The article considers the possibility of evaluating the psychophysiological state of a learner in the e-learning system. A logistic model was built, based on the regression analysis of the experimental data, allowing to evaluate the ability of the learner for effective learning before he enters the system. Galvanic skin response was proposed as a means to control the state of the learner upon learning. A network model was developed, describing the work of the e-learning system considering the psychophysiological state of the learner.

The construction of almost periodic sequences is needed for the analysis of the cycles’ detection methods, identification of symbolic sequences’ features and sensitivity analysis. Two probabilistic models of noise are proposed for constructing almost periodic symbolic sequences. Models provide various types of noise in a periodic sequence, such as changing, adding and deleting characters. Thus, on the basis of a periodic symbolic sequence, an almost periodic sequence is constructed. It is necessary to ensure a given level of noise in the constructed almost periodic sequence. The re - quired level of simulated noise is guaranteed by a two-level model, in which the positions for simulated noise are determined at the first level, based on the discrete random variable, chosen by the researcher. At the second level, the necessary changes are made at the corresponding positions using a random variable that simulates the noise itself. The second model is based on simulated noise with probability (depending on the noise level) in each element of the sequence. The observed noise level is calculated based on the Levenshtein distance between the original periodic sequence and the almost periodic sequence that we constructed. The observed noise level is always somewhat less than the level of the noise simulated, since when cal - culating the Levenshtein distance, a shorter way of obtaining a noisy sequence from a periodic one can be found than the one that is used in constructing an almost periodic sequence. A comparison of the proposed models for the proximity of the noise level they provide to a given noise level is made. The computational experiment showed that the observed noise level is closer to that provided by the two-level model. The software implementation of these models will be used in future to study the algorithms for finding cycles in noisy periodic symbolic sequences.

This article is devoted to the nonlinear integral equation arising in the biological model of Ulf Dieckmann and Richard Low. A brief review of the model of foreign authors Individual-based model is made, the meaning and necessity of introducing spatial moments is described. The following is the derivation of the nonlinear equation (for the equilibrium state) from the system of dynamics of spatial moments, after the Power-3 closure. As it was supposed earlier, as a result of this closure the integral equation with nonlinear convolution is deduced. The resulting equation is transformed to a form convenient for the application of the numerical method based on the Neumann’s series. The authors developed a stable numerical method for solving the obtained integral equation. At the end of the article, a large number of examples of the use of the constructed numerical method and numerical modeling are given: a surface in the parameter space for the integral nuclei of motion and competition is constructed; the dependence of the solution of the nonlinear integral equation depending on the area of integration (the solution for these manipulations goes to the asymptote, and does not change significantly); numerical study of the integral equation for the parameter of natural mortality equal to zero. An interesting result is the existence of a nontrivial solution, the investigated nonlinear integral equation for the natural mortality parameter, d > 0. This essentially distinguishes the derived integral equation from its linear analogue, widely studied in previous works.

*Classical approaches to the construction of hash function modes, based on the using of iterative procedures, do not allow efficient processing of large amounts of data and can’t be adapted to parallel computing architectures. It applies to both the Russian cryptographic standard GOST R 34.11-2012, which determines the algorithm and procedure for calculating the hash function, as well as many other foreign standards (for example, SHA-3). The absence of standards for parallelized modes for the hash functions of GOST R 34.11-2012 creates an urgent need for the development of the domestic standard of the parallelized mode of hash code.*

*This article is devoted to the research and development of new modes of hash code generation that allow efficient parallelization of the computation process and provide cryptographic resistance satisfying modern requirements. This work continues the research carried out by the authors, and offers a fundamentally new tree mode of hash code generation ("FT-mode"), based on l-ary hash trees and allowed to use any compression mapping for a mechanism of forming tree nodes. The resistance of the mode is completely determined by the resistance of the corresponding compressive mapping. In particular, the FT-mode allows using block ciphers and substitution transformations to form nodes of a hash tree along with compression functions and hash functions. In addition, the FT-mode excludes the main functional disadvantages of the known tree modes of hash code generation that affect their operational, technical and cryptographic quality.W**ithin the framework of the present research** a number of characteristics of FT-mode are calculated, and a comparative analysis of the time and computational complexity of implementations of FT-mode and some foreign tree hash modes is carried out. The corresponding results showed that the developed mode is not inferior to any of the considered modes.*

