Likelihood and nearest-neighbor distance properties of multidimensional Poisson cluster processes

1981 ◽  
Vol 18 (4) ◽  
pp. 879-888 ◽  
Author(s):  
Michel Baudin
Keyword(s):  
Nearest Neighbor ◽  
Likelihood Function ◽  
Practical Application ◽  
Expected Number ◽  
Generating Functional ◽  
Functional Representation ◽  
Distance Properties ◽  
Poisson Cluster ◽  
Nearest Neighbor Distances ◽  
Asymptotic Developments

The probability generating functional representation of a multidimensional Poisson cluster process is utilized to derive a formula for its likelihood function, but the prohibitive complexity of this formula precludes its practical application to statistical inference. In the case of isotropic processes, it is however feasible to compute functions such as the probability Q(r) of finding no point in a disc of radius r and the probability Q(r | 0) of nearest-neighbor distances greater than r, as well as the expected number C(r | 0) of points at a distance less than r from a given point. Explicit formulas and asymptotic developments are derived for these functions in the n-dimensional case. These can effectively be used as tools for statistical analysis.

Likelihood and nearest-neighbor distance properties of multidimensional Poisson cluster processes

1981 ◽  
Vol 18 (04) ◽  
pp. 879-888 ◽  
Author(s):  
Michel Baudin
Keyword(s):  
Nearest Neighbor ◽  
Likelihood Function ◽  
Practical Application ◽  
Expected Number ◽  
Generating Functional ◽  
Functional Representation ◽  
Distance Properties ◽  
Poisson Cluster ◽  
Nearest Neighbor Distances ◽  
Asymptotic Developments

The probability generating functional representation of a multidimensional Poisson cluster process is utilized to derive a formula for its likelihood function, but the prohibitive complexity of this formula precludes its practical application to statistical inference. In the case of isotropic processes, it is however feasible to compute functions such as the probability Q(r) of finding no point in a disc of radius r and the probability Q(r | 0) of nearest-neighbor distances greater than r, as well as the expected number C(r | 0) of points at a distance less than r from a given point. Explicit formulas and asymptotic developments are derived for these functions in the n-dimensional case. These can effectively be used as tools for statistical analysis.

Application of Lattice Imaging Techniques to Amorphous Films

1975 ◽  
Vol 33 ◽  
pp. 8-9
Author(s):  
S. R. Herd ◽  
P. Chaudhari
Keyword(s):  
Nearest Neighbor ◽  
Random Network ◽  
Imaging Techniques ◽  
Network Models ◽  
Accurate Method ◽  
Direct Transmission ◽  
Lattice Imaging ◽  
Transmission Electron ◽  
Lattice Planes ◽  
Nearest Neighbor Distances

Electron diffraction and direct transmission have been used extensively to study the local atomic arrangement in amorphous solids and in particular Ge. Nearest neighbor distances had been calculated from E.D. profiles and the results have been interpreted in terms of the microcrystalline or the random network models. Direct transmission electron microscopy appears the most direct and accurate method to resolve this issue since the spacial resolution of the better instruments are of the order of 3Å. In particular the tilted beam interference method is used regularly to show fringes corresponding to 1.5 to 3Å lattice planes in crystals as resolution tests.

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.

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.

STUDY OF THERMODYNAMIC PROPERTIES OF ZINC-BLENDE-TYPE SEMICONDUCTORS: TEMPERATURE AND PRESSURE DEPENDENCES

2011 ◽  
Vol 25 (12n13) ◽  
pp. 1041-1051 ◽  
Author(s):  
HO KHAC HIEU ◽  
VU VAN HUNG
Keyword(s):  
Nearest Neighbor ◽  
Thermodynamic Quantities ◽  
Atomic Displacements ◽  
Zinc Blende ◽  
The Mean ◽  
Temperature And Pressure ◽  
Analytical Expressions ◽  
Theoretical Results ◽  
Nearest Neighbor Distances ◽  
Statistical Moment Method

Using the statistical moment method (SMM), the temperature and pressure dependences of thermodynamic quantities of zinc-blende-type semiconductors have been investigated. The analytical expressions of the nearest-neighbor distances, the change of volumes and the mean-square atomic displacements (MSDs) have been derived. Numerical calculations have been performed for a series of zinc-blende-type semiconductors: GaAs , GaP , GaSb , InAs , InP and InSb . The agreement between our calculations and both earlier other theoretical results and experimental data is a support for our new theory in investigating the temperature and pressure dependences of thermodynamic quantities of semiconductors.

