Home About us Contact
|
Home About us Contact | ||
|
|
||
Point Patterns (point + pattern)
Kinds of Point Patterns Terms modified by Point Patterns Selected AbstractsOrder Distance in Regular Point PatternsGEOGRAPHICAL ANALYSIS, Issue 3 2009Masashi Miyagawa This article examines the kth nearest neighbor distance for three regular point patterns: square, triangular, and hexagonal lattices. The probability density functions of the kth nearest distance and the average kth nearest distances are theoretically derived for k=1, 2, ,, 7. As an application of the kth nearest distance, we consider a facility location problem with closing of facilities. The problem is to find the optimal regular pattern that minimizes the average distance to the nearest open facility. Assuming that facilities are closed independently and at random, we show that the triangular lattice is optimal if at least 68% of facilities are open by comparing the upper and lower bounds of the average distances. El siguiente artículo examina la distancia de los k-vecinos más cercanos en látices cuadrados, triangulares y hexagonales. La funciones de densidad de probabilidad para las distancias k-más próximas y para las k-promedio más próximas son derivadas teóricamente para k=1,2,,7. Con el fin de demostrar una aplicación de la distancia k-más próxima los autores utilizan un ejemplo de localización y clausura de instalaciones. El objetivo es identificar el patrón regular óptimo que minimice la distancia promedio a la instalación abierta más cercana. Bajo el supuesto que las instalaciones cierran independientemente y aleatoriamente, y comparando los límites extremos superiores e inferiores de las distancias promedio, los autores demuestran que el patrón triangular es el óptimo si es que por lo menos 68 por ciento de las instalaciones permanecen abiertas. [source] Local Indicators of Network-Constrained Clusters in Spatial Point PatternsGEOGRAPHICAL ANALYSIS, Issue 3 2007Ikuho Yamada The detection of clustering in a spatial phenomenon of interest is an important issue in spatial pattern analysis. While traditional methods mostly rely on the planar space assumption, many spatial phenomena defy the logic of this assumption. For instance, certain spatial phenomena related to human activities are inherently constrained by a transportation network because of our strong dependence on the transportation system. This article thus introduces an exploratory spatial data analysis method named local indicators of network-constrained clusters (LINCS), for detecting local-scale clustering in a spatial phenomenon that is constrained by a network space. The LINCS method presented here applies to a set of point events distributed over the network space. It is based on the network K -function, which is designed to determine whether an event distribution has a significant clustering tendency with respect to the network space. First, an incremental K -function is developed so as to identify cluster size more explicitly than the original K -function does. Second, to enable identification of cluster locations, a local K -function is derived by decomposing and modifying the original network K -function. The local K -function LINCS, which is referred to as KLINCS, is tested on the distribution of 1997 highway vehicle crashes in the Buffalo, NY area. Also discussed is an adjustment of the KLINCS method for the nonuniformity of the population at risk over the network. As traffic volume can be seen as a surrogate of the population exposed to a risk of vehicle crashes, the spatial distribution of vehicle crashes is examined in relation to that of traffic volumes on the network. The results of the KLINCS analysis are validated through a comparison with priority investigation locations (PILs) designated by the New York State Department of Transportation. [source] Book Review: Statistical Analysis of Spatial Point Patterns.BIOMETRICAL JOURNAL, Issue 3 2005By Peter J. Diggle No abstract is available for this article. [source] Nonparametric One-way Analysis of Variance of Replicated Bivariate Spatial Point PatternsBIOMETRICAL JOURNAL, Issue 1 2004Sabine Landau Abstract A common problem in neuropathological studies is to assess the spatial patterning of cells on tissue sections and to compare spatial patterning between disorder groups. For a single cell type, the cell positions constitute a univariate point process and interest focuses on the degree of spatial aggregation. For two different cell types, the cell positions constitute a bivariate point process and the degree of spatial interaction between the cell types is of interest. We discuss the problem of analysing univariate and bivariate spatial point patterns in the one-way design where cell patterns have been obtained for groups of subjects. A bootstrapping procedure to perform a nonparametric one-way analysis of variance of the spatial aggregation of a univariate point process has been suggested by Diggle, Lange and Bene, (1991). We extend their replication-based approach to allow the comparison of the spatial interaction of two cell types between groups, to include planned comparisons (contrasts) and to assess whole groups against complete spatial randomness and spatial independence. We also accommodate several replicate tissue sections per subject. An advantage of our approach is that it can be applied when processes are not stationary, a common problem in brain tissue sections since neurons are arranged in cortical layers. We illustrate our methods by applying them to a neuropathological study to investigate abnormalities in the functional relationship between neurons and astrocytes in HIV associated dementia. