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A theoretical model is proposed in this work for the evaluation of composition‐dependent thermophysical properties such as the isothermal compressibility, velocity of sound and Debye temperature of liquid binary alloys. Using a square‐well (SW) model potential function under mean spherical model approximation, the composition‐dependent atomic‐level structural functions of Al1‐xCux, Ag1‐xCux, Au1‐xCux, Ag1‐xAlx, and Au1‐xAgx alloys have been determined and compared with available experimental data. An extensive computation was done to calculate the composition‐dependent isothermal compressibility through the structure factor in the long wavelength limit (k→0), and then we employed this data to investigate the velocity of sound in the considered melts. This yields the fundamental maximum frequency with which the constituent particles are vibrating in the melts and is used to determine the composition‐dependent Debye temperature, ΘD. The computed Debye temperature of considered melts using the Square‐well potential function is found to be in satisfactory agreement with the available DFT and MD simulation results. [ABSTRACT FROM AUTHOR]

We give details and derivations for the Noether invariance theory that characterizes the spatial equilibrium structure of inhomogeneous classical many-body systems, as recently proposed and investigated for bulk systems (Sammüller et al 2023 Phys. Rev. Lett. 130 268203). Thereby an intrinsic thermal symmetry against a local shifting transformation on phase space is exploited on the basis of the Noether theorem for invariant variations. We consider the consequences of the shifting that emerge at second order in the displacement field that parameterizes the transformation. In a natural way the standard two-body density distribution is generated. Its second spatial derivative is thereby balanced by two further and different two-body correlation functions, which respectively introduce thermally averaged force correlations and force gradients in a systematic and microscopically sharp way into the framework. Separate exact self and distinct sum rules express this balance. We exemplify the validity of the theory on the basis of computer simulations for the Lennard–Jones gas, liquid, and crystal, the Weeks–Chandler–Andersen fluid, monatomic Molinero–Moore water at ambient conditions, a three-body-interacting colloidal gel former, the Yukawa and soft-sphere dipolar fluids, and for isotropic and nematic phases of Gay–Berne particles. We describe explicitly the derivation of the sum rules based on Noether's theorem and also give more elementary proofs based on partial phase space integration following Yvon's theorem. [ABSTRACT FROM AUTHOR]

Analyzing the spatial patterns and associations among tree species may help to elucidate the importance of the ecological processes behind population formation and the mechanisms of species coexistence. To explore this mechanism, we mapped and studied eight dominant tree species in Korean pine broad-leaved mixed forests in a temperate forest region in Jilin Province, Northeast China. The spatial distribution patterns and spatial associations of the eight dominant tree species at different life history stages and spatial scales were analyzed using the second-order spatial point pattern method based on pair correlation functions. The results indicated the following: (1) The diameter class structure of all individuals in the plots showed an obvious "L" shape, indicating that the community was well regenerated and belonged to a growing stand. (2) The distribution of trees was affected by scale, size, and habitat heterogeneity. The degree of aggregation decreased as the diameter class increased. (3) Out of the 56 pairs of individuals, a small number showed a significant correlation, while most were negatively correlated. It is concluded that seed dispersal limitations, competitive ability, and topography and light requirements may influence the spatial distribution and association of species to maintain species coexistence and diversity in Korean pine broad-leaved mixed forests. The results can provide insights into the ecological processes of population assembly, the mechanisms of species coexistence, and the relationship between forest management and restoration. [ABSTRACT FROM AUTHOR]

Abstract Plants interact locally in many ways and the processes involved (e.g. competition for resources, natural regeneration, mortality or subsequent succession) are complex. These processes give rise to characteristic spatial patterns that vary over time. The corresponding spatial data, that is the locations of individuals and their specific characteristics (e.g. trees of a certain species and their diameters), are known as point patterns, and their statistical analysis can be used to study the underlying processes and their changes due to environmental scenarios. A special application of point pattern analysis is their numerical reconstruction, which is classically used (a) to generate null models that can be contrasted with observed patterns and (b) to evaluate the information contained in observed data using various summary statistics. Sometimes, the reconstructed datasets are also used to initialise individual‐based or agent‐based plant models with realistic but artificially generated data in order to analyse or forecast the development of plant systems. Previous reconstruction methods of point patterns consider only one mark, or they consider several marks but neglect their correlations. We introduce a method that considers individual locations and two marks simultaneously (in our example information on tree species, and diameter at breast height). The method uses different summary statistics of the second‐order point pattern analysis, such as the pair correlation function and the mark correlation function. By successively modifying the reconstructed spatial pattern, the distance (also called energy), measured in terms of differences in the summary statistics between the generated pattern and the observed pattern, is minimised and a high statistical similarity is achieved. After testing the method on different datasets, the suitability of our method for reconstructing complex spatial forest stands, including the spatial relationships of all considered marks, is shown. The presented method is a powerful tool for generating point pattern data. With minor changes, it even enables the reconstruction of forest stands and plant systems larger than those used to collect the inventory data, and although we used two marks only to demonstrate the power of the method, it is easy to include more marks.

