The authors consider the inverse problem of restoring the coefficient in a nonlinear equation of a dynamic model of a homogeneous biological population of organisms structured according to age. The model allows for the dependence of parameters of the vital activity of individuals on the population size. Some coefficients of the model are nonlocal and have an integral structure. Conditions for the uniqueness of the solution of the inverse problem are established.
An attack–defense model is considered in which the attack can deliver several strikes on defense points to maximize the damage. A way of creating a solution to a zero-sum game in mixed strategies is developed.
The diffusive logistic model of information dissemination in a social network is considered in the form of a one-dimensional nonstationary parabolic equation. The problem of parametric identification is posed as an extremum problem for searching the parameter in the form of a spatially distributed social network capacity. Gradient means of optimization are applied. The results demonstrate uniform convergence to an exact solution in the approach with a controllable descent direction.
Additive (splitting) schemes are used to contruct effective computational algorithms for approximately solving initial-boundary value problems for nonstationary partial differential equations. Splitting schemes are normally used when the main operator of a problem has an additive representation. Problems where the operator at the time derivative of a solution is split are also of interest. For first-order evolution equations, we propose splitting schemes based on transforming the original equation to an equivalent system of equations.
The authors discuss generative intelligence systems for image synthesis, describes one (DALL (cdot) E 2) in detail, and provide familiar examples of the use of such systems. The advisability of preparing such a review lies in the current situation in the field of generative intelligence, many inflated expectations and fears, and a practical lack of descriptions and analyses of scenarios for their use in business. This review will be useful to anyone who wishes to understand the real capabilities and limitations of such systems.
A description is given of algorithms for converting linear controlled systems with interval parameters from a state-space representation to a representation in the form of transfer functions and vice versa. Results are accompanied by computational examples demonstrating the capabilities and limitations of the proposed approach.
The problem of testing pharmaceuticals on their bioequivalence is considered. Investigations of drug bioequivalence are the basis for reproducing drugs that confirm their efficiency and safety. The main way of verifying drug bioequivalence is to conduct two one-sided Schuirmann tests. Two one-sided tests have been used for many years and proven their validity for proving equivalent bioavailability, but in some situations (missing data, the necessity of considering not only the aggregate metrics but also the shape of the concentration–time curve) there is a need to establish more accurately the differences between the concentration–time curves. The authors present a new criterion that is more sensitive to the differences between characteristics that affect drug bioavailability and reduce the risk for patients. In should be noted that the new criterion generalizes the Schuirmann criterion and preserves its useful properties.
A study is performed of the algebraic properties of the Hadamard product (Schur product, component-wise product) of linear error-correcting codes. The complexity of constructing a product basis using known multiplier bases is discussed. The concept is introduced of quotient, quasi-quotient, and maximal inclusion quasi-quotient obtained from the Hadamard division of one linear code by another. An explicit form of the maximum Hadamard division quasi-quotient is established. A criterion is proved for the existence of a given code of an inverse code in a semiring formed by linear codes of length (n) with the operations of sum and product of Hadamard codes. The explicit form of codes that have a reverse code in this semiring is described.
An improved lower bound is found for the bilinear complexity of the multiplication of arbitrary matrices over finite fields.
The need to detect pathogenic microorganisms in the human body as quickly as possible is an important problem in medicine. One of today’s most common approaches of solving it is based on sowing biological material on nutrient media and then observing the growth of colonies. This technique has certain disadvantages associated mainly with the human factor, which can lead to errors in the final diagnosis. The aim of this work was to develop technologies for the intelligent processing of data from microbiological analyses based on photographic images of Petri dishes. This would reduce dependence on the human factor and improve key indicators of data processing. Results show that the developed heuristic and neural network approaches of detecting and classifying colonies of microorganisms are superior to those of existing ptocedures. They allow the automation of key stages of microbiological examination and thus can be applied in practice.
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