Distribution Of Nearest-neighbor Distances Research Articles

KNNDM CV: k-fold nearest-neighbour distance matching cross-validation for map accuracy estimation

Abstract. Random and spatial cross-validation (CV) methods are commonly used to evaluate machine-learning-based spatial prediction models, and the performance values obtained are often interpreted as map accuracy estimates. However, the appropriateness of such approaches is currently the subject of controversy. For the common case where no probability sample for validation purposes is available, in Milà et al. (2022) we proposed the nearest-neighbour distance matching (NNDM) leave-one-out (LOO) CV method. This method produces a distribution of geographical nearest-neighbour distances (NNDs) between test and training locations during CV that matches the distribution of NNDs between prediction and training locations. Hence, it creates predictive conditions during CV that are comparable to what is required when predicting a defined area. Although NNDM LOO CV produced largely reliable map accuracy estimates in our analysis, as a LOO-based method, it cannot be applied to the large datasets found in many studies. Here, we propose a novel k-fold CV strategy for map accuracy estimation inspired by the concepts of NNDM LOO CV: the k-fold NNDM (kNNDM) CV. The kNNDM algorithm tries to find a k-fold configuration such that the empirical cumulative distribution function (ECDF) of NNDs between test and training locations during CV is matched to the ECDF of NNDs between prediction and training locations. We tested kNNDM CV in a simulation study with different sampling distributions and compared it to other CV methods including NNDM LOO CV. We found that kNNDM CV performed similarly to NNDM LOO CV and produced reasonably reliable map accuracy estimates across sampling patterns. However, compared to NNDM LOO CV, kNNDM resulted in significantly reduced computation times. In an experiment using 4000 strongly clustered training points, kNNDM CV reduced the time spent on fold assignment and model training from 4.8 d to 1.2 min. Furthermore, we found a positive association between the quality of the match of the two ECDFs in kNNDM and the reliability of the map accuracy estimates. kNNDM provided the advantages of our original NNDM LOO CV strategy while bypassing its sample size limitations.

Structural studies of local environments in high-symmetry quasicrystals

The statistics of how the local environment of a particle looks like, e.g., given by the distribution of nearest neighbor distances or the sizes of Voronoi cells, is important as a starting point for the calculation of many material properties like electronic or photonic band structures. Here we study local environments that occur in quasicrystals with large rotational symmetry. Both with analytical considerations based on geometric arguments and with an analysis of a large number of numerically created patches of high-symmetry quasicrystals we find that the Voronoi area’s distribution reaches a bimodal curve and that in the limit of large rotational symmetries the distribution of nearest neighbor distance converges against a universal curve, where 27.7% of the vertices have their nearest neighbor at a normalized distance equal to 1, while for the other 72.3% the nearest neighbor is at a distance less than 1. Therefore, the statistics of local environments is non-trivial but independent of the specific rotational symmetry. Thus properties that only depend on local environments are expected to be universal for all high-symmetry quasicrystals.

Heart failure (HF) alters distribution and spatial association profiles of calmodulin (CaM) and CaM target protein mRNAs.

Aberrant Ca-CaM signaling has been implicated in various congenital and acquired cardiac pathologies, including arrhythmia, hypertrophy, and HF. We examined the impact of HF induced by trans-aortic constriction (TAC) on the distribution of the three CaM mRNAs (Calm 1,2 and 3) and their key protein target mRNAs (Ryr2, Scn5a, Camk2d, NOS1 and Cacna1c) in cardiomyocytes, using fluorescence in situ hybridization (RNAScope™). HF resulted in specific changes in the pattern of localization of Calms, manifested in redistribution of Calm3 from the cell periphery towards the perinuclear area and enhanced Calm2 attraction to the perinuclear area compared to sham myocytes. Additionally, HF resulted in redistribution of mRNAs for certain CaM target mRNAs. Particularly, NOS1 localization shifted from the cell periphery towards the perinuclear area, Cacna1c, Camk2d and Scn5a abundance increased at the perinuclear area, and Ryr2 attracted even closer to the cell periphery in HF myocytes compared to sham myocytes. The strength of non-random attraction/repulsion was measured as the maximal deviation between the observed distribution of nearest neighbor distances from the distribution predicted under complete spatial randomness. Consistent with the observed alterations in abundance and distribution of CaM and CaM target mRNAs, HF resulted in increased attraction between Calm1 and Scn5a, Ryr2 and Camk2d, between Calm2 and Ryr2 and Camk2d; and between Calm3 and NOS1 and Scn5a. In contrast, the attraction between Calm3 and Ryr2 decreased in HF myocytes compared to sham. Collectively, these results suggest distribution of Calms and their association with key target protein mRNAs undergo substantial alterations in heart failure. These results have new important implications for organization of Ca signaling in normal and diseased heart.

