1,877 research outputs found
Enhanced electron correlations at the SrxCa1-xVO3 surface
We report hard x-ray photoemission spectroscopy measurements of the
electronic structure of the prototypical correlated oxide SrxCa1-xVO3. By
comparing spectra recorded at different excitation energies, we show that 2.2
keV photoelectrons contain a substantial surface component, whereas 4.2 keV
photoelectrons originate essentially from the bulk of the sample.
Bulk-sensitive measurements of the O 2p valence band are found to be in good
agreement with ab initio calculations of the electronic structure, with some
modest adjustments to the orbital-dependent photoionization cross sections. The
evolution of the O 2p electronic structure as a function of the Sr content is
dominated by A-site hybridization. Near the Fermi level, the correlated V 3d
Hubbard bands are found to evolve in both binding energy and spectral weight as
a function of distance from the vacuum interface, revealing higher correlation
at the surface than in the bulk
Stochastic Chemical Reactions in Micro-domains
Traditional chemical kinetics may be inappropriate to describe chemical
reactions in micro-domains involving only a small number of substrate and
reactant molecules. Starting with the stochastic dynamics of the molecules, we
derive a master-diffusion equation for the joint probability density of a
mobile reactant and the number of bound substrate in a confined domain. We use
the equation to calculate the fluctuations in the number of bound substrate
molecules as a function of initial reactant distribution. A second model is
presented based on a Markov description of the binding and unbinding and on the
mean first passage time of a molecule to a small portion of the boundary. These
models can be used for the description of noise due to gating of ionic channels
by random binding and unbinding of ligands in biological sensor cells, such as
olfactory cilia, photo-receptors, hair cells in the cochlea.Comment: 33 pages, Journal Chemical Physic
Transition probabilities for general birth-death processes with applications in ecology, genetics, and evolution
A birth-death process is a continuous-time Markov chain that counts the
number of particles in a system over time. In the general process with
current particles, a new particle is born with instantaneous rate
and a particle dies with instantaneous rate . Currently no robust and
efficient method exists to evaluate the finite-time transition probabilities in
a general birth-death process with arbitrary birth and death rates. In this
paper, we first revisit the theory of continued fractions to obtain expressions
for the Laplace transforms of these transition probabilities and make explicit
an important derivation connecting transition probabilities and continued
fractions. We then develop an efficient algorithm for computing these
probabilities that analyzes the error associated with approximations in the
method. We demonstrate that this error-controlled method agrees with known
solutions and outperforms previous approaches to computing these probabilities.
Finally, we apply our novel method to several important problems in ecology,
evolution, and genetics
Age-Appropriate Augmented Cognitive Behavior Therapy to enhance treatment outcome for late-life depression and anxiety disorder
Determinantal Correlations of Brownian Paths in the Plane with Nonintersection Condition on their Loop-Erased Parts
As an image of the many-to-one map of loop-erasing operation \LE of random
walks, a self-avoiding walk (SAW) is obtained. The loop-erased random walk
(LERW) model is the statistical ensemble of SAWs such that the weight of each
SAW is given by the total weight of all random walks which are
inverse images of , \{\pi: \LE(\pi)=\zeta \}. We regard the Brownian
paths as the continuum limits of random walks and consider the statistical
ensemble of loop-erased Brownian paths (LEBPs) as the continuum limits of the
LERW model. Following the theory of Fomin on nonintersecting LERWs, we
introduce a nonintersecting system of -tuples of LEBPs in a domain in
the complex plane, where the total weight of nonintersecting LEBPs is given by
Fomin's determinant of an matrix whose entries are boundary
Poisson kernels in . We set a sequence of chambers in a planar domain and
observe the first passage points at which Brownian paths first enter each chamber, under the condition that the loop-erased
parts (\LE(\gamma_1),..., \LE(\gamma_N)) make a system of nonintersecting
LEBPs in the domain in the sense of Fomin. We prove that the correlation
functions of first passage points of the Brownian paths of the present system
are generally given by determinants specified by a continuous function called
the correlation kernel. The correlation kernel is of Eynard-Mehta type, which
has appeared in two-matrix models and time-dependent matrix models studied in
random matrix theory. Conformal covariance of correlation functions is
demonstrated.Comment: v3: REVTeX4, 27 pages, 10 figures, corrections made for publication
in Phys.Rev.
