794 research outputs found
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 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
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