Computerized tomography usually deals with the determination of scalar quantities from integral information along lines. During the 90's tomographic methods have been developed that enable (at least partial) recovery also of vector elds from integral information. Depending on which component of the vector eld is considered, e.g. the ones parallel or transversal to the line, diierent characteris...

Abstract The topology of vector fields offers a well known way to show a “condensed” view of the stream line behavior of a vector field. The global structure of a field can be shown without time-consuming user interaction. With regard to large data visualization, one encounters a major drawback: the necessity to analyze a whole data set, even when interested in only a small region. We show that...

‎in this paper‎, ‎we introduce the structure of a groupoid associated to a vector field‎ ‎on a smooth manifold‎. ‎we show that in the case of the $1$-dimensional manifolds‎, ‎our‎ ‎groupoid has a‎ ‎smooth structure such that makes it into a lie groupoid‎. ‎using this approach‎, ‎we associated to‎ ‎every vector field an equivalence‎ ‎relation on the lie algebra of all vector fields on the smooth...

We propose a novel local isometry based dimensionality reduction method from the perspective of vector fields, which is called parallel vector field embedding (PFE). We first give a discussion on local isometry and global isometry to show the intrinsic connection between parallel vector fields and isometry. The problem of finding an isometry turns out to be equivalent to finding orthonormal par...

We present a novel approach toward evolving artificial embryogenies, which omits the graph representation of gene regulatory networks and directly shapes the dynamics of a system, i.e., its phase space. We show the feasibility of the approach by evolving cellular differentiation, a basic feature of both biological and artificial development. We demonstrate how a spatial hierarchy formulation ca...

pseudo ricci symmetric real hypersurfaces of a complex projective space are classified and it is proved that there are no pseudo ricci symmetric real hypersurfaces of the complex projective space cpn for which the vector field ξ from the almost contact metric structure (φ, ξ, η, g) is a principal curvature vector field.