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 $O(1/\log s)$, where $s$ 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 $s$ 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

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

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 $n_s\simeq 0.96$, which is favored by current observations, the non-Gaussianity level $f_{NL}$ seen in island will generally lie between 30 $\sim$ 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

Luminosity Profiles of Merger Remnants

Using published luminosity and molecular gas profiles of the late-stage mergers NGC 3921, NGC 7252 and Arp 220, we examine the expected luminosity profiles of the evolved merger remnants, especially in light of the massive CO complexes that are observed in their nuclei. For NGC 3921 and NGC 7252 we predict that the resulting luminosity profiles will be characterized by an r^{1/4} law. In view of previous optical work on these systems, it seems likely that they will evolve into normal ellipticals as regards their optical properties. Due to a much higher central molecular column density, Arp 220 might not evolve such a ``seamless'' light profile. We conclude that ultraluminous infrared mergers such as Arp 220 either evolve into ellipticals with anomalous luminosity profiles, or do not produce many low-mass stars out of their molecular gas complexes.Comment: Final refereed version. Note new title. 4 pages, 2 encapsulated color figures, uses emulateapj.sty. Accepted to ApJL. Also available at http://www.cv.nrao.edu/~jhibbard/Remnants/remnants.htm

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

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 $O((\log_2(n))^3 |E|)$ time, where $n$ is the number of nodes and $|E|$ 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 $\rho$ is large but not necessarily infinite. Specifically, we consider an asymptotic expansion of the two-locus sampling formula in inverse powers of $\rho$ 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

Large density amplification measured on jets ejected from a magnetized plasma gun

Observation of a large density amplification in the collimating plasma jet ejected from a coplanar coaxial plasma gun is reported. The jet velocity is ~30 km s^-1 and the electron density increases from ~10^20 to 10^(22–23) m^-3. In previous spheromak experiments, electron density of the order 10^(19–21) m^-3 had been measured in the flux conserver region, but no density measurement had been reported for the source gun region. The coplanar geometry of our electrodes permits direct observation of the entire plasma dynamics including the source region. Analysis of Stark broadened spectral lines shows that the electron density increases by a factor of 100 as the jet collimates, with a peak density of up to 10^(22–23) m^-3. The observed density amplification is interpreted according to an MHD theory that explains collimation of current-carrying plasma-filled magnetic flux tubes. Issues affecting interpretation of Stark broadened line profiles and the possibility of using the high-density plasma jet for tokamak fuel injection are discussed