28,852 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
Scope and Mechanistic Study of the Ruthenium-Catalyzed \u3cem\u3eortho\u3c/em\u3e-C−H Bond Activation and Cyclization Reactions of Arylamines with Terminal Alkynes
The cationic ruthenium hydride complex [(PCy3)2(CO)(CH3CN)2RuH]+BF4- was found to be a highly effective catalyst for the C−H bond activation reaction of arylamines and terminal alkynes. The regioselective catalytic synthesis of substituted quinoline and quinoxaline derivatives was achieved from the ortho-C−H bond activation reaction of arylamines and terminal alkynes by using the catalyst Ru3(CO)12/HBF4·OEt2. The normal isotope effect (kCH/kCD = 2.5) was observed for the reaction of C6H5NH2 and C6D5NH2 with propyne. A highly negative Hammett value (ρ = −4.4) was obtained from the correlation of the relative rates from a series of meta-substituted anilines, m-XC6H4NH2, with σp in the presence of Ru3(CO)12/HBF4·OEt2 (3 mol % Ru, 1:3 molar ratio). The deuterium labeling studies from the reactions of both indoline and acyclic arylamines with DC⋮CPh showed that the alkyne C−H bond activation step is reversible. The crossover experiment from the reaction of 1-(2-amino-1-phenyl)pyrrole with DC⋮CPh and HC⋮CC6H4-p-OMe led to preferential deuterium incorporation to the phenyl-substituted quinoline product. A mechanism involving rate-determining ortho-C−H bond activation and intramolecular C−N bond formation steps via an unsaturated cationic ruthenium acetylide complex has been proposed
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
Quilting Stochastic Kronecker Product Graphs to Generate Multiplicative Attribute Graphs
We describe the first sub-quadratic sampling algorithm for the Multiplicative
Attribute Graph Model (MAGM) of Kim and Leskovec (2010). We exploit the close
connection between MAGM and the Kronecker Product Graph Model (KPGM) of
Leskovec et al. (2010), and show that to sample a graph from a MAGM it suffices
to sample small number of KPGM graphs and \emph{quilt} them together. Under a
restricted set of technical conditions our algorithm runs in time, where is the number of nodes and is the number of edges
in the sampled graph. We demonstrate the scalability of our algorithm via
extensive empirical evaluation; we can sample a MAGM graph with 8 million nodes
and 20 billion edges in under 6 hours
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
Analytic Photometric Redshift Estimator for Type Ia Supernovae From the Large Synoptic Survey Telescope
Accurate and precise photometric redshifts (photo-z's) of Type Ia supernovae
(SNe Ia) can enable the use of SNe Ia, measured only with photometry, to probe
cosmology. This dramatically increases the science return of supernova surveys
planned for the Large Synoptic Survey Telescope (LSST). In this paper we
describe a significantly improved version of the simple analytic photo-z
estimator proposed by Wang (2007) and further developed by Wang, Narayan, and
Wood-Vasey (2007). We apply it to 55,422 simulated SNe Ia generated using the
SNANA package with the LSST filters. We find that the estimated errors on the
photo-z's, \sigma_{z_{phot}}/(1+z_{phot}), can be used as filters to produce a
set of photo-z's that have high precision, accuracy, and purity. Using SN Ia
colors as well as SN Ia peak magnitude in the i band, we obtain a set of
photo-z's with 2 percent accuracy (with \sigma(z_{phot}-z_{spec})/(1+z_{spec})
= 0.02), a bias in z_{phot} (the mean of z_{phot}-z_{spec}) of -9 X 10^{-5},
and an outlier fraction (with |(z_{phot}-z_{spec})/(1+z_{spec})|>0.1) of 0.23
percent, with the requirement that \sigma_{z_{phot}}/(1+z_{phot})<0.01. Using
the SN Ia colors only, we obtain a set of photo-z's with similar quality by
requiring that \sigma_{z_{phot}}/(1+z_{phot})<0.007; this leads to a set of
photo-z's with 2 percent accuracy, a bias in z_{phot} of 5.9 X 10^{-4}, and an
outlier fraction of 0.32 percent.Comment: 10 pages, 8 figures, 2 tables. Revised version, accepted by MNRA
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