Composition of Carbon Clusters in Implanted Silicon Using Atom Probe Tomography.

Atom probe tomography was employed to observe and derive the composition of carbon clusters in implanted silicon. This value, which is of interest to the microelectronic industry when considering ion implantation defects, was estimated not to exceed 2 at%. This measurement has been done by fitting the distribution of first nearest neighbor distances between monoatomic carbon ions (C+ and C2+). Carbon quantification has been considerably improved through the detection of molecular ions, using lower electric field conditions as well as equal proportions of 12C and 13C. In these conditions and using another quantification method, we have shown that the carbon content in clusters approaches 50 at%. This result very likely indicates that clusters are nuclei of the SiC phase.

Reassignment of magic numbers for icosahedral Au clusters: 310, 564, 928 and 1426.

Icosahedral Au clusters with three and four shells of atoms are found to deviate significantly from the commonly assumed Mackay structures. By introducing additional atoms in the surface shell and creating a vacancy in the center of the cluster, the calculated energy per atom can be lowered significantly, according to several different descriptions of the interatomic interaction. Analogous icosahedral structures with five and six shells of atoms are generated using the same structural motifs and are similarly found to be more stable than Mackay icosahedra. The lowest energy per atom obtained here is for clusters containing 310, 564, 928 and 1426 atoms, as compared with the commonly assumed magic numbers of 309, 561, 923 and 1415. Some of the vertices in the optimized clusters have a hexagonal ring of atoms, rather than a pentagon, with the vertex atom missing. An inner shell atom in some cases moves outwards by more than an Ångström into the surface shell at such a vertex site. This feature, as well as the wide distribution of nearest-neighbor distances in the surface layer, can strongly influence the properties of icosahedral clusters, for example catalytic activity. The structural optimization is initially carried out using the GOUST method with atomic forces estimated with the EMT empirical potential function, but the atomic coordinates are then refined by minimization using electron density functional theory (DFT) or Gaussian approximation potential (GAP). A single energy barrier is found to separate the Mackay icosahedron from a lower energy structure where a string of atoms moves outwards in a concerted manner from the center so as to create a central vacancy while placing an additional atom in the surface shell.

Simulating feldspar luminescence phenomena using R

Kinetic models have been used extensively for modeling and numerical simulation of luminescence phenomena and dating techniques for various dosimetric materials. Several comprehensive models have been implemented for quartz, which allow simulation of complex sequences of irradiation and thermal/optical events in nature and in the laboratory. In this paper, we present a simple and accurate way of simulating similarly complex sequences in feldspars. We introduce the open-access R scripts Feldspar Simulation Functions (FSF) for kinetic model simulation of luminescence phenomena in feldspars. These R functions offer useful numerical tools to perform luminescence simulations in a user-friendly manner. The mathematical framework of four different types of previously published models is presented in a uniform way, and the models are simulated with FSF. While previously published versions of these four models require numerical integration of the differential equations, the FSF circumvent the need for numerical integration by using accurate summations over the finite range of the model parameters. The simulation process can be understood easily by creating transparent sequences of events consisting of these compact R functions. The key physical concept of the FSF is that irradiation and thermal/optical treatments of feldspars change the distribution of nearest neighbor (NN) distances in donor-acceptor pairs. These changes are described using analytical equations within the four models examined in this paper. The NN distribution at the end of one simulation stage becomes the initial distribution for the next stage in the sequences of events being simulated. Several practical examples and possible applications and extensions of the FSF are discussed.

