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## On Stability of Probability Laws with Respect to Small Violations of Algorithmic Randomness

Theory of Computing Systems. 2016. P. 403-423.

V'yugin V.

We study a stability property of probability laws with respect to small violations of algorithmic randomness. Some sufficient

condition of stability is presented in terms of Schnorr tests of algorithmic randomness. Most probability laws, like the

strong law of large numbers, the law of iterated logarithm, and even Birkhoff's pointwise ergodic theorem for ergodic

transformations, are stable in this sense. Nevertheless, the phenomenon of instability occurs in ergodic theory. Firstly, the stability property of Birkhoff's ergodic theorem is non-uniform. Moreover, a computable non-ergodic measure-preserving transformation can be constructed such that the ergodic theorem is non-stable.

Springer, 2013

Vladimir Arnold was one of the great mathematical scientists of our time. He is famous for both the breadth and the depth of his work. At the same time he is one of the most prolific and outstanding mathematical authors. This second volume of his Collected Works focuses on hydrodynamics, bifurcation theory, and algebraic geometry. ...

Added: February 20, 2013

Minabutdinov A., Записки научных семинаров ПОМИ РАН 2016 Т. 448 С. 177-200

We prove existence of limiting curves (describing deviations in ergodic theorem) for cylindrical functions for Polynomial adic systems. For a general ergodic measure-preserving transformation and a summable function we give necessary condition of a limiting curve to exist. Our work generalizes results by E'. Janvresse, T. de la Rue and Y. Velenik. ...

Added: October 14, 2016

Blank M., Nonlinearity 2017 Vol. 30 No. 12 P. 4649-4664

The classical Birkhoff ergodic theorem in its most popular version says that the
time average along a single typical trajectory of a dynamical system is equal
to the space average with respect to the ergodic invariant distribution. This
result is one of the cornerstones of the entire ergodic theory and its numerous
applications. Two questions related to this subject ...

Added: July 16, 2018

Milovanov A., Theory of Computing Systems 2017 Vol. 61 No. 2 P. 521-535

Algorithmic statistics is a part of algorithmic information theory (Kolmogorov complexity theory) that studies the following task: given a finite object x (say, a binary string), find an `explanation' for it, i.e., a simple finite set that contains x and where x is a `typical element'. Both notions (`simple' and `typical') are defined in terms ...

Added: June 27, 2016

Blank M., [б.и.], 2017

We study typical points with respect to ergofic averaging of a general dynamical system. ...

Added: February 10, 2018

Danilov V., Rakhel M., Russian Journal of Mathematical Physics 2021 Vol. 28 No. 2 P. 179-187

In this paper, we show how to construct an asymptotic representation of the fundamental solution to the Cauchy problem for degenerate linear parabolic equations. ...

Added: June 6, 2021

Akopov A. S., Beklaryan L. A., Saghatelyan A. K., Environmental Modelling and Software 2019 Vol. 116 P. 7-25

Urban greenery such as trees can effectively reduce air pollution in a natural and eco-friendly way. However, how to spatially locate and arrange greenery in an optimal way remains as a challenging task. We developed an agent-based model of air pollution dynamics to support the optimal allocation and configuration of tree clusters in a city. The Pareto ...

Added: February 24, 2019

Lanham : University Press of America, 2012

The history of logic and analytic philosophy in Central and Eastern Europe is still known to very few people. As an exception to the rule, only two scientific schools became internationally popular: the Vienna Circle and the Lvov-Warsaw School. Nevertheless, the countries included in this region have not only joint history, but also joint cultural ...

Added: February 13, 2013

Malyshev D., Discrete Mathematics 2015 Vol. 338 No. 11 P. 1860-1865

We completely determine the complexity status of the 3-colorability problem for hereditary graph classes defined by two forbidden induced subgraphs with at most five vertices. ...

Added: April 7, 2014

Nicol R., Chapman S., Vertes P. et al., Journal of Neurophysiology (США) 2012 Vol. 107 No. 5 P. 1421-1430

How do human brain networks react to dynamic changes in the sensory environment? We measured rapid changes in brain network organization in response to brief, discrete, salient auditory stimuli. We estimated network topology and distance parameters in the immediate central response period, <1 s following auditory presentation of standard tones interspersed with occasional deviant tones ...

Added: October 23, 2014

Decrouez G. G., Hall P., Bernoulli: a journal of mathematical statistics and probability 2013 Vol. 19 No. 4 P. 1268-1293

Motivated by a problem arising when analysing data from quarantine searches, we explore properties of distributions of sums of independent means of independent lattice-valued random variables. The aim is to determine the extent to which approximations to those sums require continuity corrections. We show that, in cases where there are only two different means, the ...

Added: September 29, 2014

P. : Université Paris 13 - Paris Sorbonne Cité, 2013

In this workshop we will bring together participants who have solutions for one or more of the following problems: How can mutual understanding be optimized with the help of technology in hospitals where both patients and professionals have varying language skills, cultural backgrounds and cognitive capacities? Can domain ontologies, natural language processing tools, multilingual knowledge-based ...

