Shifts with decidable language and non-computable entropy

Automata, Logic and Semantic

Computational Complexity of Iterated Maps on the Interval (Extended Abstract)

The exact computation of orbits of discrete dynamical systems on the interval is considered. Therefore, a multiple-precision floating point approach based on error analysis is chosen and a general algorithm is presented. The correctness of the algorithm is shown and the computational complexity is analyzed. As a main result, the computational complexity measure considered here is related to the Ljapunow exponent of the dynamical system under consideration

Exogenous Ether Lipids Predominantly Target Mitochondria

Ether lipids are ubiquitous constituents of cellular membranes with no discrete cell biological function assigned yet. Using fluorescent polyene-ether lipids we analyzed their intracellular distribution in living cells by microscopy. Mitochondria and the endoplasmic reticulum accumulated high amounts of ether-phosphatidylcholine and ether-phosphatidylethanolamine. Both lipids were specifically labeled using the corresponding lyso-ether lipids, which we established as supreme precursors for lipid tagging. Polyfosine, a fluorescent analogue of the anti-neoplastic ether lipid edelfosine, accumulated to mitochondria and induced morphological changes and cellular apoptosis. These data indicate that edelfosine could exert its pro-apoptotic power by targeting and damaging mitochondria and thereby inducing cellular apoptosis. In general, this study implies an important role of mitochondria in ether lipid metabolism and intracellular ether lipid trafficking

Computability of Topological Pressure for Sofic Shifts with Applications in Statistical Physics

The topological pressure of dynamical systems theory is examined from a computability theoretic point of view. It is shown that for sofic shift dynamical systems, the topological pressure is a computable function. This result is applied to a certain class of one dimensional spin systems in statistical physics. As a consequence, the specific free energy of these spin systems is computable. Finally, phase transitions of these systems are considered. It turns out that the critical temperature is recursively approximable

Computing a Solution of Feigenbaum's Functional Equation in Polynomial Time

Lanford has shown that Feigenbaum's functional equation has an analytic solution. We show that this solution is a polynomial time computable function. This implies in particular that the so-called first Feigenbaum constant is a polynomial time computable real number

Shifts with Decidable Language and Non-Computable Entropy

We consider subshifts of the full shift of all binary bi-infinite sequences. On the one hand, the topological entropy of any subshift with computably co-enumerable language is a right-computable real number between 0 and 1. We show that, on the other hand, any right-computable real number between 0 and 1, whether computable or not, is the entropy of some subshift with even polynomial time decidable language. In addition, we show that computability of the entropy of a subshift does not imply any kind of computability of the language of the subshift

Computing a Solution of Feigenbaum's Functional Equation in Polynomial Time

Lanford has shown that Feigenbaum's functional equation has an analyticsolution. We show that this solution is a polynomial time computable function.This implies in particular that the so-called first Feigenbaum constant is apolynomial time computable real number.Comment: CCA 2012, Cambridge, UK, 24-27 June 201

Computing a Solution of Feigenbaum's Functional Equation in Polynomial Time

Lanford has shown that Feigenbaum's functional equation has an analytic solution. We show that this solution is a polynomial time computable function. This implies in particular that the so-called first Feigenbaum constant is a polynomial time computable real number.Comment: CCA 2012, Cambridge, UK, 24-27 June 201