The Kolmogorov constant is fundamental in stochastic models of turbulence. To explain the reasons for observed variations of this quantity, it is calculated for two flows by various methods and data. Velocity fluctuations are considered as the sum of contributions due to anisotropy, acceleration fluctuations and stochastic forcing that is controlled by the Kolmogorov constant. It is shown that ...

Monte-Carlo simulations featuring Kolmogorov phase screens have long been used in understanding both the effects of atmospheric turbulence on imaging and the performance of turbulence mitigation methods. We have developed a new, high fidelity, non-Kolmogorov phase screen model that allows the orientation of anisotropy to vary arbitrarily. Our model is used to generate simulated video sequences ...

Several experiments showed that the classical Kolmogorov power spectral density of the refractive-index sometimes does not properly describe the statistics of the atmosphere. In this paper we show an experimental testbed able to generate non-classical Kolmogorov turbulence by using a liquid crystal spatial light modulator. The testbed is used at Naval Postgraduate School for laboratory investig...

Kolmogorov complexity has intellectual roots in the areas of information theory, computability theory and probability theory. Despites its remarkably simple basis, it has some striking applications in Complexity Theory. The subject was developed by the Russian mathematician Andrei N. Kolmogorov (1903–1987) as an approach to the notion of random sequences and to provide an algorithmic approach t...

We continue the investigation of the path-connected geometry on the Cantor space and the related notions of dilution and compressibility described in [1]. These ideas are closely related to the notions of effective Hausdorff and packing dimensions of reals, and we argue that this geometry provides the natural context in which to study them. In particular we show that every regular real can be m...

What follows is a survey of the field of Kolmogorov complexity. Kolmogorov complexity, named after the mathematician Andrej Nikolaevič Kolmogorov, is a measure of the algorithmic complexity of a certain object (represented as a string of symbols) in terms of how hard it is to describe it. This measure dispenses with the need to know the probability distribution that rules a certain object (in g...

Given noisy observations Xi = θi + Zi, i = 1, . . . , n, with noise Zi iid ∼ N(0, σ), we wish to recover the signal θ with small mean-squared error. We consider the Minimum Kolmogorov Complexity Estimator (MKCE), defined roughly as the n-vector θ̂(X) solving the problem min Y K(Y ) subject to ‖X − Y ‖2l2n ≤ σ 2 · n, where K(Y ) denotes the length of the shortest computer program that can compute...

We introduce the study of Kolmogorov complexity with error. For a metric d, we define Ca(x) to be the length of a shortest program p which prints a string y such that d(x, y) ≤ a. We also study a conditional version of this measure Ca,b(x|y) where the task is, given a string y′ such that d(y, y′) ≤ b, print a string x′ such that d(x, x′) ≤ a. This definition admits both a uniform measure, where...

We survey diverse approaches to the notion of information: from Shannon entropy to Kolmogorov complexity. Two of the main applications of Kolmogorov complexity are presented: randomness and classification. The survey is divided in two parts in the same volume. Part I is dedicated to information theory and the mathematical formalization of randomness based on Kolmogorov complexity. This last app...