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In this paper, we consider the conjugate gradient method for solving the problem of minimizing a quadratic function with additive noise in the gradient. Three concepts of noise were considered: antagonistic noise in the linear term, stochastic noise in the linear term and noise in the quadratic term, as well as combinations of the first and second with the last. It was experimentally obtained that error accumulation is absent for any of the considered concepts, which differs from the folklore opinion that, as in accelerated methods, error accumulation must take place. The paper gives motivation for why the error may not accumulate. The dependence of the solution error both on the magnitude (scale) of the noise and on the size of the solution using the conjugate gradient method was also experimentally investigated. Hypotheses about the dependence of the error in the solution on the noise scale and the size (2-norm) of the solution are proposed and tested for all the concepts considered. It turned out that the error in the solution (by function) linearly depends on the noise scale. The work contains graphs illustrating each individual study, as well as a detailed description of numerical experiments, which includes an account of the methods of noise of both the vector and the matrix.

In this paper the problem of automated building of a citation graph from a collection of scientific documents is considered as a sequence of machine learning tasks. The overall data processing technology is described which consists of six stages: preprocessing, metainformation extraction, bibliography lists extraction, splitting bibliography lists into separate bibliography records, standardization of each bibliography record, and record linkage. The goal of this paper is to provide a survey of approaches and algorithms suitable for each stage, motivate the choice of the best combination of algorithms, and adapt some of them for multilingual bibliographies processing. For some of the tasks new algorithms and heuristics are proposed and evaluated on the mixed English and Russian documents corpora.

The paper investigates a potential solution to the problem of Self-Interference Cancellation (SIC) encountered in the design of In-Band Full-Duplex (IBFD) communication systems. The suppression of selfinterference is implemented in the digital domain using multilayer nonlinear models adapted via the gradient descent method. The presence of local optima and saddle points in the adaptation of multilayer models prevents the use of second-order methods due to the indefinite nature of the Hessian matrix.

This work proposes the use of the Mixed Newton Method (MNM), which incorporates information about the second-order mixed partial derivatives of the loss function, thereby enabling a faster convergence rate compared to traditional first-order methods. By constructing the Hessian matrix solely with mixed second-order partial derivatives, this approach mitigates the issue of “getting stuck” at saddle points when applying the Mixed Newton Method for adapting multilayer nonlinear self-interference compensators in full-duplex system design.

The Hammerstein model with complex parameters has been selected to represent nonlinear selfinterference. This choice is motivated by the model’s ability to accurately describe the underlying physical properties of self-interference formation. Due to the holomorphic property of the model output, the Mixed Newton Method provides a “repulsion” effect from saddle points in the loss landscape.

The paper presents convergence curves for the adaptation of the Hammerstein model using both the Mixed Newton Method and conventional gradient descent-based approaches. Additionally, it provides a derivation of the proposed method along with an assessment of its computational complexity.

The static three-level game-theoretic model of three-level control system of the ship’s water ballast is built. The methods of hierarchical control in view of requirements of keeping the system in the given state are used. A comparison of the results of study of the model in terms of $\Gamma_1$ and $\Gamma_2$ Germeyer’s games is conducted. Numerical calculations for some typical cases are given.

This article describes possible improvements for the simultaneous multi-stage transport model code for speeding up computations and improving the model detailing. The model consists of two blocks, where the first block is intended to calculate the correspondence matrix, and the second block computes the equilibrium distribution of traffic flows along the routes. The first block uses a matrix of transport costs that calculates a matrix of correspondences. It describes the costs (time in our case) of travel from one area to another. The second block presents how exactly the drivers (agents) are distributed along the possible paths. So, knowing the distribution of the flows along the paths, it is possible to calculate the cost matrix. Equilibrium in a two-stage traffic flow model is a fixed point of a sequence of the two described models. Thus, in this paper we report an attempt to influence the calculation speed of Dijkstra’s algorithm part of the model. It is used to calculate the shortest path from one point to another, which should be re-calculated after each iteration of the flow distribution part. We also study and implement the road pricing in the model code, as well as we replace the Sinkhorn algorithm in the calculation of the correspondence matrix part with its faster implementation. In the beginning of the paper, we provide a short theoretical overview of the transport modelling motivation; we discuss current approaches to the modelling and provide an example for demonstration of how the whole cycle of multi-stage transport modelling works.

