Statistical approach to normalization of feature vectors and clustering of mixed datasets

Normalization of feature vectors of datasets is widely used in a number of fields of data mining, in particular in cluster analysis, where it is used to prevent features with large numerical values from dominating in distance-based objective functions. In this study, a unified statistical approach to normalization of all attributes of mixed databases, when different metrics are used for numerical and categorical data, is proposed. After the proposed normalization, the contributions of both numerical and categorical attributes to a specified objective function are statistically the same. Formulae for the statistically normalized Minkowski mixed p-metrics are given in an explicit way. It is shown that the classic z-score standardization and the min–max normalization are particular cases of the statistical normalization, when the objective function is, respectively, based on the Euclidean or the Tchebycheff (Chebyshev) metrics. Finally, clustering of several benchmark datasets is performed with non-normalized and introduced normalized mixed metrics using either the k-prototypes (for p=2) or another algorithm (for p≠2)

Evaluation of adhesive and elastic properties of polymers by the BG method

The work of adhesion and the elastic contact modulus of the pair of interacting materials are a prerequesite in order to study adhesive interactions between solids. For small material samples, the contact modulus is usually evaluated by depth-sensing indentation of sharp indenters, while the work of adhesion is determined by direct measurements of pull-off force of a sphere. These measurements are unstable due to the instability of the load–displacement diagrams under tension, and they can be greatly affected by the roughness of the contacting solids. Using experiments for polyvinylsiloxane samples, it is shown how the work of adhesion and the elastic contact modulus of materials may be quantified using the BG method. This is a non-direct method based on an inverse analysis of a stable region of the experimental force–displacement curves. The BG method is simple and robust. Nevertheless, the extracted values of both characteristics vary within the same polymer sample due to contact areas that possess interacting polymer molecules in various orientations. It was found that the average values of characteristics are very stable and the work of adhesion of polymers may be treated as a material parameter in statistical sense

Evaluation of adhesive and elastic properties of materials by depth-sensing indentation of spheres

Work of adhesion is the crucial material parameter for application of theories of adhesive contact. It is usually determined by experimental techniques based on the direct measurements of pull-off force of a sphere. These measurements are unstable due to instability of the load-displacement diagrams at tension, and they can be greatly affected by roughness of contacting solids. We show how the values of work of adhesion and elastic contact modulus of materials may be quantified using a new indirect approach (the Borodich–Galanov (BG) method) based on an inverse analysis of a stable region of the force-displacements curve obtained from the depth-sensing indentation of a sphere into an elastic sample. Using numerical simulations it is shown that the BG method is simple and robust. The crucial difference between the proposed method and the standard direct experimental techniques is that the BG method may be applied only to compressive parts of the force-displacements curves. Finally, the work of adhesion and the elastic modulus of soft polymer (polyvinylsiloxane) samples are extracted from experimental load-displacement diagrams

On one-sided estimates for row-finite systems of ordinary differential equations

summary:We prove an existence and uniqueness theorem for row-finite initial value problems. The right-hand side of the differential equation is supposed to satisfy a one-sided matrix Lipschitz condition with a quasimonotone row-finite matrix which has an at most countable spectrum