Nearest-neighbor Distance Distributions Research Articles

Observation of Weibull, Lognormal, and Gamma Distributions in Electrodeposited Cu and Cu-Ag Particles.

In this work, the nearest-neighbor distances and Voronoi cell features of Cu-Ag deposits were analyzed and fitted with Lognormal, Weibull, and Gamma distributions. The nearest-neighbor distance distributions of the samples were compared with those of complete spatially random points, showing spatial inhomogeneity due to the nucleation exclusion effect. The radial distribution function was calculated, showing both influences from the grain size and the nucleation exclusion effect. Voronoi cells were generated based on the shape of the grains. The size, occupancy, and coordination of the Voronoi cells were examined and fitted. The results show that although the Cu-Ag deposits seemed to be governed by the instantaneous nucleation mode, the spatial distribution of the nuclei was more impacted by the nucleation exclusion effect than the Cu-only samples. This behavior is also justified by the grain size distribution generated with Voronoi cell size and occupancy distributions.

Mean nearest-neighbor distance in random 2D binary mixtures

The two-dimensional, mean nearest-neighbor distances, in random sequential addition hard disc computer-generated patterns with mixtures of two circle diameters, have been studied. The mean nearest-neighbor distance at a given area fraction is a quadratic polynomial function of the circle diameter standard deviation. Deviations from the uniform case may be either positive or negative, with large deviations (10–25%) at large circle diameter standard deviations. Nearest-neighbor distance distributions for binary mixture patterns may be well fit by skewed normal distributions.

Dimensional crossover in the nearest-neighbor statistics of random points in a quasi-low-dimensional system

In this work, we study the effects of geometric confinement on the point statistics in a quasi-low-dimensional system. Specifically, we focus on the nearest-neighbor statistics. Accordingly, we have performed comprehensive numerical simulations of binomial point process on quasi-one-dimensional rectangle strips for different values of the confinement ratio defined as the ratio of the strip width to the mean nearest-neighbor distance. We found that the nearest-neighbor distance distributions (NNDDs) conform to an extreme value Weibull distribution with the shape parameter depending on the confinement ratio, while the process intensity remains constant. This finding reveals the reduction of effective spatial degrees of freedom in a quasi-low-dimensional system under the geometric confinement. The scale dependence of the number of effective spatial degrees of freedom is found to obey the crossover ansatz. We stress that the functional form of the crossover ansatz is determined by the nature of the studied point process. Accordingly, different physical processes in the quasi-low-dimensional system obey different crossover ansatzes. The relevance of these results for quasi-low-dimensional systems is briefly highlighted.

Statistical Modeling and Characterization of Induced Seismicity Within the Western Canada Sedimentary Basin

AbstractIn western Canada, there has been an increase in seismic activity linked to anthropogenic energy‐related operations including conventional hydrocarbon production, wastewater fluid injection, and, more recently, hydraulic fracturing (HF). Statistical modeling and characterization of the space, time, and magnitude distributions of the seismicity are vital for a better understanding of induced earthquake processes and development of forecasting models. In this work, a statistical analysis of the seismicity in the Western Canada Sedimentary Basin was performed across past and present time periods by utilizing a compiled earthquake catalog for Alberta and eastern British Columbia. Specifically, the interevent space‐time distance distributions of earthquakes were studied using the nearest‐neighbor distance (NND) method. Additionally, the frequency‐magnitude statistics and aftershock parameters of several clusters were analyzed using the Gutenberg‐Richter relation and the epidemic‐type aftershock sequence model. The results suggest that recent regional changes in the NND distributions, namely, a disproportionate increase in loosely and tightly clustered seismic activity over time, are unnatural and likely due to the rise in HF operations for the development of unconventional resources. It is concluded that both these loosely and tightly clustered earthquake subpopulations differ measurably from what may be the region's tectonic seismic activity. Additionally, HF treatments have a greater probability of triggering swarm‐like sequences that sharply spike the seismicity rate and are characterized by larger Gutenberg‐Richter b values. In contrast, conventional production and wastewater disposal operations largely trigger loosely clustered activity with more typical magnitude occurrence distributions.

