A method for recognizing infrasound acoustic signals for two types of sources based on the analysis of the shape of their wavelet spectra is proposed. The idea of constructing this form is based on the principal component method. Morphological image analysis methods are used to search for characteristic areas. The proposed method makes it possible to effectively solve the problem of multiclass classification of acoustic signals.

The method of effective modes is used for quantifying the dynamics of energy redistribution between different kinds of motions in water clusters upon their excitation within the long-wavelength infrared range < 2000 cm(-1). Three kinds of vibrations were considered, namely, radial and angular distortions of H bonds and bending vibrations of the molecules. Dynamics of the clusters (described in the Born-Oppenheimer approximation with the electronic problem solved at the MP2 level) was promoted by the initial excitation of particular kinds of motions or their combinations with the total activation energy per molecule in a range of 1.2-4.6 kcal/mol. Gross contributions of the different kinds of motion to the leading effective modes of clusters were determined as functions of time, which made it possible to estimate the dynamic coupling. The coupling of motions depends on the number of water molecules as well as on the activation energy and its initial distribution over particular degrees of freedom. The energy initially concentrated on radial distortions can be transferred directly to the angular distortions, and the corresponding mean dynamic coupling parameter reaches a maximum of 5.0 x 10(11) to 6.0 x 10(11) s(-1 )at the initial kinetic energy per molecule similar to 3.2-3.5 kcal/mol. It decreases with an increase in the flexibility of the cluster. When the energy is initially concentrated on the angular distortion modes, its relaxation toward the lower-frequency radial modes is usually indirect and requires the mediating role of bending vibrations whose temporary contribution to the dynamics can be as high as 25-30%. The angular-to-radial distortion coupling parameter is lower by nearly half than the radial-to-angular one. When angular distortions are initially activated concurrently with the bending vibrations, the prevailing energy relaxation channel is the activation of radial distortions. Upon the initial excitation of bending vibrations, the energy can be kept by the modes with no noticeable redistribution for up to 2 or 3 ps, being later redistributed in a cascade process at first to angular and then to radial distortions.

A method for the analysis of internal dynamics of nonlinear weakly bound polymolecular systems based on the effective-mode approach is proposed. The method enables one to estimate the number of the governing collective degrees of freedom of the system of interest at a preset accuracy under particular conditions and analyze the character of the modes depending on the activation energy of the system and the duration of its dynamic propagation, which provides qualitative and quantitative information about the coupling of diverse motions and the respective energy redistribution. The method is applied to the analysis of the dynamics of small water clusters stabilized by hydrogen bonds, which are unique spectacular examples of the systems with a pronounced coupling between the intramolecular and substantially delocalized intermolecular oscillations. The dynamic trajectories were generated in the adiabatic approximation at the Born-Oppenheimer level with the use of the quantum chemical description of selected clusters at the MP2/6-311++G(d, p) level. The initial conditions corresponded to different variants of the excitation of low-frequency normal modes, and the dynamic runs were carried out at a time step of 0.5 fs and the whole duration of 50 to 100 ps. Different prevailing characters of the cluster dynamics were identified depending on the molecular size, the total activation energy, and the mean potential-energy-increment to kinetic-energy-increment ratio, from an efficient accumulation of the excess kinetic energy on the effective modes of the cluster to the dissociation of the cluster into constituting fragments. The signs of the corresponding processes in the overlap matrices of the effective-mode vectors, kinetic-energy distribution over the modes, and the correlation between the number of the modes and the mean kinetic energy of the cluster are distinguished.

A new decomposition method (decomposition into N and U-waves) of infrasonic signals corresponding to partial reflection of N-wave sounding pulses from anisotropic atmospheric layers and recorded in areas of geometric shadow at large distances from explosions and volcanic eruptions is presented. The decomposition method makes it possible to determine the vertical gradients of the effective sound speed (sound speed plus wind speed in the direction of propagation) that are not available for determination by other methods.

This article provides an overview of the fundamental research directions being pursued at the Faculty of Physics of Lomonosov Moscow State University under the guidance of Professor Yuri Petrovich Pyt’ev. These research directions can be categorized into three primary areas: methods of morphological analysis of images and signals, theory of computer-aided measuring systems, and methods related to the theory of possibilities and subjective mathematical modeling. The article elucidates the foundational ideas and concepts of these directions, contemplates alternative approaches to address similar challenges, and offers both model-based and application-driven examples utilizing the methods corresponding to these directions and their combinations.