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Statistical Analysis and Modelling of Spatial Point Patterns by ILLIAN, J., PENTTINEN, A., STOYAN, H., and STOYAN, D.BIOMETRICS, Issue 3 2009Jesper MøllerArticle first published online: 14 SEP 200 No abstract is available for this article. [source] Spatial point-process statistics: concepts and application to the analysis of lead contamination in urban soil,ENVIRONMETRICS, Issue 4 2005Christian Walter Abstract This article explores the use of spatial point-process analysis as an aid to describe topsoil lead distribution in urban environments. The data used were collected in Glebe, an inner suburb of Sydney. The approach focuses on the locations of punctual events defining a point pattern, which can be statistically described through local intensity estimates and between-point distance functions. F -, G - and K -surfaces of a marked spatial point pattern were described and used to estimate nearest distance functions over a sliding band of quantiles belonging to the marking variable. This provided a continuous view of the point pattern properties as a function of the marking variable. Several random fields were simulated by selecting points from random, clustered or regular point processes and diffusing them. Recognition of the underlying point process using variograms derived from dense sampling was difficult because, structurally, the variograms were very similar. Point-event distance functions were useful complimentary tools that, in most cases, enabled clear recognition of the clustered processes. Spatial sampling quantile point pattern analysis was defined and applied to the Glebe data set. The analysis showed that the highest lead concentrations were strongly clustered. The comparison of this data set with the simulation confidence limits of a Poisson process, a short-radius clustered point process and a geostatistical simulation showed a random process for the third quartile of lead concentrations but strong clustering for the data in the upper quartile. Thus the distribution of topsoil lead concentrations over Glebe may have resulted from several contamination processes, mainly from regular or random processes with large diffusion ranges and short-range clustered processes for the hot spots. Point patterns with the same characteristics as the Glebe experimental pattern could be generated by separate additive geostatistical simulation. Spatial sampling quantile point patterns statistics can, in an easy and accurate way, be used complementarily with geostatistical methods. Copyright © 2005 John Wiley & Sons, Ltd. [source] Using neutral landscapes to identify patterns of aggregation across resource pointsECOGRAPHY, Issue 3 2006Jill Lancaster Many organisms are aggregated within resource patches and aggregated spatially across landscapes with multiple resources. Such patchy distributions underpin models of population regulation and species coexistence, so ecologists require methods to analyse spatially-explicit data of resource distribution and use. I describe a method for analysing maps of resources and testing hypotheses about how resource distribution influences the distribution of organisms, where resource patches can be described as points in a landscape and the number of organisms on each resource point is known. Using a mark correlation function and the linearised form of Ripley's K-function, this version of marked point pattern analysis can characterise and test hypotheses about the spatial distribution of organisms (marks) on resource patches (points). The method extends a version of point pattern analysis that has wide ecological applicability, it can describe patterns over a range of scales, and can detect mixed patterns. Statistically, Monte Carlo permutations are used to estimate the difference between the observed and expected values of the mark correlation function. Hypothesis testing employs a flexible neutral landscape approach in which spatial characteristics of point patterns are preserved to some extent, and marks are randomised across points. I describe the steps required to identify the appropriate neutral landscape and apply the analysis. Simulated data sets illustrate how the choice of neutral landscape can influence ecological interpretations, and how this spatially-explicit method and traditional dispersion indices can yield different interpretations. Interpretations may be general or context-sensitive, depending on information available about the underlying point pattern and the neutral landscape. An empirical example of caterpillars exploiting food plants illustrates how this technique might be used to test hypotheses about adult oviposition and larval dispersal. This approach can increase the value of survey data, by making it possible to quantify the distribution of resource points in the landscape and the pattern of resource use by species. [source] Spatial point-process statistics: concepts and application to the analysis of lead contamination in urban soil,ENVIRONMETRICS, Issue 4 2005Christian Walter Abstract This article explores the use of spatial point-process analysis as an aid to describe topsoil lead distribution in urban environments. The data used were collected in Glebe, an