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  • Publication . Article . Other literature type . Preprint . 2016
    Open Access English
    Authors: 
    Eyal Elyashiv; Shmuel Sattath; Tina T. Hu; Alon Strutsovsky; Graham McVicker; Peter Andolfatto; Graham Coop; Guy Sella;
    Publisher: Public Library of Science (PLoS)
    Country: United States
    Project: NSF | Collaborative Research: A... (1262645)

    © 2016 Elyashiv et al. Natural selection at one site shapes patterns of genetic variation at linked sites. Quantifying the effects of “linked selection” on levels of genetic diversity is key to making reliable inference about demography, building a null model in scans for targets of adaptation, and learning about the dynamics of natural selection. Here, we introduce the first method that jointly infers parameters of distinct modes of linked selection, notably background selection and selective sweeps, from genome-wide diversity data, functional annotations and genetic maps. The central idea is to calculate the probability that a neutral site is polymorphic given local annotations, substitution patterns, and recombination rates. Information is then combined across sites and samples using composite likelihood in order to estimate genome-wide parameters of distinct modes of selection. In addition to parameter estimation, this approach yields a map of the expected neutral diversity levels along the genome. To illustrate the utility of our approach, we apply it to genome-wide resequencing data from 125 lines in Drosophila melanogaster and reliably predict diversity levels at the 1Mb scale. Our results corroborate estimates of a high fraction of beneficial substitutions in proteins and untranslated regions (UTR). They allow us to distinguish between the contribution of sweeps and other modes of selection around amino acid substitutions and to uncover evidence for pervasive sweeps in untranslated regions (UTRs). Our inference further suggests a substantial effect of other modes of linked selection and of adaptation in particular. More generally, we demonstrate that linked selection has had a larger effect in reducing diversity levels and increasing their variance in D. melanogaster than previously appreciated.

  • Publication . Article . Preprint . 2014
    Open Access English
    Authors: 
    Kerner, Dmitry;
    Project: EC | DURFEE (334347)

    Consider rectangular matrices over a local ring R. In the previous work we have obtained criteria for block-diagonalization of such matrices, i.e. U A V=A_1\oplus A_2, where U,V are invertible matrices over R. In this short note we extend the criteria to the decomposability of quiver representations over R. Preliminary brief announcement

  • Open Access English
    Authors: 
    Biskup, Marek; Louidor, Oren;
    Project: EC | MOTTPROXIMITY (276923), NSF | Large Scale Phenomena in ... (1407558)

    We study the extremal process associated with the Discrete Gaussian Free Field on the square lattice and elucidate how the conformal symmetries manifest themselves in the scaling limit. Specifically, we prove that the joint process of spatial positions ($x$) and centered values ($h$) of the extreme local maxima in lattice versions of a bounded domain $D\subset\mathbb C$ converges, as the lattice spacing tends to zero, to a Poisson point process with intensity measure $Z^D(dx)\otimes e^{-\alpha h}d h$, where $\alpha$ is a constant and $Z^D$ is a random a.s.-finite measure on $D$. The random measures $\{Z^D\}$ are naturally interrelated; restrictions to subdomains are governed by a Gibbs-Markov property and images under analytic bijections $f$ by the transformation rule $(Z^{f(D)}\circ f)(d x)\overset{\text{law}}=|f'(x)|^4\, Z^D(d x)$. Conditions are given that determine the laws of these measures uniquely. These identify $Z^D$ with the critical Liouville Quantum Gravity associated with the Continuum Gaussian Free Field. Comment: 58 pages, 4 figs, version to appear in Commun. Math. Phys

  • Publication . Article . Other literature type . Preprint . 2022
    Open Access English
    Authors: 
    Laura Sberna; Stanislav Babak; Sylvain Marsat; Andrea Caputo; Giulia Cusin; Alexandre Toubiana; Enrico Barausse; Chiara Caprini; Tito Dal Canton; Alberto Sesana; +1 more
    Project: EC | GRU (101007855), EC | LDMThExp (682676), EC | GRAMS (815673), EC | B Massive (818691)

    Binaries of relatively massive black holes like GW190521 have been proposed to form in dense gas environments, such as the disks of Active Galactic Nuclei (AGNs), and they might be associated with transient electromagnetic counterparts. The interactions of this putative environment with the binary could leave a significant imprint at the low gravitational wave frequencies observable with the Laser Interferometer Space Antenna (LISA). We show that LISA will be able to detect up to ten GW190521-like black hole binaries, with sky position errors $\lesssim1$ deg$^2$. Moreover, it will measure directly various effects due to the orbital motion around the supermassive black hole at the center of the AGN, especially the Doppler modulation and the Shapiro time delay. Thanks to a careful treatment of their frequency domain signal, we were able to perform the full parameter estimation of Doppler and Shapiro-modulated binaries as seen by LISA. We find that the Doppler and Shapiro effects will allow for measuring the AGN parameters (radius and inclination of the orbit around the AGN, central black hole mass) with up to percent-level precision. Properly modeling these low-frequency environmental effects is crucial to determine the binary formation history, as well as to avoid biases in the reconstruction of the source parameters and in tests of general relativity with gravitational waves. 13+4 pages, 7+1 figures v3: corrected typo in Fig 5

  • Publication . Preprint . Article . 2003
    Open Access English
    Authors: 
    Cohen, R.; Dolev, D.; Havlin, S.; Kalisky, T.; Mokryn, O.; Shavitt, Y.;

    In this paper we model the tomography of scale free networks by studying the structure of layers around an arbitrary network node. We find, both analytically and empirically, that the distance distribution of all nodes from a specific network node consists of two regimes. The first is characterized by rapid growth, and the second decays exponentially. We also show that the nodes degree distribution at each layer is a power law with an exponential cut-off. We obtain similar results for the layers surrounding the root of multicast trees cut from such networks, as well as the Internet. All of our results were obtained both analytically and on empirical Interenet data.

