The Experts below are selected from a list of 225 Experts worldwide ranked by ideXlab platform

David Sankoff - One of the best experts on this subject based on the ideXlab platform.

  • A Continuous Analog of run length distributions reflecting accumulated fractionation events.
    BMC bioinformatics, 2016
    Co-Authors: David Sankoff
    Abstract:

    We propose a new, Continuous model of the fractionation process (duplicate gene deletion after polyploidization) on the real line. The aim is to infer how much DNA is deleted at a time, based on segment lengths for alternating deleted (invisible) and undeleted (visible) regions. After deriving a number of analytical results for "one-sided" fractionation, we undertake a series of simulations that help us identify the distribution of segment lengths as a gamma with shape and rate parameters evolving over time. This leads to an inference procedure based on observed length distributions for visible and invisible segments. We suggest extensions of this mathematical and simulation work to biologically realistic discrete models, including two-sided fractionation.

  • A Continuous Analog of run length distributions reflecting accumulated fractionation events
    BMC Bioinformatics, 2016
    Co-Authors: David Sankoff
    Abstract:

    Abstract Background We propose a new, Continuous model of the fractionation process (duplicate gene deletion after polyploidization) on the real line. The aim is to infer how much DNA is deleted at a time, based on segment lengths for alternating deleted (invisible) and undeleted (visible) regions. Results After deriving a number of analytical results for “one-sided” fractionation, we undertake a series of simulations that help us identify the distribution of segment lengths as a gamma with shape and rate parameters evolving over time. This leads to an inference procedure based on observed length distributions for visible and invisible segments. Conclusions We suggest extensions of this mathematical and simulation work to biologically realistic discrete models, including two-sided fractionation

Vincent Vargas - One of the best experts on this subject based on the ideXlab platform.

  • Levy multiplicative chaos and star scale invariant random measures
    Annals of Probability, 2014
    Co-Authors: Rémi Rhodes, Julien Sohier, Vincent Vargas
    Abstract:

    In this article, we consider the Continuous Analog of the celebrated Mandelbrot star equation with infinitely divisible weights. Mandelbrot introduced this equation to characterize the law of multiplicative cascades. We show existence and uniqueness of measures satisfying the aforementioned Continuous equation. We obtain an explicit characterization of the structure of these measures, which reflects the constraints imposed by the Continuous setting. In particular, we show that the Continuous equation enjoys some specific properties that do not appear in the discrete star equation. To that purpose, we define a Levy multiplicative chaos that generalizes the already existing constructions.

  • Limiting laws of supercritical branching random walks
    arXiv: Probability, 2012
    Co-Authors: Julien Barral, Rémi Rhodes, Vincent Vargas
    Abstract:

    In this note, we make explicit the law of the renormalized supercritical branching random walk, giving credit to a conjecture formulated in a previous works of the authors for a Continuous Analog of the branching random walk. Also, in the case of a branching random walk on a homogeneous tree, we express the law of the corresponding limiting renormalized Gibbs measures, confirming, in this discrete model, conjectures formulated by physicists about the Poisson-Dirichlet nature of the jumps in the limit, and precising the conjecture by giving the spatial distribution of these jumps.

  • Lognormal scale invariant random measures
    Probability Theory and Related Fields, 2012
    Co-Authors: Romain Allez, Rémi Rhodes, Vincent Vargas
    Abstract:

    In this article, we consider the Continuous Analog of the celebrated Mandelbrot star equation with lognormal weights. Mandelbrot introduced this equation to characterize the law of multiplicative cascades. We show existence and uniqueness of measures satisfying the aforementioned Continuous equation; these measures fall under the scope of the Gaussian multiplicative chaos theory developed by J.P. Kahane in 1985 (or possibly extensions of this theory). As a by product, we also obtain an explicit characterization of the covariance structure of these measures. We also prove that qualitative properties such as long-range independence or isotropy can be read off the equation.

I. V. Puzynin - One of the best experts on this subject based on the ideXlab platform.

L. H. Harper - One of the best experts on this subject based on the ideXlab platform.

  • Duality Theorems for a Continuous Analog of Ford-Fulkerson Flows in Networks
    Advances in Applied Mathematics, 1993
    Co-Authors: J. D. Chavez, L. H. Harper
    Abstract:

    T. C. Hu and K. Jacobs independently proposed Continuous Analogs of Ford-Fulkerson flows in networks. Their models are different, but both showed that there are difficulties in obtaining maxflow = mincut theorems. In this paper, using a definition of Continuous networks which has already been shown to be natural and useful for solving combinatorial problems, we prove that there is no duality gap.

  • A Continuous Analog of Ford-Fulkerson flows in networks and its application to a problem of Rota
    Advances in Applied Mathematics, 1991
    Co-Authors: L. H. Harper
    Abstract:

    Given a poset Q, a natural question to ask is “What is the largest subset of Q having no comparable elements?” In 1928 E. Sperner [SP] showed that for Q = B,, the set of all subsets of an n-set ordered by containment, the answer is Bn,,n,2,, its largest rank. Subsequently, sets of incomparable elements have become known as Sperner sets; the general maximization problem as the Sperner problem, and the property of a graded poset that the solution be the largest rank as the Sperner property. In 1970 G.-C. Rota [RO] asked if II,, the lattice of partitions of an n-set, ordered by refinement, has the Sperner property. E. R. Canfield showed in 1976 [CA] that the answer to Rota’s question is “not for n sufficiently large.” Follow-on papers by J. B. Shearer [SHI, J.C. Sha and D. J. Kleitman [SK] simplified Canfield’s argument and lowered the bound on II to 3.4 x 106. None of these studies, however, gave any additional information about the asymptotic growth of Sperner sets (e.g., can they grow significantly faster than the largest rank?). Meanwhile the present author [HA 1; HA 2; HA 31 developed a notion of morphism for the weighted Sperner problem, showing that Rota’s question is equivalent to that for the weighted poset II,/s,, = {a E 2: 1%~~ = n], partially ordered by the cone K, = (Zcq, j(6, + Sj ai+j)Jai,j 2 01, ai being 0 except in component i where it is 1, II,/S, has rank function r-(v) = Cy= iui, and weights w(u) = n!/IJ~,,(i!h,!. Since II,/s,, is embedded in R”, the possibility of passing to a Continuous limit presented itself, the limit object being infinite dimensional (a

T. L. Boyadjiev - One of the best experts on this subject based on the ideXlab platform.

  • NAA - Stability and Bifurcation of the Magnetic Flux Bound States in Stacked Josephson Junctions
    Lecture Notes in Computer Science, 2009
    Co-Authors: Ivan C. Christov, Stefka Dimova, T. L. Boyadjiev
    Abstract:

    The static distributions of the magnetic flux in stacked Josephson junctions are investigated numerically. To solve the nonlinear boundary value problem an iterative algorithm, based on the Continuous Analog of Newton method is constructed. The linearized problems at every iteration step are solved by the Galerkin finite element method. In order to study the stability of possible distributions a Sturm-Liouville problem is generated. A minimal eigenvalue equal to zero means a bifurcation of the corresponding solution. The subspace iteration method is used to find the smallest eigenvalues and the corresponding eigenvectors.