17,375 research outputs found
Rare events in networks with internal and external noise
We study rare events in networks with both internal and external noise, and
develop a general formalism for analyzing rare events that combines
pair-quenched techniques and large-deviation theory. The probability
distribution, shape, and time scale of rare events are considered in detail for
extinction in the Susceptible-Infected-Susceptible model as an illustration. We
find that when both types of noise are present, there is a crossover region as
the network size is increased, where the probability exponent for large
deviations no longer increases linearly with the network size. We demonstrate
that the form of the crossover depends on whether the endemic state is
localized near the epidemic threshold or not
Enhancing noise-induced switching times in systems with distributed delays
The paper addresses the problem of calculating the noise-induced switching rates in systems with
delay-distributed kernels and Gaussian noise. A general variational formulation for the switching
rate is derived for any distribution kernel, and the obtained equations of motion and boundary conditions
represent the most probable, or optimal, path, which maximizes the probability of escape.
Explicit analytical results for the switching rates for small mean time delays are obtained for the
uniform and bi-modal (or two-peak) distributions. They suggest that increasing the width of the distribution
leads to an increase in the switching times even for longer values of mean time delays for
both examples of the distribution kernel, and the increase is higher in the case of the two-peak distribution.
Analytical predictions are compared to the direct numerical simulations and show excellent
agreement between theory and numerical experiment
The Algebras of Large N Matrix Mechanics
Extending early work, we formulate the large N matrix mechanics of general
bosonic, fermionic and supersymmetric matrix models, including Matrix theory:
The Hamiltonian framework of large N matrix mechanics provides a natural
setting in which to study the algebras of the large N limit, including
(reduced) Lie algebras, (reduced) supersymmetry algebras and free algebras. We
find in particular a broad array of new free algebras which we call symmetric
Cuntz algebras, interacting symmetric Cuntz algebras, symmetric
Bose/Fermi/Cuntz algebras and symmetric Cuntz superalgebras, and we discuss the
role of these algebras in solving the large N theory. Most important, the
interacting Cuntz algebras are associated to a set of new (hidden) local
quantities which are generically conserved only at large N. A number of other
new large N phenomena are also observed, including the intrinsic nonlocality of
the (reduced) trace class operators of the theory and a closely related large N
field identification phenomenon which is associated to another set (this time
nonlocal) of new conserved quantities at large N.Comment: 70 pages, expanded historical remark
Scaling in activated escape of underdamped systems
Noise-induced escape from a metastable state of a dynamical system is studied
close to a saddle-node bifurcation point, but in the region where the system
remains underdamped. The activation energy of escape scales as a power of the
distance to the bifurcation point. We find two types of scaling and the
corresponding critical exponents.Comment: 9 page
Large rare fluctuations in systems with delayed dissipation
We study the probability distribution and the escape rate in systems with
delayed dissipation that comes from the coupling to a thermal bath. To
logarithmic accuracy in the fluctuation intensity, the problem is reduced to a
variational problem. It describes the most probable fluctuational paths, which
are given by acausal equations due to the delay. In thermal equilibrium, the
most probable path passing through a remote state has time reversal symmetry,
even though one cannot uniquely define a path that starts from a state with
given system coordinate and momentum. The corrections to the distribution and
the escape activation energy for small delay and small noise correlation time
are obtained in the explicit form.Comment: 9 page
Generalized Supersymmetric Perturbation Theory
Using the basic ingredient of supersymmetry, we develop a simple alternative
approach to perturbation theory in one-dimensional non-relativistic quantum
mechanics. The formulae for the energy shifts and wave functions do not involve
tedious calculations which appear in the available perturbation theories. The
model applicable in the same form to both the ground state and excited bound
states, unlike the recently introduced supersymmetric perturbation technique
which, together with other approaches based on logarithmic perturbation theory,
are involved within the more general framework of the present formalism.Comment: 13 pages article in LaTEX (uses standard article.sty). No Figures.
Sent to Ann. Physics (2004
Modeling urban street patterns
Urban streets patterns form planar networks whose empirical properties cannot
be accounted for by simple models such as regular grids or Voronoi
tesselations. Striking statistical regularities across different cities have
been recently empirically found, suggesting that a general and
details-independent mechanism may be in action. We propose a simple model based
on a local optimization process combined with ideas previously proposed in
studies of leaf pattern formation. The statistical properties of this model are
in good agreement with the observed empirical patterns. Our results thus
suggests that in the absence of a global design strategy, the evolution of many
different transportation networks indeed follow a simple universal mechanism.Comment: 4 pages, 5 figures, final version published in PR
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