Regular Path Queries (RPQs) are a type of graph query where answers are pairs of nodes connected by a sequence of edges matching a regular expression. We study the techniques to process such queries on a distributed graph of data. While many techniques assume the location of each data element (node or edge) is known, when the components of the distributed system are autonomous, the data will be...

Seymour’s famous decomposition theorem for regular matroids states that any totally unimodular (TU) matrix can be constructed through a series of composition operations called k-sums starting from network matrices and their transposes and two compact representation matrices B1, B2 of a certain ten element matroid. Given that B1, B2 are binet matrices we examine the k-sums of network and binet m...

Several of the more commonly used triangle quality measures are analyzed and compared. Proofs are provided to verify that they do exhibit the expected extremal properties. The asymptotic behavior of these measures is investigated and a number of useful results are derived. It is shown that some of the quality measures are equivalent, in the sense of displaying the same extremal and asymptotic b...

Let G be a simple and simply connected complex linear algebraic group, with Lie algebra g. Let ρ : G → AutV be an irreducible finite-dimensional representation of G, and let ρ∗ : g → EndV be the induced representation of g. The goal of this paper is to study ρ∗, and in particular to give normal forms for the action of ρ∗(X) for regular elements X of g. Of course, when X is semisimple, the actio...

We derive explicit formulas for the eigenvalues and eigenvectors of the Discrete Laplacian on a rectangular grid for the standard finite difference and finite element methods in 1D, 2D, and 3D. Periodic, Dirichlet, Neumann, and mixed boundary conditions are all considered. We show how the higher dimensional operators can be written as sums of tensor products of one dimensional operators, and th...

Abstract We demonstrate, through separation of variables and estimates from the semiclassical analysis of the Schrödinger operator, that the eigenvalues of an elliptic operator defined on a compact hypersurface in Rn can be found by solving an elliptic eigenvalue problem in a bounded domain Ω ⊂ Rn. The latter problem is solved using standard finite element methods on the Cartesian grid. We also...

The dynamic behavior of magnetically driven microsystems is investigated in this study. An experimental setup designed to simulate the dynamic response of a micro-roller element moving in rectilinear path under influence of an external magnetic field is presented. Results of element response to step excitation field are discussed and an analytical model for the response based on a lumped capaci...

An adaptive finite element strategy is employed to solve the Perona-Malik model as modified by Catté, Lions, Morel and Coll for image processing by (often highly) nonlinear diffusion. FEMLAB® and MATLAB® are used to implement the experiments and they prove to be very suitable tools to run this type of problem. Refinement and coarsening of the grids are used as needed and the approach leads to u...

In the paper a balanced Neumann Neumann algorithm for the reduced HCT finite element nonmatching meshes is discussed. The overall discretization is done using a mortar technique which is based on the application of an approximate matching condition for the discrete functions. The algorithms are analyzed using the abstract Schwarz framework, proving an almost optimal condition bound which is ind...

Providing realistic interactive simulation requires a powerful animation method with a highly detailed rendering. Based on continuum mechanics, the finite element method needs a volumetric representation of the object to animate. This paper proposes an automatic method for building meshes that are well adapted to interactive simulation starting from miscellaneous input data. Contrary to commonl...