Showing papers by "Santa Fe Institute published in 1992"
TL;DR: In this article, a statistical approach for identifying nonlinearity in time series is described, which first specifies some linear process as a null hypothesis, then generates surrogate data sets which are consistent with this null hypothesis and finally computes a discriminating statistic for the original and for each of the surrogate sets.
3,405 citations
TL;DR: In this article, a human DNA sequence containing mostly intron segments, those that do not code for proteins, and a "symbolic spectrum" is calculated for a human sequence.
Abstract: Mutual information function, which is an alternative to correlation function for symbolic sequences, and a "symbolic spectrum" are calculated for a human DNA sequence containing mostly intron segments, those that do not code for proteins. It is observed that the mutual information function of this sequence decays very slowly, and the correlation length is extremely long (at least 800 bases). The symbolic spectrum of the sequence at very low frequencies can be approximated by 1/fα, where f is the frequency and α ranges from 0.5 to 0.85. It is suggested that the existence of the repetitive patterns in the sequence is mainly responsible for the observed long-range correlation. A possible connection between this long-range correlation and those in music notes is also briefly discussed.
411 citations
TL;DR: In this paper, a closed-form solution to principal component analysis in the limit of small window widths is derived, which explains the relationship between delays, derivatives, and principal components, and shows how the singular spectrum scales with dimension and delay time.
213 citations
TL;DR: This paper aims at understanding the statistical features of nucleic acid sequences from the knowledge of the dynamical process that produces them, and it is observed that intron sequences (noncoding sequences) tend to have longer correlation lengths than exon sequences (protein-c coding sequences).
Abstract: This paper aims at understanding the statistical features of nucleic acid sequences from the knowledge of the dynamical process that produces them. Two studies are carried out: first, mutual information function of the limiting sequences generated by simple sequence manipulation dynamics with replications and mutations are calculated numerically (sometimes analytically). It is shown that elongation and replication can easily produce long-range correlations. These long range correlations could be destroyed in various degrees by mutation in different sequence manipulation models. Second, mutual information functions for several human nucleic acids sequences are determined. It is observed that intron sequences (noncoding sequences) tend to have longer correlation lengths than exon sequences (protein-coding sequences).
91 citations
TL;DR: In this article, a class of kinetic equations describing catalysed and template induced replication, and mutation is introduced, are split into two vector fields, a replication and a mutation field, considered as a perturbation of the replicator equation.
Abstract: A class of kinetic equations describing catalysed and template induced replication, and mutation is introduced. This ODE in its most general form is split into two vector fields, a replication and a mutation field. The mutation field is considered as a perturbation of the replicator equation. The perturbation expansion is a Taylor series in a mutation parameter lambda. First, second and higher order contributions are computed by means of the conventional Rayleigh-Schrodinger approach. Qualitative shift in the positions of rest points and limit cycles on the boundary of the physically meaningful part of concentration space are predicted from flow topologies. The results of the topological analysis are summarized in two theorems which turned out to be useful in applications: the rest point migration theorem (RPM) and the limit cycle migration theorem (LCM). Quantitative expressions for the shifts of rest points are computed directly from the perturbation expansion. The concept is applied to a collection of selected examples from biophysical chemistry and biology.
88 citations
TL;DR: A model of how the local scent laying and scent following of individual ants leads to collective decision making in groups of ants is studied, where the behavior of the individual ants is completely described by a local choice function based on their observed local behavior.
58 citations
TL;DR: The dynamics of nonlocal cellular automata are studied and the question of whether a three-input cellular automaton rule contains the three fundamental logical gates: two-input rules AND and OR, and one-input rule NOT is asked.
Abstract: Dynamical systems with nonlocal connections have potential applications to economic and biological systems. This paper studies the dynamics of nonlocal cellular automata. In particular, all two-state, three-input nonlocal cellular automata are classified according to the dynamical behavior starting from random initial configurations and random wirings, although it is observed that sometimes a rule can have different dynamical behaviors with different wirings. The nonlocal cellular automata rule space is studied using a mean-field parametrization which is ideal for the situation of random wiring. Nonlocal cellular automata can be considered as computers carrying out computation at the level of each component. Their computational abilities are studied from the point of view of whether they contain many basic logical gates. In particular, I ask the question of whether a three-input cellular automaton rule contains the three fundamental logical gates: two-input rules AND and OR, and one-input rule NOT. A particularly interesting “edge-of-chaos” nonlocal cellular automaton, the rule 184, is studied in detail. It is a system of coupled “selectors” or “multiplexers.” It is also part of the Fredkin's gate—a proposed fundamental gate for conservative computations. This rule exhibits irregular fluctuations of density, large coherent structures, and long transient times.
