This article presents the analysis of approaches to data warehouse construction based on relational and NoSQL solutions and lists the limitations of the relational approach to data mining. The contradiction between data presentation in the real subject domain and the model of data presentation in the relational and NoSQL approaches is revealed. The revealed contradiction is related to the temporality of the values of individual data attributes, the variability of the composition of these attributes, and structure of connections between them. A new logical model of the data warehouse with dynamic structure is proposed. The model is based on the concept of the object as a container for properties storage. Each property of the object includes the property name and two property values without reference and with reference, that are relevant at a given time. The reference property value points to an object whose name is interpreted as the value of the property at a given time. A formal description of the model with allocation of the necessary functionality to manipulate objects and their properties (selectors, predicates, constructors) is given and the necessary control structures are introduced. Substantiation of the proposed model, called an OP-model is given on the basis of compliance with the logical ER data model. It is proved that any ER data model can be implemented in the OP-model. At the same time, the advantages of the OP-model are indicated, they are associated with the possibility of changing connections between entities due to changes in the reference value at a particular time. The potential for scalability of data warehouse due to the unique identification of each object is noted. 

In the paper we consider a method for a reliability allocation problem (RAP) of distributed computer systems (DCS) under cost constraints. In this problem we maximize reliability of DCS under constraints of system cost. The article describes considered fault tolerance mechanisms. The mathematical formulation of RAP is provided. RAP is widely discussed in the literature. A detailed description of the method is ensured. The applied method is an evolutionary algorithm with an adaptive logic control procedure. The adaptive logic control procedure analyzes the results of evolutionary algorithm work in each generation and, based on this information, adjusts parameters. The key feature of the proposed method is the use of an adaptive hybrid genetic algorithm. The results of experiments with the implemented method are presented. This method was implemented as a pilot system which works in cooperation with DYANA simulation environment. Finally, future plans for the development of the presented method and tools are briefly described. 

The code C on a group G, induced by the code N on a subgroup H, has the property that for decoding the code C one can use the decoder for the code N. Therefore, if N has an efficient algorithm for decoding, we can build a class of induced codes with known decoding algorithms. This feature is used in this paper to build the code McEliece-type public key cryptosystems on induced group codes. For this cryptosystem we described operations of encryption and decryption, an analysis of the resistance to the attack on the private key is proposed, and also weak keys are highlighted, which is used while breaking McEliece-type cryptosystem on the induced code C is reduced to breaking this cryptosystem on the code N. It is shown that a practically resistant cryptosystem on the induced code C can be built on the code N with small length. Based on the proposed cryptosystem a common protocol for open channel key generation is developed.

A standard problem of DBMSs usage is a lack of efficiency and high cost of the access to the stored data. The acceptable level of system performance may be achieved by query optimization technics that determine the most efficient way to execute a given query by its modification and considering possible query execution plans. The goal of this paper is to prove the efficiency of the query minimization algorithms based on minimization of the query restriction by elimination of the redundant conditions. The paper represents minimization algorithms based on the mathematical transformations, which detect and remove redundant conditions from query restriction to simplify it. It includes minimization algorithms based on “condition absorption”, prime implicants, and a set of linear inequalities minimization technics. The paper also includes theoretical justification of the efficiency of minimization approach to the query optimization based on restriction simplification. We also observe experimental results of the implementation of these optimization techniques and their influence on the query processing speed. In the end, we represent an observation of the query minimization impact on the whole optimization process 

Let V be a smooth projective variety over a global field k = κ(C) of rational functions on a smooth projective curve C over a finite field Fq of characteristic p. Assume that there is a projective flat Fq-morphism π : X → C, where X is a smooth projective variety and the generic scheme fiber of π is isomorphic to a variety V (we call π : X → C an arithmetic model of a variety V ).

M. Artin conjectured the finiteness of the Brauer group Br(X) classifying sheaves of Azumaya algebras on X modulo similitude. It is well known that the group Br(X) is contained in the cohomological Brauer group

Br′(X)=H2(X,G ). et m

By definition, the non−p component of the cohomological Brauer group Br′(X) coincides with the direct sum of the l-primary components of the group Br′(X) for all prime numbers l different from the characteristic p. It is known that the structure of k-variety on V yields the canonical morphism of the groups Br(k) → Br′(V ).

