The first edition of this book was greeted with broad interest from readers en gaged in various disciplines of biophysics. I received many stimulating and en couraging responses, however, some of the book's reviewers wanted to stress the fact that an extensive literature of network theory was not included or reported in the book. But the main aspect of the book is intended to be substantive rather than methodical: networks simply serve as a remedy for doing some first steps in analysing and modelling complex biological systems. For an advanced stage in the investigation of a particular system it may be appropriate to replace the pheno menological network method by more detailed techniques like statistical equations or computer simulations. According to this intention, the second edition of the book has been enlarged by further biological examples for network analysis, not by more network theory. There is a completely new section on a network model for photoreception. For this section I am obliged to J. Tiedge who did most of the detailed calculation and to my colleague Professor Stieve with whom we have had a very fruitful cooperation. Also I would like to mention that this work has been sponsored by the "Deutsche Forschungsgemei nschaft" i n the "Sonderforschungsberei ch 160". Recent results for excitable systems represented by feedback networks have also been included in the second edition, especially for limit cycle networks.

Biological Network Analysis: Trends, Approaches, Graph Theory, and Algorithms considers three major biological networks, including Gene Regulatory Networks (GRN), Protein-Protein Interaction Networks (PPIN), and Human Brain Connectomes. The book's authors discuss various graph theoretic and data analytics approaches used to analyze these networks with respect to available tools, technologies, standards, algorithms and databases for generating, representing and analyzing graphical data. As a wide variety of algorithms have been developed to analyze and compare networks, this book is a timely resource. - Presents recent advances in biological network analysis, combining Graph Theory, Graph Analysis, and various network models - Discusses three major biological networks, including Gene Regulatory Networks (GRN), Protein-Protein Interaction Networks (PPIN) and Human Brain Connectomes - Includes a discussion of various graph theoretic and data analytics approaches

In recent years, significant advances have been made in the development of chemistry and computer science integration into the fields of biomedical and chemical engineering, applying quantum principles to practical, macro-world science. Methodologies and Applications for Chemoinformatics and Chemical Engineering brings together innovative research, new concepts, and novel developments in the application of informatics tools for applied chemistry and computer science. This book is essential amongst chemists, engineers, and researchers in providing mutual communication between academics and industry professionals around the world.

This volume contains selected papers presented at the Fourth Asian Symposium on Computer Mathematics. There are 39 peer-reviewed contributions together with full papers and extended abstracts by the four invited speakers, G.H. Gonnet, D. Lazard, W. McCune and W.-T. Wu, and these cover some of the most significant advances in computer mathematics, including algebraic, symbolic, numeric and geometric computation, automated mathematical reasoning, mathematical software, and computer-aided geometric design.

An international conference. titled Nonlinear Phenomena in Chemical Dynamics was held in Bordeaux on September 7-11, 1981. The present volume contains the text of lectures and abstracts of posters presented during the meeting. This conference is part of a series of scientific multidisciplinary meetings in which chemistry is involved at various levels. Amongst the most recent ones let us mention Aachen 1979, Bielefeld 1979, New York 1979, Elmau 1981. In addition, this meeting is a direct extension of the first one that took place in Bordeaux in 1978 on the topic "Far from equilibrium: instabilities and structures," at the conclusions of which we could write (cf. Far fram Equilibrium, Springer Series in Synergetics, Vol. 3): "The three key words, far fram equilibriUm, instabilities and structuPes, best illustrate the new concepts which emerge from the description of the dynamics of various systems relevant to many different research areas. " The present proceedings show how much these remarks have remained true, even though substantial progress has been achieved during the three last years. To get a ,deeper experimental knowledge of open reacting systems, to model and simulate reaction-diffusion systems, to develop the mathematical theory of dynamical sys tems, these are the main direction~ in current investigations.

This book contains the invited papers of an international symposium on synergetics; which was held at Schlol3 Elmau, Bavaria, FRG, April 27 to May 1, 1981. At our previous meetings on synergetics the self-organized formation of structures in quite different disciplines stood in the foreground of our interest. More recently it has turned out that phenomena characterized by the word "chaos" appear in various disciplines, and again far-reaching analogies in the behavior of quite different systems become visible. Therefore this meeting was devoted not only to problems connected with the occurrence of ordered structures but also to most recent results obtained in the study of chaotic motion. In the strict mathematical sense we are dealing here with deterministic chaos, i. e. , irregular motion described by deter ministic equations. While in this relatively young fieJd of research computer ex periments and computer simulations predominated in the past, there now seems to be a change of trend, namely to study certain regular features of chaos by analytical metbods. I think considerable progress has been achieved in this respect quite recently. This theoretical work is paralleled by a number of very beautiful experi ments in different fields, e. g. , fluid dynamics, solid-state physics, and chemistry. For the first time at this kind of meeting we have included plasma physics, which presents a number of most fascinating problems with respect to instabilities, formation of structures, and related phenomena.

