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Chaos and Nonlinear Dynamics: Application to Financial Markets
 Journal of Finance
, 1991
"... After the stock market crash of October 19, 1987, interest in nonlinear dynamics, especially deterministic chaotic dynamics, has increased in both the financial press and the academic literature. This has come about because the frequency of large moves in stock markets is greater than would be expec ..."
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Cited by 185 (3 self)
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After the stock market crash of October 19, 1987, interest in nonlinear dynamics, especially deterministic chaotic dynamics, has increased in both the financial press and the academic literature. This has come about because the frequency of large moves in stock markets is greater than would be expected
"Theoretical mathematics”: Toward a cultural synthesis of mathematics and theoretical physics
 BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY
, 1993
"... Is speculative mathematics dangerous? Recent interactions between physics and mathematics pose the question with some force: traditional mathematical norms discourage speculation, but it is the fabric of theoretical physics. In practice there can be benefits, but there can also be unpleasant and de ..."
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Cited by 40 (1 self)
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Is speculative mathematics dangerous? Recent interactions between physics and mathematics pose the question with some force: traditional mathematical norms discourage speculation, but it is the fabric of theoretical physics. In practice there can be benefits, but there can also be unpleasant and destructive consequences. Serious caution is required, and the issue should be considered before, rather than after, obvious damage occurs. With the hazards carefully in mind, we propose a framework that should allow a healthy and positive role for speculation.
A Comparison Of Genetic Algorithms And Other Machine Learning Systems On A Complex Classification Task From Common Disease Research
, 1995
"... The thesis project is an investigation of some wellknown machine learning systems and evaluates their utility when applied to a classification task from the field of human genetics. This commondisease research task, an inquiry into genetic and biochemical factors and their association with a fami ..."
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Cited by 18 (1 self)
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The thesis project is an investigation of some wellknown machine learning systems and evaluates their utility when applied to a classification task from the field of human genetics. This commondisease research task, an inquiry into genetic and biochemical factors and their association with a family history of coronary artery disease (CAD), is more complex than many pursued in machine learning research, due to interactions and the inherent noise in the dataset. The task also differs from most pursued in machine learning research because there is a desire to explain the dataset with a small number of rules, even at the expense of accuracy, so that they will be more accessible to medical researchers who are unaccustomed to dealing with disjunctive explanations of data. Furthermore, there is as...
Principles and applications of chaotic systems
 Communications of the ACM
, 1995
"... the behavioral elements of chaos introduces a wide array of commercial applications to enhance, manipulate, or better control many current technical functions. 96 November 1995/Vol. 38, No. 11 COMMUNICATIONS OF THE ACM There lies a behavior between rigid regularity and randomness based on pure chanc ..."
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Cited by 10 (1 self)
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the behavioral elements of chaos introduces a wide array of commercial applications to enhance, manipulate, or better control many current technical functions. 96 November 1995/Vol. 38, No. 11 COMMUNICATIONS OF THE ACM There lies a behavior between rigid regularity and randomness based on pure chance. It’s called a chaotic system, or chaos for short [5]. Chaos is all around us. Our notions of physical motion or dynamic systems have encompassed the precise clocklike ticking of periodic systems and the vagaries of dicethrowing chance, but have often been overlooked as a way to account for the more commonly
Complex patterns generated by next nearest neighbors cellular automata
 Computer & Graphics
, 1989
"... included Abstract. A greater number of complicated patterns can be produced by cellular automata rules with next nearest neighbors in the updating, than those with only nearest neighbors couplings. Some patterns can be identified as gliders moving on the background, while other rules have more intri ..."
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Cited by 7 (1 self)
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included Abstract. A greater number of complicated patterns can be produced by cellular automata rules with next nearest neighbors in the updating, than those with only nearest neighbors couplings. Some patterns can be identified as gliders moving on the background, while other rules have more intriguing configurations called “creatures ” which move irregularly on the background. Sometimes, even the distinction between creatures and the background disappear, and the patterns look strikingly similar to those generated by probabilistic rules, even though the rules used are strictly deterministic. The question of how the complicated behaviors of biological systems can be explained in terms of the simple laws of physics motivated Von Neumann and Ulam to propose the use of cellular automaton [1], a fully discretized dynamical system with local couplings. It is indeed found that some specially designed 2dimensional cellular automata can mimic the least selfreproduction behaviors [2]. Although we lack the general criteria on what types of cellular automata rules can produce what behaviors, it is widely appreciated nowadays that simple rules can lead to complex dynamics [3, 4]. The simplest type of cellular automata are on a 1dimensional lattice with 2 state values at each site, and with nearest neighbors couplings: a t+1 i = f(ati−1,ati,ati+1) (0.1) where a t i is the state value on site i at time t, and f() is some kind of function, usually in a tabular form, with the state values at previous time step on nearest sites as the variables. These cellular automata are thoroughly studied, and their spatialtemporal patterns can be found in the Appendix
Methods for the Analysis of ShortTerm Variability of Heart Rate and Blood Pressure in Frequency Domain
, 1997
"... Cardiovascular variability signals provide information about the functioning of the autonomous nervous system and other physiological subsystems. Because of large inter and intrasubject variability, sophisticated data analysis methods are needed to gain this information. An important approach for ..."
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Cited by 3 (0 self)
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Cardiovascular variability signals provide information about the functioning of the autonomous nervous system and other physiological subsystems. Because of large inter and intrasubject variability, sophisticated data analysis methods are needed to gain this information. An important approach for analysing signals is the analysis in the frequency domain.
EMERGENCE OF SPACETIME
, 2005
"... Starting from a background Zero Point Field (or Dark Energy) we show how an array of oscillators at the Planck scale leads to the formation of elementary particles and spacetime and also to a cosmology consistent with latest observations. 1 ..."
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Starting from a background Zero Point Field (or Dark Energy) we show how an array of oscillators at the Planck scale leads to the formation of elementary particles and spacetime and also to a cosmology consistent with latest observations. 1