3,948 research outputs found
On the Critical Behavior of D1-brane Theories
We study renormalization-group flow patterns in theories arising on D1-branes
in various supersymmetry-breaking backgrounds. We argue that the theory of N
D1-branes transverse to an orbifold space can be fine-tuned to flow to the
corresponding orbifold conformal field theory in the infrared, for particular
values of the couplings and theta angles which we determine using the discrete
symmetries of the model. By calculating various nonplanar contributions to the
scalar potential in the worldvolume theory, we show that fine-tuning is in fact
required at finite N, as would be generically expected. We further comment on
the presence of singular conformal field theories (such as those whose target
space includes a ``throat'' described by an exactly solvable CFT) in the
non-supersymmetric context. Throughout the analysis two applications are
considered: to gauge theory/gravity duality and to linear sigma model
techniques for studying worldsheet string theory.Comment: 23 pages in harvmac big, 8 figure
Non-Gaussianity in Island Cosmology
In this paper we fully calculate the non-Gaussianity of primordial curvature
perturbation of island universe by using the second order perturbation
equation. We find that for the spectral index , which is
favored by current observations, the non-Gaussianity level seen in
island will generally lie between 30 60, which may be tested by the
coming observations. In the landscape, the island universe is one of
anthropically acceptable cosmological histories. Thus the results obtained in
some sense means the coming observations, especially the measurement of
non-Gaussianity, will be significant to make clear how our position in the
landscape is populated.Comment: 5 pages, 1 eps figure, some discussions added, published versio
Open string instantons and relative stable morphisms
We show how topological open string theory amplitudes can be computed by
using relative stable morphisms in the algebraic category. We achieve our goal
by explicitly working through an example which has been previously considered
by Ooguri and Vafa from the point of view of physics. By using the method of
virtual localization, we successfully reproduce their results for multiple
covers of a holomorphic disc, whose boundary lies in a Lagrangian submanifold
of a Calabi-Yau 3-fold, by Riemann surfaces with arbitrary genera and number of
boundary components. In particular we show that in the case we consider there
are no open string instantons with more than one boundary component ending on
the Lagrangian submanifold.Comment: This is the version published by Geometry & Topology Monographs on 22
April 200
Descartes' rule of signs and the identifiability of population demographic models from genomic variation data
The sample frequency spectrum (SFS) is a widely-used summary statistic of
genomic variation in a sample of homologous DNA sequences. It provides a highly
efficient dimensional reduction of large-scale population genomic data and its
mathematical dependence on the underlying population demography is well
understood, thus enabling the development of efficient inference algorithms.
However, it has been recently shown that very different population demographies
can actually generate the same SFS for arbitrarily large sample sizes. Although
in principle this nonidentifiability issue poses a thorny challenge to
statistical inference, the population size functions involved in the
counterexamples are arguably not so biologically realistic. Here, we revisit
this problem and examine the identifiability of demographic models under the
restriction that the population sizes are piecewise-defined where each piece
belongs to some family of biologically-motivated functions. Under this
assumption, we prove that the expected SFS of a sample uniquely determines the
underlying demographic model, provided that the sample is sufficiently large.
We obtain a general bound on the sample size sufficient for identifiability;
the bound depends on the number of pieces in the demographic model and also on
the type of population size function in each piece. In the cases of
piecewise-constant, piecewise-exponential and piecewise-generalized-exponential
models, which are often assumed in population genomic inferences, we provide
explicit formulas for the bounds as simple functions of the number of pieces.
Lastly, we obtain analogous results for the "folded" SFS, which is often used
when there is ambiguity as to which allelic type is ancestral. Our results are
proved using a generalization of Descartes' rule of signs for polynomials to
the Laplace transform of piecewise continuous functions.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1264 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Fundamental limits on the accuracy of demographic inference based on the sample frequency spectrum
The sample frequency spectrum (SFS) of DNA sequences from a collection of
individuals is a summary statistic which is commonly used for parametric
inference in population genetics. Despite the popularity of SFS-based inference
methods, currently little is known about the information-theoretic limit on the
estimation accuracy as a function of sample size. Here, we show that using the
SFS to estimate the size history of a population has a minimax error of at
least , where is the number of independent segregating sites
used in the analysis. This rate is exponentially worse than known convergence
rates for many classical estimation problems in statistics. Another surprising
aspect of our theoretical bound is that it does not depend on the dimension of
the SFS, which is related to the number of sampled individuals. This means
that, for a fixed number of segregating sites considered, using more
individuals does not help to reduce the minimax error bound. Our result
pertains to populations that have experienced a bottleneck, and we argue that
it can be expected to apply to many populations in nature.Comment: 17 pages, 1 figur
On a Conjecture of Givental
These brief notes record our puzzles and findings surrounding Givental's
recent conjecture which expresses higher genus Gromov-Witten invariants in
terms of the genus-0 data. We limit our considerations to the case of a
projective line, whose Gromov-Witten invariants are well-known and easy to
compute. We make some simple checks supporting his conjecture.Comment: 13 pages, no figures; v.2: new title, minor change
An asymptotic sampling formula for the coalescent with Recombination