Determining the Ratio of the Precipitated versus Substituted Arsenic by XAFS and SIMS in Heavy Dose Arsenic Implants in Silicon

2001 ◽  
Vol 669 ◽  
Author(s):  
M. A. Sahiner ◽  
S. W. Novak ◽  
J. C. Woicik ◽  
J. Liu ◽  
V. Krishnamoorty
Keyword(s):  
Solid Solubility ◽  
Amorphous Materials ◽  
Nearest Neighbor ◽  
Secondary Ion Mass Spectrometry ◽  
Local Environment ◽  
Coordination Numbers ◽  
Annealing Conditions ◽  
X Ray Absorption ◽  
Secondary Ion ◽  
Nearest Neighbor Distances

ABSTRACTDoping silicon with arsenic by ion implantation above the solid solubility level leads to As clusters and/or precipitates in the form of monoclinic SiAs causing electrical deactivation of the dopant. Information on the local structure around the As atom, and the As concentration depth profiles is important for the implantation and annealing process in order to reduce the precipitated As and maximize the electrically activated As. In this study, we determined the local As structure and the precipitated versus substituted As for As implants in CZ (001) Si wafers, with implant energies between 20 keV and 100 keV, and implant doses ranging from 1 × 1015/cm2 to 1 × 1018/cm2. The samples were subjected to different thermal annealing conditions. We used secondary ion mass spectrometry (SIMS) and UT- MARLOWE simulations to determine the region where the As-concentration is above the solid solubility level. By x-ray absorption fine structure spectroscopy (XAFS), we probed the structure of the local environment around As. XAFS being capable of probing the short-range order in crystalline and amorphous materials provides information on the number, distance and chemical identity of the neighbors of the main absorbing atom. Using Fourier analysis, the coordination numbers (N) and the nearest-neighbor distances (R) to As atoms in the first shell were extracted from the XAFS data. When As precipitates as monoclinic SiAs, the nearest-neighbor distances and coordination numbers are ∼2.37 Å and ∼3, as opposed to ∼2.40 Å and ∼4 when As is substitutional. Based on this information, the critical implant dose where the precipitation/clustering of As starts, and the ratio of the substitutional versus cluster/precipitate form As in the samples were determined.

Assessment of Two-Dimensional Separative Systems Using Nearest-Neighbor Distances Approach. Part 1: Orthogonality Aspects

2013 ◽  
Vol 85 (20) ◽  
pp. 9449-9458 ◽  
Author(s):  
Witold Nowik ◽  
Sylvie Héron ◽  
Myriam Bonose ◽  
Mateusz Nowik ◽  
Alain Tchapla
Keyword(s):  
Nearest Neighbor ◽  
Two Dimensional ◽  
Nearest Neighbor Distances

scholarly journals Evaluating the Stability of Embedding-based Word Similarities

2018 ◽  
Vol 6 ◽  
pp. 107-119 ◽  
Author(s):  
Maria Antoniak ◽  
David Mimno
Keyword(s):  
Nearest Neighbor ◽  
Word Embeddings ◽  
Training Set ◽  
Word Associations ◽  
Training Corpus ◽  
Study Word ◽  
Highly Sensitive ◽  
The Stability ◽  
Nearest Neighbor Distances

Word embeddings are increasingly being used as a tool to study word associations in specific corpora. However, it is unclear whether such embeddings reflect enduring properties of language or if they are sensitive to inconsequential variations in the source documents. We find that nearest-neighbor distances are highly sensitive to small changes in the training corpus for a variety of algorithms. For all methods, including specific documents in the training set can result in substantial variations. We show that these effects are more prominent for smaller training corpora. We recommend that users never rely on single embedding models for distance calculations, but rather average over multiple bootstrap samples, especially for small corpora.

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