We analyze transformations of circular Laguerre-Gaussian beams with zero radial index after passage through the double-phase-ramp (DPR) converter and study the behavior of optical vortices in the propagating transformed beam. Direct and inverse DPR converters are considered, and informative features of the complete set of optical vortices are revealed. For the input beam with even azimuthal index, such a reaction may cause the sign reversal of the axial optical vortex. The results can be used for creation of light beams with prescribed singular skeleton, for the beam diagnostics, and in high-resolution metrology.

We study the system of phase singularities (‘singular skeleton’) formed when a quasi-plane wave (QPW) input beam diffracts at a double-phase-ramp (DPR) converter. The external (OV positions and 3D trajectories) and internal (ellipticity and orientation angle of the equal-intensity ellipses in the OV-core area) singular-skeleton features are investigated both theoretically and in experiments. The results are presented in comparison with the singular skeleton formed by the DPR when the incident beam is Gaussian. In contrast to the limited number of OVs in the synthesized OV chain, divergent 3D OV trajectories and variable OV morphologies depending on their off-axis distances, which is typical for the Gaussian input beam, it is shown that the QPW-generated diffracted beam carries a rectilinear chain of equidistant optical vortices (OV) with identical morphology parameters. Such singular-skeleton configurations can be useful for the applications to metrology and micromanipulation, in particular, for the multi-particle optical trapping and guiding.

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The work is aimed at establishing the boundaries of the use of models for describing signals in optoelectronic systems in calculating efficiency. A description of the signal formation process is proposed, taking into account the corpuscular and wave properties when registering signals in a wide range of intensities. A description of the statistical features of the output signals depending on the energy properties of the signal and noise components is proposed. It is shown that when describing the output signals of optoelectronic systems that register signals with different properties, Poisson and Gaussian distributions are used. The invariance of Poisson flows determines the description of an additive mixture of signal and background flows using Poisson flow. The efficiency of optoelectronic systems is calculated by the signal-to-noise ratio criterion based on the corpuscular and wave description of signals. Efficiency calculations have shown the expedience of using this criterion, provided that the statistical properties of signal and background flows are stabilized. It is shown that under the condition of changes in the energy characteristics of signals, from the point of view of the wave and corpuscular models, the statistical characteristics of the signals have different descriptions. The analysis of theoretical methods of signal analysis in optoelectronic systems is carried out, which is aimed at an adequate characteristic of the system operation, depending on the conditions of its operation. Taking into account the method of describing the process of receiving and processing signals will take into account additional statistical characteristics of signals, for example, an increase of the variance of the output signal. The use of adaptive methods for describing signals will make it possible to increase the efficiency of systems when receiving strong signals in a difficult interference environment, as well as when receiving weak signals

Models for predicting the number of patients with COVID-19 using machine learning methods have been built. The data for models are obtained from various official sources, including the World Health Organization, from the beginning of the epidemic to the present time. The data in Ukraine and India were selected to teach models for predicting the number of patients with COVID-19. Algorithms of linear regression for Ukraine and gradient boosting for India proved to be the methods that provided high accuracy of the forecast for the existing data. Data analysis was performed using the Python programming language with Sklearn library which is based on SciPy (Scientific Python). In addition, the XGboost gradient boost algorithm library was used. To develop the model, multifactor prediction of time series with the delays as predictors was chosen. It is established that the such characteristics as the date of the event, day of the week, week number, month affect to the model. Model errors are smallest and forecast accuracy were estimated with the best values of 0.83 for Ukraine and 0.75 for India. The built models allow to predict the epidemiological situation in the future, to coordinate actions in different areas of health care and to carry out reasonable preventive measures at the state level.