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

BIOE 402. Medical Technology Assessment. 2 or 3 hours. Bioentrepreneur course. Assessment of medical technology in the context of commercialization. Objectives, competition, market share, funding, pricing, manufacturing, growth, and intellectual property; many issues unique to biomedical products. Course Information: 2 undergraduate hours. 3 graduate hours. Prerequisite(s): Junior standing or above and consent of the instructor.

“Bioinformatics” 특집을 내면서

N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

https://iopscience.iop.org/article/10.1088/0031-9112/34/4/040/pdf

Stochastic Processes in Physics and Chemistry

For economical and ecological reasons, synthetic chemists are confronted with the increasing obligation of optimizing their synthetic methods. Maximizing efficiency and minimizing costs in the production of molecules and macromolecules constitutes, therefore, one of the most exciting challenges of synthetic chemistry.1-3 The ideal synthesis should produce the desired product in 100% yield and selectivity, in a safe and environmentally acceptable process.4 It is now well recognized that organometallic homogeneous catalysis offers one of the most promising approaches for solving this basic problem.2 Indeed, many of these homogeneous processes occur in high yields and selectivities and under mild reaction conditions. Most importantly, the steric and electronic properties of these catalysts can be tuned by varying the metal center and/or the ligands, thus rendering tailor-made molecular and macromolecular structures accessible.5,6 Despite the fact that various efficient methods, based on organometallic homogeneous catalysis, have been developed over the last 30 years on the laboratory scale, the industrial use of homogeneous catalytic processes is relatively limited.7 The separation of the products from the reaction mixture, the recovery of the catalysts, and the need for organic solvents are the major disadvantages in the homogeneous catalytic process. For these reasons, many homogeneous processes are not used on an industrial scale despite their benefits. Among the various approaches to address these problems, liquidliquid biphasic catalysis (“biphasic catalysis”) has emerged as one of the most important alternatives.6-11 The concept of this system implies that the molecular catalyst is soluble in only one phase whereas the substrates/products remain in the other phase. The reaction can take place in one (or both) of the phases or at the interface. In most cases, the catalyst phase can be reused and the products/substrates are simply removed from the reaction mixture by decantation. Moreover, in these biphasic systems it is possible to extract the primary products during the reaction and thus modulate the product selectivity.12 For a detailed discussion about this and other concepts of homogeneous catalyst immobilization, the reader is referred elsewhere.6,7 These biphasic systems might combine the advantages of both homogeneous (greater catalyst efficiency and mild reaction conditions) and heterogeneous (ease of catalyst recycling and separation of the products) catalysis. The advent of water-soluble organometallic complexes, especially those based on sulfonated phosphorus-containing ligands, has enabled various biphasic catalytic reactions to be conducted on an industrial scale.13-15 However, the use of water as a * Corresponding author. Fax: ++ 55 51 3316 73 04. E-mail: dupont@iq.ufrgs.br. 3667 Chem. Rev. 2002, 102, 3667−3692

https://www.chem.ccu.edu.tw/~joyce/referance/gump/IL/Chem.%20Rev.%202002,%20102,%203667.pdf

Ionic liquid (molten salt) phase organometallic catalysis.

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)

Evidence of Chaotic Dynamics of Brain Activity During the Sleep Cycle

The time-dependent properties of the Fokker–Planck equation corresponding to a zero-dimensional climate model, showing bistable behavior and subject to a weak external periodic forcing are analyzed. Conditions under which the response is amplified are found analytically. In this way the possibility of transitions between climatic states is established. The results are illustrated by the 100,000-yr periodicity of the eccentricity of the earth's orbit, in connection with glaciation cycles. DOI: 10.1111/j.2153-3490.1982.tb01786.x

Stochastic aspects of climatic transitions—response to a periodic forcing

Much of our information on climatic evolution during the past million years comes from the time series describing the isotope record of deep-sea cores. A major task of climatology is to identify, from this apparently limited amount of information, the essential features of climate viewed as a dynamic system. Using the theory of nonlinear dynamic systems we show how certain key properties of climate can be determined solely from time series data.

Is there a climatic attractor

The Fokker-Planck equation corresponding to a zero-dimensional climatic model showing bistable behavior is analyzed. A climatic potential function is introduced, whose variational properties determine the most probable states of the stationary probability distribution. A study of the time-dependent properties leads to the identification of the characteristic time scales of evolution.

https://www.tandfonline.com/doi/pdf/10.3402/tellusa.v33i3.10710

Stochastic aspects of climatic transitions–Additive fluctuations

An approach to Complexity from the perspective of fundamental science is outlined, drawing on the cross-fertilization of concepts and tools from nonlinear dynamics, statistical physics, probability and information theories, data analysis and numerical simulation. Emphasis is placed on the intertwining between different levels of description and on the probabilistic dimension of complex systems, in connection with the issue of prediction. © 2009 Academia Europaea.

/pdf/foundations-of-complex-systems-1jvksmgs9j.pdf

Catherine Nicolis

Papers

Evidence of Chaotic Dynamics of Brain Activity During the Sleep Cycle

Stochastic aspects of climatic transitions—response to a periodic forcing

Is there a climatic attractor

Stochastic aspects of climatic transitions–Additive fluctuations

Foundations of Complex Systems