1,343 research outputs found
Graphs having no quantum symmetry
We consider circulant graphs having vertices, with prime. To any such
graph we associate a certain number , that we call type of the graph. We
prove that for the graph has no quantum symmetry, in the sense that the
quantum automorphism group reduces to the classical automorphism group.Comment: 14 page
Boolean networks synchronism sensitivity and XOR circulant networks convergence time
In this paper are presented first results of a theoretical study on the role
of non-monotone interactions in Boolean automata networks. We propose to
analyse the contribution of non-monotony to the diversity and complexity in
their dynamical behaviours according to two axes. The first one consists in
supporting the idea that non-monotony has a peculiar influence on the
sensitivity to synchronism of such networks. It leads us to the second axis
that presents preliminary results and builds an understanding of the dynamical
behaviours, in particular concerning convergence times, of specific
non-monotone Boolean automata networks called XOR circulant networks.Comment: In Proceedings AUTOMATA&JAC 2012, arXiv:1208.249
P-matrices and signed digraphs
We associate a signed digraph with a list of matrices whose dimensions permit
them to be multiplied, and whose product is square. Cycles in this graph have a
parity, that is, they are either even (termed e-cycles) or odd (termed
o-cycles). The absence of e-cycles in the graph is shown to imply that the
matrix product is a P0-matrix, i.e., all of its principal minors are
nonnegative. Conversely, the presence of an e-cycle is shown to imply that
there exists a list of matrices associated with the graph whose product fails
to be a P0-matrix. The results generalise a number of previous results relating
P- and P0-matrices to graphs
The modeling of diffuse boundaries in the 2-D digital waveguide mesh
The digital waveguide mesh can be used to simulate the propagation of sound waves in an acoustic system. The accurate simulation of the acoustic characteristics of boundaries within such a system is an important part of the model. One significant property of an acoustic boundary is its diffusivity. Previous approaches to simulating diffuse boundaries in a digital waveguide mesh are effective but exhibit limitations and have not been analyzed in detail. An improved technique is presented here that simulates diffusion at boundaries and offers a high degree of control and consistency. This technique works by rotating wavefronts as they pass through a special diffusing layer adjacent to the boundary. The waves are rotated randomly according to a chosen probability function and the model is lossless. This diffusion model is analyzed in detail, and its diffusivity is quantified in the form of frequency dependent diffusion coefficients. The approach used to measuring boundary diffusion is described here in detail for the 2-D digital waveguide mesh and can readily be extended for the 3-D case
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