Random Matrices with Merging Singularities and the Painlev\'e V Equation

We study the asymptotic behavior of the partition function and the correlation kernel in random matrix ensembles of the form $\frac{1}{Z_n} \big|\det \big( M^2-tI \big)\big|^{\alpha} e^{-n\operatorname{Tr} V(M)}dM$, where $M$ is an $n\times n$ Hermitian matrix, $\alpha>-1/2$ and $t\in\mathbb R$, in double scaling limits where $n\to\infty$ and simultaneously $t\to 0$. If $t$ is proportional to $1/n^2$, a transition takes place which can be described in terms of a family of solutions to the Painlev\'e V equation. These Painlev\'e solutions are in general transcendental functions, but for certain values of $\alpha$, they are algebraic, which leads to explicit asymptotics of the partition function and the correlation kernel

Statistical Intercell Interference Modeling for Capacity-Coverage Tradeoff Analysis in Downlink Cellular Networks

Interference shapes the interplay between capacity and coverage in cellular networks. However, interference is non-deterministic and depends on various system and channel parameters including user scheduling, frequency reuse, and fading variations. We present an analytical approach for modeling the distribution of intercell interference in the downlink of cellular networks as a function of generic fading channel models and various scheduling schemes. We demonstrate the usefulness of the derived expressions in calculating location-based and average-based data rates in addition to capturing practical tradeoffs between cell capacity and coverage in downlink cellular networks.Comment: 5 pages, 7 figures, conferenc

Investigation on polynomial integrators for time-domain electromagnetics using a high-order discontinuous Galerkin method

International audienceIn this work, we investigate the application of polynomial integrators in a high-order discontinuous Galerkin method for solving the time-domain Maxwell equations. After the spatial discretization, we obtain a time-continuous system of ordinary differential equations of the form, ∂tY(t)=HY(t), where Y(t) is the electromagnetic field, H is a matrix containing the spatial derivatives, and t is the time variable. The formal solution is written as the exponential evolution operator, exp(tH), acting on a vector representing the initial condition of the electromagnetic field. The polynomial integrators are based on the approximation of exp(tH) by an expansion of the form ∑ _m=0^\infinity gm(t) Pm(H), where gm(t) is a function of time and Pm(H) is a polynomial of order m satisfying a short recursion. We introduce a general family of expansions of exp(tH) based on Faber polynomials. This family of expansions is suitable for non-Hermitian matrices, and consequently the proposed integrators can handle absorbing media and conductive materials. We discuss the efficient implementation of this technique, and based on some test problems, we compare the virtues and shortcomings of the algorithm. We also demonstrate how this scheme provides an efficient alternative to standard explicit integrators

High-Order Leap-Frog Based Discontinuous Galerkin Method for the Time-Domain Maxwell Equations on Non-Conforming Simplicial Meshes

International audienceA high-order leap-frog based non-dissipative discontinuous Galerkin time-domain method for solving Maxwell's equations is introduced and analyzed. The proposed method combines a centered approximation for the evaluation of fluxes at the interface between neighboring elements, with a Nth-order leap-frog time scheme. Moreover, the interpolation degree is defined at the element level and the mesh is refined locally in a non-conforming way resulting in arbitrary level hanging nodes. The method is proved to be stable under some CFL-like condition on the time step. The convergence of the semi-discrete approximation to Maxwell's equations is established rigorously and bounds on the global divergence error are provided. Numerical experiments with high-order elements show the potential of the method

Locally implicit discontinuous Galerkin method for time domain electromagnetics

In the recent years, there has been an increasing interest in discontinuous Galerkin time domain (DGTD) methods for the solution of the unsteady Maxwell equations modeling electromagnetic wave propagation. One of the main features of DGTD methods is their ability to deal with unstructured meshes which are particularly well suited to the discretization of the geometrical details and heterogeneous media that characterize realistic propagation problems. Such DGTD methods most often rely on explicit time integration schemes and lead to block diagonal mass matrices. However, explicit DGTD methods are also constrained by a stability condition that can be very restrictive on highly refined meshes and when the local approximation relies on high order polynomial interpolation. An implicit time integration scheme is a natural way to obtain a time domain method which is unconditionally stable but at the expense of the inversion of a global linear system at each time step. A more viable approach consists of applying an implicit time integration scheme locally in the refined regions of the mesh while preserving an explicit time scheme in the complementary part, resulting in an hybrid explicit–implicit (or locally implicit) time integration strategy. In this paper, we report on our recent efforts towards the development of such a hybrid explicit–implicit DGTD method for solving the time domain Maxwell equations on unstructured simplicial meshes. Numerical experiments for 3D propagation problems in homogeneous and heterogeneous media illustrate the possibilities of the method for simulations involving locally refined meshes

Can Integrity Replace Institutions? Theory and Evidence

Institutions are important for proper economic performance, but are replaceable by trust or other social norms. We show that when proper institutions and trust are missing, integrity of the individuals can replace them. We construct a model of a transactions-based economy with contracts preceding the transactions, and show that any one of (1) institutions, (2) trust, or (3) integrity, foster economic growth. We construct data of economic performance of social groups in Lebanon, measure integrity and other values of these groups, and use this data and data from Kenya to support one of the model’s predictions. Policy implications are discussed.economic development, institutions, integrity, Lebanon, social norms, trust