http://www.maths.qmul.ac.uk/%7Elatora/report_06.pdf

Complex networks: Structure and dynamics

1980 Preface * 1999 Preface * 1999 Acknowledgements * Introduction * 1 Circular Logic * 2 Phase Singularities (Screwy Results of Circular Logic) * 3 The Rules of the Ring * 4 Ring Populations * 5 Getting Off the Ring * 6 Attracting Cycles and Isochrons * 7 Measuring the Trajectories of a Circadian Clock * 8 Populations of Attractor Cycle Oscillators * 9 Excitable Kinetics and Excitable Media * 10 The Varieties of Phaseless Experience: In Which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways * 11 The Firefly Machine 12 Energy Metabolism in Cells * 13 The Malonic Acid Reagent ('Sodium Geometrate') * 14 Electrical Rhythmicity and Excitability in Cell Membranes * 15 The Aggregation of Slime Mold Amoebae * 16 Numerical Organizing Centers * 17 Electrical Singular Filaments in the Heart Wall * 18 Pattern Formation in the Fungi * 19 Circadian Rhythms in General * 20 The Circadian Clocks of Insect Eclosion * 21 The Flower of Kalanchoe * 22 The Cell Mitotic Cycle * 23 The Female Cycle * References * Index of Names * Index of Subjects

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/596B270197FE27DE5FABB598B6210622/S0025557200150892a.pdf/div-class-title-span-class-italic-the-geometry-of-biological-time-span-by-a-t-winfree-pp-544-dm68-corrected-second-printing-1990-isbn-3-540-52528-9-springer-div.pdf

The geometry of biological time , by A. T. Winfree. Pp 544. DM68. Corrected Second Printing 1990. ISBN 3-540-52528-9 (Springer)

https://deim.urv.cat/~alexandre.arenas/publicacions/pdf/review.pdf

Synchronization in complex networks

The combination of the compactness of networks, featuring small diameters, and their complex architectures results in a variety of critical effects dramatically different from those in cooperative systems on lattices. In the last few years, important steps have been made toward understanding the qualitatively new critical phenomena in complex networks. The results, concepts, and methods of this rapidly developing field are reviewed. Two closely related classes of these critical phenomena are considered, namely, structural phase transitions in the network architectures and transitions in cooperative models on networks as substrates. Systems where a network and interacting agents on it influence each other are also discussed. A wide range of critical phenomena in equilibrium and growing networks including the birth of the giant connected component, percolation, $k$-core percolation, phenomena near epidemic thresholds, condensation transitions, critical phenomena in spin models placed on networks, synchronization, and self-organized criticality effects in interacting systems on networks are mentioned. Strong finite-size effects in these systems and open problems and perspectives are also discussed.

/pdf/critical-phenomena-in-complex-networks-4vxnv3f75f.pdf

Critical phenomena in complex networks

Myoglobin rebinding of carbon monoxide and dioxygen after photodissociation has been observed in the temperature range between 40 and 350 K. A system was constructed that records the change in optical absorption at 436 nm smoothly and without break between 2 musec and 1 ksec. Four different rebinding processes have been found. Between 40 and 160 K, a single process is observed. It is not exponential in time, but approximately given by N(t) = (1 + t/to)-n, where to and n are temperature-dependent, ligand-concentration independent, parameters. At about 170 K, a second and at 200 K, a third concentration-independent process emerge. At 210 K, a concentration-dependent process sets in. If myoglobin is embedded in a solid, only the first three can be seen, and they are all nonexponential. In a liquid glycerol-water solvent, rebinding is exponential. To interpret the data, a model is proposed in which the ligand molecule, on its way from the solvent to the binding site at the ferrous heme iron, encounters four barriers in succession. The barriers are tentatively identified with known features of myoglobin. By computer-solving the differential equation for the motion of a ligand molecule over four barriers, the rates for all important steps are obtained. The temperature dependences of the rates yield enthalpy, entropy, and free-energy changes at all barriers. The free-energy barriers at 310 K indicate how myoglobin achieves specificity and order. For carbon monoxide, the heights of these barriers increase toward the inside; carbon monoxide consequently is partially rejected at each of the four barriers. Dioxygen, in contrast, sees barriers of about equal height and moves smoothly toward the binding site. The entropy increases over the first two barriers, indicating a rupturing of bonds or displacement of residues, and then smoothly decreases, reaching a minimum at the binding site. The magnitude of the decrease over the innermost barrier implies participation of heme and/or protein. The nonexponential rebinding observed at low temperatures and in solid samples implies that the innermost barrier has a spectrum of activation energies. The shape of the spectrum has been determined; its existence can be explained by assuming the presence of many conformational states for myoglobin. In a liquid at temperatures above about 230 K, relaxation among conformational states occurs and rebinding becomes exponential.

