数学最新文献

A single-particle cryo-electron microscopy (cryo-EM) measurement, called a micrograph, consists of multiple two-dimensional tomographic projections of a three-dimensional (3-D) molecular structure at unknown locations, taken under unknown viewing directions. All existing cryo-EM algorithmic pipelines first locate and extract the projection images, and then reconstruct the structure from the extracted images. However, if the molecular structure is small, the signal-to-noise ratio (SNR) of the data is very low, making it challenging to accurately detect projection images within the micrograph. Consequently, all standard techniques fail in low-SNR regimes. To recover molecular structures from measurements of low SNR, and in particular small molecular structures, we devise an approximate expectation-maximization algorithm to estimate the 3-D structure directly from the micrograph, bypassing the need to locate the projection images. We corroborate our computational scheme with numerical experiments and present successful structure recoveries from simulated noisy measurements.

This study aims to investigate the nontransitivity of the stochastic precedence relation. The dice were taken as an example of discrete random variables with a finite set of values. The means and variances of the dice were assumed those of the classical dice. The whole variety of nontransitive sets containing three or four dice were found in case of one or two tosses and various ways to determine the advantage. The sets that reveal the strongest property of nontransitivity were obtained according to the specific function. The hypothesis has been tested about the emergence of nontransitivity after two tosses of dice in originally transitive sets.

The article studies the issues of innovation implementation in universities. A three-level hierarchically organized model is proposed to describe the process of innovation implementation in universities. The model includes agents (followers, in whose role teachers act), supervisors (subjects of middle-level management, universities) and a principal (leader, the state). The principal (the state) is the first to announce its behavior strategy. Supervisors choose their management strategies when the principal’s choice is already known, but the agents’ choice is not yet known. Agents (teachers) make their choice when the management strategies of the other subjects are already known. Supervisors, like agents, make their choice independently of each other. The principal subsidizes the innovative development of higher education institutions by allocating funds for the development of new electronic courses. The new electronic courses being developed are considered as innovative products that contribute to the innovative development of higher education institutions. Supervisors receive subsidies from the principal for the development and implementation of innovative products. They determine the required volume of new courses issued by agents. Agents develop new electronic training courses for subsequent sale and implementation in the educational process. Supervisors keep part of the subsidies received from the principal for themselves, and transfer part to agents. Agents receive subsidies, the amount of which depends on the demand for the courses they develop, and manage the quality of the courses they develop, improving their qualifications. The possibility of corruption in the system is provided for and methods for combating it are defined. Lower and middle management entities may be subject to corruption. Agents may offer bribes to supervisors, in exchange for which they inflate the portion of subsidies transferred to agents. An analysis is conducted of how the presence of corruption affects the innovative development of universities. Thus, a dynamic three-level model is constructed, in which the dynamics are described by a difference equation reflecting the change in the general innovative level of the education system depending on the agents’ controls. Algorithms for constructing a solution for different combinations of Stackelberg games with and without feedback on control between the state and universities and between universities and teachers are indicated. In a non-antagonistic game of universities among themselves, as in a game of teachers, a Nash equilibrium is built. The results of numerical experiments are presented, their analysis is given. A number of meaningful conclusions and recommendations are made.

The article proposes a technology for validating autonomous navigation methods for unmanned aerial vehicles based on simultaneous mapping and localization (SLAM) algorithms. The proposed technology is based on experimental studies using real flight data and includes the design of validation scenarios, synchronization and spatial alignment of trajectories, as well as the calculation of a set of quantitative metrics characterizing global and local accuracy, drift accumulation, and the stability of the navigation solution. As a demonstration example, the technology was evaluated using the VINS-Fusion visual-inertial algorithm using recordings of real UAV flights. The obtained results show that the proposed approach allows comparing different SLAM solutions under the same conditions and identifying flight modes that are most sensitive to error accumulation.

A new neurodynamic model for joint optimization of the traveling salesman problem route and fuzzy cluster partitioning of a set of vertices is proposed. The model’s energy function includes three components: a Hopfield-Tank term encoding route feasibility constraints; a fuzzy means term ensuring geometric compactness of clusters; and a topological matching term penalizing for discontinuities in cluster membership between adjacent vertices along the route. An iterative minimization scheme is developed. The following convergence properties are proven: monotonic energy decrease and convergence of the energy sequence to a limit value. Computational experiments on a test example showed that the proposed model finds solutions that coincide with the global optimum, while the resulting clusters differ significantly from the results of the classical fuzzy c-means algorithm, reflecting the topology of the optimal route. The results of the study can be used for problems of delivery territory zoning, production operation planning, and condensation of large factor models.

The problem of redistributing quotas for training among structural divisions of a higher education institution is considered. The problem of redistributing quotas has a wide range of applications, in particular, in preventing environmental pollution. The article assumes that a higher education institution has several structural divisions. The management of the higher education institution allocates some quotas for training to structural divisions (SD). The head of each SD can give part of the quota of his SD to another division, receiving some compensation in return. In this case, if the quota is not given, it must be fully used in the joint venture to which it was allocated. The head of each joint venture strives to maximize his gain, expressed by his objective function. For simplicity, it can be considered that the goal of the head of each joint venture is to maximize the amount of funds accumulated in the centralized fund of this joint venture. In this case, the head of the joint venture can manage the share of the quota allocated to him, which he wants to give or receive from another joint venture. It is shown in which cases all structural divisions manage to receive optimal quotas for them as a result of redistribution. Three cases are considered: when the total value of the quota that the divisions want to give is greater than, less than or equal to the total value of the quota that other structural divisions want to acquire. Algorithms for redistributing quotas in each of these cases are proposed. The study is conducted analytically for a particular type of input functions, which are taken as power functions. Numerical examples are given and an analysis of the results obtained is given. A number of meaningful conclusions are made.