Vanadium-based solid solution alloys potentially serve as safe, high-capacity hydrogen storage materials. Low-vanadium-concentration alloys have low durability, and their hydrogen absorption and desorption amounts decrease by 20 % after 100 cycles. In this study, we conducted reverse Monte Carlo modeling on X-ray diffraction patterns and neutron pair distribution functions of the hydrogen-absorbed and desorbed samples of a V 0.10 Ti 0.36 Cr 0.54 alloy to analyze the variations in the local structure. The local structure surrounding the hydrogen atom in the hydrogen-absorbed phase exhibited minimal changes. In contrast, hydrogen occupied both tetrahedral and octahedral sites of the hydrogen-desorbed phase almost equally during the early cycles; however, the amount of hydrogen occupying the tetrahedral sites increased with the number of cycles. It is speculated that hydrogen absorption and desorption cycling induced grain refinement and/or introduced dislocations, which altered both the amount of hydrogen and the sites occupied in the desorbed phase, thereby decreasing the hydrogen storage capacity. [Display omitted] • Degradation mechanism of V–Ti–Cr hydrogen storage alloy revealed by local structure. • Decrease in hydrogen storage consistent with PDF refinements and p – c isotherms. • Cr–H and Ti–H correlations reproduced by a large atomic ensemble in RMC modeling. • Change in hydrogen occupation positions supplemented by inelastic neutron scattering. [ABSTRACT FROM AUTHOR]

The configuration of trees and their interplay offer vital perspectives into a forest community's spatial structure and plant species' coexistence mechanisms. This study aimed to investigate the spatial patterns and interactions of woody plant species in an evergreen broadleaved forest on the Con Dao Islands, Vietnam. A 4-ha study plot was established in 2022, and all trees with a diameter breast height (DBH) ≥ 5 cm were measured, identified species, and mapped. The spatial point pattern analysis method was employed to explore the spatial distribution and interactions of woody plant species in the study plot. The findings indicated that saplings (DBH < 10 cm) were mainly aggregated at a small scale of 0–10 m, whereas intermediate (10 cm ≤ DBH ≤ 20 cm) and adult (DBH > 20 cm) trees were randomly distributed. Species-area relationships and spatial patterns varied according to the life-history stages of each species and spatial scales. The results also suggested that species coexistence within the plant community was achieved through the overall effects of the diversity accumulator species, diversity repeller species, and neutral species. The ecological niche theory, unified neutral theory, and asymmetric competition principle were deemed appropriate for explaining the coexistence of woody plant species in the evergreen broadleaved forest on Con Dao Islands, Vietnam. [ABSTRACT FROM AUTHOR]

This work focuses on kernel estimation of the pair correlation function (PCF) for inhomogeneous spatial point processes. We propose a bootstrap bandwidth selector based on minimizing the mean integrated squared error (MISE). The variance term is estimated by nonparametric bootstrap, and the bias by a plug-in approach using a pilot estimator of the PCF. Kernel estimators of the PCF also require a pilot estimator of the first-order intensity. We test the performance of the bandwidth selector and the role of the pilot intensity estimator in a simulation study. The bootstrap bandwidth selector is competitive with cross-validation procedures, but the contribution of the bandwidth parameter to the goodness-of-fit of the kernel PCF estimator is minor in comparison with that of the pilot intensity function. The data-based kernel intensity estimator leads to biased kernel PCF estimators, while both kernel and parametric covariate-based intensities provide accurate estimators of the PCF. [ABSTRACT FROM AUTHOR]

Imaging platforms for generating highly multiplexed histological images are being continually developed and improved. Significant improvements have also been made in the accuracy of methods for automated cell segmentation and classification. However, less attention has focused on the quantification and analysis of the resulting point clouds, which describe the spatial coordinates of individual cells. We focus here on a particular spatial statistical method, the cross-pair correlation function (cross-PCF), which can identify positive and negative spatial correlation between cells across a range of length scales. However, limitations of the cross-PCF hinder its widespread application to multiplexed histology. For example, it can only consider relations between pairs of cells, and cells must be classified using discrete categorical labels (rather than labeling continuous labels such as stain intensity). In this paper, we present three extensions to the cross-PCF which address these limitations and permit more detailed analysis of multiplex images: topographical correlation maps can visualize local clustering and exclusion between cells; neighbourhood correlation functions can identify colocalization of two or more cell types; and weighted-PCFs describe spatial correlation between points with continuous (rather than discrete) labels. We apply the extended PCFs to synthetic and biological datasets in order to demonstrate the insight that they can generate.

Plants interact locally in many ways and the processes involved (e.g. competition for resources, natural regeneration, mortality or subsequent succession) are complex. These processes give rise to characteristic spatial patterns that vary over time. The corresponding spatial data, that is the locations of individuals and their specific characteristics (e.g. trees of a certain species and their diameters), are known as point patterns, and their statistical analysis can be used to study the underlying processes and their changes due to environmental scenarios. A special application of point pattern analysis is their numerical reconstruction, which is classically used (a) to generate null models that can be contrasted with observed patterns and (b) to evaluate the information contained in observed data using various summary statistics. Sometimes, the reconstructed datasets are also used to initialise individual‐based or agent‐based plant models with realistic but artificially generated data in order to analyse or forecast the development of plant systems.Previous reconstruction methods of point patterns consider only one mark, or they consider several marks but neglect their correlations. We introduce a method that considers individual locations and two marks simultaneously (in our example information on tree species, and diameter at breast height). The method uses different summary statistics of the second‐order point pattern analysis, such as the pair correlation function and the mark correlation function. By successively modifying the reconstructed spatial pattern, the distance (also called energy), measured in terms of differences in the summary statistics between the generated pattern and the observed pattern, is minimised and a high statistical similarity is achieved.After testing the method on different datasets, the suitability of our method for reconstructing complex spatial forest stands, including the spatial relationships of all considered marks, is shown.The presented method is a powerful tool for generating point pattern data. With minor changes, it even enables the reconstruction of forest stands and plant systems larger than those used to collect the inventory data, and although we used two marks only to demonstrate the power of the method, it is easy to include more marks. [ABSTRACT FROM AUTHOR]