The importance of development of new methods for reconstruction of an object image given its sinogram and some additional information about the object stems from the possibility of artifact presence in the reconstructed image, or its insufficient sharpness when the used additional information does not hold. The problem of recovering artifact-free images of the studied object from tomography data is considered in the framework of the theory of computer-aided measuring systems. Methods for solving it are developed. They are based on narrowing the class of possible images using less artifact-inducing information. An example of such information is the natural condition of non-negativeness of the estimated brightnesses. The main problem that arises is the large dimensionality of the images, which prevents the use of direct algorithms. One proposed method is based on local approach, namely correction of the result of unfiltered backprojection by applying a locally (in the space of the output image) optimal linear transformation. Another method processes a sinogram directly, without using backprojection, using iterative implementation of the measurement reduction technique. Examples of use of the proposed methods for processing teeth sinograms are given.

The article is dedicated to the problem of recovering gaps in data series of experimental long-term continuous high-frequency observations of carbon dioxide concentration and air temperature. The study was conducted using the observation results from an automatic eco-climatic station located in a tropical monsoon forest in southern Vietnam (Dong Nai biosphere reserve). Gaps in observation series are, as a rule, random and caused by technical malfunctions of the instrumentation. Accurately recovered observation series allow for the assessment of the temporal variability of observed parameters on different time scales. In the scope of this study, options for recovering the continuity of time series based on mathematical statistics methods—autoregression (ARIMA) and the linear prediction method—have been considered. A comparative analysis of the accuracy of gap recovering using different methods is provided.

The analysis of regional trends in surface air temperature has become particularly relevant in recent years due to climate changes caused by an increase in the average global air temperature. This paper evaluates the main trends of long-term dynamics and cyclical changes in the average monthly air temperature in several regions of Russia, analyzes the statistical significance and adequacy of the constructed models, presents their comparative characteristics, and provides a forecast of regional trends.

The detecting of infrasonic signals from impulsive sources based on the mathematical model of their wavelet spectrum forms characteristic of signals from impulsive sources (explosions, volcanic activity, and others) is proposed. This model is based on wavelet spectra analysis of infrasonic signals from different sources. Modeling is based on morphological image analysis methods that are invariant to changes in signal recording conditions. The wavelet spectrum of a signal is a function of time and frequency, i.e., it depends on two arguments varying on a rectangular grid, and the value of this function (its module or the module of its real part) is considered as image brightness. The spectrum section corresponding to a signal from a source is approximated by a piecewise constant image, and the geometric form of its spots with the same brightness determines the model of spectral images of signals from different sources. It is shown that, for different impulsive sources, the characteristic form of these spots is conserved and at the same time it significantly differs from the forms that are characteristic of the wavelet spectra of signals from other sources (microbaroms, mountain associated waves, and auroral infrasonic waves). A morphological method of searching for wavelet spectrum sections of signals that are characteristic of impulsive sources is proposed.

A new method for isolating the quasi-periodic component of a time series based on the description of its form is proposed. This form is set by alternating convex up and convex down sections, the inflection points are the form parameters. The quasi-periodic component is isolated by solving the problem of the best approximation of the presented series by quasi-periodic signals. This approach makes it possible to distinguish a component with a variable period in the time series. After morphological filtration of the component of the series modeling the daily variability, the remainder of the series becomes stationary, which allows using methods of mathematical statistics and Fourier analysis for its further study. Verification of the obtained results was carried out by comparison with the results of Fourier analysis. The effectiveness of the approach is illustrated by results of decomposition of a time series of CO2 concentration in the atmosphere.

The computed tomography allows to reconstruct the inner morphological structure of an object without physical destructing. The accuracy of digital image reconstruction directly depends on the measurement conditions of tomographic projections, in particular, on the number of recorded projections. In medicine, to reduce the dose of the patient load there try to reduce the number of measured projections. However, in a few-view computed tomography, when we have a small number of projections, using standard reconstruction algorithms leads to the reconstructed images degradation. The main feature of our approach for few-view tomography is that algebraic reconstruction is being finalized by a neural network with keeping measured projection data because the additive result is in zero space of the forward projection operator. The final reconstruction presents the sum of the additive calculated with the neural network and the algebraic reconstruction. First is an element of zero space of the forward projection operator. The second is an element of orthogonal addition to the zero space. Last is the result of applying the algebraic reconstruction method to a few-angle sinogram. The dependency model between elements of zero space of forward projection operator and algebraic reconstruction is built with neural networks. It demonstrated that realization of the suggested approach allows achieving better reconstruction accuracy and better computation time than state-of-the-art approaches on test data from the Low Dose CT Challenge dataset without increasing reprojection error.

This paper deals with the formulation and solution of problems on the empirical restoration of the subjective mathematical model of an object of study, the scheme of its measurements, and the subjective interpretation of measurement data distorted by “omissions” in studied object measurements and noise, whose mathematical model is unknown. In this paper, the relevant problem of the subjective restoration of missing measurement data is formulated, solved, and studied, and the effect of omissions on the quality of the solution of subjective modeling problems is investigated. Some results of the comparative analysis of errors in the “automatic” and subjective methods for the restoration of measurement data are presented. Formulation and solution of the mentioned problems are carried out with the mathematical formalism of subjective modeling, which provides the mathematical formulation of both the subjective model of an object of study and the subjective models of its measurements with the subjective interpretation of measurement data. For this purpose, the subjective judgements of a researcher modeler1 on the physical properties of the object of study, the means of its measurements, the mathematical properties of noise, etc., are used; all the used subjective information is based on the scientific experience of a researcher modeler and his intuition.

