349 research outputs found
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
Quantum Geometry and its Implications for Black Holes
General relativity successfully describes space-times at scales that we can
observe and probe today, but it cannot be complete as a consequence of
singularity theorems. For a long time there have been indications that quantum
gravity will provide a more complete, non-singular extension which, however,
was difficult to verify in the absence of a quantum theory of gravity. By now
there are several candidates which show essential hints as to what a quantum
theory of gravity may look like. In particular, loop quantum gravity is a
non-perturbative formulation which is background independent, two properties
which are essential close to a classical singularity with strong fields and a
degenerate metric. In cosmological and black hole settings one can indeed see
explicitly how classical singularities are removed by quantum geometry: there
is a well-defined evolution all the way down to, and across, the smallest
scales. As for black holes, their horizon dynamics can be studied showing
characteristic modifications to the classical behavior. Conceptual and physical
issues can also be addressed in this context, providing lessons for quantum
gravity in general. Here, we conclude with some comments on the uniqueness
issue often linked to quantum gravity in some form or another.Comment: 16 pages, Plenary talk at ``Einstein's Legacy in the New Millenium,''
Puri, India, December 200
The linearization method and new classes of exact solutions in cosmology
We develop a method for constructing exact cosmological solutions of the
Einstein equations based on representing them as a second-order linear
differential equation. In particular, the method allows using an arbitrary
known solution to construct a more general solution parameterized by a set of
3\textit{N} constants, where \textit{N} is an arbitrary natural number. The
large number of free parameters may prove useful for constructing a theoretical
model that agrees satisfactorily with the results of astronomical observations.
Cosmological solutions on the Randall-Sundrum brane have similar properties. We
show that three-parameter solutions in the general case already exhibit
inflationary regimes. In contrast to previously studied two-parameter
solutions, these three-parameter solutions can describe an exit from inflation
without a fine tuning of the parameters and also several consecutive
inflationary regimes.Comment: 7 page
Pressure-induced phase transition of Bi2Te3 into the bcc structure
The pressure-induced phase transition of bismuth telluride, Bi2Te3, has been
studied by synchrotron x-ray diffraction measurements at room temperature using
a diamond-anvil cell (DAC) with loading pressures up to 29.8 GPa. We found a
high-pressure body-centered cubic (bcc) phase in Bi2Te3 at 25.2 GPa, which is
denoted as phase IV, and this phase apperars above 14.5 GPa. Upon releasing the
pressure from 29.8 GPa, the diffraction pattern changes with pressure
hysteresis. The original rhombohedral phase is recovered at 2.43 GPa. The bcc
structure can explain the phase IV peaks. We assumed that the structural model
of phase IV is analogous to a substitutional binary alloy; the Bi and Te atoms
are distributed in the bcc-lattice sites with space group Im-3m. The results of
Rietveld analysis based on this model agree well with both the experimental
data and calculated results. Therefore, the structure of phase IV in Bi2Te3 can
be explained by a solid solution with a bcc lattice in the Bi-Te (60 atomic%
tellurium) binary system.Comment: 12 pages, 5 figure
Vibrational spectra, dipole moments, and conformations of acylic sulfoxides
Acyclic aliphatic and aliphatic-aromatic sulfoxides exist in the form of equilibrium mixtures of conformations. In the case of bromomethyl methyl sulfoxide, a conformational equilibrium of three forms is observed, and an equilibrium between two forms basically exists for chloromethyl methyl sulfoxide and halomethyl aryl sulfoxides. © 1981 Plenum Publishing Corporation
Inflationary universe in loop quantum cosmology
Loop quantum cosmology provides a nice solution of avoiding the big bang
singularity through a big bounce mechanism in the high energy region. In loop
quantum cosmology an inflationary universe is emergent after the big bounce, no
matter what matter component is filled in the universe. A super-inflation phase
without phantom matter will appear in a certain way in the initial stage after
the bounce; then the universe will undergo a normal inflation stage. We discuss
the condition of inflation in detail in this framework. Also, for slow-roll
inflation, we expect the imprint from the effects of the loop quantum cosmology
should be left in the primordial perturbation power spectrum. However, we show
that this imprint is too weak to be observed.Comment: 21 pages, 4 figures; accepted for publication in JCA
Investigation of conformational equilibrium in a series of some 1,3-dioxa-2-phosphorinanes
1. The IR spectra of certain 1,3-dioxa-2-phosphorinanes were studied under conditions of various polarities of the medium and temperatures, and it was shown that 2,4-dimethy1-2-thiono- and 2-chloro-2-thiono-1,3-dioxa-2-phosphorinanes are characterized by stabilization of one conformational form, while for 2-methyl-2-thiono-1,3-dioxa-2-phosphorinane a dynamic equilibrium of two conformers is realized with an appreciable dependence of their amounts on the dielectric permeability of the medium. 2. An equilibrium of three conformers was detected for 2-chloro-4-methyl-2-thiono-1,3-dioxa-2-phosphorinane. It was hypothesized that, together with the "chair" conformation of the ring with axial and equatorial positions of the P=Sbond, the conformer with an equatorial arrangement of the P=S bond and a "boat" form of the ring participates in the equilibrium. © 1973 Consultants Bureau
Mathematical Modeling of a Solar Arrays Deploying Process at Ground Tests
This paper focuses on the creating of a mathematical model of a solar array deploying process during ground tests. Lagrange equation was used to obtain the math model. The distinctive feature of this mathematical model is the possibility of taking into account the gravity compensation system influence on the construction in the deploying process and the aerodynamic resistance during ground tests
Perturbative Degrees of Freedom in Loop Quantum Gravity: Anisotropies
The relation between an isotropic and an anisotropic model in loop quantum
cosmology is discussed in detail, comparing the strict symmetry reduction with
a perturbative implementation of symmetry. While the latter cannot be done in a
canonical manner, it allows to consider the dynamics including the role of
small non-symmetric degrees of freedom for the symmetric evolution. This serves
as a model for the general situation of perturbative degrees of freedom in a
background independent quantization such as loop quantum gravity, and for the
more complicated addition of perturbative inhomogeneities. While being crucial
for cosmological phenomenology, it is shown that perturbative non-symmetric
degrees of freedom do not allow definitive conclusions for the singularity
issue and in such a situation could even lead to wrong claims.Comment: 32 page
Effective State Metamorphosis in Semi-Classical Loop Quantum Cosmology
Modification to the behavior of geometrical density at short scales is a key
result of loop quantum cosmology, responsible for an interesting phenomenology
in the very early universe. We demonstrate the way matter with arbitrary scale
factor dependence in Hamiltonian incorporates this change in its effective
dynamics in the loop modified phase. For generic matter, the equation of state
starts varying near a critical scale factor, becomes negative below it and
violates strong energy condition. This opens a new avenue to generalize various
phenomenological applications in loop quantum cosmology. We show that different
ways to define energy density may yield radically different results, especially
for the case corresponding to classical dust. We also discuss implications for
frequency dispersion induced by modification to geometric density at small
scales.Comment: Revised version; includes expanded discussion of natural
trans-Planckian modifications to frequency dispersion and robustness to
quantization ambiguities. To appear in Class. Quant. Gra
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