2,079 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
Diversities and the Geometry of Hypergraphs
The embedding of finite metrics in has become a fundamental tool for
both combinatorial optimization and large-scale data analysis. One important
application is to network flow problems in which there is close relation
between max-flow min-cut theorems and the minimal distortion embeddings of
metrics into . Here we show that this theory can be generalized
considerably to encompass Steiner tree packing problems in both graphs and
hypergraphs. Instead of the theory of metrics and minimal distortion
embeddings, the parallel is the theory of diversities recently introduced by
Bryant and Tupper, and the corresponding theory of diversities and
embeddings which we develop here.Comment: 19 pages, no figures. This version: further small correction
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
- …