A Match in Time Saves Nine: Deterministic Online Matching With Delays
We consider the problem of online Min-cost Perfect Matching with Delays
(MPMD) introduced by Emek et al. (STOC 2016). In this problem, an even number
of requests appear in a metric space at different times and the goal of an
online algorithm is to match them in pairs. In contrast to traditional online
matching problems, in MPMD all requests appear online and an algorithm can
match any pair of requests, but such decision may be delayed (e.g., to find a
better match). The cost is the sum of matching distances and the introduced
delays.
We present the first deterministic online algorithm for this problem. Its
competitive ratio is , where is the
number of requests. This is polynomial in the number of metric space points if
all requests are given at different points. In particular, the bound does not
depend on other parameters of the metric, such as its aspect ratio. Unlike
previous (randomized) solutions for the MPMD problem, our algorithm does not
need to know the metric space in advance
An Evolutionary Reduction Principle for Mutation Rates at Multiple Loci
A model of mutation rate evolution for multiple loci under arbitrary
selection is analyzed. Results are obtained using techniques from Karlin (1982)
that overcome the weak selection constraints needed for tractability in prior
studies of multilocus event models. A multivariate form of the reduction
principle is found: reduction results at individual loci combine topologically
to produce a surface of mutation rate alterations that are neutral for a new
modifier allele. New mutation rates survive if and only if they fall below this
surface - a generalization of the hyperplane found by Zhivotovsky et al. (1994)
for a multilocus recombination modifier. Increases in mutation rates at some
loci may evolve if compensated for by decreases at other loci. The strength of
selection on the modifier scales in proportion to the number of germline cell
divisions, and increases with the number of loci affected. Loci that do not
make a difference to marginal fitnesses at equilibrium are not subject to the
reduction principle, and under fine tuning of mutation rates would be expected
to have higher mutation rates than loci in mutation-selection balance. Other
results include the nonexistence of 'viability analogous, Hardy-Weinberg'
modifier polymorphisms under multiplicative mutation, and the sufficiency of
average transmission rates to encapsulate the effect of modifier polymorphisms
on the transmission of loci under selection. A conjecture is offered regarding
situations, like recombination in the presence of mutation, that exhibit
departures from the reduction principle. Constraints for tractability are:
tight linkage of all loci, initial fixation at the modifier locus, and mutation
distributions comprising transition probabilities of reversible Markov chains.Comment: v3: Final corrections. v2: Revised title, reworked and expanded
introductory and discussion sections, added corollaries, new results on
modifier polymorphisms, minor corrections. 49 pages, 64 reference
Aging in the random energy model
In this letter we announce rigorous results on the phenomenon of aging in the
Glauber dynamics of the random energy model and their relation to Bouchaud's
'REM-like' trap model. We show that, below the critical temperature, if we
consider a time-scale that diverges with the system size in such a way that
equilibrium is almost, but not quite reached on that scale, a suitably defined
autocorrelation function has the same asymptotic behaviour than its analog in
the trap model.Comment: 4pp, P
A Combinatorial Interpretation of the Free Fermion Condition of the Six-Vertex Model
The free fermion condition of the six-vertex model provides a 5 parameter
sub-manifold on which the Bethe Ansatz equations for the wavenumbers that enter
into the eigenfunctions of the transfer matrices of the model decouple, hence
allowing explicit solutions. Such conditions arose originally in early
field-theoretic S-matrix approaches. Here we provide a combinatorial
explanation for the condition in terms of a generalised Gessel-Viennot
involution. By doing so we extend the use of the Gessel-Viennot theorem,
originally devised for non-intersecting walks only, to a special weighted type
of \emph{intersecting} walk, and hence express the partition function of
such walks starting and finishing at fixed endpoints in terms of the single
walk partition functions
Universality of weak selection
Weak selection, which means a phenotype is slightly advantageous over
another, is an important limiting case in evolutionary biology. Recently it has
been introduced into evolutionary game theory. In evolutionary game dynamics,
the probability to be imitated or to reproduce depends on the performance in a
game. The influence of the game on the stochastic dynamics in finite
populations is governed by the intensity of selection. In many models of both
unstructured and structured populations, a key assumption allowing analytical
calculations is weak selection, which means that all individuals perform
approximately equally well. In the weak selection limit many different
microscopic evolutionary models have the same or similar properties. How
universal is weak selection for those microscopic evolutionary processes? We
answer this question by investigating the fixation probability and the average
fixation time not only up to linear, but also up to higher orders in selection
intensity. We find universal higher order expansions, which allow a rescaling
of the selection intensity. With this, we can identify specific models which
violate (linear) weak selection results, such as the one--third rule of
coordination games in finite but large populations.Comment: 12 pages, 3 figures, accepted for publication in Physical Review
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