Ewens sampling formula (ESF) is a one-parameter family of probability
distributions with a number of intriguing combinatorial connections. This
elegant closed-form formula first arose in biology as the stationary
probability distribution of a sample configuration at one locus under the
infinite-alleles model of mutation. Since its discovery in the early 1970s, the
ESF has been used in various biological applications, and has sparked several
interesting mathematical generalizations. In the population genetics community,
extending the underlying random-mating model to include recombination has
received much attention in the past, but no general closed-form sampling
formula is currently known even for the simplest extension, that is, a model
with two loci. In this paper, we show that it is possible to obtain useful
closed-form results in the case the population-scaled recombination rate
is large but not necessarily infinite. Specifically, we consider an asymptotic
expansion of the two-locus sampling formula in inverse powers of and
obtain closed-form expressions for the first few terms in the expansion. Our
asymptotic sampling formula applies to arbitrary sample sizes and
configurations.Comment: Published in at http://dx.doi.org/10.1214/09-AAP646 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A novel spectral method for inferring general diploid selection from time series genetic data
The increased availability of time series genetic variation data from
experimental evolution studies and ancient DNA samples has created new
opportunities to identify genomic regions under selective pressure and to
estimate their associated fitness parameters. However, it is a challenging
problem to compute the likelihood of nonneutral models for the population
allele frequency dynamics, given the observed temporal DNA data. Here, we
develop a novel spectral algorithm to analytically and efficiently integrate
over all possible frequency trajectories between consecutive time points. This
advance circumvents the limitations of existing methods which require
fine-tuning the discretization of the population allele frequency space when
numerically approximating requisite integrals. Furthermore, our method is
flexible enough to handle general diploid models of selection where the
heterozygote and homozygote fitness parameters can take any values, while
previous methods focused on only a few restricted models of selection. We
demonstrate the utility of our method on simulated data and also apply it to
analyze ancient DNA data from genetic loci associated with coat coloration in
horses. In contrast to previous studies, our exploration of the full fitness
parameter space reveals that a heterozygote advantage form of balancing
selection may have been acting on these loci.Comment: Published in at http://dx.doi.org/10.1214/14-AOAS764 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Multi-locus analysis of genomic time series data from experimental evolution.
Genomic time series data generated by evolve-and-resequence (E&R) experiments offer a powerful window into the mechanisms that drive evolution. However, standard population genetic inference procedures do not account for sampling serially over time, and new methods are needed to make full use of modern experimental evolution data. To address this problem, we develop a Gaussian process approximation to the multi-locus Wright-Fisher process with selection over a time course of tens of generations. The mean and covariance structure of the Gaussian process are obtained by computing the corresponding moments in discrete-time Wright-Fisher models conditioned on the presence of a linked selected site. This enables our method to account for the effects of linkage and selection, both along the genome and across sampled time points, in an approximate but principled manner. We first use simulated data to demonstrate the power of our method to correctly detect, locate and estimate the fitness of a selected allele from among several linked sites. We study how this power changes for different values of selection strength, initial haplotypic diversity, population size, sampling frequency, experimental duration, number of replicates, and sequencing coverage depth. In addition to providing quantitative estimates of selection parameters from experimental evolution data, our model can be used by practitioners to design E&R experiments with requisite power. We also explore how our likelihood-based approach can be used to infer other model parameters, including effective population size and recombination rate. Then, we apply our method to analyze genome-wide data from a real E&R experiment designed to study the adaptation of D. melanogaster to a new laboratory environment with alternating cold and hot temperatures
Distortion of genealogical properties when the sample is very large
Study sample sizes in human genetics are growing rapidly, and in due course
it will become routine to analyze samples with hundreds of thousands if not
millions of individuals. In addition to posing computational challenges, such
large sample sizes call for carefully re-examining the theoretical foundation
underlying commonly-used analytical tools. Here, we study the accuracy of the
coalescent, a central model for studying the ancestry of a sample of
individuals. The coalescent arises as a limit of a large class of random mating
models and it is an accurate approximation to the original model provided that
the population size is sufficiently larger than the sample size. We develop a
method for performing exact computation in the discrete-time Wright-Fisher
(DTWF) model and compare several key genealogical quantities of interest with
the coalescent predictions. For realistic demographic scenarios, we find that
there are a significant number of multiple- and simultaneous-merger events
under the DTWF model, which are absent in the coalescent by construction.
Furthermore, for large sample sizes, there are noticeable differences in the
expected number of rare variants between the coalescent and the DTWF model. To
balance the tradeoff between accuracy and computational efficiency, we propose
a hybrid algorithm that utilizes the DTWF model for the recent past and the
coalescent for the more distant past. Our results demonstrate that the hybrid
method with only a handful of generations of the DTWF model leads to a
frequency spectrum that is quite close to the prediction of the full DTWF
model.Comment: 27 pages, 2 tables, 14 figure
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