In that paper, we a suggest lightweight filtering neural network, which implements the filtering stage in the Filtered Back-Projection algorithm (FBP), but good reconstruction results are achieved not only in ideal data but also in noisy data, which a usual FBP algorithm cannot achieve. Thus, our neural network is not an only variation of Ramp filter, which is usually used then FBP algorithm, but also a denoising filter. The neural network architecture was inspired with the idea of the possibility of the Ramp filtering operation’s approximation with sufficient accuracy. The efficiency of our network was shown on the synthetic data, which imitate tomographic projections collected with low exposition. In the generation of synthetic data, we have taken into account the quantum nature of X-ray radiation, exposition time of one frame, and non-linear detector response. The FBP reconstruction time with our neural network was 13 times faster than the time of reconstruction neural network from Learned Primal-Dual Reconstruction, and our reconstruction quality 0.906 by SSIM metric, which is enough to identify most significant objects.

The development of methods for improving the quality of tomographic images is an urgent task, as the presence of artifacts and insufficient sharpness of tomography result can cause erroneous decisions in medical diagnostics, when analyzing the structure of geological cores, etc. It is assumed that several artifacts arise due to inadequate a priori information involved in constructing the result of tomography, and a two-stage method is proposed for constructing an estimate of the distribution of the absorption coefficient of the sample. At the first stage, without using a priori information about the internal structure, the methods of the theory of computer-aided measuring systems construct an estimate of the absorption coefficient, which results in a blurred image of the internal structure of the object. At the second stage, the resolution of this image is increased by the method of moving averages with coefficients calculated from the condition of maximum accuracy for estimating the brightness of the central pixel of the window. Further, this estimate is refined from the natural conditions of the non-negativeness of the estimated brightness. Examples of the application of the method for assessing the structure of a child's tooth are given.

We propose a lightweight noise-canceling filtering neural network that implements the filtering stage in the algorithm for tomographic reconstruction of convolution and back-projection (Filtered BackProjection-FBP). We substantiate the neural network architecture, selected on the basis of the possibility of approximating the ramp filtering operation with sufficient accuracy. The network performance has been demonstrated using synthetic data that mimics low-exposure tomographic projections. The quantum nature of X-ray radiation, the exposure time of one frame, and the nonlinear response of the ionizing radiation detector are taken into account when generating the synthetic data. The reconstruction time using the proposed network is 11 times shorter than that of the heavy networks selected for comparison, with the reconstruction quality in the SSIM metric above 0.9.

Methods of the linear theory of computer-aided measuring systems are well developed. They allow obtaining the most accurate estimates of the parameters of the object under study from the measurement data (the reduction of measurement), as well as monitoring the consistency of the used mathematical model with the measurement result. In this paper, these methods are generalized to a class of nonlinear estimates implemented using neural networks. Sample estimates of the accuracy of the reduction of measurements and the agreement of the model with the data are used. The approach is applied for estimating atmospheric parameters based on spectral measurements of scattered solar radiation.

This paper proposes a method and an algorithm for the reconstruction of piecewise constant signals using the registration results obtained by devices whose operation can be described by a linear fuzzifier and additive noise. The type of the linear transformation and the statistical properties of the noise are known. The number of levels of a piecewise constant signal is also assumed to be given. The dependence of the accuracy of the piecewise-constant signal reconstruction on the number of possible signal values has been studied.

The paper proposes an approach to estimate the number of modes of collective movement of particles in weakly bound molecular systems, based on the principal component analysis. The example of the water molecule cluster (H2O)(8) shows significant differences in estimates of the number of effective and normal modes and establishes energy and time threshold criteria for the applicability of the normal modes method.

The reconstruction of an image distorted by a linear transformation is a problem that is unstable with respect to the perturbation of the mathematical model of the image formation. This instability is overcome by using a priori information about the class of original images. Among the ways to use such information, there is an assumption that the original image belongs to the class of piecewise constant images. The class of piecewise constant functions can provide a good approximation for signals encountered in practice since such functions can approximate any square-integrable signal with arbitrary accuracy. On the other hand, the assumption that the brightness value of the image takes a finite set of values is plausible for some applied studies. Such a proposal, in particular, is made in the tomography, where studied samples can consist of a small number of fractions. In this paper, we propose an algorithm for reconstruction of piecewise constant signals blurred by a linear transformation and investigate the possibility of its application to the original unblurred signal estimation. For ease of implementation, the case of one-dimensional signals is considered.