The paper addresses the acceleration of cognitive modelling by automating the creation of cognitive semantics of Artificial Intelligence (AI) models considering such human abilities as free will, consciousness, unconsciousness, feelings, thoughts and experience. The problem consists of the impossibility of formalising these abilities during modelling, especially considering their uncaused character. Traditional AI tools such as knowledge management, logical ontologies and neuron networks cannot totally embrace these abilities, to understand and explain events. The paper suggests using the Hybrid AI (HAI) approach, which integrates formalisable AI and non-formalisable human abilities. This paper’s main idea consists of using a non-local approach to enrich the cognitive semantics of AI models that consider the subatomic structure of the human mind’s biological tissue. In this case, quantum operators map an AI model on relevant big data, thereby enriching the cognitive semantics. The quantum non-local approach helps to increase the quality of cognitive models and synthesise their drafts automatically. The inverse problem-solving method on topological spaces, which ensures the purposefulness and sustainability (convergence) of decision-making processes, is also used. The approach is applied in real practice during collective strategic planning and is now developing for decision-making in an emergency.

Exponential upper bounds for the convergence rate of the distribution of restorable element with partially energized standby redundancy are found, in the case where all working and repair times are bounded by an exponential random variable (upper and lower), and working and repair times can be dependent. The convergence rate of the availability factor is estimated. Найдены экспоненциальные оценки сверху скорости сходимости распределения восстанавливаемого элемента с тёплым резервом в случае, когда все рабочие и ремонтные времена ограничены экспоненциальной случайной величиной (сверху и снизу), а рабочие и ремонтные времена могут быть зависимыми. Оценена скорость сходимости коэффициента готовности.

Equations defined by locally Lipschitz continuous mappings with a parameter are considered. Implicit function theorems for this equation are obtained. The regularity condition is formulated in the terms of the Clarke Jacobian. Implicit functions estimates are derived. It is shown that the considered regularity assumptions are weaker than most of the known ones. The obtained implicit function theorems are applied to derive conditions for upper semicontinuity of the optimal value function for parameterized optimization problems.

We discuss the computation of lower partial moments for the return of the investment portfolio that consists of the assets whose incomes are modeled by variance-gamma distribution, gamma distribution, and constants. The derived formulas depend on the values of the generalized hypergeometric functions. As a corollary of the main result, we calculate the target semideviation. We also show how the obtained results generate analytical expressions for the value at risk and the expected shortfall monetary risk measures.

The paper is devoted to the problem of dense packing of objects of arbitrary geometric shape with generalization in terms of dimension. A new solution method which consists in transforming the shape of objects by voxelization and the subsequent applying the developed algorithm for placing orthogonal polyhedrons is proposed. The effectiveness of the application of the developed method is demonstrated by an example of solving the problem of generating a layout of parts on the platform of a 3D printer. The application of the developed algorithms for solving the problem of dense packing of objects inside containers of arbitrary geometric shape is shown.