390 research outputs found
Asymptotic analysis of first passage time in complex networks
The first passage time (FPT) distribution for random walk in complex networks
is calculated through an asymptotic analysis. For network with size and
short relaxation time , the computed mean first passage time (MFPT),
which is inverse of the decay rate of FPT distribution, is inversely
proportional to the degree of the destination. These results are verified
numerically for the paradigmatic networks with excellent agreement. We show
that the range of validity of the analytical results covers networks that have
short relaxation time and high mean degree, which turn out to be valid to many
real networks.Comment: 6 pages, 4 figures, 1 tabl
The fate of bezafibrate, carbamazepine, ciprofloxacin and clarithromycin in the wastewater treatment process
The progress of four pharmaceuticals (bezafibrate, carbamazepine, clarithromycin and ciprofloxacin) is followed through the treatment stages (screened sewage, settled sewage and final effluent) of a large urban wastewater treatment plant (WWTP) employing activated sludge treatment. Concentrations at the inlet to the WWTP are generally higher than those predicted from consideration of local pharmaceutical consumption and typical excretion data. Percentage removal efficiencies are variable (22.5 â 94.3%) with carbamazepine being the most resistant to elimination
Sources and pathways for pharmaceuticals in the urban water environment
The progress of five pharmaceutical compounds (bezafibrate, carbamazepine, diclofenac, ibuprofen and sulfasalazine) and one antibacterial agent (triclosan) were monitored through the treatment stages of a large sewage treatment works (STW) using activated sludge as well as in the receiving water both upstream and downstream of the effluent discharge. All except sulfasalazine were detected in the influent at concentrations ranging from 1.44-3.75 ”g/L. The analysis of prescription data has been used as a tool to predict the amount of pharmaceuticals potentially released into the catchment of the investigated sewage treatment works and the results compared with the measured influent concentrations. A reduction in concentration between influent and final effluent samples (51-97%) indicates the variable removal of these compounds and therefore their potential to be discharged into receiving surface waters. The analysis of primary and final effluents highlight the important processes involved in the removal of pharmaceuticals and indicate that sorption processes are important for bezafibrate, carbamazepine and diclofenac. These three PPCPs were observed at higher concentrations (0.07-0.35 ”g/L) downstream of the discharged effluent compared to upstream (0.02-0.04 ”g/L) although the risks that these compounds pose in the environment are not yet fully understood
Crossover between Levy and Gaussian regimes in first passage processes
We propose a new approach to the problem of the first passage time. Our
method is applicable not only to the Wiener process but also to the
non--Gaussian Lvy flights or to more complicated stochastic
processes whose distributions are stable. To show the usefulness of the method,
we particularly focus on the first passage time problems in the truncated
Lvy flights (the so-called KoBoL processes), in which the
arbitrarily large tail of the Lvy distribution is cut off. We
find that the asymptotic scaling law of the first passage time distribution
changes from -law (non-Gaussian Lvy
regime) to -law (Gaussian regime) at the crossover point. This result
means that an ultra-slow convergence from the non-Gaussian Lvy
regime to the Gaussian regime is observed not only in the distribution of the
real time step for the truncated Lvy flight but also in the
first passage time distribution of the flight. The nature of the crossover in
the scaling laws and the scaling relation on the crossover point with respect
to the effective cut-off length of the Lvy distribution are
discussed.Comment: 18pages, 7figures, using revtex4, to appear in Phys.Rev.
Desynchronization in diluted neural networks
The dynamical behaviour of a weakly diluted fully-inhibitory network of
pulse-coupled spiking neurons is investigated. Upon increasing the coupling
strength, a transition from regular to stochastic-like regime is observed. In
the weak-coupling phase, a periodic dynamics is rapidly approached, with all
neurons firing with the same rate and mutually phase-locked. The
strong-coupling phase is characterized by an irregular pattern, even though the
maximum Lyapunov exponent is negative. The paradox is solved by drawing an
analogy with the phenomenon of ``stable chaos'', i.e. by observing that the
stochastic-like behaviour is "limited" to a an exponentially long (with the
system size) transient. Remarkably, the transient dynamics turns out to be
stationary.Comment: 11 pages, 13 figures, submitted to Phys. Rev.