Supramolecular clustering of the cardiac sodium channel Nav1.5 in HEK293F cells, with and without the auxiliary β3-subunit.

Voltage‐gated sodium channels comprise an ion‐selective α‐subunit and one or more associated β‐subunits. The β3‐subunit (encoded by the SCN3B gene) is an important physiological regulator of the heart‐specific sodium channel, Nav1.5. We have previously shown that when expressed alone in HEK293F cells, the full‐length β3‐subunit forms trimers in the plasma membrane. We extend this result with biochemical assays and use the proximity ligation assay (PLA) to identify oligomeric β3‐subunits, not just at the plasma membrane, but throughout the secretory pathway. We then investigate the corresponding clustering properties of the α‐subunit and the effects upon these of the β3‐subunits. The oligomeric status of the Nav1.5 α‐subunit in vivo, with or without the β3‐subunit, has not been previously investigated. Using super‐resolution fluorescence imaging, we show that under conditions typically used in electrophysiological studies, the Nav1.5 α‐subunit assembles on the plasma membrane of HEK293F cells into spatially localized clusters rather than individual and randomly dispersed molecules. Quantitative analysis indicates that the β3‐subunit is not required for this clustering but β3 does significantly change the distribution of cluster sizes and nearest‐neighbor distances between Nav1.5 α‐subunits. However, when assayed by PLA, the β3‐subunit increases the number of PLA‐positive signals generated by anti‐(Nav1.5 α‐subunit) antibodies, mainly at the plasma membrane. Since PLA can be sensitive to the orientation of proteins within a cluster, we suggest that the β3‐subunit introduces a significant change in the relative alignment of individual Nav1.5 α‐subunits, but the clustering itself depends on other factors. We also show that these structural and higher‐order changes induced by the β3‐subunit do not alter the degree of electrophysiological gating cooperativity between Nav1.5 α‐subunits. Our data provide new insights into the role of the β3‐subunit and the supramolecular organization of sodium channels, in an important model cell system that is widely used to study Nav channel behavior.

Quantifying the spatial heterogeneity of points

ABSTRACTVariation in the spatial heterogeneity of points reflects the evolutionary process or mechanism of geographical events. The key to depicting this variation is quantifying spatial heterogeneity. In this paper, the spatial heterogeneity of a point pattern is defined as the degree of aggregation-type deviation from complete spatial randomness. In such a case, a goodness-of-fit-type statistic based on the distribution of nearest-neighbor distances called the level of heterogeneity (LH*) is regarded as a standard measurement, and a normalized version called the normalized level of heterogeneity (NLH*) is proposed for datasets with different point numbers and study region areas. Considering the complex integration calculation of LH* and NLH*, simulation experiments are implemented to test the capability of some classic nearest-neighbor statistics in quantifying spatial heterogeneity. The results showed that except for the standard LH* statistic, only Clark and Evans’ statistic (A-w) and Byth and Ripley’s statistic (H-xw) are robust. Statistics NLH*, (A-w) and (H-xw) are validated by quantifying the spatial heterogeneity of two-dimensional crime events, three-dimensional earthquake events and four-dimensional origin-destination (OD) events. The results indicate that these statistics all have a reasonable explanation in quantifying spatial heterogeneity for real-world geographical events of different types and with different dimensions. Compared with NLH*, Clark and Evans’ (A-w) statistic and Byth and Ripley’s (H-xw) statistic are recommended from the perspective of accessibility.

