We consider stochastically modeled reaction networks and prove that if a constant solution to the Kolmogorov forward equation decays fast enough relative to the transition rates, then the model is non-explosive. In particular, complex balanced reaction networks are non-explosive.

We present a brief survey of results on relations between the Kolmogorov complexity of infinite strings and several measures of information content (dimensions) known from dimension theory, information theory or fractal geometry. Special emphasis is laid on bounds on the complexity of strings in constructively given subsets of the Cantor space. Finally, we compare the Kolmogorov complexity to t...

The equivalence of universal measure, a priori probability and the negative exponential of Kolmogorov complexity is a well known result with signiicance both to the theory of Kolmogorov complexity and many of its applications. In this paper we consider deenitions for the time-bounded setting where similar equivalences hold. Unlike the unbounded case, time-bounded universal distributions give ri...

A model of laminated weak turbulence (WT) is presented. This model consists of two co-existing layers one with continuous spectra, covered by Kolmogorov ́s theory and KAM tori, and one with discrete spectra, covered by discrete classes of waves and Clipping method. Some known laboratory experiments and numerical simulations are explained in the frame of this model. A few problems which might app...

We present families of unital algebras obtained through a doubling process from a cyclic central simple algebra D = (K/F, σ, c), employing a K-automorphism τ and an element d ∈ D. These algebras appear in the construction of iterated spacetime block codes. We give conditions when these iterated algebras are division which can be used to construct fully diverse iterated codes. We also briefly lo...

The conditional in conditional Kolmogorov complexity commonly is taken to be a finite binary string. The Coding Theorem of L.A. Levin connects unconditional prefix Kolmogorov complexity with the discrete universal distribution. The least upper semicomputable code-length is up to a constant equal to the negative logarithm of the greatest lower semicomputable probability mass function. We investi...

The purpose of this thesis is to give a formal definition of quantum Kolmogorov complexity and rigorous mathematical proofs of its basic properties. Classical Kolmogorov complexity is a well-known and useful measure of randomness for binary strings. In recent years, several different quantum generalizations of Kolmogorov complexity have been proposed. The most natural generalization is due to B...