395 research outputs found
Strong and weak semiclassical limits for some rough Hamiltonians
We present several results concerning the semiclassical limit of the time
dependent Schr\"odinger equation with potentials whose regularity doesn't
guarantee the uniqueness of the underlying classical flow. Different topologies
for the limit are considered and the situation where two bicharateristics can
be obtained out of the same initial point is emphasized
Exact equations for smoothed Wigner transforms and homogenization of wave propagation
The Wigner Transform (WT) has been extensively used in the formulation of
phase-space models for a variety of wave propagation problems including
high-frequency limits, nonlinear and random waves. It is well known that the WT
features counterintuitive 'interference terms', which often make computation
impractical. In this connection, we propose the use of the smoothed Wigner
Transform (SWT), and derive new, exact equations for it, covering a broad class
of wave propagation problems. Equations for spectrograms are included as a
special case. The 'taming' of the interference terms by the SWT is illustrated,
and an asymptotic model for the Schroedinger equation is constructed and
numerically verified.Comment: 16 pages, 8 figure
Regional coherence evaluation in mild cognitive impairment and Alzheimer's disease based on adaptively extracted magnetoencephalogram rhythms
This study assesses the connectivity alterations caused by Alzheimer's disease (AD) and mild cognitive impairment (MCI) in magnetoencephalogram (MEG) background activity. Moreover, a novel methodology to adaptively extract brain rhythms from the MEG is introduced. This methodology relies on the ability of empirical mode decomposition to isolate local signal oscillations and constrained blind source separation to extract the activity that jointly represents a subset of channels. Inter-regional MEG connectivity was analysed for 36 AD, 18 MCI and 26 control subjects in δ, θ, α and β bands over left and right central, anterior, lateral and posterior regions with magnitude squared coherence—c(f). For the sake of comparison, c(f) was calculated from the original MEG channels and from the adaptively extracted rhythms. The results indicated that AD and MCI cause slight alterations in the MEG connectivity. Computed from the extracted rhythms, c(f) distinguished AD and MCI subjects from controls with 69.4% and 77.3% accuracies, respectively, in a full leave-one-out cross-validation evaluation. These values were higher than those obtained without the proposed extraction methodology
Spectral Analysis of Multi-dimensional Self-similar Markov Processes
In this paper we consider a discrete scale invariant (DSI) process with scale . We consider to have some fix number of
observations in every scale, say , and to get our samples at discrete points
where is obtained by the equality
and . So we provide a discrete time scale
invariant (DT-SI) process with parameter space . We find the spectral representation of the covariance function of
such DT-SI process. By providing harmonic like representation of
multi-dimensional self-similar processes, spectral density function of them are
presented. We assume that the process is also Markov
in the wide sense and provide a discrete time scale invariant Markov (DT-SIM)
process with the above scheme of sampling. We present an example of DT-SIM
process, simple Brownian motion, by the above sampling scheme and verify our
results. Finally we find the spectral density matrix of such DT-SIM process and
show that its associated -dimensional self-similar Markov process is fully
specified by where is
the covariance function of th and th observations of the process.Comment: 16 page
The Hurst Exponent of Fermi GRBs
Using a wavelet decomposition technique, we have extracted the Hurst exponent
for a sample of 46 long and 22 short Gamma-ray bursts (GRBs) detected by the
Gamma-ray Burst Monitor (GBM) aboard the Fermi satellite. This exponent is a
scaling parameter that provides a measure of long-range behavior in a time
series. The mean Hurst exponent for the short GRBs is significantly smaller
than that for the long GRBs. The separation may serve as an unbiased criterion
for distinguishing short and long GRBs.Comment: Accepted for publication in Monthly Notices of the Royal Astronomical
Societ
Time-frequency detection of Gravitational Waves
We present a time-frequency method to detect gravitational wave signals in
interferometric data. This robust method can detect signals from poorly modeled
and unmodeled sources. We evaluate the method on simulated data containing
noise and signal components. The noise component approximates initial LIGO
interferometer noise. The signal components have the time and frequency
characteristics postulated by Flanagan and Hughes for binary black hole
coalescence. The signals correspond to binaries with total masses between to and with (optimal filter) signal-to-noise ratios of 7
to 12. The method is implementable in real time, and achieves a coincident
false alarm rate for two detectors 1 per 475 years. At this false
alarm rate, the single detector false dismissal rate for our signal model is as
low as 5.3% at an SNR of 10. We expect to obtain similar or better detection
rates with this method for any signal of similar power that satisfies certain
adiabaticity criteria. Because optimal filtering requires knowledge of the
signal waveform to high precision, we argue that this method is likely to
detect signals that are undetectable by optimal filtering, which is at present
the best developed detection method for transient sources of gravitational
waves.Comment: 24 pages, 5 figures, uses REVTE
On the origin of intermittency in wave turbulence
Using standard signal processing tools, we experimentally report that
intermittency of wave turbulence on the surface of a fluid occurs even when two
typical large-scale coherent structures (gravity wave breakings and bursts of
capillary waves on steep gravity waves) are not taken into account. We also
show that intermittency depends on the power injected into the waves. The
dependence of the power-law exponent of the gravity-wave spectrum on the
forcing amplitude cannot be also ascribed to these coherent structures.
Statistics of these both events are studied.Comment: To be published in EP
Frequency decoding of periodically timed action potentials through distinct activity patterns in a random neural network
Frequency discrimination is a fundamental task of the auditory system. The
mammalian inner ear, or cochlea, provides a place code in which different
frequencies are detected at different spatial locations. However, a temporal
code based on spike timing is also available: action potentials evoked in an
auditory-nerve fiber by a low-frequency tone occur at a preferred phase of the
stimulus-they exhibit phase locking-and thus provide temporal information about
the tone's frequency. In an accompanying psychoacoustic study, and in agreement
with previous experiments, we show that humans employ this temporal information
for discrimination of low frequencies. How might such temporal information be
read out in the brain? Here we demonstrate that recurrent random neural
networks in which connections between neurons introduce characteristic time
delays, and in which neurons require temporally coinciding inputs for spike
initiation, can perform sharp frequency discrimination when stimulated with
phase-locked inputs. Although the frequency resolution achieved by such
networks is limited by the noise in phase locking, the resolution for realistic
values reaches the tiny frequency difference of 0.2% that has been measured in
humans.Comment: 16 pages, 5 figures, and supplementary informatio
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