There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1（PfPMP1）与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用，在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员，通过启动转录不同的var基因变异体为抗原变异提供了分子基础。

疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A

I have developed "tennis elbow" from lugging this book around the past four weeks, but it is worth the pain, the effort, and the aspirin. It is also worth the (relatively speaking) bargain price. Including appendixes, this book contains 894 pages of text. The entire panorama of the neural sciences is surveyed and examined, and it is comprehensive in its scope, from genomes to social behaviors. The editors explicitly state that the book is designed as "an introductory text for students of biology, behavior, and medicine," but it is hard to imagine any audience, interested in any fragment of neuroscience at any level of sophistication, that would not enjoy this book. The editors have done a masterful job of weaving together the biologic, the behavioral, and the clinical sciences into a single tapestry in which everyone from the molecular biologist to the practicing psychiatrist can find and appreciate his or

Principles of Neural Science

A comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium is presented, with emphasis on comparisons between theory and quantitative experiments. Examples include patterns in hydrodynamic systems such as thermal convection in pure fluids and binary mixtures, Taylor-Couette flow, parametric-wave instabilities, as well as patterns in solidification fronts, nonlinear optics, oscillatory chemical reactions and excitable biological media. The theoretical starting point is usually a set of deterministic equations of motion, typically in the form of nonlinear partial differential equations. These are sometimes supplemented by stochastic terms representing thermal or instrumental noise, but for macroscopic systems and carefully designed experiments the stochastic forces are often negligible. An aim of theory is to describe solutions of the deterministic equations that are likely to be reached starting from typical initial conditions and to persist at long times. A unified description is developed, based on the linear instabilities of a homogeneous state, which leads naturally to a classification of patterns in terms of the characteristic wave vector q0 and frequency ω0 of the instability. Type Is systems (ω0=0, q0≠0) are stationary in time and periodic in space; type IIIo systems (ω0≠0, q0=0) are periodic in time and uniform in space; and type Io systems (ω0≠0, q0≠0) are periodic in both space and time. Near a continuous (or supercritical) instability, the dynamics may be accurately described via "amplitude equations," whose form is universal for each type of instability. The specifics of each system enter only through the nonuniversal coefficients. Far from the instability threshold a different universal description known as the "phase equation" may be derived, but it is restricted to slow distortions of an ideal pattern. For many systems appropriate starting equations are either not known or too complicated to analyze conveniently. It is thus useful to introduce phenomenological order-parameter models, which lead to the correct amplitude equations near threshold, and which may be solved analytically or numerically in the nonlinear regime away from the instability. The above theoretical methods are useful in analyzing "real pattern effects" such as the influence of external boundaries, or the formation and dynamics of defects in ideal structures. An important element in nonequilibrium systems is the appearance of deterministic chaos. A greal deal is known about systems with a small number of degrees of freedom displaying "temporal chaos," where the structure of the phase space can be analyzed in detail. For spatially extended systems with many degrees of freedom, on the other hand, one is dealing with spatiotemporal chaos and appropriate methods of analysis need to be developed. In addition to the general features of nonequilibrium pattern formation discussed above, detailed reviews of theoretical and experimental work on many specific systems are presented. These include Rayleigh-Benard convection in a pure fluid, convection in binary-fluid mixtures, electrohydrodynamic convection in nematic liquid crystals, Taylor-Couette flow between rotating cylinders, parametric surface waves, patterns in certain open flow systems, oscillatory chemical reactions, static and dynamic patterns in biological media, crystallization fronts, and patterns in nonlinear optics. A concluding section summarizes what has and has not been accomplished, and attempts to assess the prospects for the future.

/pdf/pattern-formation-outside-of-equilibrium-1601b9znum.pdf

Pattern formation outside of equilibrium

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)

Part I: Overview 1 Introduction - A Bit of History 2 Fundamentals 3 Apparatus 4 Chemical Oscillations: Synthesis 5 Chemical Oscillations: Analysis 6 Waves and Patterns 7 Computational Tools Part II: Special Topics 8 Complex Oscillations and Chaos 9 Transport and External Field Effects 10 Delays and Differential Delay Equations 11 Polymer Systems 12 Coupled Oscillators 13 Biological Oscillators 14 Turing Patterns 15 Stirring and Mixing Effects Appendix I Demonstrations A11 The Briggs-Rauscher Reaction A12 The Belousov-Zhabotinsky Reaction A13 BZ Waves A14 A Propagating pH Front Appendix 2 Experiments for the Undergraduate Lab A21 Frontal Polymerization A22 Oscillations in the Homogeneous Belousov-Zhabotinsky Reaction A23 Unstirred BZ System: "Measuring Rate Constants with a Ruler" Bibliography

An Introduction to Nonlinear Chemical Dynamics: Oscillations, Waves, Patterns, and Chaos

Chemical reactions with nonlinear kinetic behavior can give rise to a remarkable set of spatiotemporal phenomena. These include periodic and chaotic changes in concentration, traveling waves of chemical reactivity, and stationary spatial (Turing) patterns. Although chemists were initially skeptical of the existence and the relevance of these phenomena, much progress has been made in the past two decades in characterizing, designing, modeling, and understanding them. Several nonlinear dynamical phenomena in chemical systems provide simpler analogues of behaviors found in biological systems.

http://hopf.chem.brandeis.edu/pubs/pub236%20rep.pdf

Nonlinear Chemical Dynamics: Oscillations, Patterns, and Chaos

Recent experiments on the chlorite-iodide-malonic acid-starch reaction in a gel reactor give the first evidence of the existence of the symmetry breaking, reaction-diffusion structures predicted by Turing in 1952. A five-variable model that describes the temporal behavior of the system is reduced to a two-variable model, and its spatial behavior is analyzed. Structures have been found with wavelengths that are in good agreement with those observed experimentally. The gel plays a key role by binding key iodine species, thereby creating the necessary difference in the effective diffusion coefficients of the activator and inhibitor species, iodide and chlorite ions, respectively.

https://science.sciencemag.org/content/sci/251/4994/650.full.pdf

Modeling of turing structures in the chlorite--iodide--malonic Acid--starch reaction system.

A systematic approach is suggested to design chemical systems capable of displaying stationary, symmetry-breaking reaction diffusion patterns (Turing structures). The technique utilizes the fact that reversible complexation of an activator species to form an unreactive, immobile complex reduces the effective diffusion constant of the activator, thereby facilitating the development of Turing patterns. The chlorine dioxide/iodine/malonic acid reaction is examined as an example, and it is suggested that a similar phenomenon may occur in some biological pattern formation processes.

https://www.pnas.org/content/pnas/89/9/3977.full.pdf

A chemical approach to designing Turing patterns in reaction-diffusion systems.

Turing structures, standing waves, oscillatory clusters, and accelerating waves have been found in the spatially extended Belousov-Zhabotinsky system dispersed in water droplets of a reverse AOT microemulsion. The variety of patterns is determined by the tunable microstructure of the medium, i.e., by the concentration and size of water droplets. We propose a simple model to describe this system.

/pdf/pattern-formation-in-a-tunable-medium-the-belousov-3v7m8wjuw5.pdf

Irving R. Epstein

Papers

An Introduction to Nonlinear Chemical Dynamics: Oscillations, Waves, Patterns, and Chaos

Nonlinear Chemical Dynamics: Oscillations, Patterns, and Chaos

Modeling of turing structures in the chlorite--iodide--malonic Acid--starch reaction system.

A chemical approach to designing Turing patterns in reaction-diffusion systems.

Pattern formation in a tunable medium: the Belousov-Zhabotinsky reaction in an aerosol OT microemulsion.