weakness of gravity on distances> ∼ 1 mm is due to the existence of n ≥ 2 new compact spatial dimensions large compared to the weak scale. The Planck scale MPl ∼ G −1/2 N is not a fundamental scale; its enormity is simply a consequence of the large size of the new dimensions. While gravitons can freely

field theories. This leads to a new proposal for a definition of M-theory which could be extended to include five or four non-compact dimensions. 1

In this paper, we propose a new method for index-ing large amounts of point and spatial data in high-dimensional space. An analysis shows that index structures such as the R*-tree are not adequate for indexing high-dimensional data sets. The major problem of R-tree-based index structures

for learning M 3 networks based on a compact quadratic program formulation. We provide a new theoretical bound for generalization in structured domains. Experiments on the task of handwritten character recognition and collective hypertext classification demonstrate very significant gains over previous

A well-known open question in differential geometry is the question of whether a given compact Riemannian manifold is necessarily conformally equivalent to one of constant scalar curvature. This problem is known as the Yamabe problem because it was formulated by Yamabe [8] in 1960, While Yamabe

with a small dissipative correction. The new system can be solved by underresolved stable numerical discretizations without using either Riemann solvers spatially or a nonlinear system of algebraic equations solver temporally. Numerical results for 1-D and 2-D problems are presented. The second order

Locally weighted projection regression (LWPR) is a new algorithm for incremental nonlinear function approximation in high dimensional spaces with redundant and irrelevant input dimensions. At its core, it employs nonparametric regression with locally linear models. In order to stay computationally

and purely Lagrangian schemes for interface resolution. The method is presented in three spatial dimensions.

. In contrast to acquisition-based noise reduction methods we propose a postprocess based on anisotropic diffusion. Extensions of this new technique support 3-D and multi-echo MRI, incorporating higher spatial and spectral dimensions. The procedure overcomes the major drawbacks of conventional filter methods

Abstract: The realization of global symmetries can depend on the geometry of the underlying space. In particular, compactification can lead to spontaneous breaking of such symmetries. Four–dimensional QCD with fundamental representation fermions embedded in a space with one compact spatial