The paper considers the problems of mathematical description of deontological aspects influencing the behavior of decision makers. A methodology is proposed for correlating utilitarian (material) and deontological (value) aspects in their decision-making, taking into account their psychological characteristics. A mathematical model is proposed for the joint consideration of utilitarian and deontological factors in decision-making in various situations. Some patterns related to this consideration are identified, and their formal description is given. The model shows that there is a tendency for a gradual decrease in the level of deontology in evaluating alternatives when making decisions (compared to what the outside world inclines to) towards greater utilitarianism. Over time, this trend begins to influence public opinion and society’s attitude to moral norms, gradually reducing the overall level of morality in society. This process can be stopped only by constantly and purposefully maintaining a high level of deontology by society and the state (ideological work, promotion of traditional values, educational work at school, etc.), otherwise society will inevitably become utilitarian over time, focusing exclusively on material factors when making decisions.

In the future, it is planned to use the developed tools for analyzing specific situations, including for analyzing the patterns of civilizational cycles: the rise and fall of the Roman Empire, the USSR, and modern Western civilization).

We show that basic properties of some models of monopolistic competition are described using families of hypergeometric functions. The results obtained by building a general equilibrium model in a multisector economy producing a differentiated good in $n$ high-tech sectors in which single-product firms compete monopolistically using the same technology. Homogeneous (traditional) sector is characterized by perfect competition. Workers are motivated to find a job in high-tech sectors as wages are higher there. However, they are at risk to remain unemployed. Unemployment persists in equilibrium by labor market imperfections. Wages are set by firms in high-tech sectors as a result of negotiations with employees. It is assumed that individuals are homogeneous consumers with identical preferences that are given the separable utility function of general form. In the paper the conditions are found such that the general equilibrium in the model exists and is unique. The conditions are formulated in terms of the elasticity of substitution $\mathfrak{S}$ between varieties of the differentiated good which is averaged over all consumers. The equilibrium found is symmetrical with respect to the varieties of differentiated good. The equilibrium variables can be represented as implicit functions which properties are associated elasticity $\mathfrak{S}$ introduced by the authors. A complete analytical description of the equilibrium variables is possible for known special cases of the utility function of consumers, for example, in the case of degree functions, which are incorrect to describe the response of the economy to changes in the size of the markets. To simplify the implicit function, we introduce a utility function defined by two one-parameter families of hypergeometric functions. One of the families describes the pro-competitive, and the other — anti-competitive response of prices to an increase in the size of the economy. A parameter change of each of the families corresponds to all possible values of the elasticity $\mathfrak{S}$. In this sense, the hypergeometric function exhaust natural utility function. It is established that with the increase in the elasticity of substitution between the varieties of the differentiated good the difference between the high-tech and homogeneous sectors is erased. It is shown that in the case of large size of the economy in equilibrium individuals consume a small amount of each product as in the case of degree preferences. This fact allows to approximate the hypergeometric functions by the sum of degree functions in a neighborhood of the equilibrium values of the argument. Thus, the change of degree utility functions by hypergeometric ones approximated by the sum of two power functions, on the one hand, retains all the ability to configure parameters and, on the other hand, allows to describe the effects of change the size of the sectors of the economy.

Deposit benchmark interest rates are a policy implemented by banking regulators to calculate the interest rates offered to depositors, maintaining equitable and competitive rates within the financial industry. It functions as a benchmark for determining the pricing of different banking products, expenses, and financial choices. The benchmark rate will have a direct impact on the amount of money deposited, which in turn will determine the amount of money available for lending.We are motivated to analyze the influence of deposit benchmark interest rates on the dynamics of banking loans. This study examines the issue using a difference equation of banking loans. In this process, the decision on the loan amount in the next period is influenced by both the present loan volume and the information on its marginal profit. An analysis is made of the loan equilibrium point and its stability. We also analyze the bifurcations that arise in the model. To ensure a stable banking loan, it is necessary to set the benchmark rate higher than the flip value and lower than the transcritical bifurcation values. The confirmation of this result is supported by the bifurcation diagram and its associated Lyapunov exponent. Insufficient deposit benchmark interest rates might lead to chaotic dynamics in banking lending. Additionally, a bifurcation diagram with two parameters is also shown. We do numerical sensitivity analysis by examining contour plots of the stability requirements, which vary with the deposit benchmark interest rate and other parameters. In addition, we examine a nonstandard difference approach for the previous model, assess its stability, and make a comparison with the standard model. The outcome of our study can provide valuable insights to the banking regulator in making informed decisions regarding deposit benchmark interest rates, taking into account several other banking factors.