A Tractable Model for Wirelessly Powered Networks With Energy Correlation

In the analysis of large-scale wirelessly powered networks, the energy correlation is often ignored. While this leads to remarkably simple results for key performance metrics, it is typically not realistic and accurate. Considering the accuracy, tractability, and practicability tradeoffs, this paper introduces and promotes the Poisson disk process (PDP) as a model for the energized nodes that succeed in harvesting energy. To show that the model leads to analytically tractable results in several cases of interest, we derive its first and second moment densities, which fully characterize the PDP. Besides, we also provide tight bounds for its probability generating functional as well as its contact and nearest-neighbor distance distributions. Then, to show that the model is relevant for wirelessly powered networks-which all have positive energy correlation-we provide two approaches to fit the PDP to a given energized point process incorporating practical energy harvesting factors. Further, we derive the success probability in the information transmission phase, where the distribution of the active transmitters is modeled by a PDP. It turns out that the resulting PDP can closely model the distribution of actual energized nodes in terms of the success probability and other statistics while preserving analytical tractability.

Semi-Poisson nearest-neighbor distance statistics for a 2D dissipative map

Typical pseudotrajectories of 2D ergodic maps are known to possess Wignerian nearest-neighbor distance distributions (NNDDs). In the case of 2D chaotic dissipative maps, bounded aperiodic pseudotrajectories typically evolve on planar strange attractors. In this microarticle, the hypothesis that such pseudotrajectories should possess NNDDs that are intermediate between the Poisson and Wigner distributions is put forward and a rare example for which the intermediate distribution can be clearly identified is presented. In particular, it is demonstrated numerically that typical pseudotrajectories evolving in the strange attractor of the standard 2D Ikeda map possess semi-Poissionian NNDDs.

On the Contact and Nearest-Neighbor Distance Distributions for the ${n}$ -Dimensional Matérn Cluster Process

This letter provides exact characterization of the contact and nearest-neighbor distance distributions for the ${n}$ -dimensional ( ${n}$ -D) Matern cluster process (MCP). We also provide novel upper and lower bounds to these distributions in order to gain useful insights about their behavior. The two and three dimensional versions of these results are directly applicable to the performance analyses of wireless networks modeled as MCP.

Electron Microscopic Detection of Single Membrane Proteins by a Specific Chemical Labeling.

SummaryElectron microscopy (EM) is a technology that enables visualization of single proteins at a nanometer resolution. However, current protein analysis by EM mainly relies on immunolabeling with gold-particle-conjugated antibodies, which is compromised by large size of antibody, precluding precise detection of protein location in biological samples. Here, we develop a specific chemical labeling method for EM detection of proteins at single-molecular level. Rational design of α-helical peptide tag and probe structure provided a complementary reaction pair that enabled specific cysteine conjugation of the tag. The developed chemical labeling with gold-nanoparticle-conjugated probe showed significantly higher labeling efficiency and detectability of high-density clusters of tag-fused G protein-coupled receptors in freeze-fracture replicas compared with immunogold labeling. Furthermore, in ultrathin sections, the spatial resolution of the chemical labeling was significantly higher than that of antibody-mediated labeling. These results demonstrate substantial advantages of the chemical labeling approach for single protein visualization by EM.

IGFEM-based shape sensitivity analysis of the transverse failure of a composite laminate

This manuscript presents a shape sensitivity analysis method based on an Interface-enriched Generalized Finite Element Method (IGFEM) formulation and its application to the sensitivity of the transverse failure of a fiber-reinforced composite laminate with respect to the geometrical parameters that define its microstructure. The analytical sensitivities with respect to individual fiber radius and placement are first derived within the context of a cohesive IGFEM solver specially developed to simulate the fiber/matrix debonding observed in the transverse failure of composite laminates with high fiber volume fraction. The IGFEM solver utilizes $$C^{-1}$$ continuous enrichment functions and a cohesive failure model to capture the transverse cracking associated primarily with fiber/matrix interface debonding. In addition to the sensitivities with respect to individual geometrical parameters such as the radius of individual fibers, the sensitivities of the transverse stress–strain response with respect to the parameters that define the distributions of the geometrical parameters such as the mean and standard deviation of the fiber radius and nearest-neighbor distance distributions are also derived. The sensitivity analysis is performed on realistic microstructures composed of hundreds of fibers to characterize the influence of the geometrical parameters and their distributions on the transverse failure response of the composite laminate.

