86,823 research outputs found

    On a Conjecture of Givental

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    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

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    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 ρ\rho is large but not necessarily infinite. Specifically, we consider an asymptotic expansion of the two-locus sampling formula in inverse powers of ρ\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

    Intrinsic Charm Flavor and Helicity Content in the Proton

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    Contributions to the quark flavor and spin observables from the intrinsic charm in the proton are discussed in the SU(4) quark meson fluctuation model. Our results suggest that the probability of finding the intrinsic charm in the proton is less than 1%. The intrinsic charm helicity is small and negative, Δc(0.0030.015)\Delta c \simeq -(0.003\sim 0.015). The fraction of the total quark helicity carried by the intrinsic charm is less than 2%, and c_\up/c_\dw=35/67.Comment: 4 pages, 2 tables (revised version

    Symbol error rate analysis for M-QAM modulated physical-layer network coding with phase errors

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    Recent theoretical studies of physical-layer network coding (PNC) show much interest on high-level modulation, such as M-ary quadrature amplitude modulation (M-QAM), and most related works are based on the assumption of phase synchrony. The possible presence of synchronization error and channel estimation error highlight the demand of analyzing the symbol error rate (SER) performance of PNC under different phase errors. Assuming synchronization and a general constellation mapping method, which maps the superposed signal into a set of M coded symbols, in this paper, we analytically derive the SER for M-QAM modulated PNC under different phase errors. We obtain an approximation of SER for general M-QAM modulations, as well as exact SER for quadrature phase-shift keying (QPSK), i.e. 4-QAM. Afterwards, theoretical results are verified by Monte Carlo simulations. The results in this paper can be used as benchmarks for designing practical systems supporting PNC. © 2012 IEEE

    Tractable diffusion and coalescent processes for weakly correlated loci

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    Widely used models in genetics include the Wright-Fisher diffusion and its moment dual, Kingman's coalescent. Each has a multilocus extension but under neither extension is the sampling distribution available in closed-form, and their computation is extremely difficult. In this paper we derive two new multilocus population genetic models, one a diffusion and the other a coalescent process, which are much simpler than the standard models, but which capture their key properties for large recombination rates. The diffusion model is based on a central limit theorem for density dependent population processes, and we show that the sampling distribution is a linear combination of moments of Gaussian distributions and hence available in closed-form. The coalescent process is based on a probabilistic coupling of the ancestral recombination graph to a simpler genealogical process which exposes the leading dynamics of the former. We further demonstrate that when we consider the sampling distribution as an asymptotic expansion in inverse powers of the recombination parameter, the sampling distributions of the new models agree with the standard ones up to the first two orders.Comment: 34 pages, 1 figur

    Simultaneous Multiple Surface Segmentation Using Deep Learning

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    The task of automatically segmenting 3-D surfaces representing boundaries of objects is important for quantitative analysis of volumetric images, and plays a vital role in biomedical image analysis. Recently, graph-based methods with a global optimization property have been developed and optimized for various medical imaging applications. Despite their widespread use, these require human experts to design transformations, image features, surface smoothness priors, and re-design for a different tissue, organ or imaging modality. Here, we propose a Deep Learning based approach for segmentation of the surfaces in volumetric medical images, by learning the essential features and transformations from training data, without any human expert intervention. We employ a regional approach to learn the local surface profiles. The proposed approach was evaluated on simultaneous intraretinal layer segmentation of optical coherence tomography (OCT) images of normal retinas and retinas affected by age related macular degeneration (AMD). The proposed approach was validated on 40 retina OCT volumes including 20 normal and 20 AMD subjects. The experiments showed statistically significant improvement in accuracy for our approach compared to state-of-the-art graph based optimal surface segmentation with convex priors (G-OSC). A single Convolution Neural Network (CNN) was used to learn the surfaces for both normal and diseased images. The mean unsigned surface positioning errors obtained by G-OSC method 2.31 voxels (95% CI 2.02-2.60 voxels) was improved to 1.271.27 voxels (95% CI 1.14-1.40 voxels) using our new approach. On average, our approach takes 94.34 s, requiring 95.35 MB memory, which is much faster than the 2837.46 s and 6.87 GB memory required by the G-OSC method on the same computer system.Comment: 8 page

    Determining SUSY Parameters in Chargino Pair-Production in e+ee^+e^- Collisions

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    In most supersymmetric theories, charginos χ~1,2±\tilde{\chi}^\pm_{1,2}, mixtures of charged color-neutral gauginos and higgsinos, belong to the class of the lightest supersymmetric particles. They are easy to observe at e+ee^+e^- colliders. By measuring the total cross sections and the left-right asymmetries with polarized electron beams in e+eχ~iχ~j+[i,j=1,2]e^+e^-\to\tilde{\chi}_i^-\tilde{\chi}_j^+ [i,j=1,2], the chargino masses and the gaugino-higgsino mixing angles can be determined. From these observables the fundamental SUSY parameters can be derived: the SU(2) gaugino mass M2M_2, the modulus μ|\mu| and cosΦμ\cos \Phi_\mu of the higgsino mass parameter, and tanβ=v2/v1\tan\beta = v_2/v_1, the ratio of the vacuum expectation values of the two neutral Higgs doublet fields. The solutions are unique; the CP-violating phase Φμ\Phi_\mu can be determined uniquely by analyzing effects due to the normal polarization of the charginos.Comment: 20 pages, 4 figures, uses axodraw.st

    Custodial bulk Randall-Sundrum model and B->K* l+ l'-

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    The custodial Randall-Sundrum model based on SU(2)_L X SU(2)_R X U(1)_(B-L) generates new flavor-changing-neutral-current (FCNC) phenomena at tree level, mediated by Kaluza-Klein neutral gauge bosons. Based on two natural assumptions of universal 5D Yukawa couplings and no-cancellation in explaining the observed standard model fermion mixing matrices, we determine the bulk Dirac mass parameters. Phenomenological constraints from lepton-flavor-violations are also used to specify the model. From the comprehensive study of B->K* l+ l'-, we found that only the B->K*ee decay has sizable new physics effects. The zero value position of the forward-backward asymmetry in this model is also evaluated, with about 5% deviation from the SM result. Other effective observables are also suggested such as the ratio of two differential (or partially integrated) decay rates of B->K*ee and B->K*mu mu. For the first KK gauge boson mass of M_A^(1)=2-4 TeV, we can have about 10-20% deviation from the SM results.Comment: references added with minor change

    Decoding coalescent hidden Markov models in linear time

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    In many areas of computational biology, hidden Markov models (HMMs) have been used to model local genomic features. In particular, coalescent HMMs have been used to infer ancient population sizes, migration rates, divergence times, and other parameters such as mutation and recombination rates. As more loci, sequences, and hidden states are added to the model, however, the runtime of coalescent HMMs can quickly become prohibitive. Here we present a new algorithm for reducing the runtime of coalescent HMMs from quadratic in the number of hidden time states to linear, without making any additional approximations. Our algorithm can be incorporated into various coalescent HMMs, including the popular method PSMC for inferring variable effective population sizes. Here we implement this algorithm to speed up our demographic inference method diCal, which is equivalent to PSMC when applied to a sample of two haplotypes. We demonstrate that the linear-time method can reconstruct a population size change history more accurately than the quadratic-time method, given similar computation resources. We also apply the method to data from the 1000 Genomes project, inferring a high-resolution history of size changes in the European population.Comment: 18 pages, 5 figures. To appear in the Proceedings of the 18th Annual International Conference on Research in Computational Molecular Biology (RECOMB 2014). The final publication is available at link.springer.co
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