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.

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...

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...

We use the connection of Hausdorff dimension and Kolmogorov complexity to describe a geometry on the Cantor set including concepts of angle, projections and scalar multiplication. A question related to compressibility is addressed using these geometrical ideas.

An infinite binary sequence X is Kolmogorov-Loveland (or KL) random if there is no computable non-monotonic betting strategy that succeeds on X in the sense of having an unbounded gain in the limit while betting successively on bits of X . A sequence X is KL-stochastic if there is no computable non-monotonic selection rule that selects from X an infinite, biased sequence. One of the major open ...

Conditional Kolmogorov complexity can be understood as the complexity of the problem “ ”, where is the problem “construct ” and is the problem “construct ”. Other logical operations ( ) can be interpreted in a similar way, extending Kolmogorov interpretation of intuitionistic logic and Kleene realizability. This leads to interesting problems in algorithmic information theory. Some of these ques...

Estimating forage biomass yield remotely from space is still challenging nowadays. Field experiments were conducted and ground measurements correlated to remote sensing data to estimate the forage biomass yield of Alpine-cold meadow grassland during the grass and grass-withering period in Sanjiangyuan area in Yushu county. Both Shapiro-Wilk and Kolmogorov-Smirnov two-tailed tests showed that th...