18,739 research outputs found
Dynamic Monopolies in Colored Tori
The {\em information diffusion} has been modeled as the spread of an
information within a group through a process of social influence, where the
diffusion is driven by the so called {\em influential network}. Such a process,
which has been intensively studied under the name of {\em viral marketing}, has
the goal to select an initial good set of individuals that will promote a new
idea (or message) by spreading the "rumor" within the entire social network
through the word-of-mouth. Several studies used the {\em linear threshold
model} where the group is represented by a graph, nodes have two possible
states (active, non-active), and the threshold triggering the adoption
(activation) of a new idea to a node is given by the number of the active
neighbors.
The problem of detecting in a graph the presence of the minimal number of
nodes that will be able to activate the entire network is called {\em target
set selection} (TSS). In this paper we extend TSS by allowing nodes to have
more than two colors. The multicolored version of the TSS can be described as
follows: let be a torus where every node is assigned a color from a finite
set of colors. At each local time step, each node can recolor itself, depending
on the local configurations, with the color held by the majority of its
neighbors. We study the initial distributions of colors leading the system to a
monochromatic configuration of color , focusing on the minimum number of
initial -colored nodes. We conclude the paper by providing the time
complexity to achieve the monochromatic configuration
Stability properties of the ENO method
We review the currently available stability properties of the ENO
reconstruction procedure, such as its monotonicity and non-oscillatory
properties, the sign property, upper bounds on cell interface jumps and a total
variation-type bound. We also outline how these properties can be applied to
derive stability and convergence of high-order accurate schemes for
conservation laws.Comment: To appear in Handbook of Numerical Methods for Hyperbolic Problem
Strict bounding of quantities of interest in computations based on domain decomposition
This paper deals with bounding the error on the estimation of quantities of
interest obtained by finite element and domain decomposition methods. The
proposed bounds are written in order to separate the two errors involved in the
resolution of reference and adjoint problems : on the one hand the
discretization error due to the finite element method and on the other hand the
algebraic error due to the use of the iterative solver. Beside practical
considerations on the parallel computation of the bounds, it is shown that the
interface conformity can be slightly relaxed so that local enrichment or
refinement are possible in the subdomains bearing singularities or quantities
of interest which simplifies the improvement of the estimation. Academic
assessments are given on 2D static linear mechanic problems.Comment: Computer Methods in Applied Mechanics and Engineering, Elsevier,
2015, online previe
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