inner suburb of Sydney. The approach focuses on the locations of punctual events defining a point pattern, which can be statistically described through local intensity estimates and between-point distance functions. F -, G - and K -surfaces of a marked spatial point pattern were described and used to estimate nearest distance functions over a sliding band of quantiles belonging to the marking variable. This provided a continuous view of the point pattern properties as a function of the marking variable. Several random fields were simulated by selecting points from random, clustered or regular point processes and diffusing them. Recognition of the underlying point process using variograms derived from dense sampling was difficult because, structurally, the variograms were very similar. Point-event distance functions were useful complimentary tools that, in most cases, enabled clear recognition of the clustered processes. Spatial sampling quantile point pattern analysis was defined and applied to the Glebe data set. The analysis showed that the highest lead concentrations were strongly clustered. The comparison of this data set with the simulation confidence limits of a Poisson process, a short-radius clustered point process and a geostatistical simulation showed a random process for the third quartile of lead concentrations but strong clustering for the data in the upper quartile. Thus the distribution of topsoil lead concentrations over Glebe may have resulted from several contamination processes, mainly from regular or random processes with large diffusion ranges and short-range clustered processes for the hot spots. Point patterns with the same characteristics as the Glebe experimental pattern could be generated by separate additive geostatistical simulation. Spatial sampling quantile point patterns statistics can, in an easy and accurate way, be used complementarily with geostatistical methods. Copyright © 2005 John Wiley & Sons, Ltd. [source] Using neutral landscapes to identify patterns of aggregation across resource pointsECOGRAPHY, Issue 3 2006Jill Lancaster Many organisms are aggregated within resource patches and aggregated spatially across landscapes with multiple resources. Such patchy distributions underpin models of population regulation and species coexistence, so ecologists require methods to analyse spatially-explicit data of resource distribution and use. I describe a method for analysing maps of resources and testing hypotheses about how resource distribution influences the distribution of organisms, where resource patches can be described as points in a landscape and the number of organisms on each resource point is known. Using a mark correlation function and the linearised form of Ripley's K-function, this version of marked point pattern analysis can characterise and test hypotheses about the spatial distribution of organisms (marks) on resource patches (points). The method extends a version of point pattern analysis that has wide ecological applicability, it can describe patterns over a range of scales, and can detect mixed patterns. Statistically, Monte Carlo permutations are used to estimate the difference between the observed and expected values of the mark correlation function. Hypothesis testing employs a flexible neutral landscape approach in which spatial characteristics of point patterns are preserved to some extent, and marks are randomised across points. I describe the steps required to identify the appropriate neutral landscape and apply the analysis. Simulated data sets illustrate how the choice of neutral landscape can influence ecological interpretations, and how this spatially-explicit method and traditional dispersion indices can yield different interpretations. Interpretations may be general or context-sensitive, depending on information available about the underlying point pattern and the neutral landscape. An empirical example of caterpillars exploiting food plants illustrates how this technique might be used to test hypotheses about adult oviposition and larval dispersal. This approach can increase the value of survey data, by making it possible to quantify the distribution of resource points in the landscape and the pattern of resource use by species. [source] Assessing the influence of environmental heterogeneity on bird spacing patterns: a case study with two raptorsECOGRAPHY, Issue 2 2006Thomas Cornulier Testing for aggregation or regularity in point patterns is difficult in the presence of spatial variation in abundance due to environmental heterogeneity. Using a recently developed method generalizing Ripley's K function for non homogeneous point patterns, we test the aggregation of the nests in two species of birds (little owl and Montagu's harrier) exhibiting heterogeneous distributions in response to landscape structure. We compare the results obtained under different null models accounting for environmental heterogeneity at large and/or small spatial scales. Whereas both species were initially found to form clusters at some scale, taking spatial heterogeneity into account revealed that 1) territorial little owls showed no clustering of territories when habitat availability was considered; 2) semi-colonial harriers still formed significant clusters, but part of the aggregation in this species could be explained by landscape structure alone. Our results highlight that it is feasible and highly recommended to account for non-stationarity