Nearest-Neighbor and Contact Distance Distributions for Matérn Cluster Process

In this letter, we derive the cumulative density function of the nearest neighbor and contact distance distributions of the Matern cluster process (MCP) in $\mathbb {R}^{2}$ . These results will be useful in the performance analysis of many real-world wireless networks that exhibit inter-node attraction. Using these results, we concretely demonstrate that the contact distance of the MCP stochastically dominates its nearest-neighbor distance as well as the contact distance of the homogenous Poisson point process with the same density.

Nearest-Neighbor and Contact Distance Distributions for Thomas Cluster Process

We characterize the statistics of nearest-neighbor and contact distance distributions for Thomas cluster process (TCP), which is a special case of Poisson cluster process. In particular, we derive the cumulative distribution function of the distance to the nearest point of TCP from a reference point for three different cases: 1) reference point is not a part of the point process; 2) it is chosen uniformly at random from the TCP; and 3) it is a randomly chosen point from a cluster chosen uniformly at random from the TCP. While the first corresponds to the contact distance distribution, the other two provide two different viewpoints for the nearest-neighbor distance distribution. Closed-form bounds are also provided for the first two cases.

Plant architecture and spatial structure of an early Permian woodland buried by flood waters, Sangre de Cristo Formation, New Mexico

Abstract Natural molds of 165 stems were found in life position in a 1 m-thick sandstone bed, lower Permian (Wolfcampian), Sangre de Cristo Formation, northern New Mexico. The sandstone represents a single flood event of a river sourced in the Ancestral Rocky Mountains. Most of the flood-buried plants survived and resumed growth. The stem affinities are uncertain, but they resemble coniferophytic gymnosperms, possibly dicranophylls. Stem diameters (N = 135) vary from 1 to 21 cm, with three strongly overlapping size classes. Modern forest studies predict a monotonically decreasing number (inverse square law) of individuals per size class as diameter increases. This is not seen for fossil stems ≤ 6 cm diameter, reflecting biases against preservation, exposure, and observation of smaller individuals. Stems ≥ 6 cm diameter obey the predicted inverse square law of diameter distribution. Height estimates calculated from diameter-to-height relationships of modern gymnosperms yielded heights varying from ~ 0.9 m to > 8 m, mean of ~ 3 m. Mean stand density is approximately 2 stems/m 2 (20,000 stems/hectare) for all stems > 1 cm diameter. For stems > 7.5 cm or > 10 cm diameter, density is approximately 0.24 stems/m 2 (2400 stems/hectare) and 0.14 stems/m 2 (1400 stems/hectare). Stem spatial distribution is random (Poisson). Mean all-stem nearest-neighbor distance (NND) averages 36 cm. Mean NND between stems > 7.5 cm and > 10 cm diameter is approximately 1.02 m and 1.36 m. NND increases in approximate isometry with stem diameter, indicating conformation to the same spatial packing rules found in extant forests and other fossil forests of varying ages. Nearest-neighbor distance distribution passes statistical testing for normality, but with positive skew, as often seen in extant NND distributions. The size-frequency distribution of the stems is similar to those of Jurassic, early Tertiary, and extant woodlands; the early Permian woodland distribution line has the same slope, but differs in that the overall size range increases over time (Cope's rule). The early Permian woodland is self-thinning; its volume versus density relationship shows a self-thinning exponent between − 1.25 and − 1.5, within the range seen in some extant plant stands (− 1.21 to − 1.7).

Robust estimation of distance between sets of points

This paper proposes a new methodology for computing Hausdorff distances between sets of points in a robust way. In a first step, robust nearest neighbor distance distributions between the two sets of points are obtained by considering reliability measures in the computations through a Monte Carlo scheme. In a second step, the computed distributions are operated using random variables algebra in order to obtain probability distributions of the average, minimum or maximum distances. In the last step, different statistics are computed from these distributions. A statistical test of significance, the nearest neighbor index, in addition to the newly proposed divergence and clustering indices are used to compare the computed measurements with respect to values obtained by chance. Results on synthetic and real data show that the proposed method is more robust than the standard Hausdorff distance. In addition, unlike previously proposed methods based on thresholding, it is appropriate for problems that can be modeled through point processes.