Ecosystem analysis and ecological modelling is a rapidly developing interdisciplinary branch of science used in theoretical developments in ecology and having practical applications in environmental protection. In this book, the authors introduce new holistic, particularly cybernetic, concepts into ecosystem theory and modelling, and provide a concise treatment of mathematical modelling of freshwater ecosystems which covers methods, subsystem models, applications and theoretical developments.Part I begins with a brief introduction to the principles of systems theory and their applications to ecosystems, and provides a summary of various methods of systems analysis. In Part II emphasis is laid on the pelagic processes in standing water, characterised by relatively uninvolved structures from which models can be readily developed. Part III describes applications of the technique of modelling to solutions of theoretical and practical problems, with different modelling methods and objectives being used in the various chapters. More recent developments in the methods and theory of ecosystem modelling are covered in Part IV which also includes a discussion of future trends. The book is addressed to practising ecologists and engineers in the fields of ecology, limnology, environmental protection, and water quality managements, as well as to graduate/post-graduate university students in science and engineering. Students and researchers involved in environmental applications of mathematics and cybernetics will also find the book of interest.

Biophysics is the science of physical principles underlying all processes of life, including the dynamics and kinetics of biological systems. This fully revised 2nd English edition is an introductory text that spans all steps of biological organization, from the molecular, to the organism level, as well as influences of environmental factors. In response to the enormous progress recently made, especially in theoretical and molecular biophysics, the author has updated the text, integrating new results and developments concerning protein folding and dynamics, molecular aspects of membrane assembly and transport, noise-enhanced processes, and photo-biophysics. The advances made in theoretical biology in the last decade call for a fully new conception of the corresponding sections. Thus, the book provides the background needed for fundamental training in biophysics and, in addition, offers a great deal of advanced biophysical knowledge.

First published in 1998, this volume, spanning a lifetime's research, is a highly innovative first attempt at a consistent theoretical approach to the elements, structures and dynamics of the geography of agents, settlements and trade. Cause and effect are replaced by chance within constraints. Populations are substituted for unreal representative individuals, variability for uniformity, probabilistic process for unique history. Ignorance is a major factor in interpersonal and inter-areal commercial relations so that the focus is on flows of information and their effects on the efficiency of the economy or, alternatively, on changes in its information content. Recent work on spatial arrangements in many physical and social sciences is incorporated but always interpreted from an overriding geographical viewpoint. Key concepts are locational potential, distance friction, mobility, diffusion, spatial pattern and texture, adaptability, efficiency, spatial interaction and dependence. Analytic methods include autocovariance and transfer functions, areal special densities and entropy. Various forms of self-organization of economic spatial patterns are examined.

A NATO Advanced Research Workshop entitled New Methods for the Study of Molecular Aggregates was held at Tbe Lodge at Kananaskis Village, Alberta, Canada from 16 -20 June 1996. In fact the meeting was entirely concerned with the problem of analyzing biomolecular complexes, so the title of these proceedings has been altered to give a more precise description of the content. Tbe workshop was hosted by the time-of-flight group of the Department of Physics at the University of Manitoba, and was attended by 64 participants from around the world. '!\venty-one invited talks were given and 27 papers were presented as posters. Of the 48 contributions, 22 papers (12 orals, 10 posters) are included in these proceedings. Tbe subject of the conference was the investigation of noncovalent biomolecular complexes, with particular focus on the application of mass spectrometry to their characterization. '!\vo new ionization techniques introduced in the late 1980s, electrospray ionization (ES I) and matrix-assisted laser desorptionlionization (MALDI), resulted in a breakthrough in mass spectrometry, enabling its use in molecular weight and primary structure determination of biopolymers larger than 100 kDa. Recently it has been discovered that ESI mass spectrometry mayaiso be used to characterize complexes containing noncovalent interactions, thus opening new perspectives for supramolecular chemistry. ESI mass spectrometry has the advantage that the sampie is introduced from a homogenous solution which can be maintained at near physiological conditions of pR, concentration, and temperature.