when testing for aggregation. Further, provided that sufficient knowledge of the study system is available, this approach helps to identify behavioural and environmental components of spatial variation in abundance. Additionally, we demonstrate that accounting for large or small-scale heterogeneity affects the perception of spacing behaviours differently, so that both need to be considered. [source] Statistics for spatial functional data: some recent contributionsENVIRONMETRICS, Issue 3-4 2010P. Delicado Abstract Functional data analysis (FDA) is a relatively new branch in statistics. Experiments where a complete function is observed for each individual give rise to functional data. In this work we focus on the case of functional data presenting spatial dependence. The three classic types of spatial data structures (geostatistical data, point patterns, and areal data) can be combined with functional data as it is shown in the examples of each situation provided here. We also review some contributions in the literature on spatial functional data. Copyright © 2009 John Wiley & Sons, Ltd. [source] Spatial,temporal marked point processes: a spectrum of stochastic modelsENVIRONMETRICS, Issue 3-4 2010Eric Renshaw Abstract Many processes that develop through space and time do so in response not only to their own individual growth mechanisms but also in response to interactive pressures induced by their neighbours. The growth of trees in a forest which compete for light and nutrient resources, for example, provides a classic illustration of this general spatial,temporal growth-interaction process. Not only has its mathematical representation proved to be a powerful tool in the study and analysis of marked point patterns since it may easily be simulated, but it has also been shown to be highly flexible in terms of its application since it is robust with respect to incorrect choice of model selection. Moreover, it is highly amenable to maximum likelihood and least squares parameter estimation techniques. Currently the algorithm comprises deterministic growth and interaction coupled with a stochastic arrival and departure mechanism. So for systems with a fixed number of particles there is an inherent lack of randomness. A variety of different stochastic approaches are therefore presented, from the exact event,time model through to the associated stochastic differential equation, taking in time-increment and Tau- and Langevin-Leaping approximations en route. The main algorithm is illustrated through application to forest management and high-intensity packing of hard particle systems, and comparisons are made with the established force biased approach. Copyright © 2009 John Wiley & Sons, Ltd. [source] Description of earthquake aftershock sequences using prototype point patternsENVIRONMETRICS, Issue 3 2008Frederic Paik Schoenberg Abstract We introduce the use of prototype point patterns to characterize the behavior of a typical aftershock sequence from the global Harvard earthquake catalog. These prototypes are used not only for data description and summary but also to identify outliers and to classify sequences into groups exhibiting similar aftershock behavior. We find that a typical shallow earthquake of magnitude between 7.5 and 8.0 has approximately five aftershocks of magnitude at least 5.5, and that within an observation window of 0.113 days to 2.0 years after the mainshock, these aftershocks are roughly evenly distributed in log-time. The relative magnitudes and distances from the mainshock for the typical aftershock sequence are characterized as well. Copyright © 2007 John Wiley & Sons, Ltd. [source] Order Distance in Regular Point PatternsGEOGRAPHICAL ANALYSIS, Issue 3 2009Masashi Miyagawa This article examines the kth nearest neighbor distance for three regular point patterns: square, triangular, and hexagonal lattices. The probability density functions of the kth nearest distance and the average kth nearest distances are theoretically derived for k=1, 2, ,, 7. As an application of the kth nearest distance, we consider a facility location problem with closing of facilities. The problem is to find the optimal regular pattern that minimizes the average distance to the nearest open facility. Assuming that facilities are closed independently and at random, we show that the triangular lattice is optimal if at least 68% of facilities are open by comparing the upper and lower bounds of the average distances. El siguiente artículo examina la distancia de los k-vecinos más cercanos en látices cuadrados, triangulares y hexagonales. La funciones de densidad de probabilidad para las distancias k-más próximas y para las k-promedio más próximas son derivadas teóricamente para k=1,2,,7. Con el fin de demostrar una aplicación de la distancia k-más próxima los autores utilizan un ejemplo de localización y clausura de instalaciones. El objetivo es identificar el patrón regular óptimo que minimice la distancia promedio a la instalación abierta más cercana. Bajo el supuesto que las instalaciones cierran independientemente y aleatoriamente, y comparando los límites extremos superiores e inferiores de las distancias promedio, los autores demuestran que el patrón triangular es el óptimo si es que por lo menos 68 por ciento de las instalaciones permanecen abiertas. [source] Complex dynamics in one-dimensional CNNsINTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 1 2006István Petrás Abstract The effect