Coupling of SK channels, L-type Ca2+ channels, and ryanodine receptors in cardiomyocytes

Small-conductance Ca2+-activated K+ (SK) channels regulate the excitability of cardiomyocytes by integrating intracellular Ca2+ and membrane potentials on a beat-to-beat basis. The inextricable interplay between activation of SK channels and Ca2+ dynamics suggests the pathology of one begets another. Yet, the exact mechanistic underpinning for the activation of cardiac SK channels remains unaddressed. Here, we investigated the intracellular Ca2+ microdomains necessary for SK channel activation. SK currents coupled with Ca2+ influx via L-type Ca2+ channels (LTCCs) continued to be elicited after application of caffeine, ryanodine or thapsigargin to deplete SR Ca2+ store, suggesting that LTCCs provide the immediate Ca2+ microdomain for the activation of SK channels in cardiomyocytes. Super-resolution imaging of SK2, Cav1.2 Ca2+ channel, and ryanodine receptor 2 (RyR2) was performed to quantify the nearest neighbor distances (NND) and localized the three molecules within hundreds of nanometers. The distribution of NND between SK2 and RyR2 as well as SK2 and Cav1.2 was bimodal, suggesting a spatial relationship between the channels. The activation mechanism revealed by our study paved the way for the understanding of the roles of SK channels on the feedback mechanism to regulate the activities of LTCCs and RyR2 to influence local and global Ca2+ signaling.

Nearest-neighbour distribution of distances in crystals from extended X-ray absorption fine structure.

Extended X-ray absorption fine structure (EXAFS) is a powerful probe of the distribution of nearest-neighbour distances around selected atomic species. We consider here the effect of vibrational disorder in crystals. The potential of EXAFS for the accurate evaluation of the coefficient of bond thermal expansion and its temperature dependence is discussed, with the aim of stimulating and facilitating the comparison with the results from total scattering experiments. The meaning of the distribution asymmetry in crystals and its connection with the effective potential anharmonicity and the bond expansion is quantitatively explored by comparing the results for a number of different systems. The extent of the relative atomic vibrations perpendicular to the bond direction and the perpendicular to parallel anisotropy are correlated with the extent of lattice negative thermal expansion as well as with the ionic mobility in superionic crystals.

Thermoluminescence glow curves in preheated feldspar samples: An interpretation based on random defect distributions

Thermoluminescence (TL) glow curves from feldspar samples have been studied extensively in luminescence dating and dosimetry applications. However, the mechanism responsible for their unusual shape and behavior in preheated samples is not well understood. This paper presents new experimental TL glow curves for four types of preheated feldspar samples; an orthoclase, a sanidine and two microclines. Both the preheat temperature and the duration of the preheat are varied, before measurement of the remnant TL glow curve. Kinetic analysis of the experimental results is carried out using a recently proposed physical kinetic model which describes localized electronic recombination in a random distribution of donor-acceptor pairs, with nearest-neighbor interaction. The experimental data are analyzed using two different methods within the model. In the first method one follows the development of the distribution of nearest neighbor distances for each of the four stages of the experiment, namely irradiation followed by heating to a temperature and holding the sample at this temperature for certain time, and finally measurement of the TL glow curve. In the second method the TL glow curves are analyzed by using a single adjustable parameter in the model, which characterizes the thermal history of the sample. Good agreement is found between the two methods. However, the second method is much simpler to use in practical situations, and in principle it can be applied for any thermally or optically pretreated feldspar sample.

Differentiating induced and natural seismicity using space‐time‐magnitude statistics applied to the Coso Geothermal field

AbstractA remarkable characteristic of earthquakes is their clustering in time and space, displaying their self‐similarity. It remains to be tested if natural and induced earthquakes share the same behavior. We study natural and induced earthquakes comparatively in the same tectonic setting at the Coso Geothermal Field. Covering the preproduction and coproduction periods from 1981 to 2013, we analyze interevent times, spatial dimension, and frequency‐size distributions for natural and induced earthquakes. Individually, these distributions are statistically indistinguishable. Determining the distribution of nearest neighbor distances in a combined space‐time‐magnitude metric, lets us identify clear differences between both kinds of seismicity. Compared to natural earthquakes, induced earthquakes feature a larger population of background seismicity and nearest neighbors at large magnitude rescaled times and small magnitude rescaled distances. Local stress perturbations induced by field operations appear to be strong enough to drive local faults through several seismic cycles and reactivate them after time periods on the order of a year.

The patterning of retinal horizontal cells: normalizing the regularity index enhances the detection of genomic linkage.

