منابع مشابه
Percolation and Minimal Spanning Trees
Consider a random set V n of points in the box n; n) d , generated either by a Poisson process with density p or by a site percolation process with parameter p. We analyse the empirical distribution function F n of the lengths of edges in a minimal (Euclidean) spanning tree T n on V n. We express the limit of F n , as n ! 1, in terms of the free energies of a family of percolation processes der...
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We revisit the minimal spanning tree problem in order to develop a theory of construction and counting of the minimal spanning trees in a network. The theory indicates that the construction of such trees consists of many di erent choices, all independent of each other. These results suggest a block approach to the construction of all minimal spanning trees in the network, and an algorithm to th...
متن کاملManifold Learning with Geodesic Minimal Spanning Trees
In the manifold learning problem one seeks to discover a smooth low dimensional surface, i.e., a manifold embedded in a higher dimensional linear vector space, based on a set of measured sample points on the surface. In this paper we consider the closely related problem of estimating the manifold’s intrinsic dimension and the intrinsic entropy of the sample points. Specifically, we view the sam...
متن کاملModeling Minimal Spanning Trees with Beta Vectors
We model the distribution of normalized interpoint distances (IDs) on the minimal spanning tree (MST) using multivariate beta vectors. We define overlapping sums of the components of a Dirichlet distribution to construct multivariate beta distributions. We also use a multivariate normal copula with beta marginals to define beta vectors. Based on the ordered IDs of the MST, we define a multivari...
متن کاملCalorimeter Clustering with Minimal Spanning Trees
Clustering calorimeter hits is a complex pattern recognition problem with complexity depending on event type, energy and detector design. A successful clustering algorithm must be characterised by high efficiency and speed to cope with and to exploit the high granularity design forseen for both electromagnetic and hadronic calorimeters in a Future Linear Collider experiment. In the following we...
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ژورنال
عنوان ژورنال: The Annals of Applied Probability
سال: 2017
ISSN: 1050-5164
DOI: 10.1214/16-aap1239