We consider the nonparametric estimation of the univariate heavy tailed probability density function (pdf) with a support on [0,∞) by independent data. To this end we construct the new kernel estimator as a combination of the asymmetric gamma and weibull kernels, ss. gamma-weibullkernel. Thegammakernelis nonnegative,changestheshapedependingonthe position on the semi-axis and possess good boundary properties for a wide class of densities. Thus, we use it to estimate the pdf near the zero boundary. The weibull kernel is based on the weibull distribution which can be heavy tailed and hence we use it to estimate the tail of the unknownpdf. The theoretical asymptotic properties of the proposeddensity estimator like bias and variance are derived. We obtain the optimal bandwidth selection for the estimate as a minimum of the mean integrated squared error (MISE). Optimal rate of convergence of the MISE for the density is found.

For enhance a situational awareness of aircraft crew the method for predicting the future state of aircraft is developed. Algorithms for predicting the end point of the brake path have been developed. Algorithms have the properties of adaptation to the conditions of run. To improve the accuracy of the prediction, a correction was introduced. The statistical tests of prediction algorithms in a wide range of operational modes were performed. Statistical characteristics of prediction errors are given.

The mathematical model of the formation and functioning of a team of artificial intelligence agents with BDI architecture in a qualitative semiotic (sign) environment of functioning is considered in the work. As the basis of the mathematical model of the environment of functioning, the model of the “Group of robots–Environment” multi-agent dynamic system was chosen. A method for structuring the environment of functioning in the form of a partially ordered set of embedded subspaces of the state space of a dynamical system and a method for symbolizing the classes of states by symbol names that define these classes are proposed. Such a structure is defined as a qualitative conceptual framework of the environment and is called the semiotic environment of functioning. In terms of a qualitative semiotic functioning environment, a mathematical model of an intelligent agent with a BDI architecture is proposed and the conditions for the formation and functioning of teams of intelligent agents in this environment are formulated.

An asynchronous discrete model of nonsynaptic chemical interactions between neurons is proposed. The model significantly extends the previous work [1, 2] by novel concepts that make it more biologically plausible. In the model, neurons interact by emitting neurotransmitters to the shared extracellular space (ECS). We introduce the dynamics of membrane potentials that comprises two factors: the endogenous rates of change depending on the neuron’s firing type and the exogenous rates of change depending on the concentrations of neurotransmitters that the neuron is sensitive to. The neuron’s firing type is determined by the individual composition of endogenous rates. We consider three basic firing types: oscillatory, tonic, and reactive. Each firing type is essential for modeling central pattern generators—neural ensembles that generate rhythmic activity in the absence of external stimuli. Differences in endogenous rates of different neurons lead to asynchronous neural interactions and significant variability of phase durations in the activity patterns present in simple neural systems. The algorithm computing the behavior of the proposed model is provided.

The construction of a recommendation system for selecting one of five non-medication-based rehabilitation complexes for participants in armed conflicts and emergencies is described. Rehabilitation techniques developed at the Tomsk Science Research Institute of Balneology and Physiotherapy prevent potential chronicization of pathological processes, increase the body’s adaptive reserves, and improve quality of life in those affected by emergencies. A set of features was determined for each complex, providing the most precise identification of each complex. The principle underlying the construction of the recommendation system is instrumental in nature and the system could be used not only in rehabilitation and treatment centers, but also in other healthcare institutions.