Retinal neurons are often arranged as non-random distributions called “mosaics,” as their somata minimize proximity to neighboring cells of the same type. The horizontal cells serve as an example of such a mosaic, but little is known about the developmental mechanisms that underlie their patterning. To identify genes involved in this process, we have used three different spatial statistics to assess the patterning of the horizontal cell mosaic across a panel of genetically distinct recombinant inbred strains. To avoid the confounding effect of cell density, which varies twofold across these different strains, we computed the “real/random regularity ratio,” expressing the regularity of a mosaic relative to a randomly distributed simulation of similarly sized cells. To test whether this latter statistic better reflects the variation in biological processes that contribute to horizontal cell spacing, we subsequently compared the genomic linkage for each of these two traits, the regularity index, and the real/random regularity ratio, each computed from the distribution of nearest neighbor (NN) distances and from the Voronoi domain (VD) areas. Finally, we compared each of these analyses with another index of patterning, the packing factor. Variation in the regularity indexes, as well as their real/random regularity ratios, and the packing factor, mapped quantitative trait loci to the distal ends of Chromosomes 1 and 14. For the NN and VD analyses, we found that the degree of linkage was greater when using the real/random regularity ratio rather than the respective regularity index. Using informatic resources, we narrowed the list of prospective genes positioned at these two intervals to a small collection of six genes that warrant further investigation to determine their potential role in shaping the patterning of the horizontal cell mosaic.

Dissociation and the Development of Spatial Correlation in a Molecular Ultracold Plasma

Penning ionization initiates the evolution of a dense molecular Rydberg gas to plasma. This process selects for pairs of excited molecules separated by a distance of two Rydberg orbital diameters or less. The deactivated Penning partners predissociate, depleting the leading edge of the distribution of nearest-neighbor distances. For certain density and orbital radii, this sequence of events can form a plasma in which large distances separate a disproportionate fraction of the ions. Experimental results and model calculations suggest that the reduced potential energy of this Penning lattice significantly affects the development of strong coupling in an ultracold plasma.

Effects of aging and gender on the spatial organization of nuclei in single human skeletal muscle cells

The skeletal muscle fibre is a syncitium where each myonucleus regulates the gene products in a finite volume of the cytoplasm, i.e., the myonuclear domain (MND). We analysed aging- and gender-related effects on myonuclei organization and the MND size in single muscle fibres from six young (21-31 years) and nine old men (72-96 years), and from six young (24-32 years) and nine old women (65-96 years), using a novel image analysis algorithm applied to confocal images. Muscle fibres were classified according to myosin heavy chain (MyHC) isoform expression. Our image analysis algorithm was effective in determining the spatial organization of myonuclei and the distribution of individual MNDs along the single fibre segments. Significant linear relations were observed between MND size and fibre size, irrespective age, gender and MyHC isoform expression. The spatial organization of individual myonuclei, calculated as the distribution of nearest neighbour distances in 3D, and MND size were affected in old age, but changes were dependent on MyHC isoform expression. In type I muscle fibres, average NN-values were lower and showed an increased variability in old age, reflecting an aggregation of myonuclei in old age. Average MND size did not change in old age, but there was an increased MND size variability. In type IIa fibres, average NN-values and MND sizes were lower in old age, reflecting the smaller size of these muscle fibres in old age. It is suggested that these changes have a significant impact on protein synthesis and degradation during the aging process.

Evidence of Antiblockade in an Ultracold Rydberg Gas

We present the experimental observation of the antiblockade in an ultracold Rydberg gas recently proposed by Ates et al. [Phys. Rev. Lett. 98, 023002 (2007)]. Our approach allows the control of the pair distribution in the gas and is based on a strong coupling of one transition in an atomic three-level system, while introducing specific detunings of the other transition. When the coupling energy matches the interaction energy of the Rydberg long-range interactions, the otherwise blocked excitation of close pairs becomes possible. A time-resolved spectroscopic measurement of the Penning ionization signal is used to identify slight variations in the Rydberg pair distribution of a random arrangement of atoms. A model based on a pair interaction Hamiltonian is presented which well reproduces our experimental observations and allows one to deduce the distribution of nearest-neighbor distances.

