195 research outputs found
Inversa de matrices circulantes con tres parámetros
Utilizando técnicas relacionadas con la resolución de problemas de contorno
para ecuaciones en diferencias de segundo orden, se dan condiciones necesarias y suficientes
cientes para la invertibilidad de matrices circulantes que dependen de tres parámetros. En
los casos que existe, se da la expresión de los coeficientes de la matriz inversa reduciendo
significativamente el coste computacional. Como aplicación, se obtiene la matriz inversa
de circulantes cuyos coeficientes son progresiones aritméticas o geométricas entre otros.
Se obtiene también, la matriz inversa de una matriz tridiagonal circulante sin necesidad
de suponer la hipótesis de dominancia diagonalPeer ReviewedPostprint (author's final draft
Computing the Green function for a Dirichlet problem on spider networks
Postprint (published version
Matrix tree theorem for Schrödinger operators on networks
Postprint (published version
The group inverse of subdivision networks
In this paper, given a network and a subdivision of it, we show how the Group Inverse of the subdivision network can be related to the Group Inverse of initial given network. Our approach establishes a relationship between solutions of related Poisson problems on both networks and takes advantatge on the definition of the Group Inverse matrix.Peer ReviewedPostprint (author's final draft
Minimal contention-free matrices with application to multicasting
In this paper, we show that the multicast problem in trees can be
expressed in term of arranging rows and columns of boolean matrices.
Given a matrix with 0-1 entries, the {\em shadow}
of is defined as a boolean vector of entries such that
if and only if there is no 1-entry in the th column of
, and otherwise. (The shadow can also be seen as the
binary expression of the integer .
Similarly, every row of can be seen as the binary expression of
an integer.) According to this formalism, the key for solving a
multicast problem in trees is shown to be the following. Given a matrix with 0-1 entries, finding a matrix such
that:
1- has at most one 1-entry per column;
2- every row of (viewed as the binary expression of
an integer) is larger than the corresponding row of , ; and
3- the shadow of (viewed as an integer) is minimum.
We show that there is an algorithm that
returns for any boolean matrix .
The application of this result is the following: Given a {\em directed}
tree whose arcs are oriented from the root toward the leaves,
and a subset of nodes , there exists a polynomial-time algorithm
that computes an optimal multicast protocol from the root to all
nodes of in the all-port line model.Peer Reviewe
Effective resistances and Kirchhoff index in subdivision networks
We define a subdivision network ¿S of a given network ¿; by inserting a new vertex in every edge, so that each edge is replaced by two new edges with conductances that fulfill electrical conditions on the new network. In this work, we firstly obtain an expression for the Green kernel of the subdivision network in terms of the Green kernel of the base network. Moreover, we also obtain the effective resistance and the Kirchhoff index of the subdivision network in terms of the corresponding parameters on the base network. Finally, as an example, we carry out the computations in the case of a wheel.Peer ReviewedPostprint (author's final draft
The local spectra of regular line graphs
The local spectrum of a graph G = (V, E), constituted by the standard eigenvalues of G and their local multiplicities, plays a similar role as the global spectrum when the graph is “seen” from a given vertex. Thus, for each vertex i ∈ V , the i-local multiplicities of all the eigenvalues add up to 1; whereas the multiplicity of each eigenvalue λ of G is the sum, extended to all vertices, of its local multiplicities. In this work, using the interpretation of an eigenvector as a charge distribution on the vertices, we compute the local spectrum of the line graph LG in terms of the local spectrum of the regular graph G it derives from. Furthermore, some applications of this result are derived as, for instance, some results about the number of circuits of LG
The local spectra of line graphs
The local spectrum of a graph G = (V, E), constituted by the standard eigenvalues of G and their local multiplicities, plays a similar role as the global spectrum when the graph is “seen” from a given vertex. Thus, for each vertex i ∈ V , the i-local multiplicities of all the eigenvalues add up to 1; whereas the multiplicity of each eigenvalue λl ∈ ev G is the sum, extended to all vertices, of its local multiplicities. In this work, using the interpretation of an eigenvector as a charge distribution on the vertices, we compute the local spectrum of the line graph LG in terms of the local spectrum of the (regular o semiregular) graph G it derives from. Furthermore, some applications of this result are derived as, for instance, some results related to the number of cycles
Gossiping in chordal rings under the line model
The line model assumes long distance
calls between non neighboring processors. In this sense, the line
model is strongly related to circuit-switched networks, wormhole
routing, optical networks supporting wavelength division
multiplexing, ATM switching, and networks supporting connected mode
routing protocols.
Since the chordal rings are competitors of networks as meshes or
tori because of theirs short diameter and bounded degree, it is of
interest to ask whether they can support intensive communications
(typically all-to-all) as efficiently as these networks. We
propose polynomial algorithms to derive optimal or near optimal
gossip protocols in the chordal ring
Green’s kernel for subdivision networks
Postprint (author's final draft
- …