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

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

Effect of pressure on the Raman modes of antimony

The effect of pressure on the zone-center optical phonon modes of antimony in the A7 structure has been investigated by Raman spectroscopy. The A_g and E_g frequencies exhibit a pronounced softening with increasing pressure, the effect being related to a gradual suppression of the Peierls-like distortion of the A7 phase relative to a cubic primitive lattice. Also, both Raman modes broaden significantly under pressure. Spectra taken at low temperature indicate that the broadening is at least partly caused by phonon-phonon interactions. We also report results of ab initio frozen-phonon calculations of the A_g and E_g mode frequencies. Presence of strong anharmonicity is clearly apparent in calculated total energy versus atom displacement relations. Pronounced nonlinearities in the force versus displacement relations are observed. Structural instabilities of the Sb-A7 phase are briefly addressed in the Appendix.Comment: 10 pages, 8 figure

Counting and computing regions of DD-decomposition: algebro-geometric approach

New methods for $D$-decomposition analysis are presented. They are based on topology of real algebraic varieties and computational real algebraic geometry. The estimate of number of root invariant regions for polynomial parametric families of polynomial and matrices is given. For the case of two parametric family more sharp estimate is proven. Theoretic results are supported by various numerical simulations that show higher precision of presented methods with respect to traditional ones. The presented methods are inherently global and could be applied for studying $D$-decomposition for the space of parameters as a whole instead of some prescribed regions. For symbolic computations the Maple v.14 software and its package RegularChains are used.Comment: 16 pages, 8 figure

Phase Diagram of Pressure-induced Superconductivity and its Relation to Hall Coefficient in Bi2Te3 Single Crystal

Pressure-induced superconductivity and its relation to corresponding Hall coefficient (RH) have been reported for Bi2Te3, one of known topological insulators. A full phase diagram is presented which shows a complex dependence of the superconducting transition temperature as a function of pressure over an extensive range. High-pressure RH measurements reveal a close relation of these complex behaviors, particularly, a dramatic change of dRH/dP before structural phase transition and a pressure-induced crossover on RH in the high pressure phase were observed.Comment: 14 pages and 3 figure

High pressure transport properties of the topological insulator Bi2Se3

We report x-ray diffraction, electrical resistivity, and magnetoresistance measurements on Bi2Se3 under high pressure and low temperature conditions. Pressure induces profound changes in both the room temperature value of the electrical resistivity as well as the temperature dependence of the resistivity. Initially, pressure drives Bi2Se3 towards increasingly insulating behavior and then, at higher pressures, the sample appears to enter a fully metallic state coincident with a change in the crystal structure. Within the low pressure phase, Bi2Se3 exhibits an unusual field dependence of the transverse magnetoresistance that is positive at low fields and becomes negative at higher fields. Our results demonstrate that pressures below 8 GPa provide a non-chemical means to controllably reduce the bulk conductivity of Bi2Se3

Evolution of the number of accreting white dwarfs with shell nuclear burning and of occurrence rate of SN Ia

We analyze temporal evolution of the number of accreting white dwarfs with shell hydrogen burning in semidetached and detached binaries. We consider a stellar system in which star formation lasts for 10 Gyr with a constant rate, as well as a system in which the same amount of stars is formed in a single burst lasting for 1 Gyr. Evolution of the number of white dwarfs is confronted to the evolution of occurrence rate of events that usually are identified with SN Ia or accretion-induced collapses, i.e. with accumulation of Chandrasekhar mass by a white dwarf or a merger of a pair of CO white dwarfs with total mass not lower than the Chandrasekhar one. In the systems with a burst of star formation, at $t=$10 Gyr observed supersoft X-ray sources, most probably, are not precursors of SN Ia. The same is true for an overwhelming majority of the sources in the systems with constant star formation rate. In the systems of both kinds mergers of white dwarfs is the dominant SN Ia scenario. In symbiotic binaries, accreting CO-dwarfs do not accumulate enough mass for SN Ia explosion, while ONeMg-dwarfs finish their evolution by an accretion-induced collapse with formation of a neutron star.Comment: 11 pages, 2 figures, accepted by Astronomy Letter

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

High-pressure vibrational and optical study of Bi2Te3

We report an experimental and theoretical lattice dynamics study of bismuth telluride (Bi2Te3) up to 23 GPa together with an experimental and theoretical study of the optical absorption and reflection up to 10 GPa. The indirect bandgap of the low-pressure rhombohedral (R-3m) phase (α-Bi2Te3) was observed to decrease with pressure at a rate of −6 meV/GPa. In regard to lattice dynamics, Raman-active modes of α-Bi2Te3 were observed up to 7.4 GPa. The pressure dependence of their frequency and width provides evidence of the presence of an electronic-topological transition around 4.0 GPa. Above 7.4 GPa a phase transition is detected to the C2/m structure. On further increasing pressure two additional phase transitions, attributed to the C2/c and disordered bcc (Im-3m) phases, have been observed near 15.5 and 21.6 GPa in good agreement with the structures recently observed by means of x-ray diffraction at high pressures in Bi2Te3. After release of pressure the sample reverts back to the original rhombohedral phase after considerable hysteresis. Raman- and IR-mode symmetries, frequencies, and pressure coefficients in the different phases are reported and discussed.This work has been done under financial support from Spanish MICINN under projects MAT2008-06873-C02- 02, MAT2007-66129, Prometeo/2011-035, MAT2010-21270-C04-03/04, and CSD2007-00045 and supported by the Ministry of Education, Youth and Sports of the Czech Republic (MSM 0021627501)

On Second-Order Monadic Monoidal and Groupoidal Quantifiers

We study logics defined in terms of second-order monadic monoidal and groupoidal quantifiers. These are generalized quantifiers defined by monoid and groupoid word-problems, equivalently, by regular and context-free languages. We give a computational classification of the expressive power of these logics over strings with varying built-in predicates. In particular, we show that ATIME(n) can be logically characterized in terms of second-order monadic monoidal quantifiers