1,685 research outputs found
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
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
Analytical Solution of a Stochastic Content Based Network Model
We define and completely solve a content-based directed network whose nodes
consist of random words and an adjacency rule involving perfect or approximate
matches, for an alphabet with an arbitrary number of letters. The analytic
expression for the out-degree distribution shows a crossover from a leading
power law behavior to a log-periodic regime bounded by a different power law
decay. The leading exponents in the two regions have a weak dependence on the
mean word length, and an even weaker dependence on the alphabet size. The
in-degree distribution, on the other hand, is much narrower and does not show
scaling behavior. The results might be of interest for understanding the
emergence of genomic interaction networks, which rely, to a large extent, on
mechanisms based on sequence matching, and exhibit similar global features to
those found here.Comment: 13 pages, 5 figures. Rewrote conclusions regarding the relevance to
gene regulation networks, fixed minor errors and replaced fig. 4. Main body
of paper (model and calculations) remains unchanged. Submitted for
publicatio
Aging to non-Newtonian hydrodynamics in a granular gas
The evolution to the steady state of a granular gas subject to simple shear
flow is analyzed by means of computer simulations. It is found that, regardless
of its initial preparation, the system reaches (after a transient period
lasting a few collisions per particle) a non-Newtonian (unsteady) hydrodynamic
regime, even at strong dissipation and for states where the time scale
associated with inelastic cooling is shorter than the one associated with the
irreversible fluxes. Comparison with a simplified rheological model shows a
good agreement.Comment: 6 pages, 4 figures; v2: improved version to be published in EP
Separable and Low-Rank Continuous Games
In this paper, we study nonzero-sum separable games, which are continuous
games whose payoffs take a sum-of-products form. Included in this subclass are
all finite games and polynomial games. We investigate the structure of
equilibria in separable games. We show that these games admit finitely
supported Nash equilibria. Motivated by the bounds on the supports of mixed
equilibria in two-player finite games in terms of the ranks of the payoff
matrices, we define the notion of the rank of an n-player continuous game and
use this to provide bounds on the cardinality of the support of equilibrium
strategies. We present a general characterization theorem that states that a
continuous game has finite rank if and only if it is separable. Using our rank
results, we present an efficient algorithm for computing approximate equilibria
of two-player separable games with fixed strategy spaces in time polynomial in
the rank of the game
Langevin Trajectories between Fixed Concentrations
We consider the trajectories of particles diffusing between two infinite
baths of fixed concentrations connected by a channel, e.g. a protein channel of
a biological membrane. The steady state influx and efflux of Langevin
trajectories at the boundaries of a finite volume containing the channel and
parts of the two baths is replicated by termination of outgoing trajectories
and injection according to a residual phase space density. We present a
simulation scheme that maintains averaged fixed concentrations without creating
spurious boundary layers, consistent with the assumed physics
Structure of Extreme Correlated Equilibria: a Zero-Sum Example and its Implications
We exhibit the rich structure of the set of correlated equilibria by
analyzing the simplest of polynomial games: the mixed extension of matching
pennies. We show that while the correlated equilibrium set is convex and
compact, the structure of its extreme points can be quite complicated. In
finite games the ratio of extreme correlated to extreme Nash equilibria can be
greater than exponential in the size of the strategy spaces. In polynomial
games there can exist extreme correlated equilibria which are not finitely
supported; we construct a large family of examples using techniques from
ergodic theory. We show that in general the set of correlated equilibrium
distributions of a polynomial game cannot be described by conditions on
finitely many moments (means, covariances, etc.), in marked contrast to the set
of Nash equilibria which is always expressible in terms of finitely many
moments
Soliton and black hole solutions of su(N) Einstein-Yang-Mills theory in anti-de Sitter space
We present new soliton and hairy black hole solutions of su(N)
Einstein-Yang-Mills theory in asymptotically anti-de Sitter space. These
solutions are described by N+1 independent parameters, and have N-1 gauge field
degrees of freedom. We examine the space of solutions in detail for su(3) and
su(4) solitons and black holes. If the magnitude of the cosmological constant
is sufficiently large, we find solutions where all the gauge field functions
have no zeros. These solutions are of particular interest because we anticipate
that at least some of them will be linearly stable.Comment: 15 pages, 20 figures, minor changes, accepted for publication in
Physical Review
Efficient Stochastic Simulations of Complex Reaction Networks on Surfaces
Surfaces serve as highly efficient catalysts for a vast variety of chemical
reactions. Typically, such surface reactions involve billions of molecules
which diffuse and react over macroscopic areas. Therefore, stochastic
fluctuations are negligible and the reaction rates can be evaluated using rate
equations, which are based on the mean-field approximation. However, in case
that the surface is partitioned into a large number of disconnected microscopic
domains, the number of reactants in each domain becomes small and it strongly
fluctuates. This is, in fact, the situation in the interstellar medium, where
some crucial reactions take place on the surfaces of microscopic dust grains.
In this case rate equations fail and the simulation of surface reactions
requires stochastic methods such as the master equation. However, in the case
of complex reaction networks, the master equation becomes infeasible because
the number of equations proliferates exponentially. To solve this problem, we
introduce a stochastic method based on moment equations. In this method the
number of equations is dramatically reduced to just one equation for each
reactive species and one equation for each reaction. Moreover, the equations
can be easily constructed using a diagrammatic approach. We demonstrate the
method for a set of astrophysically relevant networks of increasing complexity.
It is expected to be applicable in many other contexts in which problems that
exhibit analogous structure appear, such as surface catalysis in nanoscale
systems, aerosol chemistry in stratospheric clouds and genetic networks in
cells
Nonlinear viscosity and velocity distribution function in a simple longitudinal flow
A compressible flow characterized by a velocity field is
analyzed by means of the Boltzmann equation and the Bhatnagar-Gross-Krook
kinetic model. The sign of the control parameter (the longitudinal deformation
rate ) distinguishes between an expansion () and a condensation ()
phenomenon. The temperature is a decreasing function of time in the former
case, while it is an increasing function in the latter. The non-Newtonian
behavior of the gas is described by a dimensionless nonlinear viscosity
, that depends on the dimensionless longitudinal rate . The
Chapman-Enskog expansion of in powers of is seen to be only
asymptotic (except in the case of Maxwell molecules). The velocity distribution
function is also studied. At any value of , it exhibits an algebraic
high-velocity tail that is responsible for the divergence of velocity moments.
For sufficiently negative , moments of degree four and higher may diverge,
while for positive the divergence occurs in moments of degree equal to or
larger than eight.Comment: 18 pages (Revtex), including 5 figures (eps). Analysis of the heat
flux plus other minor changes added. Revised version accepted for publication
in PR
- …