490 research outputs found
Exemplar Dynamics Models of the Stability of Phonological Categories
We develop a model for the stability and maintenance of phonological
categories. Examples of phonological categories are vowel sounds such as "i"
and "e". We model such categories as consisting of collections of labeled
exemplars that language users store in their memory. Each exemplar is a
detailed memory of an instance of the linguistic entity in question. Starting
from an exemplar-level model we derive integro-differential equations for the
long-term evolution of the density of exemplars in different portions of
phonetic space. Using these latter equations we investigate under what
conditions two phonological categories merge or not. Our main conclusion is
that for the preservation of distinct phonological categories, it is necessary
that anomalous speech tokens of a given category are discarded, and not merely
stored in memory as an exemplar of another category.Comment: 6 pages, COGS201
Phase Field Crystals as a Coarse-Graining in Time of Molecular Dynamics
Phase field crystals (PFC) are a tool for simulating materials at the atomic
level. They combine the small length-scale resolution of molecular dynamics
(MD) with the ability to simulate dynamics on mesoscopic time scales. We show
how PFC can be interpreted as the result of applying coarse-graining in time to
the microscopic density field of molecular dynamics simulations. We take the
form of the free energy for the phase field from the classical density
functional theory of inhomogeneous liquids and then choose coefficients to
match the structure factor of the time coarse-grained microscopic density
field. As an example, we show how to construct a PFC free energy for Weber and
Stillinger's two-dimensional square crystal potential which models a system of
proteins suspended in a membrane.Comment: 5 pages, 4 figures, typos corrected, more explanation in parts,
equilib vs non-equilib clarifie
Weak Convergence in the Prokhorov Metric of Methods for Stochastic Differential Equations
We consider the weak convergence of numerical methods for stochastic
differential equations (SDEs). Weak convergence is usually expressed in terms
of the convergence of expected values of test functions of the trajectories.
Here we present an alternative formulation of weak convergence in terms of the
well-known Prokhorov metric on spaces of random variables. For a general class
of methods, we establish bounds on the rates of convergence in terms of the
Prokhorov metric. In doing so, we revisit the original proofs of weak
convergence and show explicitly how the bounds on the error depend on the
smoothness of the test functions. As an application of our result, we use the
Strassen - Dudley theorem to show that the numerical approximation and the true
solution to the system of SDEs can be re-embedded in a probability space in
such a way that the method converges there in a strong sense. One corollary of
this last result is that the method converges in the Wasserstein distance,
another metric on spaces of random variables. Another corollary establishes
rates of convergence for expected values of test functions assuming only local
Lipschitz continuity. We conclude with a review of the existing results for
pathwise convergence of weakly converging methods and the corresponding strong
results available under re-embedding.Comment: 12 pages, 2nd revision for IMA J Numerical Analysis. Further minor
errors correcte
Complexity reduction of astrochemical networks
We present a new computational scheme aimed at reducing the complexity of the
chemical networks in astrophysical models, one which is shown to markedly
improve their computational efficiency. It contains a flux-reduction scheme
that permits to deal with both large and small systems. This procedure is shown
to yield a large speed-up of the corresponding numerical codes and provides
good accord with the full network results. We analyse and discuss two examples
involving chemistry networks of the interstellar medium and show that the
results from the present reduction technique reproduce very well the results
from fuller calculations.Comment: 9 pages, 7 figures, accepted for publication in Monthly Notices of
the Royal Astronomical Society Main Journa
Nonlinear evolution of dark matter and dark energy in the Chaplygin-gas cosmology
The hypothesis that dark matter and dark energy are unified through the
Chaplygin gas is reexamined. Using generalizations of the spherical model which
incorporate effects of the acoustic horizon we show that an initially
perturbative Chaplygin gas evolves into a mixed system containing cold dark
matter-like gravitational condensate.Comment: 11 pages, 3 figures, substantial revision, title changed, content
changed, added references, to appear in JCA
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