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The behavior of a Markov network with respect to an absorbing class: the target algorithm

Giacomo Aletti (2009)

RAIRO - Operations Research

In this paper, we face a generalization of the problem of finding the distribution of how long it takes to reach a “target” set T of states in Markov chain. The graph problems of finding the number of paths that go from a state to a target set and of finding the n-length path connections are shown to belong to this generalization. This paper explores how the state space of the Markov chain can be reduced by collapsing together those states that behave in the same way for the purposes of calculating...

The Collatz-Wielandt quotient for pairs of nonnegative operators

Shmuel Friedland (2020)

Applications of Mathematics

In this paper we consider two versions of the Collatz-Wielandt quotient for a pair of nonnegative operators A , B that map a given pointed generating cone in the first space into a given pointed generating cone in the second space. If the two spaces and two cones are identical, and B is the identity operator, then one version of this quotient is the spectral radius of A . In some applications, as commodity pricing, power control in wireless networks and quantum information theory, one needs to deal with...

The completely distributive lattice of machine invariant sets of infinite words

Aleksandrs Belovs, Jānis Buls (2007)

Discussiones Mathematicae - General Algebra and Applications

We investigate the lattice of machine invariant classes. This is an infinite completely distributive lattice but it is not a Boolean lattice. The length and width of it is c. We show the subword complexity and the growth function create machine invariant classes.

The dimension of graph directed attractors with overlaps on the line, with an application to a problem in fractal image recognition

Michael Keane, K. Károly, Boris Solomyak (2003)

Fundamenta Mathematicae

Consider a graph directed iterated function system (GIFS) on the line which consists of similarities. Assuming neither any separation conditions, nor any restrictions on the contractions, we compute the almost sure dimension of the attractor. Then we apply our result to give a partial answer to an open problem in the field of fractal image recognition concerning some self-affine graph directed attractors in space.

The entropy of Łukasiewicz-languages

Ludwig Staiger (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

The paper presents an elementary approach for the calculation of the entropy of a class of languages. This approach is based on the consideration of roots of a real polynomial and is also suitable for calculating the Bernoulli measure. The class of languages we consider here is a generalisation of the Łukasiewicz language.

The entropy of Łukasiewicz-languages

Ludwig Staiger (2010)

RAIRO - Theoretical Informatics and Applications

The paper presents an elementary approach for the calculation of the entropy of a class of languages. This approach is based on the consideration of roots of a real polynomial and is also suitable for calculating the Bernoulli measure. The class of languages we consider here is a generalisation of the Łukasiewicz language.

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