The world of hereditary classes is rich and diverse it contains a variety theoretical practical importance. Thousands results in the literature are devoted to individual only few them analyse universe as whole. To shift analysis into new level, present paper we exploit an approach, where operate by infinite families classes, rather than classes. Each family associated with graph parameter chara...

A parametric manifold can be viewed as the manifold of orbits of a (regular) foliation of a manifold by means of a family of curves. If the foliation is hypersurface orthogonal, the parametric manifold is equivalent to the 1-parameter family of hypersurfaces orthogonal to the curves, each of which inherits a metric and connection from the original manifold via orthogonal projections; this is th...

A parametric manifold is a manifold on which all tensor fields depend on an additional parameter, such as time, together with a parametric structure, namely a given (parametric) 1-form field. Such a manifold admits natural generalizations of Lie differentiation, exterior differentiation, and covariant differentiation, all based on a nonstandard action of vector fields on functions. There is a n...

This paper investigates the performance of three types of random coefficients logistic regression models; that is, models using parametric, semi-parametric, and nonparametric specifications of the distribution of the random effects. Whereas earlier studies focussed on models with a single random effect, here we look at models with multidimensional random effects (intercepts and slopes). Moreove...

This article describes a versatile approach to non-linear, non-Gaussian noise target tracking which makes use of both parametric and non-parametric techniques within a Bayesian framework. It produces a Gaussian mixture model (GMM) of a track, but resorts to a sampling technique within the tracking process to handle non-linearity. GMMs are recovered from samples using the expectation-maximisatio...

Adaptive logics (ALs) in standard format are defined in terms of a monotonic core logic L, a distinct set of ‘abnormal’ formulas and a strategy, which can be either reliability or minimal abnormality. In this article we we ask under which conditions the consequence relation of two ALs that use the same strategy are identical, and when one is a proper subrelation of the other. This results in a ...