Ultimate Fast Gyrosynchrotron Codes

The past decade has seen a dramatic increase in practical applications of microwave gyrosynchrotron emission for plasma diagnostics and three-dimensional modeling of solar flares and other astrophysical objects. This breakthrough became possible due to an apparently minor, technical development of fast gyrosynchrotron codes, which enormously reduced the computation time needed to calculate a single spectrum, while preserving the accuracy of the computation. However, the available fast codes are limited in that they can only be used for a factorized distribution over the energy and pitch angle, while the distribution of electrons over energy or pitch angle is limited to a number of predefined analytical functions. In realistic simulations, these assumptions do not hold; thus, the codes free from the mentioned limitations are called for. To remedy this situation, we extended our fast codes to work with an arbitrary input distribution function of radiating electrons. We accomplished this by implementing fast codes for a distribution function described by an arbitrary numerically defined array. In addition, we removed several other limitations of the available fast codes and improved treatment of the free–free component. The ultimate fast codes presented here allow for an arbitrary combination of the analytically and numerically defined distributions, which offers the most flexible use of the fast codes. We illustrate the code with a few simple examples.

Stochastic Crashworthiness Optimization Accounting for Simulation Noise

Finite element-based crashworthiness optimization is extensively used to improve the safety of motor vehicles. However, the responses of crash simulations are characterized by a high level of numerical noise, which can hamper the blind use of surrogate-based design optimization methods. It is therefore essential to account for the noise-induced uncertainty when performing optimization. For this purpose, a surrogate, referred to as Non-Deterministic Kriging (NDK), can be used. It models the noise as a non-stationary stochastic process, which is added to a traditional deterministic kriging surrogate. Based on the NDK surrogate, this study proposes an optimization algorithm tailored to account for both epistemic uncertainty, due to the lack of data, and irreducible aleatory uncertainty, due to the simulation noise. The variances are included within an extension of the well-known expected improvement infill criterion referred to as Modified Augmented Expected Improvement (MAEI). Because the proposed optimization scheme requires an estimate of the aleatory variance, it is approximated through a regression kriging, which is iteratively refined. The proposed algorithm is tested on a set of analytical functions and applied to the optimization of an Occupant Restraint System (ORS) during a crash.

Fuzzy Differential Subordination of the Atangana–Baleanu Fractional Integral

The present paper continues the study on the relatively new concept of fuzzy differential subordination conducted in some recently published cited papers. In this article, certain fuzzy subordination results for analytical functions involving the Atangana–Baleanu fractional integral of Bessel functions are presented. Theorems giving the best dominants for some fuzzy differential subordinations are proved, and interesting corollaries are provided with the use of particular functions as fuzzy best dominants.

On one approach to the solution of miscellaneous problems of the theory of elasticity

Herein, a miscellaneous contact problem of the theory of elasticity in the upper half-plane is considered. The boundary is a real semi-axis separated into four parts, on each of which the boundary conditions are set for the real or imaginary part of two desired analytical functions. Using new unknown functions, the problem is reduced to an inhomogeneous Riemann boundary value problem with a piecewise constant 2 × 2 matrix and four singular points. A differential equation of the Fuchs class with four singular points is constructed, the residue matrices of which are found by the logarithm method of the product of matrices. The single solution of the problem is represented in terms of Cauchy-type integrals when the solvability condition is met.

Empirical Modelling of Public Lighting Emission Functions

Study of light at night has increased in recent decades due to the recognition of its impact on the environment, potential health concerns, as well as both the financial and carbon cost of energy waste. The advent of more extensive and improved ground-based measurements together with quantifiable satellite data has revolutionised the field, and provided data to test improved theoretical models. However, “closing the loop” and finding a detailed connection between these measurements requires knowledge of the “city emission function”, the angular distribution of upwelling radiation with zenith distance. Simplified analytical functions have been superseded by more complex models involving statistical approximation of emission sources and obstructions and inversion techniques now permit the estimation of emission functions from the observed sky brightness measurements. In this paper, we present an efficient GIS-based method to model public lighting using real-world photometric data and high-resolution digital elevation maps of obstructions such as buildings and trees at a 1 m scale. We discuss the results of this work for a sample of Irish towns as well as a city area. We also compare our results to previous emission functions as well as to observed asymmetries in emission detected by satellites such as SUOMI VIIRS.

