Asymptotic Behaviour of an Empirical Nearest-Neighbour Distance Function for Stationary Poisson Cluster Processes

1988 ◽  
Vol 136 (1) ◽  
pp. 131-148 ◽  
Author(s):  
Lothar Heinrich
Keyword(s):  
Asymptotic Behaviour ◽  
Distance Function ◽  
Nearest Neighbour ◽  
Neighbour Distance ◽  
Poisson Cluster ◽  
Cluster Processes

On interpoint distances for planar Poisson cluster processes

1983 ◽  
Vol 20 (3) ◽  
pp. 513-528 ◽  
Author(s):  
Richard J. Kryscio ◽  
Roy Saunders
Keyword(s):  
Lebesgue Measure ◽  
Distance Function ◽  
Nearest Neighbor ◽  
Indicator Function ◽  
Poisson Processes ◽  
Interpoint Distance ◽  
Poisson Cluster ◽  
Cluster Processes

For stationary Poisson or Poisson cluster processes ξ on R2 we study the distribution of the interpoint distances using the interpoint distance function and the nearest-neighbor indicator function . Here Sr (x) is the interior of a circle of radius r having center x, I(t) is that subset of D which has x ∊ D and St(x) ⊂ D and χ is the usual indicator function. We show that if the region D ⊂ R2 is large, then these functions are approximately distributed as Poisson processes indexed by and , where µ(D) is the Lebesgue measure of D.

On interpoint distances for planar Poisson cluster processes

1983 ◽  
Vol 20 (03) ◽  
pp. 513-528
Author(s):  
Richard J. Kryscio ◽  
Roy Saunders
Keyword(s):  
Lebesgue Measure ◽  
Distance Function ◽  
Nearest Neighbor ◽  
Indicator Function ◽  
Poisson Processes ◽  
Interpoint Distance ◽  
Poisson Cluster ◽  
Cluster Processes

For stationary Poisson or Poisson cluster processes ξ on R2 we study the distribution of the interpoint distances using the interpoint distance function and the nearest-neighbor indicator function . Here Sr (x) is the interior of a circle of radius r having center x, I(t) is that subset of D which has x ∊ D and St (x) ⊂ D and χ is the usual indicator function. We show that if the region D ⊂ R2 is large, then these functions are approximately distributed as Poisson processes indexed by and , where µ(D) is the Lebesgue measure of D.

ELASTIC PROPERTIES OF STRAINED FCC AND HCP IRON

1993 ◽  
Vol 07 (01n03) ◽  
pp. 207-211
Author(s):  
T. KRAFT ◽  
M. METHFESSEL ◽  
M. VAN SCHILFGAARDE ◽  
M. SCHEFFLER
Keyword(s):  
Energy Cost ◽  
Interplanar Distance ◽  
Orbital Method ◽  
Full Potential ◽  
Local Spin Density Approximation ◽  
Nearest Neighbour ◽  
Density Approximation ◽  
Neighbour Distance ◽  
Large Lattice ◽  
Fcc Phase

Using the full-potential linear muffin-tin orbital method within the local spin-density approximation we analyse the influence of the nearest neighbour distance on fcc(111) or hcp(0001) iron layers. The LDA-LSDA error in describing ferromagnetic phases is determined to be at least 15 mRy/atom. As a consequence of this error, our calculations favour paramagnetic ground states. In this sense, the reported results have some model character. However, our analysis of the elastic energy cost under distortions should hold for transition metals in general. Allowing relaxations of the interplanar distance the fcc phase can become energetically favourable over the hcp phase at large lattice mismatches. The main reason for this behaviour is the enhanced stiffness of the hcp interplanar bonds due to the shortening of the axial c/a ratio.