Specification of a parametric model for the intensity function is a fundamental task in statistics for spatial point processes. It is, therefore, crucial to be able to assess the appropriateness of a suggested model for a given point pattern dataset. For this purpose, we develop a new class of semiparametric goodness-of-fit tests for the specified parametric first-order intensity, without assuming a full data generating mechanism that is needed for the existing popular Monte Carlo tests. The proposed tests crucially rely on accurate nonparametric estimation of the second-order properties of a point process. To address this we propose a new nonparametric pair correlation function (PCF) estimator for clustered spatial point processes under some mild shape constraints, which is shown to achieve uniform consistency. The proposed test statistics are computationally efficient owing to closed-form asymptotic distributions and achieve the nominal size even for testing composite hypotheses. In practice, the proposed estimation and testing procedures provide effective tools to improve parametric intensity function modeling, which is demonstrated through extensive simulation studies as well as a real data analysis of street crime activity in Washington DC. for this article are available online. [ABSTRACT FROM AUTHOR]

Investigating the spatial distributions and associations of tree populations provides better insights into the dynamics and processes that shape the forest community. Korean pine (Pinus koraiensis) is one of the most important tree species in broad-leaved Korean pine mixed forests (BKMFs), and little is known about the spatial point patterns of and associations between Korean pine and community-level woody species groups such as coniferous and deciduous trees in different developmental stages. This study investigated the spatial patterns of Korean pine (KP) trees and then analyzed how the spatial associations between KP trees and other tree species at the community level vary in different BKMFs. Extensive data collected from five relatively large sample plots, covering a substantial area within the natural distribution range of KP in northeastern China, were utilized. Uni- and bivariate pair correlation functions and mark correlation functions were applied to analyze spatial distribution patterns and spatial associations. The DBH (diameter at breast height) histogram of KP trees in northeastern China revealed that the regeneration process was very poor in the Changbai Mountain (CBS) plot, while the other four plots exhibited moderate or expanding population structures. KP trees were significantly aggregated at scales up to 10 m under the HPP null model, and the aggregation scales decreased with the increase in size classes. Positive or negative spatial associations were observed among different life stages of KP trees in different plots. The life history stages of the coniferous tree group showed positive spatial associations with KP saplings and juvenile trees at small scales, and spatial independence or negative correlations with larger KP trees at greater scales. All broad-leaved tree groups (canopy, middle, and understory layers) exhibited only slightly positive associations with KP trees at small scales, and dominant negative associations were observed at most scales. Our results demonstrate that mature KP trees have strong importance in the spatial patterns of KP populations, and site heterogeneity, limited seed dispersal, and interspecific competition characterize the spatial patterns of KP trees and community-level spatial associations with respect to KP trees, which can serve as a theoretical basis for the management and restoration of BKMFs in northeastern China. [ABSTRACT FROM AUTHOR]

We present a comprehensive study shedding light on how thermal fluctuations affect correlations in a Bose gas with contact repulsive interactions in one spatial dimension. The pair correlation function, the static structure factor, and the one-body density matrix are calculated as a function of the interaction strength and temperature with the exact ab-initio Path Integral Monte Carlo method. We explore all possible gas regimes from weak to strong interactions and from low to high temperatures. We provide a detailed comparison with a number of theories, such as perturbative (Bogoliubov and decoherent classical), effective (Luttinger liquid) and exact (ground-state and thermal Bethe Ansatz) ones. Our Monte Carlo results exhibit an excellent agreement with the tractable limits and provide a fundamental benchmark for future observations which can be achieved in atomic gases, cavity quantum-electrodynamic and superconducting-circuit platforms. [ABSTRACT FROM AUTHOR]

A fundamental problem of the optical diagnostics of the supercritical fluid (SF) structure and its statistical properties in the vicinity of the Widom line is considered. The solution of this problem requires approaches that allow us to bring the peculiarities of optical measurement data in line with the peculiarities of the state of the fluid. The results obtained in the past ten years on the problem of the Widom lines in nonpolar supercritical media are briefly reviewed. Particular attention is given to the optical measurement data in the Widom region, namely, measurements of the nonlinear contribution to the refractive index and measurements of the Rayleigh light scattering intensity. It is demonstrated that these data can serve as a base for mutually complementary methods for the optical diagnostics of an SF state. As an example, the data on small-angle light scattering by SF-CO2 were used to restore its pair correlation function, the temperature dependence of which fundamentally differs from that of the Ornstein–Zernike pair correlation function. It is noted that the method based on measuring the Rayleigh scattering intensity is general in nature and can be applied to any random unordered molecular media, including the atmosphere. [ABSTRACT FROM AUTHOR]

