25 research outputs found
Constraint Ergodic optimization for generic continuous functions
One of the fundamental results of ergodic optimization asserts that for any
dynamical system on a compact metric space with the specification property and
for a generic continuous function every invariant probability measure that
maximizes the space average of must have zero entropy. We establish the
analogical result in the context of constraint ergodic optimization, which is
introduced by Garibaldi and Lopes (2007)
Splicing Systems from Past to Future: Old and New Challenges
A splicing system is a formal model of a recombinant behaviour of sets of
double stranded DNA molecules when acted on by restriction enzymes and ligase.
In this survey we will concentrate on a specific behaviour of a type of
splicing systems, introduced by P\u{a}un and subsequently developed by many
researchers in both linear and circular case of splicing definition. In
particular, we will present recent results on this topic and how they stimulate
new challenging investigations.Comment: Appeared in: Discrete Mathematics and Computer Science. Papers in
Memoriam Alexandru Mateescu (1952-2005). The Publishing House of the Romanian
Academy, 2014. arXiv admin note: text overlap with arXiv:1112.4897 by other
author
On Commutation and Conjugacy of Rational Languages and the Fixed Point Method
The research on language equations has been active during last decades. Compared to the equations on words the equations on languages are much more difficult to solve. Even very simple equations that are easy to solve for words can be very hard for languages. In this thesis we study two of such equations, namely commutation and conjugacy equations. We study these equations on some limited special cases and compare some of these results to the solutions of corresponding equations on words. For both equations we study the maximal solutions, the centralizer and the conjugator. We present a fixed point method that we can use to search these maximal solutions and analyze the reasons why this method is not successful for all languages. We give also several examples to illustrate the behaviour of this method.Siirretty Doriast