Point process statistics in atom probe tomography

Many fresh and coastal waters are becoming increasingly turbid because of human activities, which may disrupt the visually mediated behaviours of aquatic organisms. Shoaling fish typically depend on vision to maintain collective behaviour, which has a range of benefits including protection from predators, enhanced foraging efficiency and access to mates. Previous studies of the effects of turbidity on shoaling behaviour have focussed on changes to nearest neighbour distance and average group‐level behaviours. Here, we investigated whether and how experimental shoals of three‐spined sticklebacks (Gasterosteus aculeatus) in clear (<10 Nephelometric Turbidity Units [NTU]) and turbid (~35 NTU) conditions differed in five local‐level behaviours of individuals (nearest and furthest neighbour distance, heading difference with nearest neighbour, bearing angle to nearest neighbour and swimming speed). These variables are important for the emergent group‐level properties of shoaling behaviour. We found an indirect effect of turbidity on nearest neighbour distances driven by a reduction in swimming speed, and a direct effect of turbidity which increased variability in furthest neighbour distances. In contrast, the alignment and relative position of individuals was not significantly altered in turbid compared to clear conditions. Overall, our results suggest that the shoals were usually robust to adverse effects of turbidity on collective behaviour, but group cohesion was occasionally lost during periods of instability.

The upland mesic rainforests of eastern Australia have been described as a "mesothermal archipelago" where a chain of cool mountain "islands" arise from a warm "sea" of tropical and subtropical lowlands. An endemic freshwater crayfish belonging to the genus Euastacus is found on each of these mountain "islands." The Euastacus are particularly suitable for the study of evolution because each mountain harbors a unique species, there are many taxa present providing replication within the group and, most importantly, their distribution is linear, extending along a south-north axis. This group could have evolved by "simultaneous vicariance" where there was one vicariant separation event of a widespread ancestor, or by "south to north stepping stone dispersal" where there were long distance dispersal events from neighboring mountain islands, starting in the south and proceeding north in a dispersal-colonization wave. We used pairwise genetic distances between nearest geographic neighbors as a novel way to test the two hypotheses. If diversification was due to "south to north stepping stone dispersal," then pairwise genetic distances between nearest geographic neighbors should decrease progressively the farther north the taxon pairs are found, reflecting the decreasing periods of isolation. In this case there should be a negative correlation between the south to north rank order of nearest neighbors and pairwise genetic distances. A Spearman's correlation on 16S mtDNA pairwise genetic distances and geographic rank order was not significant, indicating there was no support for the south to north stepping stone dispersal hypothesis. If simultaneous vicariance was responsible for diversification then all nearest geographic neighbor taxon pairs should have similar genetic distances and, therefore, the variance in nearest neighbor distances should be zero, or close to it. To test if the observed variance was tending towards zero we developed a randomization test where nearest neighbor taxon pairs were assigned random genetic distances and the variances calculated. The observed variance lay in the < 0.05 range of the simulated variances, providing support for the simultaneous vicariance hypothesis. The data also suggest there was simultaneous vicariance of at least two ancestral Queensland lineages. The timing of this vicariant event was probably in the Pliocene, which is consistent with the divergence times reported for other Australian mesic rainforest restricted taxa.

The upland mesic rainforests of eastern Australia have been described as a “mesothermal archipelago” where a chain of cool mountain “islands” arise from a warm “sea” of tropical and subtropical lowlands. An endemic freshwater crayfish belonging to the genus Euastacus is found on each of these mountain “islands.” The Euastacus are particularly suitable for the study of evolution because each mountain harbors a unique species, there are many taxa present providing replication within the group and, most importantly, their distribution is linear, extending along a south-north axis. This group could have evolved by “simultaneous vicariance” where there was one vicariant separation event of a widespread ancestor, or by “south to north stepping stone dispersal” where there were long distance dispersal events from neighboring mountain islands, starting in the south and proceeding north in a dispersal-colonization wave. We used pairwise genetic distances between nearest geographic neighbors as a novel way to test the two hypotheses. If diversification was due to “south to north stepping stone dispersal,” then pairwise genetic distances between nearest geographic neighbors should decrease progressively the farther north the taxon pairs are found, reflecting the decreasing periods of isolation. In this case there should be a negative correlation between the south to north rank order of nearest neighbors and pairwise genetic distances. A Spearman's correlation on 16S mtDNA pairwise genetic distances and geographic rank order was not significant, indicating there was no support for the south to north stepping stone dispersal hypothesis. If simultaneous vicariance was responsible for diversification then all nearest geographic neighbor taxon pairs should have similar genetic distances and, therefore, the variance in nearest neighbor distances should be zero, or close to it. To test if the observed variance was tending towards zero we developed a randomization test where nearest neighbor taxon pairs were assigned random genetic distances and the variances calculated. The observed variance lay in the < 0.05 range of the simulated variances, providing support for the simultaneous vicariance hypothesis. The data also suggest there was simultaneous vicariance of at least two ancestral Queensland lineages. The timing of this vicariant event was probably in the Pliocene, which is consistent with the divergence times reported for other Australian mesic rainforest restricted taxa.

