MOTIVATION Genome-wide gene expression measurements, as currently determined by the microarray technology, can be represented mathematically as points in a high-dimensional gene expression space. Genes interact with each other in regulatory networks, restricting the cellular gene expression profiles to a certain manifold, or surface, in gene expression space. To obtain knowledge about this mani...

the importance of zagros forests and interdependence of local communities to forest resources have led to complexity of its management. the role of local communities and investigating their relations toward implementation of natural resources co-management are undeniable. social network analysis (sna) approach is a new method which illustrates relations among local beneficiaries and has importa...

A shortest path connecting two vertices u and v is called a u-v geodesic. The distance between u and v, denoted by dG(u, v), is the number of edges in a u-v geodesic. A graph G with n vertices is geodesic-pancyclic if for each pair of vertices u, v ∈ V (G), every u-v geodesic lies on every cycle of length k satisfying max{2dG(u, v), 3} ≤ k ≤ n. In this paper, we study the properties for graphs ...

A natural metric in 2-manifold surfaces is to use geodesic distance. If a 2manifold surface is represented by a triangle mesh T , the geodesic metric on T can be computed exactly using computational geometry methods. Previous work for establishing the geodesic metric on T only supports using half-edge data structures; i.e., each edge e in T is split into two halves (he1, he2) and each half-edge...

In this paper, we propose a parallel and scalable approach for geodesic distance computation on triangle meshes. Our key observation is that the recovery of with heat method [1] can be reformulated as optimization its gradients subject to integrability, which solved using an efficient first-order requires no linear system solving converges quickly. Afterward, efficiently recovered by integratio...

We describe an elasting matching procedure between plane curves based on computing a minimal deformation cost between the curves. The design of the deformation cost is based on a geodesic distance deened on an innnite dimensional group acting on the curves. The geodesic paths also provide an optimal deformation process, which allows to interpolate between any plane curves.

Let M be a simply connected complete Kähler manifold and N a closed complete totally geodesic complex submanifold of M such that every minimal geodesic in N is minimal in M . Let Uν be the unit normal bundle of N in M . We prove that if a distance function ρ is differentiable at v ∈ Uν , then ρ is also differentiable at −v.

The geodesic center of a simple polygon is a point inside the polygon which minimizes the maximum internal distance to any point in the polygon. We present an algorithm which calculates the geodesic center of a simple polygon with n vertices in time O(n log n).

This paper constructs a class of complete Kähler metrics of positive holomorphic sectional curvature on C and finds that the constructed metrics satisfy the following properties: As the geodesic distance ρ → ∞, the volume of geodesic balls grows like O(ρ 2(β+1)n β+2 ) and the Riemannian scalar curvature decays like O(ρ − 2(β+1) β+2 ), where β ≥ 0.