Information systems play a serious role in modern education, providing an information basis for many disciplines. One of the main tasks in integrating information systems into the educational process is to provide a relevant search for information consolidated from heterogeneous sources. In the field of inorganic chemistry and material science, set-theoretic methods for searching for relevant information are known, which ensure the construction of a sufficiently high-quality response to user requests. However, the problem of quantifying the relevance of information retrieval in this subject area remains open. In this paper we propose a method based on weighted graphs for quantifying the relevance of information retrieval in integrated systems on inorganic substances and materials properties. The vertices of the graph are heterogeneous chemical objects (systems, substances and crystal modifications) on which a metric is determined that estimates the similarity of chemical objects. In metric space, cost definition of the path between the vertices of the graph allows us to evaluate the chemical objects similarity (relevance), that is important in enabling the search for related chemical entities and their properties in the context of an integrated information system that consolidates Russian and foreign resources on inorganic substances properties (www.imet-db.ru). Thus, a relevance metric (introduced as a value inversely proportional to the cost of the graph path) allows, from the material scientist’s point of view, to optimally rank the information that is displayed at the user's request at a single access point to consolidated information resources on inorganic substances properties. In addition to the metric on the graph, a measure is defined that is useful in finding out a complete informational description of a chemical object. The measure is used in the search for all properties of the object available in integrated resources, which is necessary when compiling a complete analytical description of a chemical object.

The article is devoted to inclusion of the topic "parallel computing" in the school informatics . Some methodical materials prepared in the course of work on the "Permian version" of a propaedeutic course of computer science (the author team is M.A. Plaksin, N.I. Ivanova, O.L. Rusakova) are described.

The complexity of the individual traveling salesman problem was analyzed by means of mathematical statistics. The complexity is defined as a number of nodes of the decision tree created by the branch and bound algorithm. We obtained approximate representations for parameters of probability distribution of the natural logarithm of the complexity. These representations are functions of the dimension of the problem. The linear function is used to construct the upper estimation for the quantiles of the natural logarithm of the complexity, in cases when the level of the quantile is more than 0.5. We also applied this formula for the lower bound of the quantiles of levels less than 0.5. Then we used the normal distribution with the parameters and as an approximation of the distribution of the natural logarithm of the complexity. We combined a nonlinear function for the parameter and linear function for and obtained a lower bound for the quantiles of the level 0.95 of the natural logarithm of the complexity. The quality of the estimations was analyzed by the experiment. In our experiment the sample’s quantiles of the level 0.95 differ from the estimation less than 0.3% in the case when the dimension of the problem in range from 45 to 50.