Merged trees in second-growth, fire-origin forests in Patagonia, Chile: positive spatial association patterns and their ecological implications

• Negative density-dependent processes have been thought to be the primary cause of shifting spatial patterns of tree populations through time. The existence of adult tree clusters might challenge this classical prediction. Here, we document the prevalence of merged stems (clustering of mature trees leading to stem fusion) in second-growth forests of Nothofagus pumilio and hypothesize that it is nonrandom but predictable in space. • We stem-mapped nine sites in second-growth edge and interior forests of fire origin and in mature forests of N. pumilio (>3500 trees) in central Patagonia, Chile. The spatial structure of stand-level and individual-level features was estimated with spatial analyses (pair-correlation function and nearest-neighbor distances). • Multistemmed trees were merged clusters of separate individuals. Merged trees were predominantly found at the edge of the second-growth forests. We found strong clustering (≤5 m) at forest edge sites and none at interior sites. Nearest-neighbor distance distributions were unimodal for unmerged trees and monotonically decreasing for merged trees; interstem distances were much smaller at the edge sites than at the interior sites. • The occurrence of merged trees at the forest edge, and the resulting high spatial aggregation of stems, is consistent with the hypothesis that establishment was probably aggregated. The spatial pattern found at the forest edge changes the standard spatial pattern sequence through time in temperate forests, altering traditional forest-stand-dynamics models.

Beyond co-localization: inferring spatial interactions between sub-cellular structures from microscopy images

BackgroundSub-cellular structures interact in numerous direct and indirect ways in order to fulfill cellular functions. While direct molecular interactions crucially depend on spatial proximity, other interactions typically result in spatial correlations between the interacting structures. Such correlations are the target of microscopy-based co-localization analysis, which can provide hints of potential interactions. Two complementary approaches to co-localization analysis can be distinguished: intensity correlation methods capitalize on pattern discovery, whereas object-based methods emphasize detection power.ResultsWe first reinvestigate the classical co-localization measure in the context of spatial point pattern analysis. This allows us to unravel the set of implicit assumptions inherent to this measure and to identify potential confounding factors commonly ignored. We generalize object-based co-localization analysis to a statistical framework involving spatial point processes. In this framework, interactions are understood as position co-dependencies in the observed localization patterns. The framework is based on a model of effective pairwise interaction potentials and the specification of a null hypothesis for the expected pattern in the absence of interaction. Inferred interaction potentials thus reflect all significant effects that are not explained by the null hypothesis. Our model enables the use of a wealth of well-known statistical methods for analyzing experimental data, as demonstrated on synthetic data and in a case study considering virus entry into live cells. We show that the classical co-localization measure typically under-exploits the information contained in our data.ConclusionsWe establish a connection between co-localization and spatial interaction of sub-cellular structures by formulating the object-based interaction analysis problem in a spatial statistics framework based on nearest-neighbor distance distributions. We provide generic procedures for inferring interaction strengths and quantifying their relative statistical significance from sets of discrete objects as provided by image analysis methods. Within our framework, an interaction potential can either refer to a phenomenological or a mechanistic model of a physico-chemical interaction process. This increased flexibility in designing and testing different hypothetical interaction models can be used to quantify the parameters of a specific interaction model or may catalyze the discovery of functional relations.

A boundary corrected expansion of the moments of nearest neighbor distributions

In this article, the moments of nearest neighbor distance distributions are examined. While the asymptotic form of such moments is well-known, the boundary effect has this far resisted a rigorous analysis. Our goal is to develop a new technique that allows a closed-form high order expansion, where the boundaries are taken into account up to the first order. The resulting theoretical predictions are tested via simulations and found to be much more accurate than the first order approximation obtained by neglecting the boundaries. While our results are of theoretical interest, they definitely also have important applications in statistics and physics. As a concrete example, we mention estimating Rényi entropies of probability distributions. Moreover, the algebraic technique developed may turn out to be useful in other, related problems including estimation of the Shannon differential entropy.© 2010 Wiley Periodicals, Inc. Random Struct. Alg., 2010

2D Quantitative Characterization of Microstructural Inhomogeneities in the Pressure Die Cast AZ91 Magnesium Alloy

Abstract Inclusions, shrinkage pores and gas pores are the major processing defects of pressure die cast AZ91 magnesium alloy. These inhomogeneities influence the mechanical properties of the material. Hence, quantitative characterization of size and arrangement of inclusions, shrinkage and gas microporosity is expected to be useful to understand the processing-property-microstructure correlation. In the present work an image analysis procedure has been explained to separately quantify the above inhomogeneities. The important parameters of image processing like montage creation, magnification selection and shrinkage pore separation are explained. The inclusions, shrinkage and gas micropores were separated by the above procedure and size, nearest neighbor distance distributions of these inhomogeneities were obtained in order to characterize the material.