Added: December 18, 2014

Malyshev D., Alekseev V., Дискретный анализ и исследование операций 2008 Т. 15 № 1 С. 3-10

Доказывается полиномиальная разрешимость задачи о независимом множестве для бесконечного семейства подмножеств класса планарных графов. ...

Added: August 31, 2012

Malyshev D., Journal of Applied and Industrial Mathematics (перевод журналов "Сибирский журнал индустриальной математики" и "Дискретный анализ и исследование операций") 2020 Vol. 14 No. 4 P. 706-721

The edge coloring problem for a graph is to minimize the number of colors that are sufficient to color all edges of the graph so that all adjacent edges receive distinct colors. The computational complexity of the problem is known for all graph classes defined by forbidden subgraphs with at most 6 edges. We improve ...

Added: January 30, 2021

Николаев М. В., Nikitin A. A., Дифференциальные уравнения 2019 Т. 55 № 9 С. 1209-1217

В работе изучается нелинейное интегральное уравнение, возникающее в результате параметрического замыкания третьего пространственного момента в модели У. Дикмана и Р. Лоу. Исследуется вопрос о существовании неподвижной точки интегрального оператора, задаваемого данным уравнением. Доказывается некомпактность полученного оператора. Формулируются условия, при которых уравнение имеет нетривиальное решение. ...

Added: November 7, 2019

Bliznets Ivan, Cygan M., Komosa P. et al., ACM Transactions on Computation Theory 2018 Vol. 10 No. 2 P. 1-32

The H-free Edge Deletion problem asks, for a given graph G and integer k, whether it is possible to delete at most k edges from G to make it H-free—that is, not containing H as an induced subgraph. The H-free Edge Completion problem is defined similarly, but we add edges instead of deleting them. The study of these two problem families has recently been the subject of intensive studies from the point of ...

Added: October 30, 2018

Beklemishev L. D., Оноприенко А. А., Математический сборник 2015 Т. 206 № 9 С. 3-20

We formulate some term rewriting systems in which the number of computation steps is finite for each output, but this number cannot be bounded by a provably total computable function in Peano arithmetic PA. Thus, the termination of such systems is unprovable in PA. These systems are derived from an independent combinatorial result known as the Worm ...

Added: March 13, 2016

Красноярск : ИВМ СО РАН, 2013

Труды Пятой Международной конференции «Системный анализ и информационные технологии» САИТ-2013 (19–25 сентября 2013 г., г.Красноярск, Россия): ...

Added: November 18, 2013

Logvenkov S. A., Штейн А. А., Российский журнал биомеханики 2013 Т. 17 № 4 С. 47-57

The mathematical modelling is performed to study the effect of the permeability of the Casparian bands to water and solutes on the formation of the root pressure. It is shown that the pressure in the xylem vessels which stops the flow across a root cut (root pressure) decreases with increase in the permeability of the ...

Added: January 30, 2014

Skoptsov K. A., Sheshenin S., Galatenko V. V. et al., International Journal of Applied Mechanics 2016 Vol. 8 No. 2 P. 1650016-01-1650016-18

We present a method for evaluating elastic properties of a composite material produced by molding a resin filled with short elastic fibers. A flow of the filled resin is simulated numerically using a mesh-free method. After that, assuming that spatial distribution and orientation of fibers are not significantly changed during polymerization, effective elastic moduli of ...

Added: May 22, 2016

Decrouez G. G., Robinson A., Risk Analysis: An International Journal 2013 Vol. 33 No. 12 P. 2142-2153

We propose a new modeling approach for inspection data that provides a more useful interpretation of the patterns of detections of invasive pests, using cargo inspection as a motivating example. Methods that are currently in use generally classify shipments according to their likelihood of carrying biosecurity risk material, given available historical and contextual data. Ideally, ...

Added: September 29, 2014

Chernyshev S. V., Cherepanov E. A., Pankratiev E. V. et al., Journal of Mathematical Sciences 2005 Vol. 128 No. 6 P. 3487-3495

Added: January 27, 2014

Bagrov A. N., Gordin V. A., Bykov P. L., Russian Meteorology and Hydrology 2014 No. 5 P. 283-291

The evaluations of the forecasts of surface air temperature and precipitation for the period July 2010 - June 2013 are presented. The forecasting of surface air temperature at 5 days and precipitation at 3 days are considered. Our complex statistical scheme uses the results of the best foreign global schemes, regional scheme COSMO-RU7. The joint ...

Added: December 7, 2013

Kotelnikova M. V., Aistov A., Вестник Нижегородского университета им. Н.И. Лобачевского. Серия: Социальные науки 2019 Т. 55 № 3 С. 183-189

The article describes a method that allows to improve the content of disciplines of the mathematical cycle by dividing them into invariant (general) and variable parts. The invariants were identified for such disciplines as «Linear algebra», «Mathematical analysis», «Probability theory and mathematical statistics» delivered to Bachelors program students of economics at several universities. Based on ...

Added: January 28, 2020