Izvestiya of Saratov University. Mathematics. Mechanics. Informatics

We present a number of low and upper bounds for Levy – Prokhorov, Wasserstein, Frechet, and Hellinger distances between probability distributions of the same or different dimensions. The weighted (or context-sensitive) total variance and Hellinger  distances are introduced. The upper and low bounds for these weighted metrics are proved. The low bounds for the minimum of different errors in sensitive hypothesis testing are proved. 

This article considers systems of subspaces of the Hardy space generated by the Szego kernel. The main result of the work is to establish the convergence of orthorecursive expansions with respect to the considered systems of subspaces. Note that the conditions for the convergence of orthorecursive expansions prove to be somewhat more restrictive compared to the previously obtained conditions for the convergence of order-preserving weak greedy algorithms and frame expansions.

A technique and a prototype of a mobile test bench for conducting experiments on uniaxial compression of biological tissue samples have been developed. The test bench consists of high-precision scales, an electronic caliper with modified grips, and a video camera. With the help of the test bench, a series of experiments (120 in total) was carried out to determine Young's modulus of atherosclerotic plaques and vascular walls removed from the human body no later than a few hours. A database of plaques and artery walls' mechanical characteristics, as close as possible to their real strength properties, has been formed. In addition, regression dependencies linking Hounsfield units and Young’s moduli of atherosclerotic plaques were constructed. The uniaxial compression technique has been verified on the Instron 3342 universal testing machine. Also, to demonstrate the applicability of the developed technique and test bench for uniaxial compression of hard tissues, experiments were conducted with 14 samples of bovine spongy bone.

Deviation of the first toe to the outside, interconnected with the deviation of the first metatarsal bone to the inside, occurs in 46% of patients of the older age group and is called valgus deformity of the first toe. The negative impact of this pathology on the quality of life of patients is the reason for seeking medical help, the gold standard of which is surgical correction, and the basic surgical technique is osteotomy (sawing the bone and fixing its fragments with implants) of the first metatarsal. At the same time, an ideal osteotomy should provide initial stability in the early postoperative period. However, a large number of ways to perform osteotomy, as well as the advantages and disadvantages of each of the surgical techniques, do not allow to consider one of them as the most successful. In this regard, the aim of the work was to develop and validate a biomechanical model of osteotomy of the first metatarsal bone to analyze its stability and reliability depending on the type of osteotomy, the degree of displacement of bone fragments, as well as the number of fastening screws. In this study, biomechanical modeling of the most commonly used variants of osteotomy of the first metatarsal bone of the foot in the surgical treatment of its valgus deformity was carried out. For this purpose, 10 models of osteotomies of a separate first metatarsal bone were created, which were then subjected to static loading to analyze their stress-strain state and assess their success. Successful (stable and reliable) treatment options were identified, as well as unsuccessful ones. Two of the ten options considered were unsuccessful – scarf type osteotomies with displacement of bone fragments by 2/3 of its diameter and fixed with a single screw. It was revealed that osteotomies of the chevron type showed higher stability in comparison with scarf osteotomies. As a result, we note that in this study, numerical experiments were conducted for the first time to compare the stability and strength of the most commonly used variants of osteotomies based on a single bone model. A biomechanical model of scarf osteotomy of the first metatarsal bone has been developed and validated on the basis of mechanical experiments.

This paper briefly describes the development of information technology tools using biometric data, in particular, human gait parameters. The problems of assessing gait parameters using a mobile phone accelerometer in real conditions are briefly described. The relevance of this research is substantiated in the field of developing algorithms for assessing biometric gait indicators based on data from wearable devices. The main approaches to the processing of wearable device accelerometer data are considered, the main shortcomings and problems in improving the quality of gait parameter estimation are indicated. The algorithm for processing data from a mobile phone accelerometer is described. In the proposed algorithm, the selection of movement patterns during gait  in the recorded data is carried out on the basis of statistical information within the “floating” time window (frequency component with the maximum contribution to the spectrum of the accelerometer signal, the duration of the selected time segments), as well as on the basis of the value of the correlation coefficient, selected time segments. At the stage of data segmentation, the time window of searching of movement segments, as well as the allowable thresholds of selecting movements by their duration, change depending on the individual characteristics of the gait and human activity. The classification of the selected segments according to the nature of gait movements is carried out on the basis of a feed-forward neural network. The sigmoid was used as the activation function for the hidden layers, and the normalized exponential function was used for the output layer. The neural network was trained using the gradient backdescent method with cross entropy as an optimization criterion. Due to the selection of segments with a high correlation coefficient, the classification of data shows the quality of distinguishing movements above 95%.