88 research outputs found
Extreme statistics for time series: Distribution of the maximum relative to the initial value
The extreme statistics of time signals is studied when the maximum is
measured from the initial value. In the case of independent, identically
distributed (iid) variables, we classify the limiting distribution of the
maximum according to the properties of the parent distribution from which the
variables are drawn. Then we turn to correlated periodic Gaussian signals with
a 1/f^alpha power spectrum and study the distribution of the maximum relative
height with respect to the initial height (MRH_I). The exact MRH_I distribution
is derived for alpha=0 (iid variables), alpha=2 (random walk), alpha=4 (random
acceleration), and alpha=infinity (single sinusoidal mode). For other,
intermediate values of alpha, the distribution is determined from simulations.
We find that the MRH_I distribution is markedly different from the previously
studied distribution of the maximum height relative to the average height for
all alpha. The two main distinguishing features of the MRH_I distribution are
the much larger weight for small relative heights and the divergence at zero
height for alpha>3. We also demonstrate that the boundary conditions affect the
shape of the distribution by presenting exact results for some non-periodic
boundary conditions. Finally, we show that, for signals arising from
time-translationally invariant distributions, the density of near extreme
states is the same as the MRH_I distribution. This is used in developing a
scaling theory for the threshold singularities of the two distributions.Comment: 29 pages, 4 figure
Renormalization group theory for finite-size scaling in extreme statistics
We present a renormalization group (RG) approach to explain universal
features of extreme statistics, applied here to independent, identically
distributed variables. The outlines of the theory have been described in a
previous Letter, the main result being that finite-size shape corrections to
the limit distribution can be obtained from a linearization of the RG
transformation near a fixed point, leading to the computation of stable
perturbations as eigenfunctions. Here we show details of the RG theory which
exhibit remarkable similarities to the RG known in statistical physics. Besides
the fixed points explaining universality, and the least stable eigendirections
accounting for convergence rates and shape corrections, the similarities
include marginally stable perturbations which turn out to be generic for the
Fisher-Tippett-Gumbel class. Distribution functions containing unstable
perturbations are also considered. We find that, after a transitory divergence,
they return to the universal fixed line at the same or at a different point
depending on the type of perturbation.Comment: 15 pages, 8 figures, to appear in Phys. Rev.
Strategies to maintain high-quality education and communication among the paediatric and neonatal intensive care community during the COVID-19 pandemic
Statistics of extremal intensities for Gaussian interfaces
The extremal Fourier intensities are studied for stationary
Edwards-Wilkinson-type, Gaussian, interfaces with power-law dispersion. We
calculate the probability distribution of the maximal intensity and find that,
generically, it does not coincide with the distribution of the integrated power
spectrum (i.e. roughness of the surface), nor does it obey any of the known
extreme statistics limit distributions. The Fisher-Tippett-Gumbel limit
distribution is, however, recovered in three cases: (i) in the non-dispersive
(white noise) limit, (ii) for high dimensions, and (iii) when only
short-wavelength modes are kept. In the last two cases the limit distribution
emerges in novel scenarios.Comment: 15 pages, including 7 ps figure
Finite-size scaling in extreme statistics
We study the convergence and shape correction to the limit distributions of
extreme values due to the finite size (FS) of data sets. A renormalization
method is introduced for the case of independent, identically distributed (iid)
variables, showing that the iid universality classes are subdivided according
to the exponent of the FS convergence, which determines the leading order FS
shape correction function as well. We find that, for the correlated systems of
subcritical percolation and 1/f^alpha stationary (alpha<1) noise, the iid shape
correction compares favorably to simulations. Furthermore, for the strongly
correlated regime (alpha>1) of 1/f^alpha noise, the shape correction is
obtained in terms of the limit distribution itself.Comment: 4 pages, 3 figure
Maximal height statistics for 1/f^alpha signals
Numerical and analytical results are presented for the maximal relative
height distribution of stationary periodic Gaussian signals (one dimensional
interfaces) displaying a 1/f^alpha power spectrum. For 0<alpha<1 (regime of
decaying correlations), we observe that the mathematically established limiting
distribution (Fisher-Tippett-Gumbel distribution) is approached extremely
slowly as the sample size increases. The convergence is rapid for alpha>1
(regime of strong correlations) and a highly accurate picture gallery of
distribution functions can be constructed numerically. Analytical results can
be obtained in the limit alpha -> infinity and, for large alpha, by
perturbation expansion. Furthermore, using path integral techniques we derive a
trace formula for the distribution function, valid for alpha=2n even integer.
