193 research outputs found
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
Total variation approximation for quasi-equilibrium distributions
Quasi-stationary distributions, as discussed by Darroch & Seneta (1965), have
been used in biology to describe the steady state behaviour of population
models which, while eventually certain to become extinct, nevertheless maintain
an apparent stochastic equilibrium for long periods. These distributions have
some drawbacks: they need not exist, nor be unique, and their calculation can
present problems. In this paper, we give biologically plausible conditions
under which the quasi-stationary distribution is unique, and can be closely
approximated by distributions that are simple to compute.Comment: 16 page
Estimation of the transmission dynamics of Theileria equi and Babesia caballi in horses
For the evaluation of the epidemiology of Theileria equi and Babesia caballi in a herd of 510 horses in SW Mongolia, several mathematical models of the transmission dynamics were constructed. Because the field data contain information on the presence of the parasite (determined by PCR) and the presence of antibodies (determined by IFAT), the models cater for maternal protection with antibodies, susceptible animals, infected animals and animals which have eliminated the parasite and also allow for age-dependent infection in susceptible animals. Maximum likelihood estimation procedures were used to estimate the model parameters and a Monte Carlo approach was applied to select the best fitting model. Overall, the results are in line with previous experimental work, and add evidence that the epidemiology of T. equi differs from that of Babesia spp. The presented modelling approach provides a useful tool for the investigation of some vector-borne diseases and the applied model selection procedure avoids asymptotical assumptions that may not be adequate for the analysis of epidemiological field dat
Genetic differentiation in Scottish populations of the pine beauty moth Panolis flammea (Lepidoptera: Noctuidae)
Pine beauty moth, Panolis flammea (Denis & Schiffermüller), is a recent but persistent pest of lodgepole pine plantations in Scotland, but exists naturally at low levels within remnants and plantations of Scots pine. To test whether separate host races occur in lodgepole and Scots pine stands and to examine colonization dynamics, allozyme, randomly amplified polymorphic DNA (RAPD) and mitochondrial variation were screened within a range of Scottish samples. RAPD analysis indicated limited long distance dispersal (FST = 0.099), and significant isolation by distance (P < 0.05); but that colonization between more proximate populations was often variable, from extensive to limited exchange. When compared with material from Germany, Scottish samples were found to be more diverse and significantly differentiated for all markers. For mtDNA, two highly divergent groups of haplotypes were evident, one group contained both German and Scottish samples and the other was predominantly Scottish. No genetic differentiation was evident between P. flammea populations sampled from different hosts, and no diversity bottleneck was observed in the lodgepole group. Indeed, lodgepole stands appear to have been colonized on multiple occasions from Scots pine sources and neighbouring populations on different hosts are close to panmixia.A.J. Lowe, B.J. Hicks, K. Worley, R.A. Ennos, J.D. Morman, G. Stone and A.D. Wat
Smallest small-world network
Efficiency in passage times is an important issue in designing networks, such
as transportation or computer networks. The small-world networks have
structures that yield high efficiency, while keeping the network highly
clustered. We show that among all networks with the small-world structure, the
most efficient ones have a single ``center'', from which all shortcuts are
connected to uniformly distributed nodes over the network. The networks with
several centers and a connected subnetwork of shortcuts are shown to be
``almost'' as efficient. Genetic-algorithm simulations further support our
results.Comment: 5 pages, 6 figures, REVTeX
Variations on the Seventh Route to Relativity
As motivated in the full abstract, this paper further investigates Barbour,
Foster and O Murchadha (BFO)'s 3-space formulation of GR. This is based on
best-matched lapse-eliminated actions and gives rise to several theories
including GR and a conformal gravity theory. We study the simplicity postulates
assumed in BFO's work and how to weaken them, so as to permit the inclusion of
the full set of matter fields known to occur in nature.
We study the configuration spaces of gravity-matter systems upon which BFO's
formulation leans. In further developments the lapse-eliminated actions used by
BFO become impractical and require generalization. We circumvent many of these
problems by the equivalent use of lapse-uneliminated actions, which furthermore
permit us to interpret BFO's formulation within Kuchar's generally covariant
hypersurface framework. This viewpoint provides alternative reasons to BFO's as
to why the inclusion of bosonic fields in the 3-space approach gives rise to
minimally-coupled scalar fields, electromagnetism and Yang--Mills theory. This
viewpoint also permits us to quickly exhibit further GR-matter theories
admitted by the 3-space formulation. In particular, we show that the spin-1/2
fermions of the theories of Dirac, Maxwell--Dirac and Yang--Mills--Dirac, all
coupled to GR, are admitted by the generalized 3-space formulation we present.
Thus all the known fundamental matter fields can be accommodated. This
corresponds to being able to pick actions for all these theories which have
less kinematics than suggested by the generally covariant hypersurface
framework. For all these theories, Wheeler's thin sandwich conjecture may be
posed, rendering them timeless in Barbour's sense.Comment: Revtex version; Journal-ref adde
The Fourier Transform of Poisson Multinomial Distributions and its Algorithmic Applications
An -Poisson Multinomial Distribution (PMD) is a random variable of
the form , where the 's are independent random
vectors supported on the set of standard basis vectors in In
this paper, we obtain a refined structural understanding of PMDs by analyzing
their Fourier transform. As our core structural result, we prove that the
Fourier transform of PMDs is {\em approximately sparse}, i.e., roughly
speaking, its -norm is small outside a small set. By building on this
result, we obtain the following applications:
{\bf Learning Theory.} We design the first computationally efficient learning
algorithm for PMDs with respect to the total variation distance. Our algorithm
learns an arbitrary -PMD within variation distance using a
near-optimal sample size of and runs in time
Previously, no algorithm with a
runtime was known, even for
{\bf Game Theory.} We give the first efficient polynomial-time approximation
scheme (EPTAS) for computing Nash equilibria in anonymous games. For normalized
anonymous games with players and strategies, our algorithm computes a
well-supported -Nash equilibrium in time The best
previous algorithm for this problem had running time
where , for any
{\bf Statistics.} We prove a multivariate central limit theorem (CLT) that
relates an arbitrary PMD to a discretized multivariate Gaussian with the same
mean and covariance, in total variation distance. Our new CLT strengthens the
CLT of Valiant and Valiant by completely removing the dependence on in the
error bound.Comment: 68 pages, full version of STOC 2016 pape
Survival of branching random walks in random environment
We study survival of nearest-neighbour branching random walks in random
environment (BRWRE) on . A priori there are three different
regimes of survival: global survival, local survival, and strong local
survival. We show that local and strong local survival regimes coincide for
BRWRE and that they can be characterized with the spectral radius of the first
moment matrix of the process. These results are generalizations of the
classification of BRWRE in recurrent and transient regimes. Our main result is
a characterization of global survival that is given in terms of Lyapunov
exponents of an infinite product of i.i.d. random matrices.Comment: 17 pages; to appear in Journal of Theoretical Probabilit
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