DISCREPANCY PARAMETERS OF APPROXIMATIONS OF DISCRETELY SPECIFIED DEPENDENCIES BY ANALYTICAL FUNCTIONS AND SEARCH CRITERIA FOR OPTIMAL VALUES OF THEIR COEFFICIENTS

Universal discrepancy parameters of approximations of discretely specified dependencies by analytical functions and search criteria for optimal values of their coefficients, as well as analysis of features of their application are described. Discrepancy parameters of approximations, which do not depend on the ranges of variation of the values of functions and the number of points of a discretely specified dependence, are proposed. They can be effective for objectively comparing the quality of approximations of any dependencies by any functions. Approximations of a discretely specified dependence of the mathematical expectation of the equivalent electrical resistance of a layer of aluminum granules during spark-erosion dispersion in water on the instantaneous values of the discharge current are carried out. As approximating functions, we chose a power function with an exponent factor –1 and a function based on exponential. Using the criteria of the least approximation error, the optimal values of the coefficients of both approximating functions are founded. It is shown in which cases it is advisable to use the combined search criteria for the optimal values of the coefficients of the approximating functions, and in which are enough simple one-component ones. Ref. 27, fig. 2, tables 2.

circMine: a comprehensive database to integrate, analyze and visualize human disease–related circRNA transcriptome

Many circRNA transcriptome data were deposited in public resources, but these data show great heterogeneity. Researchers without bioinformatics skills have difficulty in investigating these invaluable data or their own data. Here, we specifically designed circMine (http://hpcc.siat.ac.cn/circmine and http://www.biomedical-web.com/circmine/) that provides 1 821 448 entries formed by 136 871 circRNAs, 87 diseases and 120 circRNA transcriptome datasets of 1107 samples across 31 human body sites. circMine further provides 13 online analytical functions to comprehensively investigate these datasets to evaluate the clinical and biological significance of circRNA. To improve the data applicability, each dataset was standardized and annotated with relevant clinical information. All of the 13 analytic functions allow users to group samples based on their clinical data and assign different parameters for different analyses, and enable them to perform these analyses using their own circRNA transcriptomes. Moreover, three additional tools were developed in circMine to systematically discover the circRNA–miRNA interaction and circRNA translatability. For example, we systematically discovered five potential translatable circRNAs associated with prostate cancer progression using circMine. In summary, circMine provides user-friendly web interfaces to browse, search, analyze and download data freely, and submit new data for further integration, and it can be an important resource to discover significant circRNA in different diseases.

Accounting and analytical support for the management of monetary assets in forestry enterprises

The subject of research: theoretical and practical problems of forming a system of accounting and analytical support for monetary assets management. The purpose of the study is to develop scientific approaches and methodical recommendations for the development of accounting and analytical support for monetary assets management in forestry enterprises. Method or methodology for conducting research. The methodological basis of the study is general theoretical methods of scientific knowledge, the main approaches and framework of accounting and analytical support of the management system, which are highlighted in the works of domestic and foreign scientists. To reach the research tasks the following methods were used: dialectical method of cognition – to analyze legislative and regulatory documents and scientific works of scientists concerning the formation of an effective system of accounting and analytical support for monetary assets management; analysis and synthesis – to study and generalize the foreign and domestic experience of theoretical and methodological fundamentals of the accounting and analysis of the monetary assets; abstract logical – for theoretical generalizations and formulation of conclusions. The field of application of results. The results of the study can be used in the practice of forestry enterprises to improve management efficiency. The results of research and conclusions. Based on the study, the essence of monetary assets is revealed, their role in ensuring the functioning of forestry enterprises is determined. The importance of building a system of accounting and analytical support for monetary assets management is substantiated; its components are characterized, and the problematic aspects of accounting and analytical functions implementation in generating the information for managing forestry enterprises’ monetary assets and cash flows are determined. The enterprises of the forestry complex need the cash flows balancing and replenishment for more efficient financing of their activities. Enterprise management should be based on the analysis and evaluation of cash flows using the information generated by the accounting and analysis system. Thus, the use of information about monetary assets should become an important element in assessing the quality of enterprise management, and lead to improving the efficiency of cash flow use and forecasting.

Gradient-Enhanced Multifidelity Neural Networks for High-Dimensional Function Approximation

In this work, a novel multifidelity machine learning (ML) algorithm, the gradient-enhanced multifidelity neural networks (GEMFNN) algorithm, is proposed. This is a multifidelity extension of the gradient-enhanced neural networks (GENN) algorithm as it uses both function and gradient information available at multiple levels of fidelity to make function approximations. Its construction is similar to the multifidelity neural networks (MFNN) algorithm. The proposed algorithm is tested on three analytical functions, a one, two, and a 20 variable function. Its performance is compared to the performance of neural networks (NN), GENN, and MFNN, in terms of the number of samples required to reach a global accuracy of 0.99 of the coefficient of determination (R2). The results showed that GEMFNN required 18, 120, and 600 high-fidelity samples for the one, two, and 20 dimensional cases, respectively, to meet the target accuracy. NN performed best on the one variable case, requiring only ten samples, while GENN worked best on the two variable case, requiring 120 samples. GEMFNN worked best for the 20 variable case, while requiring nearly eight times fewer samples than its nearest competitor, GENN. For this case, NN and MFNN did not reach the target global accuracy even after using 10,000 high-fidelity samples. This work demonstrates the benefits of using gradient as well as multifidelity information in NN for high-dimensional problems.