The problem of obtaining accurate estimates of the number of reconstructions for words over a binary alphabet is considered. Subwords of different lengths from a given set are joined by the method of overlapping end characters. It is only possible to connect a pair of subwords where the last character of the first subword is the same as the first character of the second. When superimposing a pair of suitable subwords on one character of two identical ones (at the end of the first and at the beginning of the second subword) only one, is included in the reconstruction. An approach based on combining truncated subwords consisting of the first and last characters of a subword is proposed. When building a reconstruction, instead of the subwords from a given set, truncated words of the form “00”, “01”, “10” and “11” are connected. The number of reconstructions is under the assumption that each of the truncated subwords corresponds to a unique subword in a given set of subwords. As a result, when combining the words “00” and “00”, two reconstructions are possible, corresponding to combining the original subwords “0x0” and “0y0” into “0x0y0” and “0y0x0”, where x and y are different sequences of binary alphabet characters, one of which may be empty (but not both simultaneously). Such an approach made it possible to determine the conditions for the existence of reconstruction from a given set of subwords of various lengths. It is noted under what conditions, concerning the number of truncated subwords of each type, reconstruction is impossible. For example, reconstruction by a set of subwords containing only subwords of the form “00” and “11” is not possible. It is also impossible to combine all the subwords of a given set if the number of truncated subwords of the form “01” and “10” differs by more than one. For various cases allowing for complete reconstruction, formulas of the exact number of reconstructions are obtained. The exact number of reconstructions depends on the presence or absence of subwords corresponding to truncated subwords of each type. Since the possibility of reconstruction mainly depends on the ratio of the number of subwords of the form “01” and “10”, a model with the possibility of word inversions was also considered. It is assumed that the set of subwords for reconstruction contains only words of the form “00”, “01” and “11”. Some of the words of the form “01” are written in the reverse order and become words of the form “10”. If the words “01” were an even number, then half of the words “01” would be converted to “01”, otherwise, half of the nearest even number would be. In the latter case, from the set of subwords of the form “01”, two variants of the sets of subwords of the form “01” and “10” are obtained, in one, there are more subwords “01”, in the other “10”. For each case, formulas are given for the exact number of reconstructions, provided that the subwords in the given set are unique, as well as the asymmetry of the subwords generating truncated subwords of the form “00” and “11”.

The article contains the methodological materials for inclusion of the topic “Parallel Computing” in the school informatics. The computer games “Tank crew”, “Swarm of robots”, “Firefighting vehicles” are considered. The goal of the first game is to program joint actions of tank crew members. The plot of the second game is the putting on foot the space expedition. For this goal, a group of robots should load containers with fuel and food into spacecrafts. Under uniting efforts of several robots, systemic effect is emerged: their physical and intellectual abilities increase. For programming, it means change in the number of performers and their capabilities. In the third game a group of fire engines should fight fire. The game includes the systemic effect of combining the efforts of fire engines, and two new aspects: two levels of parallelism (parallel actions of vehicles and crew members of each vehicle) and dynamic changes in the environment (combustion of objects and the spread of fire depending on the direction and strength of the wind). In the 2018/19 academic year this game is used in interregional Internet contests for schoolchildren and students “Parallel programming – from the cradle (2018)!” and “TRIZformatashka-2019” (interregional competition in informatics, systems analysis and theory of inventive problem solving (TRIZ)).

The article is devoted to the preparation of methodological materials for the inclusion of the topic "Parallel computing" in the school course of informatics. The set of tasks for the division "Swarm of Robots" are considered. The tasks were tested at the competition "TRIZformaska-2017" - an inter-regional competition in informatics, system analysis and the theory of solving inventive problems (TRIZ) for schoolchildren and students.

It is shown that the logarithm of the complexity (number of nodes in the decision tree of a branch and bound algorithm) of the individual traveling salesman problem is approximately normally distributed. We use a linear regression model (logarithm of the complexity — standard normal distribution) to estimate parameters of normal distribution, which fit the sample. Borders of the interval, which contains 90% of the sample of the logarithm of the complexity, are also given.

Perfectly-secret ciphers according to the Claude Shannon’s theory, which are considered as unbreakable, and more specifically random keystream ciphers, are discussed. An analysis of the sources mentioned in the reference list showed that all of them come to the point that the perfect ciphers according to Claude Shannon’s theory are unbreakable. The article introduces some concepts, such as: the probabilistic model of cipher; the perfect cipher, which is secure against a plaintext recovery ciphertext-only attack; the perfect cipher, which is secure against a key recovery ciphertext-only attack; effective plaintext or key recovery attack; ineffective plaintext or key recovery attack; decipherable model of cipher; undecipherable model cipher. The introduced concepts were used to clarify Shannon’s mathematical model and to prove that a statement about unbreakability of the perfect ciphers according to the Claude Shannon’s theory, including random keystream cipher, were wrong. The purpose of the article is to attract the attention of specialists to the problem of developing methods for decrypting Vizhener cipher and using them in solving the problem of determining the cipher key of a random gamming according to a ciphertext, as well as developing methods for estimating the complexity and reliability of deciphering the cipher class in question.