Главная

Gabriel H. Tucci

  1. Traffic Analysis in Random Delaunay Tessellations and Other Graphs.

    Пт, 03/23/2012 - 15:01 — SomNambul
    Authors: Gabriel H. Tucci, John D. Hobby
    Subjects: Differential Geometry
    Abstract

    In this work we study the degree distribution, the maximum vertex and edge
    flow in non-uniform random Delaunay triangulations when geodesic routing is
    used. We also investigate the vertex and edge flow in Erd\"os-Renyi random
    graphs, geometric random graphs, expanders and random $k$-regular graphs.
    Moreover we show that adding a random matching to the original graph can
    considerably reduced the maximum vertex flow.

  2. Scaling of Congestion in Small World Networks.

    Пнд, 01/23/2012 - 15:01 — SomNambul
    Authors: Gabriel H. Tucci, Iraj Saniee
    Subjects: Metric Geometry
    Abstract

    In this report we show that in a planar exponentially growing network
    consisting of $N$ nodes, congestion scales as $O(N^2/\log(N))$ independently of
    how flows may be routed. This is in contrast to the $O(N^{3/2})$ scaling of
    congestion in a flat polynomially growing network. We also show that without
    the planarity condition, congestion in a small world network could scale as low
    as $O(N^{1+\epsilon})$, for arbitrarily small $\epsilon$.

  3. New Methods for Handling Singular Sample Covariance Matrices.

    Ср, 11/02/2011 - 15:01 — SomNambul
    Authors: Ke Wang, Gabriel H. Tucci
    Subjects: Probability
    Abstract

    The estimation of a covariance matrix from an insufficient amount of data is
    one of the most common problems in fields as diverse as multivariate
    statistics, wireless communications, signal processing, biology, learning
    theory and finance. In \cite{MTS}, a new approach to handle singular covariance
    matrices was suggested. The main idea was to use dimensionality reduction in
    conjunction with an average over the unitary matrices.

  4. Asymptotic Traffic Flow in an Hyperbolic Network II: Non-uniform Traffic.

    Втр, 10/19/2010 - 15:01 — SomNambul
    Authors: Gabriel H. Tucci, Yuliy Baryshnikov
    Subjects: Group Theory
    Abstract

    In this work we study the asymptotic traffic behavior in Gromov's hyperbolic
    spaces when the traffic decays exponentially with the distance. We prove that
    under general conditions, there exist a phase transition between local and
    global traffic.

  5. Asymptotic Traffic Flow in an Hyperbolic Network I: Definition and Properties of the Core.

    Втр, 10/19/2010 - 15:01 — SomNambul
    Authors: Gabriel H. Tucci, Yuliy Baryshnikov
    Subjects: Group Theory
    Abstract

    In this work we study the asymptotic traffic behavior for Gromov's hyperbolic
    networks as the size of the network increases. We prove that under certain mild
    hypothesis the traffic in a large hyperbolic network tends to pass through a
    finite set of highly congested nodes. These nodes will be called the ``core" of
    the network. We provide a formal definition of the core in a very general
    context and we study the properties of this set for hyperbolic graphs.

  6. A Random Matrix--Theoretic Approach to Handling Singular Covariance Estimates.

    Втр, 10/05/2010 - 15:01 — SomNambul
    Authors: Gabriel H. Tucci, Thomas L. Marzetta, Steven H. Simon
    Subjects: Probability
    Abstract

    In many practical situations we would like to estimate the covariance matrix
    of a set of variables from an insufficient amount of data. More specifically,
    if we have a set of $N$ independent, identically distributed measurements of an
    $M$ dimensional random vector the maximum likelihood estimate is the sample
    covariance matrix. Here we consider the case where $N<M$ such that this
    estimate is singular and therefore fundamentally bad. We present a radically
    new approach to deal with this situation.

  7. Lack of Spectral Gap and Hyperbolicity in Asymptotic Erd\"os-Renyi Random Graphs.

    Чт, 09/30/2010 - 15:01 — SomNambul
    Authors: Gabriel H. Tucci, Onuttom Narayan, Iraj Saniee
    Subjects: Probability
    Abstract

    In this work, we prove the absence of a spectral gap for the normalized
    Laplacian of the Erd\"os-Renyi random graph $G(n,p)$ when $p=\frac{d}{n}$ for
    $d>1$ as $n\to\infty$. We also prove that for any positive $\delta$ the
    Erd\"os-Renyi random graph has a positive probability of containing
    $\delta$-fat triangles as $n\to\infty$.

  8. A Note on Averages over Random Matrix Ensembles.

    Втр, 10/06/2009 - 17:01 — SomNambul
    Authors: Gabriel H. Tucci
    Subjects: Probability
    Abstract

    In this work we find a closed form expression for matrix averages over the
    Gaussian ensemble. More precisely, given an $n\times n$ Hermitian matrix $A$
    and a continuous function $f(x)$ we find a closed form expression for the
    expectation $\E(\mathrm{Tr}(f(XAX^{*})))$ where $X$ is a Gaussian $n\times n$
    matrix with complex independent and identically distributed entries of zero
    mean and variance 1. Taking $f(x)=\log(1+x)$ this gives us another formula for
    the capacity of the MIMO communication channel and taking $f(x)=(1+x)^{-1}$
    gives us the minimum MMSE achieved by a linear receiver.

Math-arch

RSS-материал