Dynamics of ligand binding to myoglobin

The nature of the Arrhenius activation energy and frequency factor is reexamined in terms of information now becoming available on the microscopic aspects of collisional reactions. It is pointed out that the activation energy is not generally equal to the threshold for reaction, and its correct conceptual meaning is discussed. The temperature dependence of this quantity and its relation to the threshold energy is developed for a number of representative forms of the energy dependence of the reaction cross-section (excitation function). The uses and limitations of the activation energy as a means of evaluating thresholds, excitation functions, and the presence of tunneling processes are discussed.

The Meaning and Use of the Arrhenius Activation Energy

A new kind of instability is predicted for a system involving activator and inhibitor kinetics in a reactive flow. It is shown that a differential flow of activator and inhibitor, achievable, e.g., by selectively binding one component to a support, can destabilize the spatially homogeneous state of the system in a similar way as differential diffusivity does in the case of the Turing instability. The differential-flow-induced chemical instability is of the traveling-wave type. It is free from the restrictions of the Turing instability on the diffusion coefficients and can thus be expected to occur in a wide variety of natural and artificial systems

Chemical instability induced by a differential flow.

We present necessary and sufficient conditions on the stability matrix of a general n(≥2)-dimensional reaction-diffusion system which guarantee that its uniform steady state can undergo a Turing bifurcation. The necessary (kinetic) condition, requiring that the system be composed of an unstable (or activator) and a stable (or inhibitor) subsystem, and the sufficient condition of sufficiently rapid inhibitor diffusion relative to the activator subsystem are established in three theorems which form the core of our results. Given the possibility that the unstable (activator) subsystem involves several species (dimensions), we present a classification of the analytically deduced Turing bifurcations into p (1 ≤p≤ (n− 1)) different classes. For n = 3 dimensions we illustrate numerically that two types of steady Turing pattern arise in one spatial dimension in a generic reaction-diffusion system. The results confirm the validity of an earlier conjecture [12] and they also characterise the class of so-called strongly stable matrices for which only necessary conditions have been known before [23, 24]. One of the main consequences of the present work is that biological morphogens, which have so far been expected to be single chemical species [1–9], may instead be composed of two or more interacting species forming an unstable subsystem.

/pdf/turing-instabilities-in-general-systems-58et6nojq9.pdf

Turing instabilities in general systems.

We have experimentally verified the prediction that a homogeneous steady state of an activator-inhibitor system can be destabilized by a differential flow of the key species, rather than by their differential diffusivity for Turing instability. Traveling waves are generated by a flow of Belousov-Zhabotinsky reactants through a tube containing ferroin immobilized on a cation exchanger. Without flow the system resides in a homogeneous steady state. This mechanism of spatiotemporal pattern formation avoids the restrictions of the Turing instability on the diffusion coefficients and can thus be expected to operate in a larger class of chemical, physical, and biological systems.

Self-organization induced by the differential flow of activator and inhibitor.

A simple plasma ion source which is capable of delivering beams of 1×10−6 A at 200 eV and 0.1–0.2 eV energy spread is described. Gas efficiencies of the order of percents are obtained. This source was found to be very successful in experiments using low energy beams in the electron volt region.

Michael Menzinger

Papers

The Meaning and Use of the Arrhenius Activation Energy

Chemical instability induced by a differential flow.

Turing instabilities in general systems.

Self-organization induced by the differential flow of activator and inhibitor.

High Intensity, Low Energy Spread Ion Source for Chemical Accelerators