Symbolic dynamics from signed matrices
نویسندگان
چکیده
منابع مشابه
Symbolic Dynamics from Signed Matrices
We consider a method for assigning a sofic shift to a (not necessarily nonnegative integer) matrix by associating to it a directed graph with some vertices labelled 1 and the rest 2 (the decomposition of the vertices is arbitrary in applications the choice should be natural). We can detect positive topological entropy for this sofic shift by comparing the characteristic polynomial of the origin...
متن کاملSpectra of signed adjacency matrices
A signed adjacency matrix is a {−1, 0, 1}-matrix A obtained from the adjacency matrix A of a simple graph G by symmetrically replacing some of the 1’s of A by −1’s. Bilu and Linial have conjectured that if G is k-regular, then some A has spectral radius ρ(A) ≤ 2 √ k − 1. If their conjecture were true then, for each fixed k > 2, it would immediately guarantee the existence of infinite families o...
متن کاملP-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,...
متن کاملOn Matrices with Signed Null-Spaces
We denote by Q(A) the set of all matrices with the same sign pattern as A. A matrix A has signed null-space provided there exists a set S of sign patterns such that the set of sign patterns of vectors in the null-space of à is S for each à ∈ Q(A). Some properties of matrices with signed null-spaces are investigated.
متن کاملDynamics over Signed Networks
A signed network is a network with each link associated with a positive or negative sign. Models for nodes interacting over such signed networks, where two types of interactions are defined along the positive and negative links, respectively, arise from various biological, social, political, and economical systems. As modifications to the conventional DeGroot dynamics for positive links, two ba...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete and Continuous Dynamical Systems
سال: 2004
ISSN: 1078-0947
DOI: 10.3934/dcds.2004.11.621