In many real applications related with Geostatistics, medical imaging and material science, the real observations have asymmetric, and heavy-tailed multivariate distributions. These observations are spatially correlated and they could be modelled by the skew random fields. However, certain statistical analysis problems require giving analytical expectations of some integral geometric characteri...

We present an efficient algorithm to compute Euler characteristic curves of gray scale images of arbitrary dimension. In various applications the Euler characteristic curve is used as a descriptor of an image. Our algorithm is the first streaming algorithm for Euler characteristic curves. The usage of streaming removes the necessity to store the entire image in RAM. Experiments show that our im...

Geometrical properties of the extreme Kerr black holes in the topological sectors of nonextreme and extreme configurations are studied. We find that the Euler characteristic plays an essential role to distinguish these two kinds of extreme black holes. The relationship between the geometrical properties and the intrinsic thermodynamics

For any connected component H0 of the space of real meromorphic function we build a compactification N(H0) of the space H0. Then we express the Euler characteristics of the spaces H0 and N(H0) in terms of topological invariants of functions from H0.

We prove that Yuzvinskii’s entropy addition formula can not be extended for the action of certain finitely generated nonamenable groups. 1991 AMS CLASSIFICATION NUMBERS: 22D40, 58F03

We calculate the E-polynomials of certain twisted GL(n,C)character varieties Mn of Riemann surfaces by counting points over finite fields using the character table of the finite group of Lie-type GL(n,Fq) and a theorem proved in the appendix by N. Katz. We deduce from this calculation several geometric results, for example, the value of the topological Euler characteristic of the associated PGL...

In this paper, I give an explicit formula for the intersection indices of the Chern classes (defined earlier by the author) of an arbitrary reductive group with hypersurfaces. This formula has the following applications. First, it allows to compute explicitly the Euler characteristic of complete intersections in reductive groups thus extending the beautiful result by D. Bernstein and Khovanskii...

We propose a novel method for the description of spatial patterns formed by a coverage of point sets representing galaxy samples. This method is based on a complete family of morphological measures known as Minkowski functionals, which includes the topological Euler characteristic and geometric descriptors to specify the content, shape and connectivity of spatial sets.

Let I (:z: ,y ,z) be a homogeneous polynomial With. rational coefficients. Let C, be the real projective curve defined by ! = 0" and suppos~ that C/ is nonsingular. It is well known that C/ is essentially a finite collection of disjoint circles, all except possibly one of which lie in th~ projective plane Rp2 in such a way as to have both an interior (homeomorphic to a disk), and an exterior (h...