3,399 research outputs found
On Max-Stable Processes and the Functional D-Norm
We introduce a functional domain of attraction approach for stochastic
processes, which is more general than the usual one based on weak convergence.
The distribution function G of a continuous max-stable process on [0,1] is
introduced and it is shown that G can be represented via a norm on functional
space, called D-norm. This is in complete accordance with the multivariate case
and leads to the definition of functional generalized Pareto distributions
(GPD) W. These satisfy W=1+log(G) in their upper tails, again in complete
accordance with the uni- or multivariate case.
Applying this framework to copula processes we derive characterizations of
the domain of attraction condition for copula processes in terms of tail
equivalence with a functional GPD.
\delta-neighborhoods of a functional GPD are introduced and it is shown that
these are characterized by a polynomial rate of convergence of functional
extremes, which is well-known in the multivariate case.Comment: 22 page
Identification of evolutionarily conserved, functional noncoding elements in the promoter region of the sodium channel gene SCN8A
SCN8A is a major neuronal sodium channel gene expressed throughout the central and peripheral nervous systems. Mutations of SCN8A result in movement disorders and impaired cognition. To investigate the basis for the tissue-specific expression of SCN8A, we located conserved, potentially regulatory sequences in the human, mouse, chicken, and fish genes by 5′ RACE of brain RNA and genomic sequence comparison. A highly conserved 5′ noncoding exon, exon 1c, is present in vertebrates from fish to mammals and appears to define the ancestral promoter region. The distance from exon 1c to the first coding exon increased tenfold during vertebrate evolution, largely by insertion of repetitive elements. The mammalian gene acquired three novel, mutually exclusive noncoding exons that are not represented in the lower vertebrates. Within the shared exon 1c, we identified four short sequence elements of 10-20 bp with an unusually high level of evolutionary conservation. The conserved elements are most similar to consensus sites for the transcription factors Pou6f1/Brn5, YY1, and REST/NRSF. Introduction of mutations into the predicted Pou6f1 and REST sites reduced promoter activity in transfected neuronal cells. A 470-bp promoter fragment containing all of the conserved elements directed brain-specific expression of the LacZ reporter in transgenic mice. Transgene expression was highest in hippocampal neurons and cerebellar Purkinje cells, consistent with the expression of the endogenous gene. The compact cluster of conserved regulatory elements in SCN8A provides a useful target for molecular analysis of neuronal gene expression
Multiplicative processes and power laws
[Takayasu et al., Phys. Rev.Lett. 79, 966 (1997)] revisited the question of
stochastic processes with multiplicative noise, which have been studied in
several different contexts over the past decades. We focus on the regime, found
for a generic set of control parameters, in which stochastic processes with
multiplicative noise produce intermittency of a special kind, characterized by
a power law probability density distribution. We briefly explain the physical
mechanism leading to a power law pdf and provide a list of references for these
results dating back from a quarter of century. We explain how the formulation
in terms of the characteristic function developed by Takayasu et al. can be
extended to exponents , which explains the ``reason of the lucky
coincidence''. The multidimensional generalization of (\ref{eq1}) and the
available results are briefly summarized. The discovery of stretched
exponential tails in the presence of the cut-off introduced in \cite{Taka} is
explained theoretically. We end by briefly listing applications.Comment: Extended version (7 pages). Phys. Rev. E (to appear April 1998
A method for mechanical generation of radio frequency fields in nuclear magnetic resonance force microscopy
We present an innovative method for magnetic resonance force microscopy
(MRFM) with ultra-low dissipation, by using the higher modes of the mechanical
detector as radio frequency (rf) source. This method allows MRFM on samples
without the need to be close to an rf source. Furthermore, since rf sources
require currents that give dissipation, our method enables nuclear magnetic
resonance experiments at ultra-low temperatures. Removing the need for an
on-chip rf source is an important step towards a MRFM which can be widely used
in condensed matter physics.Comment: 7 pages, 5 figures, to be submitted to Physical Review Applie
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
Extreme value distributions and Renormalization Group
In the classical theorems of extreme value theory the limits of suitably
rescaled maxima of sequences of independent, identically distributed random
variables are studied. So far, only affine rescalings have been considered. We
show, however, that more general rescalings are natural and lead to new limit
distributions, apart from the Gumbel, Weibull, and Fr\'echet families. The
problem is approached using the language of Renormalization Group
transformations in the space of probability densities. The limit distributions
are fixed points of the transformation and the study of the differential around
them allows a local analysis of the domains of attraction and the computation
of finite-size corrections.Comment: 16 pages, 5 figures. Final versio
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