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Increased electrocardiogram (ECG) spatial QRS-T wave angle is a recognised risk factor. Standard evaluation of the angle requires deriving orthogonal ECG leads, either by general transformation matrices into XYZ leads or by singular value decomposition (SVD). This study shows that the transformation is not needed, and that the spatial QRS-T angle can be calculated directly from the original ECG leads. The direct computation was tested using long-term 12-lead ECGs of 523 healthy volunteers (259 females). A total of 659,313 individual 10-second ECG samples were obtained providing 7,350,733 individual beats which were analysed both by the direct method using 8 algebraically independent leads and by the conventional XYZ and SVD transformations. On average, the results of the direct non-transformation method were closer to the SVD-based results (averaged differences below 1 degree) than to the XYZ-based results (averaged differences below 2 degrees). The subject-specific regressions to the underlying heart rate showed that the proposed direct method was significantly more reproducible ( p  < 0.0001) and that it showed more compact variability within individual ECG samples ( p  < 0.0001). Thus, the study shows not only that the QRS-T angle can be computed without any orthogonal transformation but that the results of the direct computation are also more precise.

Image processing systems are currently used to solve many applied problems. The article is devoted to the identification of negative factors affecting the growth of grain in different periods of harvesting, using a program implemented in the MATLAB software environment, based on aerial photographs. The program is based on the Law’s textural mask method and successive clustering. This paper presents the algorithm of the program and shows the results of image processing by highlighting the uniformity of the image. To solve the problem, the spectral luminance coefficient (SBC), normalized difference vegetation index (NDVI), Law’s textural mask method, and clustering are used. This approach is general and has great potential for identifying objects and territories with different boundary properties on controlled aerial photographs using groups of images of the same surface taken at different vegetation periods. That is, the applicability of sets of Laws texture masks with original image enhancement for the analysis of experimental data on the identification of pest outbreaks is being investigated.

New numerical algorithms for differentiating matrix orthogonal transformations are constructed. They do not require that the derivatives of the orthogonal transformation matrix be available. An example is given how these algorithms can be applied to the numerically stable calculation of a solution to the discrete-time matrix Riccati sensitivity equation.

The dimensional statistics approach of principal component analysis is utilized in this paper to transform a set of variable observations using orthogonal transformation to convert the data to a new coordinate. The original observations data are summed linearly by selecting appropriate values through cross-validation and calculating the spatial data of works with literary elements. Determine a sufficient number of basis functions selected mainly based on the fluctuation of time variables. The number of students who believe that reading classic works enhances scientific literacy was 92.56%, with the highest contribution of linguistic and literary elements found to be 92.56%. The uniqueness and richness of children's literature can enhance character-building and overall core literacy of students, as indicated by this.

Wildfires have significant environmental and socio-economic impacts, affecting ecosystems and people worldwide. Over the coming decades, it is expected that the intensity and impact of wildfires will grow depending on the variability of climate parameters. Although Bulgaria is not situated within the geographical borders of the Mediterranean region, which is one of the most vulnerable regions to the impacts of temperature extremes, the climate is strongly influenced by it. Forests are amongst the most vulnerable ecosystems affected by wildfires. They are insufficiently adapted to fire, and the monitoring of fire impacts and post-fire recovery processes is of utmost importance for suggesting actions to mitigate the risk and impact of that catastrophic event. This paper investigated the forest vegetation recovery process after a wildfire in the Ardino region, southeast Bulgaria from the period between 2016 and 2021. The study aimed to present a monitoring approach for the estimation of the post-fire vegetation state with an emphasis on fire-affected territory mapping, evaluation of vegetation damage, fire and burn severity estimation, and assessment of their influence on vegetation recovery. The study used satellite remotely sensed imagery and respective indices of greenness, moisture, and fire severity from Sentinel-2. It utilized the potential of the landscape approach in monitoring processes occurring in fire-affected forest ecosystems. Ancillary data about pre-fire vegetation state and slope inclinations were used to supplement our analysis for a better understanding of the fire regime and post-fire vegetation damages. Slope aspects were used to estimate and compare their impact on the ecosystems’ post-fire recovery capacity. Soil data were involved in the interpretation of the results.

MR diffusion kurtosis imaging (DKI) was proposed recently to study the deviation of water diffusion from Gaussian distribution. Mean kurtosis, the directionally averaged kurtosis, has been shown to be useful in assessing pathophysiological changes, thus yielding another dimension of information to characterize water diffusion in biological tissues. In this study, orthogonal transformation of the 4th order diffusion kurtosis tensor was introduced to compute the diffusion kurtoses along the three eigenvector directions of the 2nd order diffusion tensor. Such axial ( K //) and radial ( K ┴) kurtoses measured the kurtoses along the directions parallel and perpendicular, respectively, to the principal diffusion direction. DKI experiments were performed in normal adult ( N = 7) and formalin-fixed rat brains ( N = 5). DKI estimates were documented for various white matter (WM) and gray matter (GM) tissues, and compared with the conventional diffusion tensor estimates. The results showed that kurtosis estimates revealed different information for tissue characterization. For example, K // and K ┴ under formalin fixation condition exhibited large and moderate increases in WM while they showed little change in GM despite the overall dramatic decrease of axial and radial diffusivities in both WM and GM. These findings indicate that directional kurtosis analysis can provide additional microstructural information in characterizing neural tissues.

This computationally oriented book describes and explains the mathematical relationships among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and conjugate gradient algorithms. The book bridges different mathematical areas to obtain algorithms to estimate bilinear forms involving two vectors and a function of the matrix. The first part of the book provides the necessary mathematical background and explains the theory. The second part describes the applications and gives numerical examples of the algorithms and techniques developed in the first part. Applications addressed in the book include computing elements of functions of matrices; obtaining estimates of the error norm in iterative methods for solving linear systems and computing parameters in least squares and total least squares; and solving ill-posed problems using Tikhonov regularization. This book will interest researchers in numerical linear algebra and matrix computations, as well as scientists and engineers working on problems involving computation of bilinear forms.

An important part of the well-known iterative closest point algorithm (ICP) is the variational problem. Several variants of the variational problem are known, such as point-to-point, point-to-plane, generalized ICP, and normal ICP (NICP). This paper proposes a closed-form exact solution for orthogonal registration of point clouds based on the generalized point-to-point ICP algorithm. We use points and normal vectors to align 3D point clouds, while the common point-to-point approach uses only the coordinates of points. The paper also presents a closed-form approximate solution to the variational problem of the NICP. In addition, the paper introduces a regularization approach and proposes reliable algorithms for solving variational problems using closed-form solutions. The performance of the algorithms is compared with that of common algorithms for solving variational problems of the ICP algorithm. The proposed paper is significantly extended version of Makovetskii et al. (CCIS 1090, 217–231, 2019).

This article discusses a large number of textural features and integral transformations for the analysis of texture-type images. It also discusses the description and analysis of the features of applying existing methods for segmenting texture areas in images and determining the advantages and disadvantages of these methods and the problems that arise in the segmentation of texture areas in images. The purpose of the ongoing research is to use methods and determine the effectiveness of methods for the analysis of aerospace images, which are a combination of textural regions of natural origin and artificial objects. Currently, the automation of the processing of aerospace information, in particular images of the earth’s surface, remains an urgent task. The main goal is to develop models and methods for more efficient use of information technologies for the analysis of multispectral texture-type images in the developed algorithms. The article proposes a comprehensive approach to these issues, that is, the consideration of a large number of textural features by integral transformation to eventually create algorithms and programs applicable to solving a wide class of problems in agriculture.