420 research outputs found
Rapid convergence of time-averaged frequency in phase synchronized systems
Numerical and experimental evidence is presented to show that many phase
synchronized systems of non-identical chaotic oscillators, where the chaotic
state is reached through a period-doubling cascade, show rapid convergence of
the time-averaged frequency. The speed of convergence toward the natural
frequency scales as the inverse of the measurement period. The results also
suggest an explanation for why such chaotic oscillators can be phase
synchronized.Comment: 6 pages, 9 figure
Extreme value statistics and return intervals in long-range correlated uniform deviates
We study extremal statistics and return intervals in stationary long-range
correlated sequences for which the underlying probability density function is
bounded and uniform. The extremal statistics we consider e.g., maximum relative
to minimum are such that the reference point from which the maximum is measured
is itself a random quantity. We analytically calculate the limiting
distributions for independent and identically distributed random variables, and
use these as a reference point for correlated cases. The distributions are
different from that of the maximum itself i.e., a Weibull distribution,
reflecting the fact that the distribution of the reference point either
dominates over or convolves with the distribution of the maximum. The
functional form of the limiting distributions is unaffected by correlations,
although the convergence is slower. We show that our findings can be directly
generalized to a wide class of stochastic processes. We also analyze return
interval distributions, and compare them to recent conjectures of their
functional form
Simple model for 1/f noise
We present a simple stochastic mechanism which generates pulse trains
exhibiting a power law distribution of the pulse intervals and a
power spectrum over several decades at low frequencies with close to
one. The essential ingredient of our model is a fluctuating threshold which
performs a Brownian motion. Whenever an increasing potential hits the
threshold, is reset to the origin and a pulse is emitted. We show that
if increases linearly in time, the pulse intervals can be approximated
by a random walk with multiplicative noise. Our model agrees with recent
experiments in neurobiology and explains the high interpulse interval
variability and the occurrence of noise observed in cortical
neurons and earthquake data.Comment: 4 pages, 4 figure
Networks of Recurrent Events, a Theory of Records, and an Application to Finding Causal Signatures in Seismicity
We propose a method to search for signs of causal structure in spatiotemporal
data making minimal a priori assumptions about the underlying dynamics. To this
end, we generalize the elementary concept of recurrence for a point process in
time to recurrent events in space and time. An event is defined to be a
recurrence of any previous event if it is closer to it in space than all the
intervening events. As such, each sequence of recurrences for a given event is
a record breaking process. This definition provides a strictly data driven
technique to search for structure. Defining events to be nodes, and linking
each event to its recurrences, generates a network of recurrent events.
Significant deviations in properties of that network compared to networks
arising from random processes allows one to infer attributes of the causal
dynamics that generate observable correlations in the patterns. We derive
analytically a number of properties for the network of recurrent events
composed by a random process. We extend the theory of records to treat not only
the variable where records happen, but also time as continuous. In this way, we
construct a fully symmetric theory of records leading to a number of new
results. Those analytic results are compared to the properties of a network
synthesized from earthquakes in Southern California. Significant disparities
from the ensemble of acausal networks that can be plausibly attributed to the
causal structure of seismicity are: (1) Invariance of network statistics with
the time span of the events considered, (2) Appearance of a fundamental length
scale for recurrences, independent of the time span of the catalog, which is
consistent with observations of the ``rupture length'', (3) Hierarchy in the
distances and times of subsequent recurrences.Comment: 19 pages, 13 figure
Evolution of Structure in the Intergalactic Medium and the Nature of the Ly-alpha Forest
We have performed a detailed statistical study of the evolution of structure
in a photoionized intergalactic medium (IGM) using analytical simulations to
extend the calculation into the mildly non-linear density regime found to
prevail at z = 3. Our work is based on a simple fundamental conjecture: that
the probability distribution function of the density of baryonic diffuse matter
in the universe is described by a lognormal (LN) random field. The LN field has
several attractive features and follows plausibly from the assumption of
initial linear Gaussian density and velocity fluctuations at arbitrarily early
times. Starting with a suitably normalized power spectrum of primordial fluc-
tuations in a universe dominated by cold dark matter (CDM), we compute the
behavior of the baryonic matter, which moves slowly toward minima in the dark
matter potential on scales larger than the Jeans length. We have computed two
models that succeed in matching observations. One is a non-standard CDM model
with Omega=1, h=0.5 and \Gamma=0.3, and the other is a low density flat model
with a cosmological constant(LCDM), with Omega=0.4, Omega_Lambda=0.6 and h=.65.
