Algorithmic statistics revisited

The mission of statistics is to provide adequate statistical hypotheses (models) for observed data. But what is an "adequate" model? To answer this question, one needs to use the notions of algorithmic information theory. It turns out that for every data string $x$ one can naturally define "stochasticity profile", a curve that represents a trade-off between complexity of a model and its adequacy. This curve has four different equivalent definitions in terms of (1)~randomness deficiency, (2)~minimal description length, (3)~position in the lists of simple strings and (4)~Kolmogorov complexity with decompression time bounded by busy beaver function. We present a survey of the corresponding definitions and results relating them to each other

Algorithmic statistics: forty years later

Algorithmic statistics has two different (and almost orthogonal) motivations. From the philosophical point of view, it tries to formalize how the statistics works and why some statistical models are better than others. After this notion of a "good model" is introduced, a natural question arises: it is possible that for some piece of data there is no good model? If yes, how often these bad ("non-stochastic") data appear "in real life"? Another, more technical motivation comes from algorithmic information theory. In this theory a notion of complexity of a finite object (=amount of information in this object) is introduced; it assigns to every object some number, called its algorithmic complexity (or Kolmogorov complexity). Algorithmic statistic provides a more fine-grained classification: for each finite object some curve is defined that characterizes its behavior. It turns out that several different definitions give (approximately) the same curve. In this survey we try to provide an exposition of the main results in the field (including full proofs for the most important ones), as well as some historical comments. We assume that the reader is familiar with the main notions of algorithmic information (Kolmogorov complexity) theory.Comment: Missing proofs adde

On Algorithmic Statistics for space-bounded algorithms

Algorithmic statistics studies explanations of observed data that are good in the algorithmic sense: an explanation should be simple i.e. should have small Kolmogorov complexity and capture all the algorithmically discoverable regularities in the data. However this idea can not be used in practice because Kolmogorov complexity is not computable. In this paper we develop algorithmic statistics using space-bounded Kolmogorov complexity. We prove an analogue of one of the main result of `classic' algorithmic statistics (about the connection between optimality and randomness deficiences). The main tool of our proof is the Nisan-Wigderson generator.Comment: accepted to CSR 2017 conferenc

Qualitative Approach to Semi-Classical Loop Quantum Cosmology

Recently the mechanism was found which allows avoidance of the cosmological singularity within the semi-classical formulation of Loop Quantum Gravity. Numerical studies show that the presence of self-interaction potential of the scalar field allows generation of initial conditions for successful slow-roll inflation. In this paper qualitative analysis of dynamical system, corresponding to cosmological equations of Loop Quantum Gravity is performed. The conclusion on singularity avoidance in positively curved cosmological models is confirmed. Two cases are considered, the massless (with flat potential) and massive scalar field. Explanation of initial conditions generation for inflation in models with massive scalar field is given. The bounce is discussed in models with zero spatial curvature and negative potentials.Comment: Online at http://www.iop.org/EJ/abstract/1475-7516/2004/07/01

Investigation of the steric structure of certain compounds of the bicyclo-[4,2,0]octan-7-one series

1. The steric structure of adducts of dichloroketene and cyclohexene, dichloroketene and methyl-cyclohexene, dimethylketene and dihydropyran was investigated by the methods of dipole moments and molar Kerr constants. 2. For all the adducts, the preferential conformation of the bicyclo[4,2,0]octan-7-one system is the anti-boat conformation. 3. The adduct of dimethylketene and dihydropyran has the structure of 8,8-dimethyl-2-oxobicyclo-[4,2,0] octan-7-one. The formation of such a structure is apparently determined by the electron donor influence of the oxygen atom in dihydropyran on the process of cycloaddition. © 1974 Consultants Bureau

Approach of the NGC 1977 star cluster to the TOI-2796 host star

We study of possible encounters in past epochs of the open star cluster NGC 1977 with host stars. For this purpose, the age of the cluster was determined based on our catalog data. Stars with planetary systems were selected from the NASA Archive. The age of the cluster was determined using the color - absolute magnitude diagram and the isochron system. By extending the track of the movement of the cluster and stars in past epochs, 10 Myr. The time of the maximum approach 32 pc of the host star with planetary system TOI-2796 with the NGC 1977 are found. The place of approach in the sky is shown, this point can be considered as the place of appearance of interstellar comets. Thus, the result of our work is that the we found approach of the host star to the cluster entailed effects associated with the gravitational influence of the cluster on the nuclei of comets located in the outer parts of the Oort cloud of the planetary system. The effect of approach on comets is estimated

Dipole moments of organophosphorus compounds. 15. Polarities and polarizabilities of some acetylenic compounds

1. Effective P-Csp bond dipole moments have been calculated for the oxides of diethyl and diphenylpropynylphosphines, and for the dichloroanhydride of propynylphosphonic acid. 2. The form with gauche orientation of the phosphoryl and ethoxy groups is preferred in the 0,0-diethyl ethynyl -and 0,0-diethyl propynylphosphonates. 3. The C-CH3 bonds of the ethyl and phosphoryl groups are in gauche orientation in diethylpropynylphosphine oxide. The structure of diphenylpropynylphosphine oxide is such that the phenyl radical planes are close to ethynyl group shielding. © 1978 Plenum Publishing Corporation

Chemistry for Sustainable Development 16 (2008) 521-528 Content of Various Size and Density Particles in Cenosphere Concentrates of Volatile Coal Combustion Ashes from the Kuznetsk Coalfield

Abstract Using an aerodynamic method with the subsequent particle size analysis of the fractions obtained a separation process was carried out for cenosphere concentrates from volatile ashes of the Kuznetsk field coal combustion at the Moscow Thermal and Electric Plant TETs-22, the Belovo State Regional Power Station as well as for several cenosphere concentrate fractions obtained at the Novosibirsk Thermal and Electric Plant TETs-5. As much as 90 fractions with the various particle size (70-250 mm) and bulk density (0.16-0.52 g/cm 3 ) have been isolated from the concentrate of the Moscow TETs-22. Irrespective of particle size the bulk density of fractions with the maximal yield is equal to 0.33-0.35g/cm 3 , whereas the ratio of the apparent wall thickness to the particle diameter amounts to 0.042-0.043. The process of the aerodynamic separation of cenospheres from different concentrate sources can be satisfactorily described by theoretical dependences for the carryover of spherical particles; the deviations are caused, first of all, by a nonspherical shape of cenospheres