory finds its origin in Shannon's 1949 classic paper. In the opening chapter of this Part H. Haken develops the quantum expression of Shannon information along with an extension of Jaynes' maximum entropy principle into the quantum domain. The conditions under which entangled states and long-range coherence can be secured as necessary conditions for information processing at the quantum mechanical level, are addressed in the following chapter by S. Nicolis. A dynamical approach to information is subsequently developed in the chapter by C. Nicolis, devoted to nonlinear systems giving rise to multiple simultaneously stable states and to stochastic resonance. Different signatures of multistability and of stochastic resonance on a hierarchy of entropy-related quantities characterizing the system as an information processor are identified. Finally, in the closing chapter by W. Ebeling and R. Feistel the origin of information processing is addressed in relation to the origin and evolution of life. Central to their approach is the idea that there exists a universal process of self-organized emergence of systems capable of processing symbolic information. They coin to it the name of "ritualization transition" and discuss its status with respect to kinetic phase transitions familiar from physics.

III. Biological information processing

Undoubtedly Information processing and the very concept of Information, for that matter, find their most exciting expressions in living matter. In the opening chapter of this Part, P. Schuster addresses the information processing mechanisms responsible for the build up of an evolutionary memory within a population. The conditions under which optimality can be achieved are also analysed using computer simulations along with mathematical modelling, and connections to nonlinear dynamics and irreversible thermodynamics are suggested. Evolutionary arguments are also central in the chapter by Y. Almirantis et al, where the structure of the genome and, in particular, the distribution patterns of the distances between different groups along it are explored and correlated with known evolutionary phenomena. The ubiquity of power law behaviours is established and a model based on aggregative dynamics capable of reproducing these patterns is proposed. Pattern formation on a much larger scale associated to embryonic development is considered in the closing chapter by S. Papageorgiou. A biophysical model is proposed to explain the appearance of a sequential pattern along the anterior-posterior axis of a vertebrate embryo, in coincidence with the 3' to 5' order of the genes in the chromosome.

IV. Complexity, chaos and cognition:

This Part deals with the multiple facets of information processing by the brain, a question that has been at the center of interests of John Nicolis throughout his career. Different approaches to cognition are developed and the status of self-referential processes is discussed. In the opening chapter W. J. Freeman summarises the role of chaos in brain function from a "bottom-up approach". He discusses the state of "criticality" of the celebral cortex and its placid properties of a system at the edge of chaos, an idea that J.S. Nicolis employed in his studies of the mechanisms of cognition in the brain as a hierarchical system. W.J. Freeman, offers a discussion on the state of the art of the issue of brain waves, emerging patterns, fractality, quantum-field considerations and the role of noise in the emergence of coherent and intermittent states in brain dynamics. The spectral properties of brain recordings are studied in comparison with the spectral signatures of a Lorenz-type model, at its turbulent regime, by Provata et al. Bringing out the relevance of chaotic dynamics in understanding the phenomenology of brain recordings. F.T. Arrechi, is addressing the issue of cognition and language with respect to brain dynamics in a hierarchical system perspective via a "top down" approach. He proposes a quantum-like model where apprehension, judgment and self-consciousness could be discussed. He shows that the uncertainty in the information content of spike-train recording is ruled by a "quantum" constant, that can be given a numerical value depending on the specifics of the experimental set up. Subsequently, K. Kaneko presents a tantalizing approach to bridge the gap between dynamical systems and biological information processing. Chaotic itinerancy in high-dimensional dynamical systems, induced switches of states, and interference between slow and fast modes via "super-selection rules", also a preoccupation of J. S. Nicolis, are reviewed and applied to cell differentiation, adaptation, and memory. The necessity to expand the mathematical framework to include self-referential dynamics for such "super selection rules" is also stressed. Closing this part, I. Tsuda, discusses self-reference and chaotic itinerancy with relation to the dynamics of cognition, perception ambiguity and paradoxical games from a purely dynamical-systems point of view.

V. Dynamical games and collective behaviours:

Continuing on the theme of games C. Grebogi and coworkers address the outstanding and fundamental problem of species coexistence. They approach this problem augmenting evolutionary games with mobility for the species dynamics, under cyclic competitions, which enables them to elucidate the underlying fundamentally nonlinear mechanisms. The emerging picture is one of a complex, non-trivial, chaotic landscape for coexistence and extinction. The emergent properties of the collective behaviour of animal groups is the theme that follows where T. Bountis et al study collective behaviours and phase transitions in models of bird flocking. With an emphasis on the interplay between topological and dynamical constrains present in the complex interactions of the constituent parts, they discuss the emerging complex patterns of motion. In the same vein but with another biological model of social animal behaviour, that of ants, S.C. Nicolis presents evidence of fractal scaling laws in the ubiquitous activity of animal construction. Fractal scaling laws have also been associated with the underlying process of self-organized criticality, a theme that John Nicolis was enthusiastically and frequently discussing in his work and teaching. Y.-P. Gunji offers his view of an extended self-organised criticality in asynchronously tuned cellular automata. He provides a link with dynamical games based on cellular automata, distributed in space, and demonstrates the subtleties in information flow of synchronous versus asynchronous updating for their local states. He demonstrates that asynchronous information updating is the main formative cause of self-organized criticality.

Closing the volume, O. E. Rössler dialogues here with John Nicolis and invites us in a journey on the theme of scientific revolution crossing space-time barriers, from Heraclitus to Hubble.

The general approach followed and the ideas put forward in this volume will prove useful to students, researchers and the general public attracted by the interdisciplinary approach to science. .

Quotes From the Book:

"Mapping the continuous description of a system into a discrete set of states also means that the original, fine grained dynamics induces a symbolic dynamics describing how the sequence of letters from an alphabet unfold in time. This provides a natural link with the information theory view of chaos pioneered by John Nicolis." Chapter 4, Coarse Graining Approach to Chaos, by Donal MacKernan.

"Our interest [...] is focused on the self-organization of information, on the way how a physical system can be enabled to create symbols and the related symbol-processing machinery out of ordinary pre-biological roots."

Chapter 9, Selforganization of Symbols and Information, by Werner Ebeling and Rainer Feistel.

"The late Professor J.S. Nicolis always emphasized [...]the relevance of a dynamical systems approach to biology. In particular, viewing the genome as a "biological text" captures the dynamical character of both the evolution and function of the organisms in the form of correlations indicating the presence of a long-range order. This genomic structure can be expressed in forms reminiscent of natural languages and several temporal and spatial traces left by the functioning of dynamical systems: Zipf laws, self-similarity and fractality".

Chapter 11 Long-Range Order and Fractality in the Structure and Organization of Eukaryotic Genomes, by Dimitris Polychronopoulos, Giannis Tsiagkas, Labrini Athanasopoulou, Diamantis Sellis and Yannis Almirantis.

"In the last decades a wholistic approach has emerged aiming at explaining the complex phenomena of life. In this direction different branches of Science like Chemistry, Physics, Mathematics have contributed. Systems Biology consists of this inter-disciplinary field where the development of powerful computational techniques plays a fundamental role. This new field aims at discovering emerging properties at the level of cells, tissues, organisms, populations functioning as a whole system."

Chapter 12, Towards Resolving the Enigma of HOX Gene Collinearity, by Spyros Papageorgiou

The book retails at major bookstores at US$148 (hardcover). More information about the book can be found at


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