In both models, the variance of the density distribution function grows with
time, reaching unity at about z=4, where the simulation yields spectra that
closely resemble the Ly-alpha forest absorption seen in the spectra of high z
quasars. The calculations also successfully predict the observed properties of
the Ly-alpha forest clouds and their evolution from z=4 down to at least z=2,
assuming a constant intensity for the metagalactic UV background over this
redshift range. However, in our model the forest is not due to discrete clouds,
but rather to fluctuations in a continuous intergalactic medium. (This is an
abreviated abstract; the complete abstract is included with the manuscript.)Comment: Wrong Fig. 10 is corrected. Our custom made postscript is available
at ftp://hut4.pha.jhu.edu/incoming/igm, or contact Arthur Davidsen
([email protected]) for nice hardcopies; accepted for publication in Ap
Far-ultraviolet Spectroscopy of Venus and Mars at 4 A Resolution with the Hopkins Ultraviolet Telescope on Astro-2
Far-ultraviolet spectra of Venus and Mars in the range 820-1840 A at 4 A
resolution were obtained on 13 and 12 March 1995, respectively, by the Hopkins
Ultraviolet Telescope (HUT), which was part of the Astro-2 observatory on the
Space Shuttle Endeavour. Longward of 1250 A, the spectra of both planets are
dominated by emission of the CO Fourth Positive band system and strong OI and
CI multiplets. In addition, CO Hopfield-Birge bands, B - X (0,0) at 1151 A and
C - X (0,0) at 1088 A, are detected for the first time, and there is a weak
indication of the E - X (0,0) band at 1076 A in the spectrum of Venus. The B -
X band is blended with emission from OI 1152. Modeling the relative intensities
of these bands suggests that resonance fluorescence of CO is the dominant
source of the emission, as it is for the Fourth Positive system. Shortward of
Lyman-alpha, other emission features detected include OII 834, OI lambda 989,
HI Lyman-beta, and NI 1134 and 1200. For Venus, the derived disk brightnesses
of the OI, OII, and HI features are about one-half of those reported by Hord et
al. (1991) from Galileo EUV measurements made in February 1990. This result is
consistent with the expected variation from solar maximum to solar minimum. The
ArI 1048, 1066 doublet is detected only in the spectrum of Mars and the derived
mixing ratio of Ar is of the order of 2%, consistent with previous
determinations.Comment: 8 pages, 5 figures, accepted for publication in ApJ, July 20, 200
Evolution in random fitness landscapes: the infinite sites model
We consider the evolution of an asexually reproducing population in an
uncorrelated random fitness landscape in the limit of infinite genome size,
which implies that each mutation generates a new fitness value drawn from a
probability distribution . This is the finite population version of
Kingman's house of cards model [J.F.C. Kingman, \textit{J. Appl. Probab.}
\textbf{15}, 1 (1978)]. In contrast to Kingman's work, the focus here is on
unbounded distributions which lead to an indefinite growth of the
population fitness. The model is solved analytically in the limit of infinite
population size and simulated numerically for finite . When
the genome-wide mutation probability is small, the long time behavior of
the model reduces to a point process of fixation events, which is referred to
as a \textit{diluted record process} (DRP). The DRP is similar to the standard
record process except that a new record candidate (a number that exceeds all
previous entries in the sequence) is accepted only with a certain probability
that depends on the values of the current record and the candidate. We develop
a systematic analytic approximation scheme for the DRP. At finite the
fitness frequency distribution of the population decomposes into a stationary
part due to mutations and a traveling wave component due to selection, which is
shown to imply a reduction of the mean fitness by a factor of compared to
the limit.Comment: Dedicated to Thomas Nattermann on the occasion of his 60th birthday.
Submitted to JSTAT. Error in Section 3.2 was correcte
Structure of a large social network
We study a social network consisting of over individuals, with a
degree distribution exhibiting two power scaling regimes separated by a
critical degree , and a power law relation between degree and
local clustering. We introduce a growing random model based on a local
interaction mechanism that reproduces all of the observed scaling features and
their exponents. Our results lend strong support to the idea that several very
different networks are simultenously present in the human social network, and
these need to be taken into account for successful modeling.Comment: 5 pages, 5 figure
Possibility between earthquake and explosion seismogram differentiation by discrete stochastic non-Markov processes and local Hurst exponent analysis
The basic purpose of the paper is to draw the attention of researchers to new
possibilities of differentiation of similar signals having different nature.
One of examples of such kind of signals is presented by seismograms containing
recordings of earthquakes (EQ's) and technogenic explosions (TE's). We propose
here a discrete stochastic model for possible solution of a problem of strong
EQ's forecasting and differentiation of TE's from the weak EQ's. Theoretical
analysis is performed by two independent methods: with the use of statistical
theory of discrete non-Markov stochastic processes (Phys. Rev. E62,6178 (2000))
and the local Hurst exponent. Time recordings of seismic signals of the first
four dynamic orthogonal collective variables, six various plane of phase
portrait of four dimensional phase space of orthogonal variables and the local
Hurst exponent have been calculated for the dynamic analysis of the earth
states. The approaches, permitting to obtain an algorithm of strong EQ's
forecasting and to differentiate TE's from weak EQ's, have been developed.Comment: REVTEX +12 ps and jpg figures. Accepted for publication in Phys. Rev.
E, December 200
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