A Lightweight Learning Method for Stochastic Configuration Networks Using Non-Inverse Solution

Stochastic configuration networks (SCNs) face time-consuming issues when dealing with complex modeling tasks that usually require a mass of hidden nodes to build an enormous network. An important reason behind this issue is that SCNs always employ the Moore–Penrose generalized inverse method with high complexity to update the output weights in each increment. To tackle this problem, this paper proposes a lightweight SCNs, called L-SCNs. First, to avoid using the Moore–Penrose generalized inverse method, a positive definite equation is proposed to replace the over-determined equation, and the consistency of their solution is proved. Then, to reduce the complexity of calculating the output weight, a low complexity method based on Cholesky decomposition is proposed. The experimental results based on both the benchmark function approximation and real-world problems including regression and classification applications show that L-SCNs are sufficiently lightweight.

A method for determining stoichiometric coefficients using minors of a matrix

Spinel materials often have complex structures and as a result, balancing of reactions with these compounds by traditional methods become very time consuming. A method to calculate the stoichiometric coefficients for chemical reactions using first a modified matrix-inverse method and then an optimised method is proposed. Both methods are explored using linear algebra and the result demonstrated using a typical chromite reduction reaction.

A METHOD FOR DETERMINING STOICHIOMETRIC COEFFICIENTS USING MINORS OF A MATRIX

Spinel materials often have complex structures and as a result, balancing of reactions with these compounds by traditional methods become very time consuming. A method to calculate the stoichiometric coefficients for chemical reactions using first a modified matrix-inverse method and then an optimised method is proposed. Both methods are explored using linear algebra and the result demonstrated using a typical chromite reduction reaction.

A new method for determining stoichiometric coefficients using minors of a matrix

Spinel materials often have complex structures and as a result, balancing of reactions with these compounds by traditional methods become very time consuming. A method to calculate the stoichiometric coefficients for chemical reactions using first a modified matrix-inverse method and then an optimised method is proposed. Both methods are explored using linear algebra and the result demonstrated using a typical chromite reduction reaction.

A new method for determining stoichiometric coefficients using minors of a matrix

The motivation of this study was the investigation into the metallothermic reduction of chromite ores. Spinel materials have complex structures and as a result, balancing of the reduction reactions by traditional methods become very time consuming. A method to calculate the stoichiometric coefficients for chemical reactions using first a modified matrix-inverse method and then a new optimised method is proposed. The mathematical basis of both methods is explored using matrix algebra and then demonstrated using a typical chromite reduction reaction.

Probabilistic Inverse Method for Source Localization Applied to ETEX and the 2017 Case of Ru-106 including Analyses of Sensitivity to Measurement Data

In recent years, cases of unexplained, elevated levels of radioactive particles have demonstrated an increasing need for efficient and robust source localization methods. In this study, a Bayesian method for source localization is developed and applied to two cases. First, the method is validated against the European tracer experiment (ETEX) and then applied to the still unaccounted for release of Ru-106 in the fall of 2017. The ETEX dataset, however, differs significantly from the Ru-106 dataset with regard to time resolution and the distance from the release site to the nearest measurements. Therefore, sensitivity analyses are conducted in order to test the method’s sensitivity to these parameters. The analyses show that the resulting source localization depends on both the observed temporal resolution and the existence of sampling stations close to the source. However, the method is robust, in the sense that reducing the amount of information in the dataset merely reduces the accuracy, and hence, none of the results are contradictory. When applied to the Ru-106 case, the results indicate that the Southern Ural region is the most plausible release area, and, as hypothesized by other studies, that the Mayak nuclear facility is the most likely release location.

Generalized variational principles of the Benney-Lin equation arising in fluid dynamics

Variational principle is important since it can not only reveal the possible solution structures of the equation but also provide the conservation laws in an energy form. Unfortunately, not all the differential equations can find their variational forms. In this work, the Benney-Lin equation is studied and its two different generalized variational principles are successfully established by using the semi-inverse method. The derivation process is given in detail. The finding in this work is expected to give a insight into the study of the nonlinear partial differential equations arising in fluid dynamics.