4,410 research outputs found
Connecting deterministic and stochastic metapopulation models
In this paper, we study the relationship between certain stochastic and
deterministic versions of Hanski's incidence function model and the spatially
realistic Levins model. We show that the stochastic version can be well
approximated in a certain sense by the deterministic version when the number of
habitat patches is large, provided that the presence or absence of individuals
in a given patch is influenced by a large number of other patches. Explicit
bounds on the deviation between the stochastic and deterministic models are
given.Comment: The final publication is available at Springer via
http://dx.doi.org/10.1007/s00285-015-0865-
Local approximation of a metapopulation's equilibrium
We consider the approximation of the equilibrium of a metapopulation model,
in which a finite number of patches are randomly distributed over a bounded
subset of Euclidean space. The approximation is good when a large
number of patches contribute to the colonization pressure on any given
unoccupied patch, and when the quality of the patches varies little over the
length scale determined by the colonization radius. If this is the case, the
equilibrium probability of a patch at being occupied is shown to be close
to , the equilibrium occupation probability in Levins's model, at any
point not too close to the boundary, if the local colonization
pressure and extinction rates appropriate to are assumed. The approximation
is justified by giving explicit upper and lower bounds for the occupation
probabilities, expressed in terms of the model parameters. Since the patches
are distributed randomly, the occupation probabilities are also random, and we
complement our bounds with explicit bounds on the probability that they are
satisfied at all patches simultaneously
Interacting vector fields in Relativity without Relativity
Barbour, Foster and \'{O} Murchadha have recently developed a new framework,
called here {\it{the 3-space approach}}, for the formulation of classical
bosonic dynamics. Neither time nor a locally Minkowskian structure of spacetime
are presupposed. Both arise as emergent features of the world from
geodesic-type dynamics on a space of 3-dimensional metric--matter
configurations. In fact gravity, the universal light cone and Abelian gauge
theory minimally coupled to gravity all arise naturally through a single common
mechanism. It yields relativity -- and more -- without presupposing relativity.
This paper completes the recovery of the presently known bosonic sector within
the 3-space approach. We show, for a rather general ansatz, that 3-vector
fields can interact among themselves only as Yang--Mills fields minimally
coupled to gravity.Comment: Replaced with final version accepted by Classical and Quantum Gravity
(14 pages, no figures
On the emergence of random initial conditions in fluid limits
The paper presents a phenomenon occurring in population processes that start
near zero and have large carrying capacity. By the classical result of
Kurtz~(1970), such processes, normalized by the carrying capacity, converge on
finite intervals to the solutions of ordinary differential equations, also
known as the fluid limit. When the initial population is small relative to
carrying capacity, this limit is trivial. Here we show that, viewed at suitably
chosen times increasing to infinity, the process converges to the fluid limit,
governed by the same dynamics, but with a random initial condition. This random
initial condition is related to the martingale limit of an associated linear
birth and death process
The Definition of Mach's Principle
Two definitions of Mach's principle are proposed. Both are related to gauge
theory, are universal in scope and amount to formulations of causality that
take into account the relational nature of position, time, and size. One of
them leads directly to general relativity and may have relevance to the problem
of creating a quantum theory of gravity.Comment: To be published in Foundations of Physics as invited contribution to
Peter Mittelstaedt's 80th Birthday Festschrift. 30 page
Leptons, quarks, and their antiparticles from a phase-space perspective
It is argued that antiparticles may be interpreted in macroscopic terms
without explicitly using the concept of time and its reversal. The appropriate
framework is that of nonrelativistic phase space. It is recalled that a quantum
version of this approach leads also, alongside the appearance of antiparticles,
to the emergence of `internal' quantum numbers identifiable with weak isospin,
weak hypercharge and colour, and to the derivation of the Gell-Mann-Nishijima
relation, while simultaneously offering a preonless interpretation of the
Harari-Shupe rishon model. Furthermore, it is shown that - under the assumption
of the additivity of canonical momenta - the approach entails the emergence of
string-like structures resembling mesons and baryons, thus providing a
different starting point for the discussion of quark unobservability.Comment: Talk given at Fifth Int. Workshop DICE2010 Space-Time-Matter,
Castiglioncello, Italy, September 13-17, 201
A law of large numbers approximation for Markov population processes with countably many types
When modelling metapopulation dynamics, the influence of a single patch on
the metapopulation depends on the number of individuals in the patch. Since the
population size has no natural upper limit, this leads to systems in which
there are countably infinitely many possible types of individual. Analogous
considerations apply in the transmission of parasitic diseases. In this paper,
we prove a law of large numbers for rather general systems of this kind,
together with a rather sharp bound on the rate of convergence in an
appropriately chosen weighted norm.Comment: revised version in response to referee comments, 34 page
Poisson approximations for the Ising model
A -dimensional Ising model on a lattice torus is considered. As the size
of the lattice tends to infinity, a Poisson approximation is given for the
distribution of the number of copies in the lattice of any given local
configuration, provided the magnetic field tends to and the
pair potential remains fixed. Using the Stein-Chen method, a bound is given
for the total variation error in the ferromagnetic case.Comment: 25 pages, 1 figur
Quenched QCD at finite density
Simulations of quenched at relatively small but {\it nonzero} chemical
potential on lattices indicate that the nucleon
screening mass decreases linearly as increases predicting a critical
chemical potential of one third the nucleon mass, , by extrapolation.
The meson spectrum does not change as increases over the same range, from
zero to . Past studies of quenched lattice QCD have suggested that
there is phase transition at . We provide alternative
explanations for these results, and find a number of technical reasons why
standard lattice simulation techniques suffer from greatly enhanced
fluctuations and finite size effects for ranging from to
. We find evidence for such problems in our simulations, and suggest
that they can be surmounted by improved measurement techniques.Comment: 23 pages, Revte
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