Iurie Caraus

We present a new update to MetaboAnalyst (version 4.0) for comprehensive metabolomic data analysis, interpretation, and integration with other omics data. Since the last major update in 2015, MetaboAnalyst has continued to evolve based on user feedback and technological advancements in the field. For this year's update, four new key features have been added to MetaboAnalyst 4.0, including: (1) real-time R command tracking and display coupled with the release of a companion MetaboAnalystR package; (2) a MS Peaks to Pathways module for prediction of pathway activity from untargeted mass spectral data using the mummichog algorithm; (3) a Biomarker Meta-analysis module for robust biomarker identification through the combination of multiple metabolomic datasets and (4) a Network Explorer module for integrative analysis of metabolomics, metagenomics, and/or transcriptomics data. The user interface of MetaboAnalyst 4.0 has been reengineered to provide a more modern look and feel, as well as to give more space and flexibility to introduce new functions. The underlying knowledgebases (compound libraries, metabolite sets, and metabolic pathways) have also been updated based on the latest data from the Human Metabolome Database (HMDB). A Docker image of MetaboAnalyst is also available to facilitate download and local installation of MetaboAnalyst. MetaboAnalyst 4.0 is freely available at http://metaboanalyst.ca.

In this article we obtained that the collocation methods are stable in according with the small perturbations of coefficients, kernels and right part of studied equations. We proved that the condition number of the approximate operator exists and bounded. The condition number of collocation methods is appropriated with condition number for exact singular integro- differential equations.

In this article we elaborate the numerical schemes of the collocation and quadrature- interpolation methods for the approximate solution of the singular integro-differential equations when the kernel has a weak singularity. The equations are defined on the arbitrary smooth closed contour of complex plane. The collocation and quadrature-interpolation methods are based on the descritization using Fejer points. Theoretical background for these methods is to be laid in classical Holder spaces.

Abstract: In present paper we elaborated the numerical schemes of reduction methods for approximative solution of Singular Integro- Differential Equations with kernels of Cauchy type. The equations are defined on the arbitrary smooth closed contours of complex plane. The researched methods are based on the Faber-Laurent polynomials. Theoretical background of reduction methods has been obtained in Generalized Hölder spaces. Singular Integro- differential equations, Faber-Laurent polynomials, Generalized Hölder spaces 1