Background and aims – Understanding the spatial patterns and associations of tree species with their conspecific and heterospecific neighbours is critical for sustainable management of their stands. This study assessed the intra- and interspecific spatial structure of six life stages in Afzelia africana, a keystone multipurpose and endangered tree species in a tropical savanna of Benin.Material and methods – Three plots of 4 ha each were demarcated on three sites along a conservation gradient (hunting zone – core conservation zone). Individuals of A. africana (irrespective of their diameter at breast height) and heterospecific trees (dbh ≥ 5 cm) were mapped. Tree spatial patterns and associations were determined using univariate and bivariate pair correlation functions. The distance to the nearest neighbour was further used to assess tree-to-tree distance.Key results – We found variable spatial patterns across sites. In the core zone where wildlife density is high, most life stages had a random distribution. In contrast, in the hunting zone where wildlife density is low, the species spatial distribution changed from a predominantly aggregative pattern during early stages to a less aggregative or random spatial pattern for very large adults. Most pairs of life stages showed neutral associations, except for small and large adults, which had positive association between themselves on two sites. We also found that A. africana tree spatial distribution was unrelated to heterospecific trees.Conclusion – We suggest that bush fire, seed dispersion, predation, and local environment would have contributed to the observed patterns.

Investigating the spatial distributions and associations of tree populations provides better insights into the dynamics and processes that shape the forest community. Korean pine (Pinus koraiensis) is one of the most important tree species in broad-leaved Korean pine mixed forests (BKMFs), and little is known about the spatial point patterns of and associations between Korean pine and community-level woody species groups such as coniferous and deciduous trees in different developmental stages. This study investigated the spatial patterns of Korean pine (KP) trees and then analyzed how the spatial associations between KP trees and other tree species at the community level vary in different BKMFs. Extensive data collected from five relatively large sample plots, covering a substantial area within the natural distribution range of KP in northeastern China, were utilized. Uni- and bivariate pair correlation functions and mark correlation functions were applied to analyze spatial distribution patterns and spatial associations. The DBH (diameter at breast height) histogram of KP trees in northeastern China revealed that the regeneration process was very poor in the Changbai Mountain (CBS) plot, while the other four plots exhibited moderate or expanding population structures. KP trees were significantly aggregated at scales up to 10 m under the HPP null model, and the aggregation scales decreased with the increase in size classes. Positive or negative spatial associations were observed among different life stages of KP trees in different plots. The life history stages of the coniferous tree group showed positive spatial associations with KP saplings and juvenile trees at small scales, and spatial independence or negative correlations with larger KP trees at greater scales. All broad-leaved tree groups (canopy, middle, and understory layers) exhibited only slightly positive associations with KP trees at small scales, and dominant negative associations were observed at most scales. Our results demonstrate that mature KP trees have strong importance in the spatial patterns of KP populations, and site heterogeneity, limited seed dispersal, and interspecific competition characterize the spatial patterns of KP trees and community-level spatial associations with respect to KP trees, which can serve as a theoretical basis for the management and restoration of BKMFs in northeastern China.

Termite mounds contribute to the heterogeneity and productivity of many semi‐arid ecosystems worldwide. Regular spatial patterns of termite mounds are well documented but the underlying pattern‐building mechanisms remain to be clarified. This study analysed a comprehensive data set of Macrotermes michaelseni mound metrics, spatial patterns and dynamics, recorded 12 years apart within 1 km2 of Namibian thornbush savanna. We used both unmarked and marked point pattern analyses to assess spatial distributions of termite mounds. We recorded 485 termite mounds in 2007 and 2019. Out of the investigated 142 active termite mounds in 2007, 81 were active 12 years later. Only 2% (n = 3/129) of remnant mound sites in 2007 were newly colonised in 2019. All mounds were distributed at regular distances. Mounds higher than 2 m and long‐term active mounds (active in 2007 and 2019) showed high regularity. Mounds up to 0.7 m height and new mounds occurred in clusters and showed a spatial repulsion to large and long‐term active colonies. The spatial distribution of Boscia albitrunca trees generally clustered around termite mounds, but did not cluster around young colonies. The results contradict the hypothesis of preferred colony settlement on previously inhabited mound sites. Remnant mounds are relatively unlikely to be recolonised when recently abandoned. The observed spatial patterns show that intraspecific competition between large colonies is the decisive factor for regular spatial patterns of termite colonies, whereas small and young colonies are limited to unoccupied patches. Surrounding trees are a pattern‐building factor of only secondary importance. The spatio‐temporal scale in our study reveals general trends of termite mound life histories and spatial pattern‐building mechanisms. Availability of not previously inhabited sites form the patterns of founding new colonies. Well‐established mounds are highly regulated by intraspecific competition. This highlights that termites contribute to ecosystem heterogeneity through self‐organised spatial regularity. [ABSTRACT FROM AUTHOR]

We study the analogue of the Montgomery's pair correlation function F (α) for a family of Γ 1 (q) L-functions. Assuming the Generalized Riemann Hypothesis, we evaluate this analogous pair correlation function in the range | α | < 2 , where the off-diagonal terms also contribute to the main term. As applications, we obtain that more than 93.5% of the low-lying zeros of Γ 1 (q) L-functions are simple, and we achieve upper and lower bounds for the number of pairs of zeros which are closer than β times the average spacing apart. [ABSTRACT FROM AUTHOR]

