443 research outputs found
Validation and Calibration of Models for Reaction-Diffusion Systems
Space and time scales are not independent in diffusion. In fact, numerical
simulations show that different patterns are obtained when space and time steps
( and ) are varied independently. On the other hand,
anisotropy effects due to the symmetries of the discretization lattice prevent
the quantitative calibration of models. We introduce a new class of explicit
difference methods for numerical integration of diffusion and
reaction-diffusion equations, where the dependence on space and time scales
occurs naturally. Numerical solutions approach the exact solution of the
continuous diffusion equation for finite and , if the
parameter assumes a fixed constant value,
where is an odd positive integer parametrizing the alghorithm. The error
between the solutions of the discrete and the continuous equations goes to zero
as and the values of are dimension
independent. With these new integration methods, anisotropy effects resulting
from the finite differences are minimized, defining a standard for validation
and calibration of numerical solutions of diffusion and reaction-diffusion
equations. Comparison between numerical and analytical solutions of
reaction-diffusion equations give global discretization errors of the order of
in the sup norm. Circular patterns of travelling waves have a maximum
relative random deviation from the spherical symmetry of the order of 0.2%, and
the standard deviation of the fluctuations around the mean circular wave front
is of the order of .Comment: 33 pages, 8 figures, to appear in Int. J. Bifurcation and Chao
Non-Markovian Levy diffusion in nonhomogeneous media
We study the diffusion equation with a position-dependent, power-law
diffusion coefficient. The equation possesses the Riesz-Weyl fractional
operator and includes a memory kernel. It is solved in the diffusion limit of
small wave numbers. Two kernels are considered in detail: the exponential
kernel, for which the problem resolves itself to the telegrapher's equation,
and the power-law one. The resulting distributions have the form of the L\'evy
process for any kernel. The renormalized fractional moment is introduced to
compare different cases with respect to the diffusion properties of the system.Comment: 7 pages, 2 figure
Suppressor of sable [Su(s)] and Wdr82 down-regulate RNA from heat-shock-inducible repetitive elements by a mechanism that involves transcription termination
Although RNA polymerase II (Pol II) productively transcribes very long genes in vivo, transcription through extragenic sequences often terminates in the promoter-proximal region and the nascent RNA is degraded. Mechanisms that induce early termination and RNA degradation are not well understood in multicellular organisms. Here, we present evidence that the suppressor of sable [su(s)] regulatory pathway of Drosophila melanogaster plays a role in this process. We previously showed that Su(s) promotes exosome-mediated degradation of transcripts from endogenous repeated elements at an Hsp70 locus (Hsp70-αβ elements). In this report, we identify Wdr82 as a component of this process and show that it works with Su(s) to inhibit Pol II elongation through Hsp70-αβ elements. Furthermore, we show that the unstable transcripts produced during this process are polyadenylated at heterogeneous sites that lack canonical polyadenylation signals. We define two distinct regions that mediate this regulation. These results indicate that the Su(s) pathway promotes RNA degradation and transcription termination through a novel mechanism
Non-equilibrium Phase Transitions with Long-Range Interactions
This review article gives an overview of recent progress in the field of
non-equilibrium phase transitions into absorbing states with long-range
interactions. It focuses on two possible types of long-range interactions. The
first one is to replace nearest-neighbor couplings by unrestricted Levy flights
with a power-law distribution P(r) ~ r^(-d-sigma) controlled by an exponent
sigma. Similarly, the temporal evolution can be modified by introducing waiting
times Dt between subsequent moves which are distributed algebraically as P(Dt)~
(Dt)^(-1-kappa). It turns out that such systems with Levy-distributed
long-range interactions still exhibit a continuous phase transition with
critical exponents varying continuously with sigma and/or kappa in certain
ranges of the parameter space. In a field-theoretical framework such
algebraically distributed long-range interactions can be accounted for by
replacing the differential operators nabla^2 and d/dt with fractional
derivatives nabla^sigma and (d/dt)^kappa. As another possibility, one may
introduce algebraically decaying long-range interactions which cannot exceed
the actual distance to the nearest particle. Such interactions are motivated by
studies of non-equilibrium growth processes and may be interpreted as Levy
flights cut off at the actual distance to the nearest particle. In the
continuum limit such truncated Levy flights can be described to leading order
by terms involving fractional powers of the density field while the
differential operators remain short-ranged.Comment: LaTeX, 39 pages, 13 figures, minor revision
Factors associated with failed treatment : an analysis of 121,744 women embarking on their first IVF cycles
Peer reviewedPublisher PD
Branching and annihilating Levy flights
We consider a system of particles undergoing the branching and annihilating
reactions A -> (m+1)A and A + A -> 0, with m even. The particles move via
long-range Levy flights, where the probability of moving a distance r decays as
r^{-d-sigma}. We analyze this system of branching and annihilating Levy flights
(BALF) using field theoretic renormalization group techniques close to the
upper critical dimension d_c=sigma, with sigma<2. These results are then
compared with Monte-Carlo simulations in d=1. For sigma close to unity in d=1,
the critical point for the transition from an absorbing to an active phase
occurs at zero branching. However, for sigma bigger than about 3/2 in d=1, the
critical branching rate moves smoothly away from zero with increasing sigma,
and the transition lies in a different universality class, inaccessible to
controlled perturbative expansions. We measure the exponents in both
universality classes and examine their behavior as a function of sigma.Comment: 9 pages, 4 figure
Perturbative Linearization of Reaction-Diffusion Equations
We develop perturbative expansions to obtain solutions for the initial-value
problems of two important reaction-diffusion systems, viz., the Fisher equation
and the time-dependent Ginzburg-Landau (TDGL) equation. The starting point of
our expansion is the corresponding singular-perturbation solution. This
approach transforms the solution of nonlinear reaction-diffusion equations into
the solution of a hierarchy of linear equations. Our numerical results
demonstrate that this hierarchy rapidly converges to the exact solution.Comment: 13 pages, 4 figures, latex2
Electrophysiological correlates of high-level perception during spatial navigation
We studied the electrophysiological basis of object recognition by recording scalp\ud
electroencephalograms while participants played a virtual-reality taxi driver game.\ud
Participants searched for passengers and stores during virtual navigation in simulated\ud
towns. We compared oscillatory brain activity in response to store views that were targets or\ud
nontargets (during store search) or neutral (during passenger search). Even though store\ud
category was solely defined by task context (rather than by sensory cues), frontal ...\ud
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Analysis of a spatial Lotka-Volterra model with a finite range predator-prey interaction
We perform an analysis of a recent spatial version of the classical
Lotka-Volterra model, where a finite scale controls individuals' interaction.
We study the behavior of the predator-prey dynamics in physical spaces higher
than one, showing how spatial patterns can emerge for some values of the
interaction range and of the diffusion parameter.Comment: 7 pages, 7 figure
Are Damage Spreading Transitions Generically in the Universality Class of Directed Percolation?
We present numerical evidence for the fact that the damage spreading
transition in the Domany-Kinzel automaton found by Martins {\it et al.} is in
the same universality class as directed percolation. We conjecture that also
other damage spreading transitions should be in this universality class, unless
they coincide with other transitions (as in the Ising model with Glauber
dynamics) and provided the probability for a locally damaged state to become
healed is not zero.Comment: 10 pages, LATE
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