Clustering and nearest neighbour distances in atom-probe tomography

The measurement of chemical composition of tiny clusters is a tricky problem in both atom-probe tomography experiments and atomic simulations. A new approach relying on the distribution of the first nearest neighbour (1NN) distances between solute atoms in the 3D space composed of A and B atoms was developed. This new approach, the 1NN method, is shown to be an elegant way to get the composition of tiny B-enriched clusters embedded in a random AB solid solution. The theoretical statistical distributions of first neighbour distances P( r) for both random solid solution and solute-enriched clusters finely dispersed in a depleted matrix are established. It is shown that the most probable distance of P( r) gives directly the phase composition. Applications of this model to both one-phase SiGe alloy and boron-doped silicon containing small clusters indicate that this new approach is quite reliable.

Analysis of polygonal terrain landforms on Earth and Mars through spatial point patterns

AbstractIn this paper, we explain the successive steps by which spatial point pattern analysis (SPPA) can be used to describe the variety of polygonal terrain morphologies observed both on Earth and on Mars. In this context, a point is defined as a polygon trough intersection with identifiable spatial coordinates. This definition corresponds to a key step in our approach: obtaining observed 2‐D spatial point patterns from digitized images. The distribution of nearest‐neighbor (NN) distances provides the quantitative basis sought to characterize objectively the overall polygonal network geometry as completely random, regular, or intermediate. In the cases of regular geometry, the distribution of NN distances can be advantageously modeled, which completes the effectiveness of the statistical approach and method based on SPPA. Copyright © 2008 John Wiley & Sons, Ltd.

STATISTICAL INFERENCE USING THEGORKPOINT PATTERN SPATIAL STATISTICS

Spatial point pattern analysis provides a statistical method to compare an observed spatial pattern against a hypothesized spatial process model. The G statistic, which considers the distribution of nearest neighbor distances, and the K statistic, which evaluates the distribution of all neighbor distances, are commonly used in such analyses. One method of employing these statistics involves building a simulation envelope from the result of many simulated patterns of the hypothesized model. Specifically, a simulation envelope is created by calculating, at every distance, the minimum and maximum results computed across the simulated patterns. A statistical test is performed by evaluating where the results from an observed pattern fall with respect to the simulation envelope. However, this method, which differs from P. Diggle's suggested approach, is invalid for inference because it violates the assumptions of Monte Carlo methods and results in incorrect type I error rate performance. Similarly, using the simulation envelope to estimate the range of distances over which an observed pattern deviates from the hypothesized model is also suspect. The technical details of why the simulation envelope provides incorrect type I error rate performance are described. A valid test is then proposed, and details about how the number of simulated patterns impacts the statistical significance are explained. Finally, an example of using the proposed test within an exploratory data analysis framework is provided.

Trade-offs between social behaviour and foraging by sheep in heterogeneous pastures

In heterogeneous pastures, groups of sheep may have to alter their social behaviour in order to graze patches of preferred vegetation. In this event, patch size, inter-patch distance and the contrast between patch and background vegetation are likely to affect behaviour. In this experiment, groups of five female Scottish Blackface sheep grazed for 2-h periods in 0.1ha grass plots containing seven 1.5mx1.5m patches of improved vegetation, with inter-patch distances of 1.5, 6 or 11.5m. Background vegetation was of either medium or poor quality. Control plots contained no patches. On average, sheep spent 44% of the time grazing patches, although patches comprised only 1.6% of the total plot area. Inter-patch distance did not affect accumulated time spent grazing patches during the first 30min, but patch residence time and the number of sheep on a patch increased with inter-patch distance. The distribution of nearest neighbour distances was altered when patches were 6 or 11.5m apart, compared to no patches. Accumulated time spent grazing patches and the number of sheep on a patch were greater with poor than medium backgrounds. Sheep visited patches frequently and for short periods and it is suggested that sheep often moved off patches as a result of competition. The results provide evidence that sheep make trade-offs between social and foraging behaviour and demonstrate the importance of interactions between social spacing and the size and spacing of vegetation patches, when sheep forage in heterogeneous pastures.