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

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

Pair plasma relaxation time scales

By numerically solving the relativistic Boltzmann equations, we compute the time scale for relaxation to thermal equilibrium for an optically thick electron-positron plasma with baryon loading. We focus on the time scales of electromagnetic interactions. The collisional integrals are obtained directly from the corresponding QED matrix elements. Thermalization time scales are computed for a wide range of values of both the total energy density (over 10 orders of magnitude) and of the baryonic loading parameter (over 6 orders of magnitude). This also allows us to study such interesting limiting cases as the almost purely electron-positron plasma or electron-proton plasma as well as intermediate cases. These results appear to be important both for laboratory experiments aimed at generating optically thick pair plasmas as well as for astrophysical models in which electron-positron pair plasmas play a relevant role.Comment: Phys. Rev. E, in pres

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

Geometric structures of the N,N-dimethylamides and N-methylanilides of arylsulfonic acids

1. Dipole moments and components of the poiarizability tensor have been calculated for the S-N bond in the sulfamides. 2. The aryl radicals in the N,N-dimethylsulfamides project out of the C-S-N plane by an angle of 66 ±10°. 3. In the arylsulfanilides, the angle of rotation around the S-N bond is 270 t{combining short stroke overlay} 30°. 4. The fact that the angle of aryl rotation at the N atom is not dependent on the nature of the substituent is an indication that there is only negligible conjugation between the aromatic ring and the unshared electron pair of the nitrogen. © 1980 Plenum Publishing Corporation

НОВІТНІ ПІДХОДИ ДО КОРЕКЦІЇ БОЛЬОВОГО СИНДРОМУ У ХВОРИХ З ОБЛІТЕРУЮЧИМ АТЕРОСКЛЕРОЗОМ НИЖНІХ КІНЦІВОК, ЩО ПРООПЕРОВАНІ МЕТОДОМ ЕНДОВАСКУЛЯРНОЇ БАЛОНОПЛАСТИКИ

Purpose. In order to optimize the intraoperative anesthesia tactics we used epidural anesthesia.Materials and methods. There were 40 patients. They were randomized into 2 groups of 20 people. Patients of I group performed analgosedation, group – II epidural analgesia.Results. The use of epidural anesthesia sol. 0.125% bupivacaine in the volume of 30 ml with the addition of 0.12 mg of sol. Buprenorphine provided adequate levels of both intra- and postoperative analgesia of balonplastics of obliterating atherosclerosis of the lower limbs.З метою оптимізувати інтраопераційну анестезіологічну тактику, для знеболювання було використано епідуральну аналгезію.Матеріали і методи. 40 пацієнтів були рандомізовано розподілені на дві групи по 20 осіб. Хворим І групи проводилась аналгоседація, ІІ групи – епідуральна анестезія.Результати. Застосування епідуральної анестезії розчином 0,125% бупівакаїну в об’ємі 30 мл з додавання 0,12 мг розчину бупренорфіну забезпечувало адекватний рівень як інтра-, так і післяопераційної аналгезії при балонопластиці облітеруючого атеросклерозу нижніх кінцівок

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