scholarly journals Markov properties of cluster processes

1996 ◽  
Vol 28 (2) ◽  
pp. 346-355 ◽  
Author(s):  
A. J. Baddeley ◽  
M. N. M. Van Lieshout ◽  
J. Møller
Keyword(s):  
Poisson Process ◽  
Point Process ◽  
Markov Property ◽  
Nearest Neighbour ◽  
Finite Range ◽  
Cluster Process ◽  
Cluster Point Process ◽  
Poisson Cluster ◽  
Markov Properties ◽  
Uniformly Bounded

We show that a Poisson cluster point process is a nearest-neighbour Markov point process [2] if the clusters have uniformly bounded diameter. It is typically not a finite-range Markov point process in the sense of Ripley and Kelly [12]. Furthermore, when the parent Poisson process is replaced by a Markov or nearest-neighbour Markov point process, the resulting cluster process is also nearest-neighbour Markov, provided all clusters are non-empty. In particular, the nearest-neighbour Markov property is preserved when points of the process are independently randomly translated, but not when they are randomly thinned.

A cluster process representation of a self-exciting process

1974 ◽  
Vol 11 (3) ◽  
pp. 493-503 ◽  
Author(s):  
Alan G. Hawkes ◽  
David Oakes
Keyword(s):  
Point Processes ◽  
Generating Functional ◽  
Cluster Process ◽  
Process Representation ◽  
Age Dependent ◽  
Birth Processes ◽  
Poisson Cluster ◽  
Cluster Processes

It is shown that all stationary self-exciting point processes with finite intensity may be represented as Poisson cluster processes which are age-dependent immigration-birth processes, and their existence is established. This result is used to derive some counting and interval properties of these processes using the probability generating functional.

Setting Attribute Weights for Nearest Neighbor Learning Algorithms Using C4.5

1997 ◽  
Vol 11 (03) ◽  
pp. 405-415 ◽  
Author(s):  
Charles X. Ling ◽  
John J. Parry ◽  
Handong Wang
Keyword(s):  
Machine Learning ◽  
Decision Trees ◽  
Distance Function ◽  
Nearest Neighbor ◽  
Learning Algorithms ◽  
Simple Approach ◽  
Nearest Neighbour ◽  
Attribute Weights ◽  
New Methods

Nearest Neighbour (NN) learning algorithms utilize a distance function to determine the classification of testing examples. The attribute weights in the distance function should be set appropriately. We study situations where a simple approach of setting attribute weights using decision trees does not work well, and design three improvements. We test these new methods thoroughly using artificially generated datasets and datasets from the machine learning repository.

Count distributions, orderliness and invariance of Poisson cluster processes

1979 ◽  
Vol 16 (02) ◽  
pp. 261-273 ◽  
Author(s):  
Larry P. Ammann ◽  
Peter F. Thall
Keyword(s):  
Present Article ◽  
Generating Functional ◽  
Cluster Process ◽  
Multiple Events ◽  
Poisson Cluster Process ◽  
Finite Dimensional ◽  
The Family ◽  
Moment Measures ◽  
Poisson Cluster ◽  
Cluster Processes

The probability generating functional (p.g.fl.) of a non-homogeneous Poisson cluster process is characterized in Ammann and Thall (1977) via a decomposition of the KLM measure of the process. This p.g.fl. representation is utilized in the present article to show that the family 𝒟 of Poisson cluster processes with a.s. finite clusters is invariant under a class of cluster transformations. Explicit expressions for the finite-dimensional count distributions, product moment measures, and the distribution of clusters are derived in terms of the KLM measure. It is also shown that an element of 𝒟 has no multiple events iff the points of each cluster are a.s. distinct.

scholarly journals Unified Analysis of HetNets Using Poisson Cluster Processes Under Max-Power Association

2019 ◽  
Vol 18 (8) ◽  
pp. 3797-3812 ◽  
Author(s):  
Chiranjib Saha ◽  
Harpreet S. Dhillon ◽  
Naoto Miyoshi ◽  
Jeffrey G. Andrews
Keyword(s):  
Poisson Cluster ◽  
Cluster Processes
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