The inverse Henderson problem refers to the determination of the pair potential which specifies the interactions in an ensemble of classical particles in continuous space, given the density and the equilibrium pair correlation function of these particles as data. For a canonical ensemble in a bounded domain, it has been observed that this pair potential minimizes a corresponding convex relative entropy functional, and that the Newton iteration for minimizing this functional coincides with the so-called inverse Monte Carlo (IMC) iterative scheme. In this paper, we show that in the thermodynamic limit analogous connections exist between the specific relative entropy introduced by Georgii and Zessin and a proper formulation of the IMC iteration in the full space. This provides a rigorous variational framework for the inverse Henderson problem, valid within a large class of pair potentials, including, for example, Lennard-Jones-type potentials. It is further shown that the pressure is strictly convex as a function of the pair potential and the chemical potential, and that the specific relative entropy at fixed density is a strictly convex function of the pair potential. At a given reference potential and a corresponding density in the gas phase, we determine the gradient and the Hessian of the specific relative entropy, and we prove that the Hessian extends to a symmetric positive semidefinite quadratic functional in the space of square integrable perturbations of this potential. [ABSTRACT FROM AUTHOR]

[Display omitted] Reverse Monte Carlo (RMC) simulations are widely used to reconstruct 3-dimensional (3D) metallic glass (MG) structure from neutron/X-ray diffraction data, but their reliability is debated. Here, we employ RMC to simulate a Zr 50 Cu 50 MG's structure using two types of "experimental" inputs as constraints, one with a total pair correlation function (TPCF) and the other with 3 partial PCFs (PPCFs), all of which were generated from a 3D glass structure obtained from molecular dynamics (MD) simulations of the same alloy. This MD-generated structure is then used as a benchmark to evaluate RMC's accuracy. Notably, both methods can replicate the MG's TPCFs, and total bond-angle/bond-length distributions. However, only the PPCFs-constrained RMC is able to re-produce the local structure, as manifested by nearly replicated partial bond-length/bond-angle distributions, partial coordination numbers, atomic volume, etc. This work demonstrates that PPCFs can impose stricter constraints than a TPCF does, significantly improving the reliability of RMC simulations. [ABSTRACT FROM AUTHOR]

A study is performed of the feasibility of consequences from the Bogolyubov–Born–Green (BBG) equation for fluids and amorphous bodies with hybrid potentials of a certain type ("B-theorem"). Using liquid thallium as an example, it is shown that with a fluid having a multiparticle embedded atom model (EAM) potential, the B-theorem is valid for moderate values of the parameter of hybridization, as it is for pair potentials. The reason for this feasibility is that the EAM potential at a given temperature is equivalent to an effective pair potential for liquids with a dense structure, due to the BBG equation. [ABSTRACT FROM AUTHOR]

Populus euphratica Oliv. (Euphrates poplar), as the dominant tree species of desert riparian forests along the Central Asian inland rivers, plays a critical role in protecting arid land ecosystems. In recent decades, climate change and excessive water resources utilization activities have led to the environmental degradation of desert riparian forests along the Tarim River in northwest China. Understanding the forest stand structure and spatial distribution pattern provide important guidance for monitoring forest dynamics in support of sustainable management. However, few studies have examined how riparian forests stand attributes differ in response to environmental heterogeneity. In this study, terrestrial laser scanning (TLS) was applied to acquire a total of 1648 individual P. euphratica tree's 3D structure attributes within 18 plots along the upper, middle, and lower reaches of the Tarim River, which included tree height (TH), diameter at breast height (DBH), crown diameter (CD), crown projection area (CPA), stand density index (SDI), age structure ratios, and spatial pattern. The results showed that the average tree segmentation and structure determination accuracies of TLS were 93.2 and 94.6%. From the upper to the lower reaches, the average TH and CD decreased by 3.8 and 0.3 m, while the DBH increased by 4.2 cm. The SDI and CPA exhibited the following order: upper reaches (454 n ha–1, 82.3%) > middle reaches (382 n ha–1, 67.3%) > lower reaches (263 n ha–1, 39.1%), the differences were significant at 0.05 level. The population age structure changed from growing population in the upper reaches to stable population in the middle and a temporarily stable population in the lower reaches. The pair correlation g(r) function determined random distribution pattern in the upper reaches [g(r) = 1.2], an aggregated pattern in the middle [g(r) = 3.1], and lower reaches [g(r) = 9.7]. The decline in groundwater depth and soil moisture increased aggregated distribution pattern (R = 0.67 and 0.56, P < 0.05) of the P. euphratica along the mainstream of Tarim River. The results enrich our understanding of the current development stage of P. euphratica , which is important for optimizing management strategies and realizing the sustainability of floodplain ecosystems. [ABSTRACT FROM AUTHOR]

