Extreme Situations Prediction by MultidimenSional Heterogeneous Time Series Using Logical Decision Functions

* The work is supported by RFBR, grant 04-01-00858-a

Multidimensional Heterogeneous Variable Prediction Based on Experts’ Statements

* The work was supported by the RFBR under Grant N07-01-00331a.

On Multidimensional Analogue of Marchaud Formula for Fractional Riesz-Type Derivatives in Domains in R^n

2000 Mathematics Subject Classification: 26A33, 42B20

A Bimodality Test in High Dimensions

We present a test for identifying clusters in high dimensional data based on the k-means algorithm when the null hypothesis is spherical normal. We show that projection techniques used for evaluating validity of clusters may be misleading for such data. In particular, we demonstrate that increasingly well-separated clusters are identified as the dimensionality increases, when no such clusters exist. Furthermore, in a case of true bimodality, increasing the dimensionality makes identifying the correct clusters more difficult. In addition to the original conservative test, we propose a practical test with the same asymptotic behavior that performs well for a moderate number of points and moderate dimensionality. ACM Computing Classification System (1998): I.5.3.

Exact Solutions of Nonlocal BVPs for the Multidimensional Heat Equations

MSC 2010: 44A35, 44A45, 44A40, 35K20, 35K05

Automatized Generation of Personalized Learning Paths through Aspects in Multidimensional Spaces

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2016