The article investigates stability analysis in the shortest path problem. We consider a directed graph in which all optimal paths from a source to a sink pass through a certain vertex. For such vertices, we introduce a definition of a vertex stability radius and research its features. A comparison with other results devoted to stability analysis is provided. Several explanatory and practical examples are presented.

For arbitrary continuous functions on the interval [0, 1], we obtain an interpolation formula based on known values of these functions on some uniform grid. No additional assumptions about the functions are required. The construction of such a formula is connected with the properties of local Bernstein polynomials and the Riemann zeta function. Numerical results for the interpolation of functions of the Riemann, Weierstrass, Besicovitch, and Takagi types are presented.

The paper studies the performance of a distributed computing system using Markov chains and queuing theory. The system under study possesses a buffer capacity of N and M servers. Service time is distributed exponentially. Customers entering the system in a Poisson flow consist of a random number of tasks ranging from 1 to K. The probability that a customer contains $k$ tasks is $b_k$, and the normalization condition is satisfied: $\sum _{k=1} ^{K} b_{k} = 1$. Each individual task is serviced on a separate server. The order of service is determined by the FIFO principle. The paper describes a system using a Markov chain and provides formulas for calculating its performance characteristics. It compares the performance characteristics computed analytically to those obtained from a real distributed computing system.

Currently, systems based on multidimensional membership functions are being actively researched and developed. Most algorithms for determining the parameters of fuzzy membership functions are developed on the basis of one-dimensional membership functions. The fuzzy rules generated by these algorithms often overlap and cannot act as independent rules. The overlap of fuzzy rules in fuzzy systems does not allow one to evaluate the reliability of individual fuzzy rules and at the same time creates limitations in extracting knowledge from fuzzy systems. In this article, a neuro-fuzzy neural system will be built based on a multidimensional Gaussian membership function with the ability to describe the relationship of interaction between input variables, and at the same time, the generated fuzzy rules are capable of independent operation.

In the current paper the question of the resource-saving tasks distribution in the robotic groups is under consideration. As a wide range of computational tasks in robotics are performed in a distributed manner, tasks can be assigned to the devices with a relatively low computational capacity. At the same time, data preprocessing, machine learning, SLAM problems are computationally complex, and so the participants of the computational process can be overloaded, while the latter causes the deterioration of average residual life of the computational nodes within the robots. In this paper the problem of resource-saving tasks distribution is formulated as structural-parametric multiobjective one, with paying attention to the workload of those robots in the group, which have to transmit sensor data. The general solution technique is proposed based on global problem decomposition, local time constraints estimations and simulated annealing technique. The a priory time estimations are used according to the tasks graph analysis, as well as time constraints are divided into shares considering the number of transit nodes. Also, some selected experimental results are presented, as well as comparison with the previously conducted results are made.