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Populus euphratica Oliv. (Euphrates poplar), as the dominant tree species of desert riparian forests along the Central Asian inland rivers, plays a critical role in protecting arid land ecosystems. In recent decades, climate change and excessive water resources utilization activities have led to the environmental degradation of desert riparian forests along the Tarim River in northwest China. Understanding the forest stand structure and spatial distribution pattern provide important guidance for monitoring forest dynamics in support of sustainable management. However, few studies have examined how riparian forests stand attributes differ in response to environmental heterogeneity. In this study, terrestrial laser scanning (TLS) was applied to acquire a total of 1648 individual P. euphratica tree’s 3D structure attributes within 18 plots along the upper, middle, and lower reaches of the Tarim River, which included tree height (TH), diameter at breast height (DBH), crown diameter (CD), crown projection area (CPA), stand density index (SDI), age structure ratios, and spatial pattern. The results showed that the average tree segmentation and structure determination accuracies of TLS were 93.2 and 94.6%. From the upper to the lower reaches, the average TH and CD decreased by 3.8 and 0.3 m, while the DBH increased by 4.2 cm. The SDI and CPA exhibited the following order: upper reaches (454 n ha–1, 82.3%) > middle reaches (382 n ha–1, 67.3%) > lower reaches (263 n ha–1, 39.1%), the differences were significant at 0.05 level. The population age structure changed from growing population in the upper reaches to stable population in the middle and a temporarily stable population in the lower reaches. The pair correlation g(r) function determined random distribution pattern in the upper reaches [g(r) = 1.2], an aggregated pattern in the middle [g(r) = 3.1], and lower reaches [g(r) = 9.7]. The decline in groundwater depth and soil moisture increased aggregated distribution pattern (R = 0.67 and 0.56, P < 0.05) of the P. euphratica along the mainstream of Tarim River. The results enrich our understanding of the current development stage of P. euphratica, which is important for optimizing management strategies and realizing the sustainability of floodplain ecosystems.

The effects of parameters used for tuning the interionic pair interaction of the Ashcroft's pseudopotential model on the temperature-dependent atomic transport properties of liquid Al have been studied employing the Universal Scaling Laws (USLs) and Hard Sphere (HS) theories of liquid metals. Temperature-dependent effective HS diameter and excess entropy are the key ingredients of the applied theories. We have calculated them by using Ashcroft's empty core (EMC) pseudopotential and the variational modified hypernetted chain (VMHNC) integral equation theory of liquid. Obtained results clearly suggest that the core radius in the interaction plays a major role in determining atomic transport properties of liquid Al for both USLs and HS theory. It is also observed that USLs are more sensitive than HS theories in response to variation of core radius. [ABSTRACT FROM AUTHOR]

This paper introduces a new approach to inferring the second‐order properties of a multivariate log Gaussian Cox process (LGCP) with a complex intensity function. We assume a semi‐parametric model for the multivariate intensity function containing an unspecified complex factor common to all types of points. Given this model, we construct a second‐order conditional composite likelihood to infer the pair correlation and cross pair correlation functions of the LGCP. Crucially this likelihood does not depend on the unspecified part of the intensity function. We also introduce a cross‐validation method for model selection and an algorithm for regularized inference that can be used to obtain sparse models for cross pair correlation functions. The methodology is applied to simulated data as well as data examples from microscopy and criminology. This shows how the new approach outperforms existing alternatives where the intensity functions are estimated non‐parametrically. [ABSTRACT FROM AUTHOR]

Spatial point pattern analysis usually concerns identifying features in an observation window where there is also noise. This identification traditionally begins with studying the second-order properties of the point pattern, and it may be done locally by using local second-order characteristics (LISA). Some properties of this local structure solve the problem of classification into feature and clutter points. This paper proposes an estimator for local pair correlation LISA functions, discusses some of its properties and considers a particular distance to measure dissimilarities. Two classification procedures to separate feature from clutter points are described. One of them adopts multidimensional scaling and support vector machines, and the other employs bagged clustering. Simulations demonstrate the performance of the method, and it is applied to a dataset concerning earthquakes in a seismic nest located in Colombia. [ABSTRACT FROM AUTHOR]

Point processes are popular models for data consisting of a random configuration of points, such as positions of trees of a given species in a forest stand, locations of earthquakes' epicentres or positions of proteins in a cell membrane. Pair correlation function is a functional summary characteristic quantifying the interactions between pairs of points of the process at different distances. In practice, kernel estimators of the pair correlation function are mostly used, which require the user to choose the bandwidth of the smoothing kernel. When looking for the optimal bandwidth, higher order terms of the variance of the estimator are often neglected. We present the detailed formulas for the variance and argue that the higher order terms contribute the most to the variance and should not be ignored. Furthermore, we adapt a well‐known variance approximation formula to accommodate the popular translation edge correction factor. We compare the original and the adjusted approximation formula to the exact variance obtained by numerical integration and to the empirical variance obtained from simulated realizations. We conclude that the variance approximations do not perform well and that modern cross‐validation approaches to bandwidth selection should be preferred in practice. [ABSTRACT FROM AUTHOR]

Microbial life on plant leaves is characterized by a multitude of interactions between leaf colonizers and their environment. While the existence of many of these interactions has been confirmed, their spatial scale or reach often remained unknown. In this study, we applied spatial point pattern analysis to 244 distribution patterns of Pantoea agglomerans and Pseudomonas syringae on bean leaves. The results showed that bacterial colonizers of leaves interact with their environment at different spatial scales. Interactions among bacteria were often confined to small spatial scales up to 5-20 μm, compared to interactions between bacteria and leaf surface structures such as trichomes which could be observed in excess of 100 μm. Spatial point-pattern analyses prove a comprehensive tool to determine the different spatial scales of bacterial interactions on plant leaves and will help microbiologists to better understand the interplay between these interactions.

