2,698 research outputs found
Generalized Rayleigh and Jacobi processes and exceptional orthogonal polynomials
We present four types of infinitely many exactly solvable Fokker-Planck
equations, which are related to the newly discovered exceptional orthogonal
polynomials. They represent the deformed versions of the Rayleigh process and
the Jacobi process.Comment: 17 pages, 4 figure
Early appraisal of the fixation probability in directed networks
In evolutionary dynamics, the probability that a mutation spreads through the
whole population, having arisen in a single individual, is known as the
fixation probability. In general, it is not possible to find the fixation
probability analytically given the mutant's fitness and the topological
constraints that govern the spread of the mutation, so one resorts to
simulations instead. Depending on the topology in use, a great number of
evolutionary steps may be needed in each of the simulation events, particularly
in those that end with the population containing mutants only. We introduce two
techniques to accelerate the determination of the fixation probability. The
first one skips all evolutionary steps in which the number of mutants does not
change and thereby reduces the number of steps per simulation event
considerably. This technique is computationally advantageous for some of the
so-called layered networks. The second technique, which is not restricted to
layered networks, consists of aborting any simulation event in which the number
of mutants has grown beyond a certain threshold value, and counting that event
as having led to a total spread of the mutation. For large populations, and
regardless of the network's topology, we demonstrate, both analytically and by
means of simulations, that using a threshold of about 100 mutants leads to an
estimate of the fixation probability that deviates in no significant way from
that obtained from the full-fledged simulations. We have observed speedups of
two orders of magnitude for layered networks with 10000 nodes
Consequences of an incorrect model specification on population growth
We consider stochastic differential equations to model the growth of a population ina randomly varying environment. These growth models are usually based on classical deterministic models, such as the logistic or the Gompertz models, taken as approximate models of the "true" (usually unknown) growth rate. We study the effect of the gap between the approximate and the "true" model on model predictions, particularly on asymptotiv behavior and mean and variance of the time to extinction of the population
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
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
Minimal Absent Words in Prokaryotic and Eukaryotic Genomes
Minimal absent words have been computed in genomes of organisms from all domains of life. Here, we explore different sets of minimal absent words in the genomes of 22 organisms (one archaeota, thirteen bacteria and eight eukaryotes). We investigate if the mutational biases that may explain the deficit of the shortest absent words in vertebrates are also pervasive in other absent words, namely in minimal absent words, as well as to other organisms. We find that the compositional biases observed for the shortest absent words in vertebrates are not uniform throughout different sets of minimal absent words. We further investigate the hypothesis of the inheritance of minimal absent words through common ancestry from the similarity in dinucleotide relative abundances of different sets of minimal absent words, and find that this inheritance may be exclusive to vertebrates
Recommended from our members
Determination of the Critical Concentration of Neutrophils Required to Block Bacterial Growth in Tissues
We showed previously that the competition between bacterial killing by neutrophils and bacterial growth in stirred serum-containing suspensions could be modeled as the competition between a first-order reaction (bacterial growth) and a second-order reaction (bacterial killing by neutrophils). The model provided a useful parameter, the critical neutrophil concentration (CNC), below which bacterial concentration increased and above which it decreased, independent of the initial bacterial concentration. We report here that this model applies to neutrophil killing of bacteria in three-dimensional fibrin matrices and in rabbit dermis. We measured killing of 103–108 colony forming units/ml Staphylococcus epidermidis by 105–108 human neutrophils/ml in fibrin gels. The CNC was ∼4 × 106 neutrophils/ml gel in the presence of normal serum and ∼1.6 × 107 neutrophils/ml gel in the presence of C5-deficient serum. Application of our model to published data of others on killing of ∼5 × 107 to 2 × 108 E. coli/ml rabbit dermis yielded CNCs from ∼4 × 106 to ∼8 × 106 neutrophils/ml dermis. Thus, in disparate tissues and tissuelike environments, our model fits the kinetics of bacterial killing and gives similar lower limits (CNCs) to the neutrophil concentration required to control bacterial growth
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
- …