From the latter we extract the small argument asymptote of the distribution
function whose analytic continuation to arbitrary alpha > 1 is found to be in
agreement with simulations. Comparison of the extreme and roughness statistics
of the interfaces reveals similarities in both the small and large argument
asymptotes of the distribution functions.Comment: 17 pages, 8 figures, RevTex
Diffusion in normal and critical transient chaos
In this paper we investigate deterministic diffusion in systems which are
spatially extended in certain directions but are restricted in size and open in
other directions, consequently particles can escape. We introduce besides the
diffusion coefficient D on the chaotic repeller a coefficient which
measures the broadening of the distribution of trajectories during the
transient chaotic motion. Both coefficients are explicitly computed for
one-dimensional models, and they are found to be different in most cases. We
show furthermore that a jump develops in both of the coefficients for most of
the initial distributions when we approach the critical borderline where the
escape rate equals the Liapunov exponent of a periodic orbit.Comment: 4 pages Revtex file in twocolumn format with 2 included postscript
figure
1/f Noise and Extreme Value Statistics
We study the finite-size scaling of the roughness of signals in systems
displaying Gaussian 1/f power spectra. It is found that one of the extreme
value distributions (Gumbel distribution) emerges as the scaling function when
the boundary conditions are periodic. We provide a realistic example of
periodic 1/f noise, and demonstrate by simulations that the Gumbel distribution
is a good approximation for the case of nonperiodic boundary conditions as
well. Experiments on voltage fluctuations in GaAs films are analyzed and
excellent agreement is found with the theory.Comment: 4 pages, 4 postscript figures, RevTe
Roughness distributions for 1/f^alpha signals
The probability density function (PDF) of the roughness, i.e., of the
temporal variance, of 1/f^alpha noise signals is studied. Our starting point is
the generalization of the model of Gaussian, time-periodic, 1/f noise,
discussed in our recent Letter [T. Antal et al., PRL, vol. 87, 240601 (2001)],
to arbitrary power law. We investigate three main scaling regions,
distinguished by the scaling of the cumulants in terms of the microscopic scale
and the total length of the period. Various analytical representations of the
PDF allow for a precise numerical evaluation of the scaling function of the PDF
for any alpha. A simulation of the periodic process makes it possible to study
also non-periodic signals on short intervals embedded in the full period. We
find that for alpha=<1/2 the scaled PDF-s in both the periodic and the
non-periodic cases are Gaussian, but for alpha>1/2 they differ from the
Gaussian and from each other. Both deviations increase with growing alpha. That
conclusion, based on numerics, is reinforced by analytic results for alpha=2
and alpha->infinity. We suggest that our theoretical and numerical results open
a new perspective on the data analysis of 1/f^alpha processes.Comment: 12 pages incl. 6 figures, with RevTex4, for A4 paper, in v2 some
references were correcte
Atherosclerosis of the descending aorta predicts cardiovascular events: a transesophageal echocardiography study
PURPOSE: Previous studies have shown that atherosclerosis of the descending aorta detected by transesophageal echocardiography (TEE) is a good marker of coexisting coronary artery disease. The aim of our study was to evaluate whether the presence of atherosclerosis on the descending aorta during TEE has any prognostic impact in predicting cardiovascular events. MATERIAL AND METHODS: The study group consisted of 238 consecutive in-hospital patients referred for TEE testing (135 males, 103 females, mean age 58 +/- 11 years) with a follow up of 24 months. The atherosclerotic lesions of the descending aorta were scored from 0 (no atherosclerosis) to 3 (plaque >5 mm and/or "complex" plaque with ulcerated or mobile parts). RESULTS: Atherosclerosis was observed in 102 patients, (grade 3 in 16, and grade 2 in 86 patients) whereas 136 patients only had an intimal thickening or normal intimal surface. There were 57 cardiovascular events in the follow-up period. The number of events was higher in the 102 patients with (n = 34) than in the 136 patients without atherosclerosis (n = 23, p < 0.01). The frequency of events was in close correlation with the severity of the atherosclerosis of the descending aorta. Fifty percent of the patients with grade 3 experienced cardiovascular events. Excluding patients with subsequent revascularization, the multivariate analysis only left ventricular function with EF < 40% (HR 3.0, CI 1.3–7.1) and TEE atherosclerotic plaque >=2 (HR 2.4, CI 1.0–5.5) predicted hard cardiovascular events. CONCLUSION: Atherosclerosis of the descending aorta observed during transesophageal echocardiography is a useful predictor of cardiovascular events
- …