We present a comprehensive study shedding light on how thermal fluctuations affect correlations in a Bose gas with contact repulsive interactions in one spatial dimension. The pair correlation function, the static structure factor, and the one-body density matrix are calculated as a function of the interaction strength and temperature with the exact ab-initio Path Integral Monte Carlo method. We explore all possible gas regimes from weak to strong interactions and from low to high temperatures. We provide a detailed comparison with a number of theories, such as perturbative (Bogoliubov and decoherent classical), effective (Luttinger liquid) and exact (ground-state and thermal Bethe Ansatz) ones. Our Monte Carlo results exhibit an excellent agreement with the tractable limits and provide a fundamental benchmark for future observations which can be achieved in atomic gases, cavity quantum-electrodynamic and superconducting-circuit platforms.

Background and aims - Understanding the spatial patterns and associations of tree species with their conspecific and heterospecific neighbours is critical for sustainable management of their stands. This study assessed the intra- and interspecific spatial structure of six life stages in Afzelia africana, a keystone multipurpose and endangered tree species in a tropical savanna of Benin. Material and methods - Three plots of 4 ha each were demarcated on three sites along a conservation gradient (hunting zone - core conservation zone). Individuals of A. africana (irrespective of their diameter at breast height) and heterospecific trees (dbh = 5 cm) were mapped. Tree spatial patterns and associations were determined using univariate and bivariate pair correlation functions. The distance to the nearest neighbour was further used to assess tree-to-tree distance. Key results - We found variable spatial patterns across sites. In the core zone where wildlife density is high, most life stages had a random distribution. In contrast, in the hunting zone where wildlife density is low, the species spatial distribution changed from a predominantly aggregative pattern during early stages to a less aggregative or random spatial pattern for very large adults. Most pairs of life stages showed neutral associations, except for small and large adults, which had positive association between themselves on two sites. We also found that A. africana tree spatial distribution was unrelated to heterospecific trees. Conclusion - We suggest that bush fire, seed dispersion, predation, and local environment would have contributed to the observed patterns. [ABSTRACT FROM AUTHOR]

In this contribution we provide an overview of the recent advances allowed by the use of fluorescence microscopy methods in the study of transcriptional processes and their interplay with the chromatin architecture in living cells. Although the use of fluorophores to label nucleic acids dates back at least to about half a century ago, (1) two recent breakthroughs have effectively opened the way to use fluorescence routinely for specific and quantitative probing of chromatin organization and transcriptional activity in living cells: namely, the possibility of labeling first the chromatin loci and then the mRNA synthesized from a gene using fluorescent proteins. In this contribution we focus on methods that can probe rapid dynamic processes by analyzing fast fluorescence fluctuations.

We describe efficient algorithms and open-source code for the second-order statistical analysis of point events on a linear network. Typical summary statistics are adaptations of Ripley's K-function and the pair correlation function to the case of a linear network, with distance measured by the shortest path in the network. Simple implementations consume substantial time and memory. For an efficient implementation, the data structure representing the network must be economical in its use of memory, but must also enable rapid searches to be made. We have developed such an efficient implementation in C with an R interface written as an extension to the R package spatstat. The algorithms handle realistic large networks, as we demonstrate using a database of all road accidents recorded in Western Australia.

The aim of this study was to determine the spatial pattern and intra-specific interactions of Anagyris foetida shrubs in its unique habitat in the Zagros forests. For this purpose, 1-ha sample plot which is covered by relatively pure Anagyris foetida was established. The spatial location of each individual was calculated using azimuth and distance measurement. Furthermore, the biometric characteristics of the individuals were measured. Then, the spatial pattern of the shrubs were determined using the nearest-neighbor and pair correlation functions. In addition, the spatial correlation of shrubs size was determined using Mark correlation and Mark variogram functions. The measurement of biometric characteristics of shrubs showed that the mean collar diameter, height, crown area and number of sprouts were 5.15cm, 2.36m, 5.6m2 and 12.59, respectively. The density was 231 shrubs per hectare. Based on the results of the spatial pattern analysis, the shrubs were aggregated at small spatial scales and tend to follow random distribution pattern at larger distances although the results of the pair correlation function (g) showed an aggregation at distances 13-17m. The results of the Mark correlation and Mark variogram functions showed no spatial correlation among shrubs for the biometrics characteristics implying that the shrubs arrangement by their size follows complete randomness. It was concluded that although there is a positive interaction (aggregation) in small spatial scales, no specific spatial structure was observed. The size of the shrubs was not spatially correlated and the neighboring shrubs were randomly distributed with different sizes.

Ant community structure in natural and anthropogenic ecosystems depends on the combination of several factors not easy to elucidate according to the complexity of habitat structures and anthropogenic disturbances. We investigated the influence of tree distribution pattern on the spatial distribution of dominant ant species, and the spatial relationship between dominant and associated ant species in secondary forest, cocoa farms, and palm groves at Mfou around Yaoundé city. Nine plots of 30 × 30 m each were set up around the study area including three each from every habitat type. Each plot was mapped and the Cartesian coordinated of each tree was recorded. Ants were collected on the trees using a pitfall trap and visual catch. The spatial distribution pattern of the trees and numerical dominant species were analyzed using Besag's function and spatial relationship between numerical dominant and associated ant species with pair correlation function. Trees distribution fits random models in cocoa farms and secondary forests, while in palm groves they fit regular models. Numerical dominant species also fit the same distribution pattern according to the distribution of the trees in the corresponding habitat. Spatial correlation analysis showed that the establishment of a positive or negative relationship between dominant and associated ant species depends on the distance which separates the nest of the colonies to the foraging area. Around the nest of the colonies, dominant ant species repulse all other ant species despite their territorial defensive behavior and created a safety cord intensively protected. Over this perimeter, the workers invest more in food searching than in the defense of territory and favor the establishment of a positive relationship. [ABSTRACT FROM AUTHOR]