of boundary conditions on the global dynamics of cellular neural networks (CNNs) is investigated. As a case study one-dimensional template CNNs are considered. It is shown that if the off-diagonal template elements have opposite sign, then the boundary conditions behave as bifurcation parameters and can give rise to a very rich and complex dynamic behaviour. In particular, they determine the equilibrium point patterns, the transition from stability to instability and the occurrence of several bifurcation phenomena leading to strange and/or chaotic attractors and to the coexistence of several attractors. Then the influence of the number of cells on the global dynamics is studied, with particular reference to the occurrence of hyperchaotic behaviour. Copyright © 2006 John Wiley & Sons, Ltd. [source] CMPZ, an algorithm for the efficient comparison of periodic structuresJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 1 2006R. Hundt The systematic comparison of the atomic structure of solid compounds has become an important task in crystallography, chemistry, physics and materials science, in particular in the context of structure prediction and structure determination of crystalline solids. In this work, an efficient and robust algorithm for the comparison of periodic structures is presented, which is based on the mapping of the point patterns of the two structures into each other. This algorithm has been implemented as the module CMPZ in the structure visualization and analysis program KPLOT. [source] Multigenerational analysis of spatial structure in the terrestrial, food-deceptive orchid Orchis masculaJOURNAL OF ECOLOGY, Issue 2 2009Hans Jacquemyn Summary 1In long-lived, terrestrial orchids, strong aggregation of adults and recruits within populations and pronounced spatial association between recruits and adults can be expected when seed dispersal is limited, probabilities of seed germination decrease with increasing distance from mother plants and/or not all mother plants contribute to future generations. When individuals are distributed evenly across life-history stages, these processes can also be expected to result in a significant fine-scale spatial genetic structure in recruits that will persist into the adult-stage class. 2We combined detailed spatial genetic and point pattern analyses across different generations with parentage analyses to elucidate the role of the diverse processes that might determine spatial structure in Orchis mascula. 3Analyses of spatial point patterns showed a significant association between adults and recruits and similar clustering patterns for both. Weak, but highly significant spatial genetic structure was observed in adults and recruits, but no significant differences were observed across life stages, indicating that the spatial genetic structure present in recruits persists into the adult stage. 4Parentage analyses highlighted relatively short seed dispersal distances (median offspring-recruitment distance: 1.55 and 1.70 m) and differential contribution of mother plants to future generations. 5Persistence of fine-scale spatial genetic structure from seedlings into the adult stage class is consistent with the life history of O. mascula, whereas relatively large dispersal distances of both pollen and seeds compared to the fine-scale clustering of adults and seedlings suggest overlapping seed shadows and mixing of genotypes within populations as the major factors explaining the observed weak spatial genetic structure. 6Nonetheless, comparison of the spatial association between recruits and adults with the genetic analysis of offspring-parent distances suggests that the tight clustering of recruits around adults was probably caused by decreasing probabilities of seed germination with increasing distance from mother plants. 7Synthesis. This study shows that the approach presented here, which combines spatial genetic and spatial pattern analyses with parentage analyses, may be broadly applied to other plant species to elucidate the processes that determine spatial structure within their populations. [source] Wavelet analysis for detecting anisotropy in point patternsJOURNAL OF VEGETATION SCIENCE, Issue 2 2004Michael S. Rosenberg Although many methods have been proposed for analysing point locations for spatial pattern, previous methods have concentrated on clumping and spacing. The study of anisotropy (changes in spatial pattern with direction) in point patterns has been limited by lack of methods explicitly designed for these data and this purpose; researchers have been constrained to choosing arbitrary test directions or converting their data into quadrat counts and using methods designed for continuously distributed data. Wavelet analysis, a booming approach to studying spatial pattern, widely used in mathematics and physics for signal analysis, has started to make its way into the ecological literature. A simple adaptation of wavelet analysis is proposed for the detection of anisotropy in point patterns. The method is illustrated with both simulated and field data. This approach can easily be used for both global and local spatial analysis. [source] A grid-based method for sampling and analysing spatially ambiguous plantsJOURNAL OF VEGETATION SCIENCE, Issue 4 2001Jeffrey S. Fehmi Hickman (1993). Abstract. Spatial data can provide much information about the interrelations of plants and the relationship between individuals and the