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Itamar Procaccia

Bio: Itamar Procaccia is an academic researcher from Weizmann Institute of Science. The author has contributed to research in topics: Scaling & Turbulence. The author has an hindex of 57, co-authored 467 publications receiving 30604 citations. Previous affiliations of Itamar Procaccia include Niels Bohr Institute & The Chinese University of Hong Kong.


Papers
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Journal ArticleDOI
TL;DR: In this paper, the correlation exponent v is introduced as a characteristic measure of strange attractors which allows one to distinguish between deterministic chaos and random noise, and algorithms for extracting v from the time series of a single variable are proposed.

5,239 citations

Journal ArticleDOI
TL;DR: In this article, a measure of strange attractors is introduced which offers a practical algorithm to determine their character from the time series of a single observable, and the relation of this measure to fractal dimension and information-theoretic entropy is discussed.
Abstract: A new measure of strange attractors is introduced which offers a practical algorithm to determine their character from the time series of a single observable. The relation of this new measure to fractal dimension and information-theoretic entropy is discussed.

4,323 citations

Journal ArticleDOI
TL;DR: A description of normalized distributions (measures) lying upon possibly fractal sets; for example those arising in dynamical systems theory, focusing upon the scaling properties of such measures, which are characterized by two indices: \ensuremath{\alpha}, which determines the strength of their singularities; and f, which describes how densely they are distributed.
Abstract: We propose a description of normalized distributions (measures) lying upon possibly fractal sets; for example those arising in dynamical systems theory. We focus upon the scaling properties of such measures, by considering their singularities, which are characterized by two indices: \ensuremath{\alpha}, which determines the strength of their singularities; and f, which describes how densely they are distributed. The spectrum of singularities is described by giving the possible range of \ensuremath{\alpha} values and the function f(\ensuremath{\alpha}). We apply this formalism to the ${2}^{\ensuremath{\infty}}$ cycle of period doubling, to the devil's staircase of mode locking, and to trajectories on 2-tori with golden-mean winding numbers. In all cases the new formalism allows an introduction of smooth functions to characterize the measures. We believe that this formalism is readily applicable to experiments and should result in new tests of global universality.

2,696 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that fractals in general and strange attractors in particular are characterized by an infinite number of generalized dimensions Dq, q > 0, which correspond to exponents associated with ternary, quaternary and higher correlation functions.

1,577 citations


Cited by
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08 Dec 2001-BMJ
TL;DR: There is, I think, something ethereal about i —the square root of minus one, which seems an odd beast at that time—an intruder hovering on the edge of reality.
Abstract: 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 …

33,785 citations

01 May 1993
TL;DR: Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems.
Abstract: Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

29,323 citations

28 Jul 2005
TL;DR: PfPMP1)与感染红细胞、树突状组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�ly.
Abstract: 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。

18,940 citations

Book
01 Jan 1998
TL;DR: An introduction to a Transient World and an Approximation Tour of Wavelet Packet and Local Cosine Bases.
Abstract: Introduction to a Transient World. Fourier Kingdom. Discrete Revolution. Time Meets Frequency. Frames. Wavelet Zoom. Wavelet Bases. Wavelet Packet and Local Cosine Bases. An Approximation Tour. Estimations are Approximations. Transform Coding. Appendix A: Mathematical Complements. Appendix B: Software Toolboxes.

17,693 citations

Journal ArticleDOI
TL;DR: In this paper, a generalized form of entropy was proposed for the Boltzmann-Gibbs statistics with the q→1 limit, and the main properties associated with this entropy were established, particularly those corresponding to the microcanonical and canonical ensembles.
Abstract: With the use of a quantity normally scaled in multifractals, a generalized form is postulated for entropy, namelyS q ≡k [1 – ∑ i=1 W p i q ]/(q-1), whereq∈ℝ characterizes the generalization andp i are the probabilities associated withW (microscopic) configurations (W∈ℕ). The main properties associated with this entropy are established, particularly those corresponding to the microcanonical and canonical ensembles. The Boltzmann-Gibbs statistics is recovered as theq→1 limit.

8,239 citations