39 citations
Proceedings Article•
30 Nov 1992TL;DR: It turns out that the evidence procedure's MAP estimate for neural nets is, in toto, approximation error, and the exact result neither has to be re-calculated for every new data set, nor requires the running of computer code.
Abstract: The Bayesian "evidence" approximation has recently been employed to determine the noise and weight-penalty terms used in back-propagation. This paper shows that for neural nets it is far easier to use the exact result than it is to use the evidence approximation. Moreover, unlike the evidence approximation, the exact result neither has to be re-calculated for every new data set, nor requires the running of computer code (the exact result is closed form). In addition, it turns out that the evidence procedure's MAP estimate for neural nets is, in toto, approximation error. Another advantage of the exact analysis is that it does not lead one to incorrect intuition, like the claim that using evidence one can "evaluate different priors in light of the data". This paper also discusses sufficiency conditions for the evidence approximation to hold, why it can sometimes give "reasonable" results, etc.
36 citations
01 Jan 1992
TL;DR: A nonlinear forecasting algorithm is used to attempt to identify how much of the irregularity in an aperiodic time series is due to low-dimensional chaos, as opposed to high-dimensional noise.
Abstract: Many natural and experimental time series are generated by a combination of coherent, low-dimensional dynamics and stochastic, high-dimensional dynamics. A famous example is the sunspot time series. In the first part of this paper a nonlinear forecasting algorithm is used to attempt to identify how much of the irregularity in an aperiodic time series is due to low-dimensional chaos, as opposed to high-dimensional noise. The algorithm is applied to experimentally generated time series from coupled diodes, fluid turbulence and flame dynamics, and compared to dimension calculations. Theoretical results concerning the limitations of such forecasting algorithms in the presence of noise are reviewed in the second part of the paper. These results use a combination of ideas from dynamical systems and statistics. In particular, the state space reconstruction problem is investigated using properties of likelihood functions at low noise levels.
21 citations
TL;DR: The simulations show that the average transient time Tave increases algebraically with system size N, Tave∼Nα, with α≈1.08, and that the density of propagating objects (gliders) decays with time as ngl∼-γ with γ≈0.64.
TL;DR: In this article, the use of Dirac's variational principle as applied to a class of nonlinear Schrodinger equations, i ∂ψ ∂t +∇ 2 ψ+g| ψ ∗ ψ| K ψ = 0, in d spatial dimensions for arbitrary nonlinearity parameter K and for Gaussian initial data at t = 0.
TL;DR: In this article, the static kinks in scalar field theories with V[φ] = - 1 2 m 2 φ 2 + gφ 2n were studied.
02 Oct 1992
TL;DR: In this paper, it was shown that photograph-type memories can only tell us about the past, and not the future, and that the second law implies that the collapsing can only proceed from the past to the future.
Abstract: A memory is a system for transferring informationfrom one moment in time to another. Photograph-type memories work by exploiting a collapse of state space flow which “initializes” the memory. The Landauer principle tells us that regardless of whether the collapsing proceeds from the past to the future or visa-versa, entropy must be greater on the collapsed side of such aflow. Consequently, the second law means that the collapsing can onlyproceed from the past to the future. This establishes the logical necessity of the empirical observation that photograph-type memories can only tell us about the past, and not the &we. In contrast to such systems, computer-type memories do not require initialization, and therefore need
01 Jan 1992
TL;DR: An explicit portrait of basins of attraction in disordered cellular automata networks are accessible for the first time and may offer a new approach for brain-like computation.
Abstract: An explicit portrait of basins of attraction in disordered cellular automata networks are accessible for the first time. Such networks are discrete generalisations of connectionist models. Basin of attraction (fields) may serve as the basis of a mind model, and sculpting basin fields may offer a new approach for brain-like computation.
TL;DR: In this paper, the fundamental characteristics underlying all instantiations of geometric phase shifts are reviewed with an emphasis on the fundamental properties underlying all geometric phase shift instantiations, and a review is given.
Abstract: The reanalysis of the adiabatic theorem initiated by Berry and leading to the discovery of the unexpectedly elegant geometric phase shift, has been broadened in scope by many authors; most recently, to dissipative classical dynamical systems. I review this work with an emphasis on the fundamental characteristics underlying all instantiations of geometric phase shifts.