This paper concerns space-sphere point processes, that is, point processes on the product space of ℝ d (the d-dimensional Euclidean space) and S k (the k-dimensional sphere). We consider specific classes of models for space-sphere point processes, which are adaptations of existing models for either spherical or spatial point processes. For model checking or fitting, we present the space-sphere K-function which is a natural extension of the inhomogeneous K-function for point processes on ℝ d to the case of space-sphere point processes. Under the assumption that the intensity and pair correlation function both have a certain separable structure, the space-sphere K-function is shown to be proportional to the product of the inhomogeneous spatial and spherical K-functions. For the presented space-sphere point process models, we discuss cases where such a separable structure can be obtained. The usefulness of the space-sphere K-function is illustrated for real and simulated datasets with varying dimensions d and k. [ABSTRACT FROM AUTHOR]

The most common standard estimator of the pair correlation function (PCF) of a point process has a pole at zero, which is in most cases a statistical artifact. However, sometimes it makes sense to assume that a pole really exists. We propose two independent approaches for the proof of existence of a PCF's pole and for the determination of its order. In the first, we use a summary characteristic F that transforms the PCF's pole order to the location of F's pole, while the other one uses a natural estimation method based on Ripley's K-function. These methods are applied to simulated samples of two classical point process models and two cluster point process models with special geometries. Finally, we use the approach in the statistical analysis of a classical point pattern of pine trees and a highly clustered pattern of nonmetallic inclusions in steel. [ABSTRACT FROM AUTHOR]

Summary: We study a particular marked three‐dimensional point process sample that represents a Laguerre tessellation. It comes from a polycrystalline sample of aluminium alloy material. The 'points' are the cell generators while the 'marks' are radius marks that control the size and shape of the tessellation cells. Our statistical mark correlation analyses show that the marks of the sample are in clear and plausible spatial correlation: the marks of generators close together tend to be small and similar and the form of the correlation functions does not justify geostatistical marking. We show that a simplified modelling of tessellations by Laguerre tessellations with independent radius marks may lead to wrong results. When we started from the aluminium alloy data and generated random marks by random permutation we obtained tessellations with characteristics quite different from the original ones. We observed similar behaviour for simulated Laguerre tessellations. This fact, which seems to be natural for the given data type, makes fitting of models to empirical Laguerre tessellations quite difficult: the generator points and radius marks have to be modelled simultaneously. This may imply that the reconstruction methods are more efficient than point‐process modelling if only samples of similar Laguerre tessellations are needed. We also found that literature recipes for bandwidth choice for estimating correlation functions should be used with care. [ABSTRACT FROM AUTHOR]

Summary: We introduce new estimators of the inhomogeneous K‐function and the pair correlation function of a spatial point process as well as the cross K‐function and the cross pair correlation function of a bivariate spatial point process under the assumption of second‐order intensity‐reweighted stationarity. These estimators rely on a 'global' normalisation factor which depends on an aggregation of the intensity function, while the existing estimators depend 'locally' on the intensity function at the individual observed points. The advantages of our new global estimators over the existing local estimators are demonstrated by theoretical considerations and a simulation study. [ABSTRACT FROM AUTHOR]

Cox processes are natural models for point process phenomena that are environmentally driven, but much less natural for phenomena driven primarily by interactions amongst the points. The class of log-Gaussian Cox processes (LGCPs) has an elegant simplicity, and one of its attractive features is the tractability of the multivariate normal distribution carries over, to some extent, to the associated Cox process. In the statistical analysis of spatial point patterns, it is often assumed isotropy because of a simpler interpretation and ease of analysis. However, there are many cases in which the spatial structure depends on the direction. In this paper, we introduce new families of anisotropic spatial LGCPs that are useful to model spatial anisotropic point patterns that exhibit a degree of clustering. We propose classes of families consisting of elliptical and non-elliptical models. The former can be reduced to isotropic forms after some rotations, while the latter family goes beyond this property. We derive analytical forms for the covariance of the associated random field, and some second-order characteristics. A moment-based estimation procedure is followed to make inference on the parameters that control the degree of anisotropy. The estimation procedure is evaluated through a simulation study under a variety of scenarios and various degrees of anisotropy. Our methodology is illustrated on two real datasets of earthquakes in South America and the Mediterranean Europe. [ABSTRACT FROM AUTHOR]

The pair correlation function (PCF) in a non-degenerated plasma, containing multi-species of electric charges (electrons, positive and negative ions and impurities) are calculated in a Multi-Component Plasma (MCP) model. The method stands on the use of the statistical mechanics under the mean-field theory approach where the screening and the quantum effects have been taken into account. The coupled system of the obtained nonlinear integral equations (NIES) governing the pair correlation functions are solved numerically in three-dimensional space with three different methods: Fixed Point Method (FPM), Verlet Method (VM) and Finite Difference Method (FDM). These methods generally give the same results which are in a good agreement with those obtained by the molecular dynamics simulation (MD). [ABSTRACT FROM AUTHOR]