The finiteness of the non−p component of the cohomological Brauer group Br′(X) of a variety X has been proved if

[Br′(V )/ Im[Br(k) → Br′(V )]](non −p)

is finite.
In particular, if V is a K 3 surface (in other words, V is a smooth projective simply connected surface

over a field k and the canonical class of a surface of V is trivial: Ω2V = OV ) and the characteristic of the ground field p > 2, then, by the Skorobogatov – Zarhin theorem, [Br′(V )/ Im[Br(k) → Br′(V )]](non −p) is finite, so in this case the groups Br′(X)(non−p) and Br(X)(non−p) are finite. 

This article continues a cycle of papers, which describe an approach to construction and verification of discrete PLC-programs by an LTL-specification. The approach provides a possibility of PLC-program correctness analysis by the model checking method. For the specification of the program behavior the linear-time temporal logic LTL is used. The correctness analysis of an LTL specification is performed automatically by the symbolic model checking tool Cadence SMV. 

Previously it was shown how ST-, LDand IL-programs are constructed by a correct (with verified program properties) LTL-specification. In this article a technology of CFC-program construction by an LTL-specification is described. The language CFC (Continuous Function Chart) is a variation of FBD (Function Block Diagram). FBD is a graphical language for microcircuits. CFC provides a possibility of free allocation of program components and connections on a screen. The approach to construction of CFC-programs is shown by an example. 

PLC-program representation on CFC within the approach to programming by LTL-specification differs from other representations. It gives the visualisation of a data flow from inputs to outputs. Influence and dependence between variables is explicitly shown during program execution within one PLC working cycle. In fact, CFC-program is a scheme of PLC-program data flow.

Abstract.

Asymptotic Formula for the Moments of Bernoulli Convolutions

Timofeev E. A.

Received February 8, 2016

For each λ, 0 < λ < 1, we define a random variable

∞

Yλ =(1−λ)ξnλn, n=0

where ξn are independent random variables with
P{ξn =0}=P{ξn =1}= 1.

2

The distribution of Yλ is called a symmetric Bernoulli convolution. The main result of this paper is Mn =EYλn =nlogλ22logλ(1−λ)+0.5logλ2−0.5eτ(−logλn)1+O(n−0.99),

where

is a 1-periodic function,

1k2πikx τ(x)= kα −lnλ e

k̸=0

1 (1 − λ)2πit(1 − 22πit)π−2πit2−2πitζ(2πit), 2i sh(π2t)

α(t) = −
and ζ(z) is the Riemann zeta function.

The article is published in the author’s wording.

Recently, microtask crowdsourcing has become a popular approach for addressing various data mining problems. Crowdsourcing workflows for approaching such problems are composed of several data processing stages which require consistent representation for making the work reproducible. This paper is devoted to the problem of reproducibility and formalization of the microtask crowdsourcing process. A computational model for microtask crowdsourcing based on an extended relational model and a dataflow computational model has been proposed. The proposed collaborative dataflow computational model is designed for processing the input data sources by executing annotation stages and automatic synchronization stages simultaneously. Data processing stages and connections between them are expressed by using collaborative computation workflows represented as loosely connected directed acyclic graphs. A synchronous algorithm for executing such workflows has been described. The computational model has been evaluated by applying it to two tasks from the computational linguistics field: concept lexicalization refining in electronic thesauri and establishing hierarchical relations between such concepts. The “Add–Remove–Confirm” procedure is designed for adding the missing lexemes to the concepts while removing the odd ones. The “Genus–Species–Match” procedure is designed for establishing “is-a” relations between the concepts provided with the corresponding word pairs. The experiments involving both volunteers from popular online social networks and paid workers from crowdsourcing marketplaces confirm applicability of these procedures for enhancing lexical resources. 

The problem of a routization of the movements complicated by the restrictions of different type (preceding conditions, the restrictions on the attainability of states by each movement and others) is considered. A multivariance at the movement step is permitted, it is naturally resulted in the problem about the visiting of megalopolises. The costs of movements and jobs executed when visiting megalopolises may depend on the list of tacks. This list may correspond to performed or unperformed tasks. ”Current” restrictions (on movements) may depend on the aforementioned list of tasks. The considered setting is oriented to the application with regard to a nuclear power engineering problems (the problem of decreasing irradiation of the nuclear power station staff when executing a complex of tasks under high radiation intensity) and the machine building. In the second case, which consists in controling a machine for the sheet cutting of details by the numerical program control machines, ”current” restrictions on movements may be conditioned by temperature tolerance relative to the fragments of sheet which have already been ”visited” by the cutting machine. The scheme of constructing the optimal solution based on the widely understood dynamic programming is considered in this article. The used algorithm is realized on a personal computer; the results of its application are illustrated by the modelling examples.