We construct momentum mappings for covariant Hamiltonian field theories using a generalization of symplectic geometry to the bundle LV Y of vertically adapted linear frames over the bundle of field configurations Y . Field momentum observables are vector-valued momentum mappings generated from automorphisms of Y , using the (n + k)-symplectic geometry of LV Y . These momentum observables on LV ...

We address the recovery of segmented, 3 0 descriptions of an object from intensity images. We use three views of an objectfrom slightly different viewpoints as our input. For each image we extract a hierarchy of groups based on proximity, parallelism and symmetry in a robust manner. The groups in the three images are matched by computing the epipolar geometry. For each set of matched groupsfrom...

Centrality analysis determines the importance of vertices in a network based on their connectivity within the network structure. It is a widely used technique to analyse network-structured data. A particularly important task is the comparison of different centrality measures within one network. We present three methods for the exploration and comparison of centrality measures within a network: ...

A pair of non-adjacent edges is said to be separated in a circular ordering of vertices, if the endpoints of the two edges do not alternate in the ordering. The circular separation dimension of a graph G, denoted by π◦(G), is the minimum number of circular orderings of the vertices ofG such that every pair of non-adjacent edges is separated in at least one of the circular orderings. This notion...

The k-ary n-cube is one of the most popular interconnection networks for parallel computing. This paper addresses the size of a largest connected component of a faulty k-ary n-cube. We prove that, in a k-ary n-cube (k ≥ 4 and n ≥ 2) with up to 4n – 2 faulty vertices, all fault-free vertices but at most two constitute a connected component. Moreover, this assertion holds if and only if the set o...

Boolean operations of geometric models is an essential issue in computational geometry. In this paper, we develop a simple and robust approach to perform Boolean operations on closed and open triangulated surfaces. Our method mainly has two stages: (1) We firstly find out candidate intersected-triangles pairs based on Octree and then compute the intersection lines for all pairs of triangles wit...

For a graph G = (V,E), a set S ⊆ V is a [1, 2]-set if it is a dominating set for G and each vertex v ∈ V \S is dominated by at most two vertices of S, i.e. 1 ≤ |N(v)∩S| ≤ 2. Moreover a set S ⊆ V is a total [1, 2]-set if for each vertex of V , it is the case that 1 ≤ |N(v)∩S| ≤ 2. The [1, 2]-domination number of G, denoted γ[1,2](G), is the minimum number of vertices in a [1, 2]-set. Every [1, 2...

We present a simple iterative strategy for measuring the connection strength between a pair of vertices in a graph. The method is attractive in that it has a linear complexity and can be easily parallelized. Based on an analysis of the convergence property, we propose a mutually reinforcing model to explain the intuition behind the strategy. The practical effectiveness of this measure is demons...

A balanced colouring of a graph G is a colouring of some of the vertices of G with two colours, say red and blue, such that there is the same number of vertices in each colour. The balanced decomposition number f(G) of G is the minimum integer s with the following property: For any balanced colouring of G, there is a partition V (G) = V1 ∪̇ · · · ∪̇Vr such that, for every i, Vi induces a connecte...

A Lorentz surface in an indefinite space form is called parallel if its second fundamental form is parallel. Such surfaces are locally invariant under the reflection with respect to the normal space at each point. Parallel surfaces are important in geometry as well as in general relativity since extrinsic invariants of such surfaces do not change from point to point. Parallel Lorentz surfaces i...