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

[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

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

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

http://yorke.umd.edu/Yorke_papers_most_cited_and_post2000/1983_03_GOY_PhysicaD_Crises.pdf

Crises, sudden changes in chaotic attractors, and transient chaos

http://dadun.unav.edu/bitstream/10171/2018/1/2000.PhysRep.pdf

The control of chaos: theory and applications

The extreme sensitivity of chaotic systems to tiny perturbations (the ‘butterfly effect’) can be used both to stabilize regular dynamic behaviours and to direct chaotic trajectories rapidly to a desired state. Incorporating chaos deliberately into practical systems therefore offers the possibility of achieving greater flexibility in their performance.

Using small perturbations to control chaos

The occurrence of sudden qualitative changes of chaotic (or "turbulent") dynamics is discussed and illustrated within the context of the one-dimensional quadratic map. For this case, the chaotic region can suddenly widen or disappear, and the cause and properties of these phenomena are investigated.

http://yorke.umd.edu/Yorke_papers_most_cited_and_post2000/1982_06_GOY_PRL_Crises.pdf

Chaotic attractors in crisis

The use of chaos to transmit information is described. Chaotic dynamical systems, such as electrical oscillators with very simple structures, naturally produce complex wave forms. We show that the sym- bolic dynamics of a chaotic oscillator can be made to follow a desired symbol sequence by using small perturbations, thus allowing us to encode a message in the wave form. We illustrate this using a simple numerical electrical oscillator model. PACS numbers: 05.45.+b Much of the fundamental understanding of chaotic dy- namics involves concepts from information theory, a field developed primarily in the context of practical communi- cation. Concepts from information theory used in chaos include metric entropy, topological entropy, Markov par- titions, and symbolic dynamics (1). On the other hand, because of their exponential sensitivity, chaotic systems are often said to evolve randomly. This terminology is partially justified if one regards the information obtained by detailed observation of the chaotic orbit as being less significant than the statistical properties of the orbits. The object of this Letter is to show that we can use the close connection between the theory of chaotic systems and information theory in a way that is more than purely formal. In particular, we show that the recent realization that chaos can be controlled with small perturbations (2) can be utilized to cause the symbolic dynamics of a chaotic system to track a prescribed symbol sequence, thus allowing us to encode any desired message in the sig- nal from a chaotic oscillator. The natural complexity of chaos thus provides a vehicle for information transmission in the usual sense. Furthermore, we argue that this method of communication will often have technological advantages. Specifically, assume that there is an electrical oscillator producing a large amplitude chaotic signal that one wishes to use for communication. The so-called double

http://clm.utexas.edu/compjclub/papers/Hayes1993.pdf

Celso Grebogi

Papers

Crises, sudden changes in chaotic attractors, and transient chaos

The control of chaos: theory and applications

Using small perturbations to control chaos

Chaotic attractors in crisis

Communicating with chaos.