Comparative Analysis of Viscoelastic Models Involving Fractional Derivatives of Different Orders

Mathematics Subject Classification: 74D05, 26A33

Research of the Acoustic Characteristics of the Bell "Mazepa" of the Sofia Cathedral (Kiev) and their Comparison with Characteristics of Bulgarian Bells

Experimental researches of one of the eldest bells («Mazepa»-see Appendix1) in Ukraine, are considered in the article. The spectra and spectra- time analysis of bell ringing is embodied, main frequencies of oscillation and musical intervals of sounding are determined. Comparative description of bell sounding with the known bells of Russia and Bulgaria is given.

A Comparative Analysis of Predictive Learning Algorithms on High-Dimensional Microarray Cancer Data

This research evaluates pattern recognition techniques on a subclass of big data where the dimensionality of the input space (p) is much larger than the number of observations (n). Specifically, we evaluate massive gene expression microarray cancer data where the ratio κ is less than one. We explore the statistical and computational challenges inherent in these high dimensional low sample size (HDLSS) problems and present statistical machine learning methods used to tackle and circumvent these difficulties. Regularization and kernel algorithms were explored in this research using seven datasets where κ < 1. These techniques require special attention to tuning necessitating several extensions of cross-validation to be investigated to support better predictive performance. While no single algorithm was universally the best predictor, the regularization technique produced lower test errors in five of the seven datasets studied.