In this paper the comparative analysis for quality of some interpolation non-adaptive methods of doubling the image size is carried out. We used the value of a mean square error for estimation accuracy (quality) approximation. Artifacts (aliasing, Gibbs effect (ringing), blurring, etc.) introduced by interpolation methods were not considered. The description of the doubling interpolation upscale algorithms are presented, such as: the nearest neighbor method, linear and cubic interpolation, Lanczos convolution interpolation (with a=1,2,3), and 17-point interpolation method. For each method of upscaling to twice optimal coefficients of kernel convolutions for different down-scale to twice algorithms were found. Various methods for reducing the image size by half were considered the mean value over 4 nearest points and the weighted value of 16 nearest points with optimal coefficients. The optimal weights were calculated for each method of doubling described in this paper. The optimal weights were chosen in such a way as to minimize the value of mean square error between the accurate value and the found approximation. A simple method performing correction for approximation of any algorithm of doubling size is offered. The proposed correction method shows good results for simple interpolation algorithms. However, these improvements are insignificant for complex algorithms (17-point interpolation, Lanczos a=3). According to the results of numerical experiments, the most accurate among the reviewed algorithms is the 17-point interpolation method, slightly worse is Lanczos convolution interpolation with the parameter a=3 (see the table at the end)

The paper describes some ways to accelerate solving the NP-complete Traveling Salesman Problem. The classic Little algorithm belonging to the category of ”branch and bound methods” can solve it both for directed and undirected graphs. However, for undirected graphs its operation can be accelerated by eliminating the consideration of branches examined earlier. The paper proposes changes to be made in the key operations of the algorithm to speed up its execution. It also describes the results of an experiment that demonstrated a significant acceleration of solving the problem by using an advanced algorithm. Another way to speed up the work is to parallelize the algorithm. For problems of this kind it is difficult to break the task into a sufficient number of subtasks having comparable complexity. Their parallelism arises dynamically during the execution. For such problems, it seems reasonable to use parallel-recursive algorithms. In our case the use of the library RPM ParLib developed by the author was a good choice. It allows us to develop effective applications for parallel computing on a local network using any .NET-compatible programming language. We used C# to develop the programs. Parallel applications were developed as for basic and modified algorithms, the comparing of their speed was made. Experiments were performed for the graphs with the number of vertexes up to 45 and with the number of network computers up to 16. We also investigated the acceleration that can be achieved by parallelizing the basic Little algorithm for directed graphs. The results of these experiments are also presented in the paper. 

The paper describes a mathematical model of trade flows between the territories of a region or a country in a transport network having one or more different types of marine or ground transportation. We use the approach of modeling complex communication systems to determine the most probable values of flows in case of incomplete information about the system. Transport costs between the territories are modeled within the framework of the gravity model. The payment for transportation depends on the distance between regions, the distance is estimated as the shortest way length in a given transport network or geographical distance. The mathematical formulation of the problem belongs to the class of convex mathematical programming problems and assumes the numerical solution of nonlinear optimization problem with linear constraints. Based on the model, the software is implemented as a cloud service on heterogeneous computing architectures: the simulation module is made on a highperformance server platform, management and visualization modules are produced with IACPaaS cloud platform. Communication between the platforms is established via asynchronous http-queries. For information exchange between the modules the declarative model with JSON format is developed and implemented for the objects considered in the mathematical model which are products, areas and communications. Visualization module allows to present graphically the original and the resulting matrix data and to modify the input parameters of the model interactively. The paper demonstrates the use of software for the simulation of inter-regional freight traffic of the Russian Far East region based on input data provided by open statistics sources.

Currently ”Smart building” or ”Smart house” technology is developing actively in industrialized countries. The main idea of ”smart building” or ”smart house” is to have a system which is able to identify definite situations happening in house and respond accordingly. Automated house management system is made for automated control and management and also for organization of interaction between separated systems of engineering equipment. This system includes automation subsystems of one or another engineering equipment as separated components. In order to perform study of different functioning modes of engineering subsystems and the whole system, mathematical and computer modeling needs to be used. From mathematical point of veiw description of ”Smart building” is a continuous-discrete or hybrid system consisting of interacting elements of different nature, whose behavior is described by continuous and discrete processes. In the article the authors present a computer model ”Smart building” which allows to model the work of main engineering subsystems and management algorithms. The model is created in Simulink Matlab system with ”physical modeling” library Simscape and Stateflow library. The peculiarity of this model is the use of specialized management and control algorithms which allow providing coordinated interaction of subsystems and optimizing power consumption. 

Let      ) be a projective family of surfaces (possibly with degenerations) over a smooth projective curve  . Assume that the discriminant loci       are disjoint,          for any smooth fibre     and the period map associated with the variation of Hodge structures         (where             is a smooth part of the morphism    ), is non-constant. If for generic geometric fibres     and     the following conditions hold: (i)         is an odd integer; (ii)              , then for any smooth projective model   of the fibre product         the Hodge conjecture on algebraic cycles is true. If, besides, the morphisms     are smooth,           are odd prime numbers and      , then for

The problem of integer balancing of a four-dimensional matrix is studied. The elements of the inner part (all four indices are greater than zero) of the given real matrix are summed in each direction and each two- and three-dimensional section of the matrix; the total sum is also found. These sums are placed into the elements where one or more indices are equal to zero (according to the summing directions). The problem is to find an integer matrix of the same structure, which can be produced from the initial one by replacing the elements with the largest previous or the smallest following integer. At the same time, the element with four zero indices should be produced with standard rules of rounding - off. In the article the problem of finding the maximum multiple flow in the network of any natural multiplicity   is also studied. There are arcs of three types: ordinary arcs, multiple arcs and multi-arcs. Each multiple and multi-arc is a union of   linked arcs, which are adjusted with each other. The network constructing rules are described. The definitions of a divisible network and some associated subjects are stated. There are defined the basic principles for reducing the integer balancing problem of an  -dimensional matrix ( ) to the problem of finding the maximum flow in a divisible multiple network of multiplicity  . There are stated the rules for reducing the four-dimensional balancing problem to the maximum flow problem in the network of multiplicity 5. The algorithm of finding the maximum flow, which meets the solvability conditions for the integer balancing problem, is formulated for such a network.

This paper presents an overview of some technologies that are used in modern backup systems. We consider their advantages and disadvantages. Next, we consider an example of the realisation of the backup system with files store in the database. We propose to divide the copied files into blocks of fixed length. Each block is a sequence of bytes. The block length may be adaptive, i.e. it can vary depending on the type or file size. We can store the file content in one table, and information of them such as names, attributes, and relationships between them, store in another table. The information of retained files and folders can be stored also on the client side in a hierarchical structure. It is a set of records and a model of the copied directory. The presence of such a model allows to find changes of the copied directory without additional queries to the database. If a file is modified, it is copied only the changed blocks. The model is also updated on the client side. Thus, the load on the data channel reduces. This paper presents the algorithms of saving and restoring data, and describes the factors that affect to the speed of their work. It demonstrates the dependence of the rate of saving and recovery of the fineness of the partition files, as well as the structure of the copied directory. 

In this paper a criteria of comparison of different tournament organization systems in sporting contests is offered; the criteria uses the probability of winning the fairly strongest player. Two probabilistic models have been analyzed. Calculating formulas for estimating the probability and probability density of score points gained by one or another player were obtained. Some really used tournament systems were analyzed with the stochastic modeling method. The available results also provide an order of objects presenting to experts while organizating the examination by paired comparison. An analytical estimation of probability of tournament results (or pared comparison) was obtained. In many cases it allows to avoid a time-consuming procedure of sorting out possible variants.