Noise Induced Complexity: From Subthreshold Oscillations to Spiking in Coupled Excitable Systems
We study stochastic dynamics of an ensemble of N globally coupled excitable
elements. Each element is modeled by a FitzHugh-Nagumo oscillator and is
disturbed by independent Gaussian noise. In simulations of the Langevin
dynamics we characterize the collective behavior of the ensemble in terms of
its mean field and show that with the increase of noise the mean field displays
a transition from a steady equilibrium to global oscillations and then, for
sufficiently large noise, back to another equilibrium. Diverse regimes of
collective dynamics ranging from periodic subthreshold oscillations to
large-amplitude oscillations and chaos are observed in the course of this
transition. In order to understand details and mechanisms of noise-induced
dynamics we consider a thermodynamic limit of the ensemble, and
derive the cumulant expansion describing temporal evolution of the mean field
fluctuations. In the Gaussian approximation this allows us to perform the
bifurcation analysis; its results are in good agreement with dynamical
scenarios observed in the stochastic simulations of large ensembles
Generalized Rate-Code Model for Neuron Ensembles with Finite Populations
We have proposed a generalized Langevin-type rate-code model subjected to
multiplicative noise, in order to study stationary and dynamical properties of
an ensemble containing {\it finite} neurons. Calculations using the
Fokker-Planck equation (FPE) have shown that owing to the multiplicative noise,
our rate model yields various kinds of stationary non-Gaussian distributions
such as gamma, inverse-Gaussian-like and log-normal-like distributions, which
have been experimentally observed. Dynamical properties of the rate model have
been studied with the use of the augmented moment method (AMM), which was
previously proposed by the author with a macroscopic point of view for
finite-unit stochastic systems. In the AMM, original -dimensional stochastic
differential equations (DEs) are transformed into three-dimensional
deterministic DEs for means and fluctuations of local and global variables.
Dynamical responses of the neuron ensemble to pulse and sinusoidal inputs
calculated by the AMM are in good agreement with those obtained by direct
simulation. The synchronization in the neuronal ensemble is discussed.
Variabilities of the firing rate and of the interspike interval (ISI) are shown
to increase with increasing the magnitude of multiplicative noise, which may be
a conceivable origin of the observed large variability in cortical neurons.Comment: 19 pages, 9 figures, accepted in Phys. Rev. E after minor
modification
First Passage Time Densities in Non-Markovian Models with Subthreshold Oscillations
Motivated by the dynamics of resonant neurons we consider a differentiable,
non-Markovian random process and particularly the time after which it
will reach a certain level . The probability density of this first passage
time is expressed as infinite series of integrals over joint probability
densities of and its velocity . Approximating higher order terms
of this series through the lower order ones leads to closed expressions in the
cases of vanishing and moderate correlations between subsequent crossings of
. For a linear oscillator driven by white or coloured Gaussian noise,
which models a resonant neuron, we show that these approximations reproduce the
complex structures of the first passage time densities characteristic for the
underdamped dynamics, where Markovian approximations (giving monotonous first
passage time distribution) fail
First Passage Time Densities in Resonate-and-Fire Models
Motivated by the dynamics of resonant neurons we discuss the properties of
the first passage time (FPT) densities for nonmarkovian differentiable random
processes. We start from an exact expression for the FPT density in terms of an
infinite series of integrals over joint densities of level crossings, and
consider different approximations based on truncation or on approximate
summation of this series. Thus, the first few terms of the series give good
approximations for the FPT density on short times. For rapidly decaying
correlations the decoupling approximations perform well in the whole time
domain.
As an example we consider resonate-and-fire neurons representing stochastic
underdamped or moderately damped harmonic oscillators driven by white Gaussian
or by Ornstein-Uhlenbeck noise. We show, that approximations reproduce all
qualitatively different structures of the FPT densities: from monomodal to
multimodal densities with decaying peaks. The approximations work for the
systems of whatever dimension and are especially effective for the processes
with narrow spectral density, exactly when markovian approximations fail.Comment: 11 pages, 8 figure
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