11,770 research outputs found
A new model for evolution in a spatial continuum
We investigate a new model for populations evolving in a spatial continuum.
This model can be thought of as a spatial version of the Lambda-Fleming-Viot
process. It explicitly incorporates both small scale reproduction events and
large scale extinction-recolonisation events. The lineages ancestral to a
sample from a population evolving according to this model can be described in
terms of a spatial version of the Lambda-coalescent. Using a technique of
Evans(1997), we prove existence and uniqueness in law for the model. We then
investigate the asymptotic behaviour of the genealogy of a finite number of
individuals sampled uniformly at random (or more generally `far enough apart')
from a two-dimensional torus of side L as L tends to infinity. Under
appropriate conditions (and on a suitable timescale), we can obtain as limiting
genealogical processes a Kingman coalescent, a more general Lambda-coalescent
or a system of coalescing Brownian motions (with a non-local coalescence
mechanism).Comment: 63 pages, version accepted to Electron. J. Proba
Coalescent simulation in continuous space:Algorithms for large neighbourhood size
Many species have an essentially continuous distribution in space, in which there are no natural divisions between randomly mating subpopulations. Yet, the standard approach to modelling these populations is to impose an arbitrary grid of demes, adjusting deme sizes and migration rates in an attempt to capture the important features of the population. Such indirect methods are required because of the failure of the classical models of isolation by distance, which have been shown to have major technical flaws. A recently introduced model of extinction and recolonisation in two dimensions solves these technical problems, and provides a rigorous technical foundation for the study of populations evolving in a spatial continuum. The coalescent process for this model is simply stated, but direct simulation is very inefficient for large neighbourhood sizes. We present efficient and exact algorithms to simulate this coalescent process for arbitrary sample sizes and numbers of loci, and analyse these algorithms in detail
A Heavy Fermion Can Create a Soliton: A 1+1 Dimensional Example
We show that quantum effects can stabilize a soliton in a model with no
soliton at the classical level. The model has a scalar field chirally coupled
to a fermion in 1+1 dimensions. We use a formalism that allows us to calculate
the exact one loop fermion contribution to the effective energy for a spatially
varying scalar background. This energy includes the contribution from
counterterms fixed in the perturbative sector of the theory. The resulting
energy is therefore finite and unambiguous. A variational search then yields a
fermion number one configuration whose energy is below that of a single free
fermion.Comment: 10 pages, RevTeX, 2 figures composed from 4 .eps files; v2: fixed
minor errors, added reference; v3: corrected reference added in v
Ultra-high-sensitivity two-dimensional bend sensor
A multicore fibre Fabry-Perot-based strain sensor interrogated with tandem interferometry for bend measurement is described. Curvature in two dimensions is obtained by measuring the difference in strain between three co-located low finesse Fabry-Perot interferometers formed in each core of the fibre by pairs of Bragg gratings. This sensor provides a responsivity enhancement of up to 30 times that of a previously reported fibre Bragg grating based sensor. Strain resolutions of 0.6 n epsilon/Hz(1/2) above 1 Hz are demonstrated, which corresponds to a curvature resolution of similar to 0.012 km(-1)/Hz(1/2)
The infinitesimal model with dominance
The classical infinitesimal model is a simple and robust model for the
inheritance of quantitative traits. In this model, a quantitative trait is
expressed as the sum of a genetic and a non-genetic (environmental) component
and the genetic component of offspring traits within a family follows a normal
distribution around the average of the parents' trait values, and has a
variance that is independent of the trait values of the parents. In previous
work, Barton et al.(2017), we showed that when trait values are determined by
the sum of a large number of Mendelian factors, each of small effect, one can
justify the infinitesimal model as limit of Mendelian inheritance.
In this paper, we show that the robustness of the infinitesimal model extends
to include dominance. We define the model in terms of classical quantities of
quantitative genetics, before justifying it as a limit of Mendelian inheritance
as the number, M, of underlying loci tends to infinity. As in the additive
case, the multivariate normal distribution of trait values across the pedigree
can be expressed in terms of variance components in an ancestral population and
identities determined by the pedigree. In this setting, it is natural to
decompose trait values, not just into the additive and dominance components,
but into a component that is shared by all individuals within the family and an
independent `residual' for each offspring, which captures the randomness of
Mendelian inheritance. We show that, even if we condition on parental trait
values, both the shared component and the residuals within each family will be
asymptotically normally distributed as the number of loci tends to infinity,
with an error of order 1/\sqrt{M}.
We illustrate our results with some numerical examples.Comment: 62 pages, 8 figure
Greenstone belts: Their components and structure
Greenstone sucessions are defined as the nongranitoid component of granitoid-greenstone terrain and are linear to irregular in shape and where linear are termed belts. The chemical composition of greenstones is described. Also discussed are the continental environments of greenstone successions. The effects of contact with granitoids, geophysical properties, recumbent folds and late formation structures upon greenstones are examined. Large stratigraphy thicknesses are explained
`Operational' Energy Conditions
I show that a quantized Klein-Gordon field in Minkowski space obeys an
`operational' weak energy condition: the energy of an isolated device
constructed to measure or trap the energy in a region, plus the energy it
measures or traps, cannot be negative. There are good reasons for thinking that
similar results hold locally for linear quantum fields in curved space-times. A
thought experiment to measure energy density is analyzed in some detail, and
the operational positivity is clearly manifested.
If operational energy conditions do hold for quantum fields, then the
negative energy densities predicted by theory have a will-o'-the-wisp
character: any local attempt to verify a total negative energy density will be
self-defeating on account of quantum measurement difficulties. Similarly,
attempts to drive exotic effects (wormholes, violations of the second law,
etc.) by such densities may be defeated by quantum measurement problems. As an
example, I show that certain attempts to violate the Cosmic Censorship
principle by negative energy densities are defeated.
These quantum measurement limitations are investigated in some detail, and
are shown to indicate that space-time cannot be adequately modeled classically
in negative energy density regimes.Comment: 18 pages, plain Tex, IOP macros. Expanded treatment of measurement
problems for space-time, with implications for Cosmic Censorship as an
example. Accepted by Classical and Quantum Gravit
Testing Closed String Field Theory with Marginal Fields
We study the feasibility of level expansion and test the quartic vertex of
closed string field theory by checking the flatness of the potential in
marginal directions. The tests, which work out correctly, require the
cancellation of two contributions: one from an infinite-level computation with
the cubic vertex and the other from a finite-level computation with the quartic
vertex. The numerical results suggest that the quartic vertex contributions are
comparable or smaller than those of level four fields.Comment: 14 pages, LaTeX. v2: New references to work of Beccaria and Rampino,
and Taylor. Improved numerical analysis at the end of section
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