COMPARISON OF SOLVING A STIFF EQUATION ON A SPHERE BY THE MULTI-LAYER METHOD AND METHOD OF CONTINUING AT THE BEST PARAMETER

A stiff equation, linked with the solution of singularly perturbed differential equations with the use of standard methods of numeral solutions of simple differential equations often lead to major difficulties. First difficulty is the loss of stability of the counting process, when small errors on separate steps lead to an increase in the systematic errors in general. Another difficulty is, directly linked with the first one, consists of the need of decreasing the integrating step by a lot, which leads to a major decrease in the time taken for the calculations. On an example of a boundary value problem for a differential equation of second power on a sphere, comparison of our two approaches of constructing approximate values are held. The first approach is connected with the construction of an approximate multi-layer solution of the problem and is based on the use of recurrent equalities, that come out from classical numeral methods to the interval of a non-constant length. As a result, a numeral, approximated solution is replaced with an approximate solution in form of a function, which is easier to use for adaptation, building a graph and other needs. The second approach is linked with the continuation of the solutions by the best parameter. This method allows us to decrease majorly the number of steps and increase the stability of the computing process compared to standard methods

NUMERICAL METHODS FOR SOLVING PROBLEMS WITH CONTRAST STRUCTURES

In this paper, we investigate the features of the numerical solution of Cauchy problems for nonlinear differential equations with contrast structures (interior layers). Similar problems arise in the modeling of certain problems of hydrodynamics, chemical kinetics, combustion theory, computational geometry. Analytical solution of problems with contrast structures can be obtained only in particular cases. The numerical solution is also difficult to obtain. This is due to the ill conditionality of the equations in the neighborhood of the interior and boundary layers. To achieve an acceptable accuracy of the numerical solution, it is necessary to significantly reduce the step size, which leads to an increase of a computational complexity. The disadvantages of using the traditional explicit Euler method and fourth-order Runge-Kutta method, as well as the implicit Euler method with constant and variable step sizes are shown on the example of one test problem with two boundaries and one interior layers. Two approaches have been proposed to eliminate the computational disadvantages of traditional methods. As the first method, the best parametrization is applied. This method consists in passing to a new argument measured in the tangent direction along the integral curve of the considered Cauchy problem. The best parametrization allows obtaining the best conditioned Cauchy problem and eliminating the computational difficulties arising in the neighborhood of the interior and boundary layers. The second approach for solving the Cauchy problem is a semi-analytical method developed in the works of Alexander N. Vasilyev and Dmitry A. Tarkhov their apprentice and followers. This method allows obtaining a multilayered functional solution, which can be considered as a type of nonlinear asymptotic. Even at high rigidity, a semi-analytical method allows obtaining acceptable accuracy solution of problems with contrast structures. The analysis of the methods used is carried out. The obtained results are compared with the analytical solution of the considered test problem, as well as with the results of other authors

EFSA's OpenFoodTox: An open source toxicological database on chemicals in food and feed and its future developments

Since its creation in 2002, the European Food Safety Authority (EFSA) has produced risk assessments for over 5000 substances in >2000 Scientific Opinions, Statements and Conclusions through the work of its Scientific Panels, Units and Scientific Committee. OpenFoodTox is an open source toxicological database, available both for download and data visualisation which provides data for all substances evaluated by EFSA including substance characterisation, links to EFSA's outputs, applicable legislations regulations, and a summary of hazard identification and hazard characterisation data for human health, animal health and ecological assessments. The database has been structured using OECD harmonised templates for reporting chemical test summaries (OHTs) to facilitate data sharing with stakeholders with an interest in chemical risk assessment, such as sister agencies, international scientific advisory bodies, and others. This manuscript provides a description of OpenFoodTox including data model, content and tools to download and search the database. Examples of applications of OpenFoodTox in chemical risk assessment are discussed including new quantitative structure–activity relationship (QSAR) models, integration into tools (OECD QSAR Toolbox and AMBIT-2.0), assessment of environmental footprints and testing of threshold of toxicological concern (TTC) values for food related compounds. Finally, future developments for OpenFoodTox 2.0 include the integration of new properties, such as physico-chemical properties, exposure data, toxicokinetic information; and the future integration within in silico modelling platforms such as QSAR models and physiologically-based kinetic models. Such structured in vivo, in vitro and in silico hazard data provide different lines of evidence which can be assembled, weighed and integrated using harmonised Weight of Evidence approaches to support the use of New Approach Methodologies (NAMs) in chemical risk assessment and the reduction of animal testing

High Speed and High Efficiency Travelling Wave Single-Photon Detectors Embedded in Nanophotonic Circuits

Ultrafast, high quantum efficiency single photon detectors are among the most sought-after elements in modern quantum optics and quantum communication. High photon detection efficiency is essential for scalable measurement-based quantum computation, quantum key distribution, and loophole-free Bell experiments. However, imperfect modal matching and finite photon absorption rates have usually limited the maximum attainable detection efficiency of single photon detectors. Here we demonstrate a superconducting nanowire detector atop nanophotonic waveguides which allows us to drastically increase the absorption length for incoming photons. When operating the detectors close to the critical current we achieve high on-chip single photon detection efficiency up to 91% at telecom wavelengths, with uncertainty dictated by the variation of the waveguide photon flux. We also observe remarkably low dark count rates without significant compromise of detection efficiency. Furthermore, our detectors are fully embedded in a scalable silicon photonic circuit and provide ultrashort timing jitter of 18ps. Exploiting this high temporal resolution we demonstrate ballistic photon transport in silicon ring resonators. The direct implementation of such a detector with high quantum efficiency, high detection speed and low jitter time on chip overcomes a major barrier in integrated quantum photonics

The spatial structure of Baltic Sea ferry services

Ferry service is a transport system of regular routes which links areas separated by water bodies. Sometimes ferries are the only connection of an island and the mainland which is not rare in the Baltic Sea. A typical example of this is the island of Saaremaa. Ferry service is the backbone of cargo and passenger traffic in the Baltic Sea region. This article aims to describe the spatial structure of the ferry service in the Baltic Sea. To this end, a statistical database on 101 ferry routes has been built with passenger and car traffic on each being calculated with an original methodology, which in its turn can be applied in analysing the spatial structure and traffic of ferry services in other regions. Baltic ferries account for over half of all European ferry-borne car and passenger traffic. The Baltic stands out as a region with exceptionally long ferry routes which sustain timber exports. The main cargo shipping country in the region is Sweden

Mathematical models of complex systems on the basis of artificial neural networks

Neural networking technique with models based on ordinary/partial differential equations is applied to the known incorrect problems. Solutions to such problems by routine approaches are difficult. The problem approximate solution is found as the artificial neural network output with a prescribed architecture. Network weights are determined in the stepwise network training based on the error functional minimization process in general. The case of the system parameters given in some variation intervals and the parameter set as a part of input data is considered. The construction of robust parameter neural network models is examined using some problems in classical and non-classical statements. The direct problem solution and the inverse problem regularization for the offered neural network approach are constructed uniformly. The neurocomputing results for fixed and growing neural networks are given. The supercomputer use is discussed. The neural network approach advantages and some possible generalizations are mentioned