Clustering and pair correlation function in atom probe tomography

Mg diffusion is a common problem in GaN devices with p–n junctions. Although this impurity diffusion is reported to occur through threading dislocations (TDs), no direct evidence has yet been obtained. Therefore, we tried the direct observation of Mg diffusion by atom probe tomography (APT) analysis. The n-type drift layer of the fabricated p–n diode was exposed, and etch pits were formed on the drift layer to identify the TD position. The APT analysis around TDs was carried out by lifting out the drift layer around specific etch pits using a focused ion beam to include TDs. The relationship between the etch pit shape and the TD type was confirmed by cross-sectional scanning transmission electron microscopy observation. The APT analysis of two types of etch pits formed on the mixed dislocations was performed, and Mg diffusion was clearly observed through the mixed dislocations. In this work, we show direct evidence of Mg diffusion via mixed dislocations in GaN p–n diodes and its effect on reverse leakage current.

Bone structure is generally hierarchically organized into organic (collagen, proteins, ...), inorganic (hydroxyapatite (HAP)) components. However, many fundamental mechanisms of the biomineralization processes such as HAP formation, the influence of trace elements, the mineral-collagen arrangement, etc., are not clearly understood. This is partly due to the analytical challenge of simultaneously characterizing the three-dimensional (3D) structure and chemical composition of biominerals in general at the nanometer scale, which can, in principle be achieved by atom probe tomography (APT). Yet, the hierarchical structures of bone represent a critical hurdle for APT analysis in terms of sample yield and analytical resolution, particularly for trace elements, and organic components from the collagen appear to systematically get lost from the analysis. Here, we applied in-situ metallic coating of APT specimens within the focused ion beam (FIB) used for preparing specimens, and demonstrate that the sample yield and chemical sensitivity are tremendously improved, allowing the analysis of individual collagen fibrils and trace elements such as Mg and Na. We explored a range of measurement parameters with and without coating, in terms of analytical resolution performance and determined the best practice parameters for analyzing bone samples in APT. To decipher the complex mass spectra of the bone specimens, reference spectra from pure HAP and collagen were acquired to unambiguously identify the signals, allowing us to analyze entire collagen fibrils and interfaces at the near-atomic scale. Our results open new possibilities for understanding the hierarchical structure and chemical heterogeneity of bone structures at the near-atomic level and demonstrate the potential of this new method to provide new, unexplored insights into biomineralization processes in the future. STATEMENT OF SIGNIFICANCE: Atom probe tomography (APT) is a relatively new technique for the analysis of bones, teeth or biominerals in general. APT can characterize the microstructure of materials in 3D down to the near-atomic level, combined with a high elemental sensitivity, down to parts per million. APT application to study biomineralization phenomena is plagued by low sample yield and poorer analytical performance compared to metals. Here we have overcome these limitations by in-situ metal coating of APT specimens. This can unlock future APT analysis to gain insights into fundamental biomineralization processes, e.g. collagen/hydroxyapatite interaction, influence of trace elements and a better understanding of bone diseases or bone biomineralization in general.

Basic methods of explorative statistical analysis for stationary and isotropic planar point processes are briefly and informally reviewed. At the explorative level, planar point patterns may be characterized in terms of the intensity, the K-function and the pair correlation function. These second-order functions enable one to classify a given point process as completely random, clustering or repulsive. The repulsive behaviour may be quantified by an estimate of the hard-core distance. In the exploratory approach, the statistics are essentially free from model assumptions. Second-order spatial functions have been estimated to characterize genuine planar point processes in the macroscopic domain, for example in forestry, geography and epidemiology. For light microscopy and transmission electron microscopy, two situations are distinguished, which may be summarized as the genuine planar case and the stereological case. In the genuine planar case, a direct interpretation of the results of spatial statistics is feasible. Here, monolayers in cell culture, intramembranous particles on freeze fracture specimens and amacrine cells of the retina are mentioned as examples. In the stereological case, point patterns are generated by sections through 3D structures. Here the observed point patterns may arise as the centres of sectional profiles of particles, or as centres of sectional profiles of spatial fibre processes. In both situations, exploratory spatial point process statistics allow a quantitative characterization of sectional images for the purposes of group comparisons and classification. Moreover, for spatial fibre processes it has recently been shown that the observed pair correlation function of the centres of the fibre profiles is an estimate of the reduced pair correlation function of the fibre process in 3D. Hence for fibre processes a stereological interpretation of point process statistics obtained from sections is an additional option.