  • Publication . Preprint . Article . 2011
    Open Access English
    Authors: 
    Alexander D. Rahm;
    Publisher: HAL CCSD
    Countries: France, Luxembourg, Ireland

    Note bilingue anglais/francais. We reveal a correspondence between the homological torsion of the Bianchi groups and new geometric invariants, which are effectively computable thanks to their action on hyperbolic space. We use it to explicitly compute their integral group homology and equivariant K-homology. By the Baum/Connes conjecture, which holds for the Bianchi groups, we obtain the K-theory of their reduced C*-algebras in terms of isomorphic images of the computed K-homology. We further find an application to Chen/Ruan orbifold cohomology. ______________________________ Nous mettons en é́vidence une correspondance entre la torsion homologique des groupes de Bianchi et de nouveaux invariants gé́omé́triques, calculables grâce à leur action sur l'espace hyperbolique. Nous l'utilisons pour calculer explicitement leur homologie de groupe à coefficients entiers et leur K-homologie é́quivariante. En consé́quence de la conjecture de Baum/Connes, qui est vé́rifiée pour ces groupes, nous obtenons la K-thé́orie de leurs C*-algèbres ré́duites en termes d'images isomorphes de la K-homologie calculée. Nous trouvons d'ailleurs une application à la cohomologie d'orbi-espace de Chen/Ruan.

  • Open Access English
    Authors: 
    Eyal Buks; Chunqing Deng; Jean-Luc F. X. Orgazzi; Martin Otto; Adrian Lupascu;
    Project: NSERC

    We study a system consisting of a superconducting flux qubit strongly coupled to a microwave cavity. The fundamental cavity mode is externally driven and the response is investigated in the weak nonlinear regime. We find that near the crossing point, at which the resonance frequencies of the cavity mode and qubit coincide, the sign of the Kerr coefficient changes, and consequently the type of nonlinear response changes from softening to hardening. Furthermore, the cavity response exhibits superharmonic resonances when the ratio between the qubit frequency and the cavity fundamental mode frequency is tuned close to an integer value. The nonlinear response is characterized by the method of intermodulation and both signal and idler gains are measured. The experimental results are compared with theoretical predictions and good qualitative agreement is obtained. The superharmonic resonances have potential for applications in quantum amplification and generation of entangled states of light.

  • Publication . Article . Preprint . 2008
    Open Access English
    Authors: 
    Joachim Mathiesen; Itamar Procaccia; Ido Regev;

    A classical problem in elasticity theory involves an inhomogeneity embedded in a material of given stress and shear moduli. The inhomogeneity is a region of arbitrary shape whose stress and shear moduli differ from those of the surrounding medium. In this paper we present a new, semi-analytic method for finding the stress tensor for an infinite plate with such an inhomogeneity. The solution involves two conformal maps, one from the inside and the second from the outside of the unit circle to the inside, and respectively outside, of the inhomogeneity. The method provides a solution by matching the conformal maps on the boundary between the inhomogeneity and the surrounding material. This matching converges well only for relatively mild distortions of the unit circle due to reasons which will be discussed in the article. We provide a comparison of the present result to known previous results. (10 pages, 10 figures)

  • Publication . Conference object . Preprint . Article . 2003
    Open Access English
    Authors: 
    Gérard D. Cohen; Sylvia B. Encheva; Simon Litsyn;

    Using the notion of generalized weight we improve estimates on the parameters of quantum codes obtained by Steane's construction from binary codes. This yields several new families of quantum codes. LaTeX, 10 pages

  • Open Access English
    Authors: 
    Gal Dalal; Balázs Szörényi; Gugan Thoppe;
    Project: NSF | RoL: FELS: RAISE: Does ev... (1840223)

    Policy evaluation in reinforcement learning is often conducted using two-timescale stochastic approximation, which results in various gradient temporal difference methods such as GTD(0), GTD2, and TDC. Here, we provide convergence rate bounds for this suite of algorithms. Algorithms such as these have two iterates, $\theta_n$ and $w_n,$ which are updated using two distinct stepsize sequences, $\alpha_n$ and $\beta_n,$ respectively. Assuming $\alpha_n = n^{-\alpha}$ and $\beta_n = n^{-\beta}$ with $1 > \alpha > \beta > 0,$ we show that, with high probability, the two iterates converge to their respective solutions $\theta^*$ and $w^*$ at rates given by $\|\theta_n - \theta^*\| = \tilde{O}( n^{-\alpha/2})$ and $\|w_n - w^*\| = \tilde{O}(n^{-\beta/2});$ here, $\tilde{O}$ hides logarithmic terms. Via comparable lower bounds, we show that these bounds are, in fact, tight. To the best of our knowledge, ours is the first finite-time analysis which achieves these rates. While it was known that the two timescale components decouple asymptotically, our results depict this phenomenon more explicitly by showing that it in fact happens from some finite time onwards. Lastly, compared to existing works, our result applies to a broader family of stepsizes, including non-square summable ones.

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