2,058 research outputs found
Hidden invariance in Gurzadyan-Xue cosmological models
The dark energy formula derived by Gurzadyan and Xue which leads to a value
fitting the SN data, provides a scaling relation between the physical constants
and cosmological parameters and defines a set of cosmological models. In
previous works we have considered several of those models and derived the
cosmological equations for each case. In this letter, we present the phase
portrait analysis of those models. Surprisingly we found, first, that the
separatrix in the phase space which determines the character of solutions
depends solely on the value of the current matter density. Namely, at
the equations describe Friedmannian Universe with the classical
singularity at the beginning. While at all solutions for all
models start with zero density and non vanishing scale factor. Secondly, more
remarkable, the value defining the separatrix is the same
for all models, which reveales an underlying invariance hidden in the models,
possibly, due to the basic nature of the GX-scaling.Comment: to appear in Physics Letters
Kolmogorov's Structure Functions and Model Selection
In 1974 Kolmogorov proposed a non-probabilistic approach to statistics and
model selection. Let data be finite binary strings and models be finite sets of
binary strings. Consider model classes consisting of models of given maximal
(Kolmogorov) complexity. The ``structure function'' of the given data expresses
the relation between the complexity level constraint on a model class and the
least log-cardinality of a model in the class containing the data. We show that
the structure function determines all stochastic properties of the data: for
every constrained model class it determines the individual best-fitting model
in the class irrespective of whether the ``true'' model is in the model class
considered or not. In this setting, this happens {\em with certainty}, rather
than with high probability as is in the classical case. We precisely quantify
the goodness-of-fit of an individual model with respect to individual data. We
show that--within the obvious constraints--every graph is realized by the
structure function of some data. We determine the (un)computability properties
of the various functions contemplated and of the ``algorithmic minimal
sufficient statistic.''Comment: 25 pages LaTeX, 5 figures. In part in Proc 47th IEEE FOCS; this final
version (more explanations, cosmetic modifications) to appear in IEEE Trans
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Kinetic studies of oxidative coupling of methane on samarium oxide
Kinetic behaviour of three samples of samarium oxide (cubic (Sm-1 ), monoclinic (Sm-3) and mixed cubic-monoclinic (Sm 2) ) were studied in the oxidative coupling of methane using a gradientless flow circulation system. The specific rate of C2- product formation differed by a factor of 6-8 for Sm-1 and Sm-3. The specific activity for CO formation did not depend upon the crystal structure of samarium oxide while the rate of formation of CO2 was different for the samples studied. It is proposed that formation of CO and CO2 occurs via different reaction routes. The rate of CO2 formation at high CHJO2 ratio is limited by oxidant activation or surface CO2-complex decomposition
Game interpretation of Kolmogorov complexity
The Kolmogorov complexity function K can be relativized using any oracle A,
and most properties of K remain true for relativized versions. In section 1 we
provide an explanation for this observation by giving a game-theoretic
interpretation and showing that all "natural" properties are either true for
all sufficiently powerful oracles or false for all sufficiently powerful
oracles. This result is a simple consequence of Martin's determinacy theorem,
but its proof is instructive: it shows how one can prove statements about
Kolmogorov complexity by constructing a special game and a winning strategy in
this game. This technique is illustrated by several examples (total conditional
complexity, bijection complexity, randomness extraction, contrasting plain and
prefix complexities).Comment: 11 pages. Presented in 2009 at the conference on randomness in
Madison
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