Details of the spatial structure and kinematics of the Castor and Ursa Major streams

A list of the Castor stream members is compiled based on the data from various authors. The membership probabilities for some stars are revised based on the individual apex, multiplicity, observational errors, and peculiarity. The apex of the Castor moving group is determined using the apex diagram method. The parameters of the Castor and Ursa Major streams are compared and the positions of the two streams on the apex diagram are found to differ by 225deg, implying that the two groups move in almost opposite directions. Stars of both moving groups are intermixed in space, the Castor stream occupies a smaller volume than the UMa stream and is located inside it. Our results can be useful for understanding the morphology of the Galactic disk in the Sun's vicinity

Radial velocity dispersions of star groups in M 67

High-precision measurements of radial velocities of the M 67 cluster members are used to calculate the radial-velocity dispersions in the stellar groups found earlier in the cluster's corona. The previously detected feature in one of the groups (Group 60) consisting of stars with almost identical space velocities was confirmed. The possibility of more accurate future studies of the parameters of star groups using the Gaia catalogues is discussed.Comment: 7 pages, 2 figure

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