4,474 research outputs found
Strong Structural Controllability of Signed Networks
In this paper, we discuss the controllability of a family of linear
time-invariant (LTI) networks defined on a signed graph. In this direction, we
introduce the notion of positive and negative signed zero forcing sets for the
controllability analysis of positive and negative eigenvalues of system
matrices with the same sign pattern. A sufficient combinatorial condition that
ensures the strong structural controllability of signed networks is then
proposed. Moreover, an upper bound on the maximum multiplicity of positive and
negative eigenvalues associated with a signed graph is provided
Covering a bounded set of functions by an increasing chain of slaloms
A slalom is a sequence of finite sets of length omega. Slaloms are ordered by
coordinatewise inclusion with finitely many exceptions. Improving earlier
results of Mildenberger, Shelah and Tsaban, we prove consistency results
concerning existence and non-existence of an increasing sequence of a certain
type of slaloms which covers a bounded set of functions in the Baire space
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