DCG
2007
13 years 4 months ago
2007
Given a sphere of any radius r in an n-dimensional Euclidean space, we study the coverings of this sphere with solid spheres of radius one. Our goal is to design a covering of the...
CSL
2010
Springer
13 years 5 months ago
2010
Springer
By a Euclidean logic, we understand a formal language whose variables range over subsets of Euclidean space, of some fixed dimension, and whose non-logical primitives have fixed me...
NIPS
2004
13 years 5 months ago
2004
Embedding algorithms search for low dimensional structure in complex data, but most algorithms only handle objects of a single type for which pairwise distances are specified. Thi...
ESANN
2003
13 years 5 months ago
2003
In this paper a special higher order neuron, the hypersphere neuron, is introduced. By embedding Euclidean space in a conformal space, hyperspheres can be expressed as vectors. The...
SODA
2008
ACM
13 years 5 months ago
2008
ACM
We consider the problem of embedding a metric into low-dimensional Euclidean space. The classical theorems of Bourgain, and of Johnson and Lindenstrauss say that any metric on n p...
COCOON
2008
Springer
13 years 6 months ago
2008
Springer
We use nontrivial connections between the theory of computing and the finescale geometry of Euclidean space to give a complete analysis of the dimensions of individual points in f...
CCA
2009
Springer
13 years 8 months ago
2009
Springer
We investigate the relationship between computable metric spaces (X, d, ) and (X, d, ), where (X, d) is a given metric space. In the case of Euclidean space, and are equivalent u...
ICRA
2003
IEEE
13 years 9 months ago
2003
IEEE
In this paper, we discuss the modeling of the kinematics and dynamics of compliant contact between bodies moving in Euclidean space. First, we derive the kinematic equations descr...
GIAE
2004
Springer
13 years 9 months ago
2004
Springer
This paper first gives a brief overview over some interesting descriptions of conic sections, showing formulations in the three geometric algebras of Euclidean spaces, projective ...
TPHOL
2005
IEEE
13 years 10 months ago
2005
IEEE
We describe a formalization of the elementary algebra, topology and analysis of finite-dimensional Euclidean space in the HOL Light theorem prover. (Euclidean space is RN with the...