Parallel coordinates and scatterplot matrices are widely used to visualize multi-dimensional data sets. But these visualization techniques are insufficient when the number of dimensions grows. To solve this problem, different approaches to preselect the best views or dimensions have been proposed in the last years. However, there are still several shortcomings to these methods. In this paper we...

Let (M,g) be a compact Riemannian manifold. The conformal class of g consists of all metrics g̃ = e2ug for any smooth function u. A central theme in conformal geometry is the study of properties that are common to all metrics in the same conformal class, and the understanding and classification of all the conformal classes. For this purpose it is often useful to be able to single out a unique re...

An ideal I in the free associative algebra k〈X1, . . . ,Xn〉 over a field k is shown to have a finite Gröbner basis if the algebra defined by I is commutative; in characteristic 0 and generic coordinates the Gröbner basis may even be constructed by lifting a commutative Gröbner basis and adding commutators.

In this article, we find an analytical characteristic of the type a line and derive formulae for calculating coordinates midpoints quasi-midpoints elliptic, hyperbolic, parabolic segments in extended hyperbolic space $H^3$ frame first type. The consider Cayley\,--\,Klein projective model as three-dimensional with oval quadric $\gamma$ fixed it.

Assuming that we live on a non rigid brane with TeV-scale tension, the scalar fields that control the coordinates of our brane in the extra dimensions give rise to missing energy signals at high-energy colliders with a characteristic angular and energy spectrum, identical to the one due to graviton emission in 6 extra dimensions. LEP bounds and LHC capabilities are analyzed.

Based on microarray gene expression datasets, many statistical methods have been proposed to locate the significant differentially expressed genes (marker genes) among different sample groups. Although robust models for identifying marker genes more accurately is an area of intense research, effective tools for the evaluation of results is often ignored in the literature. In this paper, we prop...

The aim of the present paper is to provide an intrinsic investigation of projective changes in Finlser geometry, following the pullback formalism. Various known local results are generalized and other new intrinsic results are obtained. Nontrivial characterizations of projective changes are given. The fundamental projectively invariant tensors, namely, the projective deviation tensor, the Weyl ...

The generalized Killing equations for the configuration space of spinning particles (spinning space) are analysed. Solutions of these equations are expressed in terms of Killing-Yano tensors. In general the constants of motion can be seen as extensions of those from the scalar case or new ones depending on the Grassmann-valued spin variables. Spinning particles, such as Dirac fermions, can be d...

The study of magnetic connectivity in the solar corona reveals a need to generalize the field line mapping technique to arbitrary geometry of the boundaries and systems of coordinates. Indeed, the global description of the connectivity in the corona requires the use of the photospheric and solar wind boundaries. Both are closed surfaces and therefore do not admit a global regular system of coor...