We study the spectrum of operators $$aT \in {\cal B}(H)$$ on a Hilbert space H where T is an isometry and belongs to commutative C*-subalgebra $$C(X) \cong A \subseteq such that formula L(a) = T*aT defines faithful transfer operator A. Based analysis C*-algebra C* (A, T) generated by aT, ∈ A, we give dynamical conditions implying σ(aT) invariant under rotation around zero, coincides with essent...

The objective is to study changes in EEG time-domain Kolmogorov entropy and cortical lateralization of brain function areas during complex problem solving mental task in healthy human subjects. EEG data for healthy subjects are acquired during complex problem solving mental task using a net of 6 electrodes. The subject was given a nontrivial multiplication problem to solve and the signals were ...

Kolmogorov complexity and Shannon entropy are conceptually different measures. However, for any recursive probability distribution, the expected value of Kolmogorov complexity equals its Shannon entropy, up to a constant. We study if a similar relationship holds for Rényi and Tsallis entropies of order α, showing that it only holds for α = 1. Regarding a time-bounded analogue relationship, we s...

We analyze the behavior of quantum dynamical entropies production from sequences of quantum approximants approaching their (chaotic) classical limit. The model of the quantized hyperbolic automorphisms of the 2-torus is examined in detail and a semi-classical analysis is performed on it using coherent states, fulfilling an appropriate dynamical localization property. Correspondence between quan...

We analyze the behavior of quantum dynamical entropies production from sequences of quantum approximants approaching their (chaotic) classical limit. The model of the quantized hyperbolic automorphisms of the 2–torus is examined in detail and a semi–classical analysis is performed on it using coherent states, fulfilling an appropriate dynamical localization property. Correspondence between quan...

Information entropy is used to summarize transcriptome data, but ignoring zero count data contained them. Ignoring zero count data causes loss of information and sometimes it was difficult to distinguish between multiple transcriptomes. Here, we estimate Kolmogorov complexity of transcriptome treating zero count data and distinguish similar transcriptome data.

A flow in a category X is an object X of X provided with an endomorphism T : X → X in X. In most of the cases X will be the category of (topological) groups and (continuous) group homomorphisms, the category of right modules over a ring R and the R-module homomorphisms, or just the category of topological (resp., measure) spaces and continuous (resp., measure preserving) maps. An isomorphism be...