Enhanced analysis of nanoporous gold by atom probe tomography

For a stationary long-range dependent point process N(.) with Palm distribution PO0, the Hurst index H =_sup{h : lim supt-o t-2h var N(0, t] = oo} is related to the moment index K - sup{k : EO(Tk) 3, it being known that equality holds for a stationary renewal process. Thus, a stationary point process for which K < 2 is necessarily long-range dependent with Hurst index greater than :. An extended example of a Wold process shows that a stationary point process can be both long-range count dependent and long-range interval dependent and have finite mean square interval length, i.e., EO(T2) <00oo.

Structures of NaCl and LiCl aqueous solutions in pores of carbon nanotubes with diameter 1 and 2 nm were evaluated by using X-ray diffraction and molecular dynamics simulations. Water intermolecular distances in carbon nanotubes with 1 and 2 nm pore diameters were more elongated and shortened than bulk water, respectively. Those were results of weakened and strengthened hydrogen bonds. The structures of aqueous solutions in carbon nanotubes were considerably different from water despite tiny amounts of ions in the pores. The nearest neighbour distances in aqueous solutions were rarely changed from that in water system in 1 nm carbon nanotubes pore, while those were longer than water in 2 nm carbon nanotubes pore. On the other hand, the second nearest neighbour distances in aqueous solutions in 1 and 2 nm pore diameter carbon nanotubes were both decreased from those in water in carbon nanotubes. Significant hydration formation and cleavage of hydrogen bonds were thus observed in 2 nm carbon nanotubes pore, because the elongated nearest neighbour and shortened second nearest neighbour distances were observed. Anomalous feature of the unchanged nearest neighbour and shortened second neighbour distances in 1 nm carbon nanotubes pore is the result that water intermolecular distance was much longer than bulk and hydrogen bonds were thus severely separated. Ions might play dominant role to connect hydrogen bonds and of course form hydration shell. Those anomalous structure changes from water to aqueous solution were observed only in extremely narrow carbon nanotubes.

Modal frequencies are widely used as damage-sensitive features in vibration-based unsupervised anomaly detection for full-scale civil structures. However, environmental variations introduce nonlinear and non-Gaussian behaviors in modal frequencies, characterized by multicentricity and substantial variance differences. These behaviors inevitably mask damage-induced frequency shifts, leading to increased false-detection rates and degraded real-time performance. To address this, this paper presents a novel unsupervised framework for early-stage anomaly detection that integrates exponential slow feature analysis (SFA) with just-in-time learning-aided standard K -nearest neighbor metrics. First, nonlinear modal features with minimum temporal variation are extracted from modal frequencies via exponential SFA for dimensionality reduction. Afterward, under the standard measurement criteria, the Euclidean squared distances between each sample in the entire training set and its nearest neighbors are computed. The standard distance for each neighbor is then modeled, with the number of neighbors automatically selected through Bayesian optimization and cross-validation. The primary purpose of this step is to ensure that the nearest neighbor distances between samples under different environmental conditions and damage conditions including abrupt anomalies or gradual degradations, are measured on a consistent scale, thereby minimizing environmental variability. After that, a robust detection indicator is derived from the mean of squared nearest neighbor distances and combined with kernel density estimation to determine an online detection threshold for outliers. The results indicate the proposed method effectively mitigates strong environmental variability without prior environmental measurements and accurately identifies anomalies in bridge modal frequencies with negligible false-positive and false-negative errors.

A new edge—corrected kernel—based estimator is proposed for the density function of the nearest neighbour distance of a stationary and isotropic point process. The performances of the new estimator and the existing estimators are compared in a simulation study. The results of the simulation study suggest that the new estimator is preferable to the existing alternatives. The use of the estimators for testing whether a spatial point pattern is consistent with the hypothesis of a Poisson process is demonstrated by a geographical example

Eriogonum inflatum Torr and Frém. (Polygonaceae) experiences unusually high population turnover for a desert perennial. For example, 20% of the individuals in the study population were dead but still rooted. Pairs of nearest neighbors which included one dead individual tended to be closer to one another than pairs of live nearest neighbors. Thus, deaths are nonrandom. Individuals which are too close to one another are most vulnerable. Nevertheless, the deaths of 20% of the individuals had no effect on the intensity of the spatial pattern of the population; survivors were just as highly aggregated as survivors and dead individuals together. I conclude that competitor-induced mortality will not have predictable effects on the spatial pattern of plant populations which consist of a mosaic of individuals of different ages and sizes.

Early-stage clustering in two Al-Mg-Zn(-Cu) alloys has been investigated using atom probe tomography and transmission electron microscopy. Cluster identification by the isoposition method and a statistical approach based on the pair correlation function have both been applied to estimate the cluster size, composition, and volume fraction from atom probe data sets. To assess the accuracy of the quantification of clusters of different mean sizes, synthesized virtual data sets were used, accounting for a simulated degraded spatial resolution. The quality of the predictions made by the two complementary methods is discussed, considering the experimental and simulated data sets.

Quantitative evaluation of spinodal decomposition in thermally aged binary Fe-35 at.% Cr alloys by correlative atom probe tomography and small angle neutron scattering analyses