environment. Spatially ambiguous plants, i.e. plants without readily identifiable loci, and plants that are profusely abundant, present non-trivial impediments to the collection and analysis of vegetation data derived from standard spatial sampling techniques. Sampling with grids of presence/absence quadrats can ameliorate much of this difficulty. Our analysis of 10 fully-mapped grassland plots demonstrates the applicability of the grid-based approach which revealed spatial dependence at a much lower sampling effort than mapping each plant. Ripley's K -function, a test commonly used for point patterns, was effective for pattern analysis on the grids and the gridded quadrat technique was an effective tool for quantifying spatial patterns. The addition of spatial pattern measures should allow for better comparisons of vegetation structure between sites, instead of sole reliance on species composition data. [source] Spatial distribution of communal nests in a colonial breeding bird: benefits without costs?AUSTRAL ECOLOGY, Issue 5 2008URS CHRISTIAN GIEßELMANN Abstract The spatial organization of individuals, or groups of individuals, within a population can provide valuable information about social organization and population dynamics. We analysed the spatial distribution of nests of the sociable weaver (Philetairus socius) on two farms in the Kalahari. Sociable weavers build large communal nests on big savannah trees, forming a pattern of trees with and without nests. We used two spatial statistics, Ripley's K and the pair correlation function, to describe characteristics of the point patterns over a range of distances. (i) At distances of 200 and 300 m, communal nests were clustered. (ii) At distances greater than 1000 m, communal nests were regularly distributed. These findings are independent of the spatial distribution of trees. Furthermore, we used Moran's I to analyse spatial autocorrelation of nest sizes. We expected negative autocorrelation because of competition between nests. But on both farms there was no significant autocorrelation of nest sizes for any distance class. The regular distribution observed at larger distances may indicate competition and/or territoriality among different nests, but the lack of spatial autocorrelation between nest sizes suggests that these interactions may happen between nest clusters rather than between single nests. This was confirmed by significant clustering of nests on small scales. We thus suggest, that colonies of P. socius consist of several nests on adjacent trees forming a cluster of subcolonies. The question why sociable weavers establish subcolonies instead of adding more chambers to the natal nest, could not simply be answered by limitation of nesting space. We suggest a strategy to avoid costs due to increasing colony size. [source] Modelling Tree Roots in Mixed Forest Stands by Inhomogeneous Marked Gibbs Point ProcessesBIOMETRICAL JOURNAL, Issue 3 2009Stefanie Eckel Abstract The aim of the paper is to apply point processes to root data modelling. We propose a new approach to parametric inference when the data are inhomogeneous replicated marked point patterns. We generalize Geyer's saturation point process to a model, which combines inhomogeneity, marks and interaction between the marked points. Furthermore, the inhomogeneity influences the definition of the neighbourhood of points. Using the maximum pseudolikelihood method, this model is then fitted to root data from mixed stands of Norway spruce (Picea abies (L.) Karst.) and European beech (Fagus sylvatica L.) to quantify the degree of root aggregation in such mixed stands. According to the analysis there is no evidence that the two root systems are not independent. [source] Nonparametric One-way Analysis of Variance of Replicated Bivariate Spatial Point PatternsBIOMETRICAL JOURNAL, Issue 1 2004Sabine Landau Abstract A common problem in neuropathological studies is to assess the spatial patterning of cells on tissue sections and to compare spatial patterning between disorder groups. For a single cell type, the cell positions constitute a univariate point process and interest focuses on the degree of spatial aggregation. For two different cell types, the cell positions constitute a bivariate point process and the degree of spatial interaction between the cell types is of interest. We discuss the problem of analysing univariate and bivariate spatial point patterns in the one-way design where cell patterns have been obtained for groups of subjects. A bootstrapping procedure to perform a nonparametric one-way analysis of variance of the spatial aggregation of a univariate point process has been suggested by Diggle, Lange and Bene, (1991). We extend their replication-based approach to allow the comparison of the spatial interaction of two cell types between groups, to include planned comparisons (contrasts) and to assess whole groups against complete spatial randomness and spatial independence. We also accommodate several replicate tissue sections per subject. An advantage of our approach is that it can be applied when processes are not stationary, a common problem in brain tissue sections since neurons are arranged in cortical layers. We illustrate our methods by applying them to a neuropathological study to investigate abnormalities in the functional relationship between neurons and astrocytes in HIV associated dementia. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | |||||||||||||