Nearest neighbor distances in uniform–random poly-dispersed microstructures

Nearest neighbor distributions are systematically studied in uniform–random microstructures containing impenetrable poly-dispersed spherical particles using computer simulation. The simulations are based on random sequential adsorption (RSA) algorithm. The computed nearest neighbor distance distributions and the mean nearest neighbor distances are unbiased and free of any edge effects. In the simulated microstructures, there are no spatial correlations among the spheres of different sizes. It is shown that the mean nearest neighbor distance 〈 D〉 depends only on the sphere volume fraction f, number density N V, and coefficient of variation (CV) of the sphere size distribution CV; it is not sensitive to the other attributes of the size distribution function such as skewness. The mean nearest neighbor distance can be calculated using the following simple equation, which is deduced from large number of simulation. 〈 D 〉 N V 1 / 3 = K 1 + B f f 0 2 / 3 − ( 1 − exp ( − C V ⋅ f ) ) where K = ( 4 / 3 π ) − 1 / 3 Γ ( 4 / 3 ) ≈ 0.55396 , B = 2 − 1 / 6 ( 4 3 π ) − 1 / 3 Γ ( 4 3 ) − 1 ≈ 1.02625 , and f 0 is the volume fraction in a closed pack structure (i.e., π / 18 or ∼0.74).

Atomic force microscopy study of the early stages of Sn phase separation on Si(111) surfaces

Sn clustering on Si(111) samples was studied during deposition at 100 °C and after an additional postdeposition anneal at 200 °C for 5 min. These conditions lead to early stage morphologies for the surface phase separation process of the thin film. We focus in this atomic force microscopy study on (i) the evolution of the partial ordering in the nearest-neighbor distance distributions observed in the late stage of phase separation and (ii) on the role of well-defined substrate defects on the development of the early stage morphology.

Track structures and dose distributions from decays of (131)I and (125)I in and around water spheres simulating micrometastases of differentiated thyroid cancer.

The disintegration of the radionuclides (131)I and (125)I and the subsequent charged-particle tracks left behind in water (as a model substance for a biological cell) are simulated by the Monte Carlo track structure simulation code PARTRAC, using new inelastic electron scattering cross sections for condensed water. Every photon and electron emitted was followed in detail, event by event, down to 10 eV. From the spatial information on the track structures, absorbed dose distributions per (131)I and (125)I decay were calculated in and around water spheres simulating micrometastases as well as in the tissue surrounding such metastases. These radionuclides were assumed to be distributed uniformly inside spheres of different diameters (0.01, 0.03, 0.1, 0.3, 1.0 and 3.0 mm). The respective electron degradation spectra, the nearest-neighbor distance distributions between inelastic events, and the distance distributions for all activations for both iodine radionuclides were calculated. The absorbed fractions of the initial electron energies, absorbed doses and energy depositions, and single-event distributions, F(1)(epsilon), inside the six water spheres described above and in the surrounding tissue were also calculated. The absorbed doses per decay inside the six water spheres, i.e., the calculated S values (listed from 0.01 to 3.0 mm), were 6.8 x 10(-4), 7.2 x 10(-5), 5.5 x 10(-6), 4.9 x 10(-7), 3.1 x 10(-8) and 1.8 x 10(-9) Gy Bq(-1) s(-1) for (131)I, and 3.4 x 10(-3), 1.7 x 10(-4), 5.1 x 10(-6), 2.0 x 10(-7), 5.6 x 10(-9) and 2.2 x 10(-10) Gy Bq(-1) s(-1) for (125)I. It is concluded that, in the treatment of thyroid cancer, the geometrical track structure properties of (125)I might be superior to those of (131)I in micrometastases with diameters less than 0.1 mm; however, in this medical context, many other factors also have to be considered.