A statistical method for the identification and aggregation of regional linguistic variation

This paper introduces a method for the analysis of regional linguistic variation. The method identifies individual and common patterns of spatial clustering in a set of linguistic variables measured over a set of locations based on a combination of three statistical techniques: spatial autocorrelation, factor analysis, and cluster analysis. To demonstrate how to apply this method, it is used to analyze regional variation in the values of 40 continuously measured, high-frequency lexical alternation variables in a 26-million-word corpus of letters to the editor representing 206 cities from across the United States.

A statistical comparison of regional phonetic and lexical variation in American English

This paper presents a statistical comparison of regional phonetic and lexical variation in American English. Both the phonetic and lexical datasets were first subjected to separate multivariate spatial analyses in order to identify the most common dimensions of spatial clustering in these two datasets. The dimensions of phonetic and lexical variation extracted by these two analyses were then correlated with each other, after being interpolated over a shared set of reference locations, in order to measure the similarity of regional phonetic and lexical variation in American English. This analysis shows that regional phonetic and lexical variation are remarkably similar in Modern American English.

"Belonging” in the gentrified Golden Horn/Halic neighbourhoods of Istanbul

Mainstream gentrification research predominantly examines experiences and motivations of the middle-class gentrifier groups, while overlooking experiences of non-gentrifying groups including the impact of in situ local processes on gentrification itself. In this paper, I discuss gentrification, neighbourhood belonging and spatial distribution of class in Istanbul by examining patterns of belonging both of gentrifiers and non-gentrifying groups in historic neighbourhoods of the Golden Horn/Halic. I use multiple correspondence analysis (MCA), a methodology rarely used in gentrification research, to explore social and symbolic borders between these two groups. I show how gentrification leads to spatial clustering by creating exclusionary practices and eroding social cohesion, and illuminate divisions that are inscribed into the physical space of the neighbourhood.

Clustering and spatial correlations of the neuronal cytoplasmic inclusions, astrocytic plaques and ballooned neurons in corticobasal degeneration

This study tested three hypotheses: (1) that there is clustering of the neuronal cytoplasmic inclusions (NCI), astrocytic plaques (AP) and ballooned neurons (BN) in corticobasal degeneration (CBD), (2) that the clusters of NCI and BN are not spatially correlated, and (3) that the lesions are correlated with disease ‘stage’. In 50% of the regions, clusters of lesions were 400–800 µm in diameter and regularly distributed parallel to the tissue boundary. Clusters of NCI and BN were larger in laminae II/III and V/VI, respectively. In a third of regions, the clusters of BN and NCI were negatively spatially correlated. Cluster size of the BN in the parahippocampal gyrus (PHG) was positively correlated with disease ‘stage’. The data suggest the following: (1) degeneration of the cortico-cortical pathways in CBD, (2) clusters of NCI and BN may affect different anatomical pathways and (3) BN may develop after the NCI in the PHG.

Higher-order co-occurrences for exploratory point pattern analysis and decision tree clustering on spatial data

Analyzing geographical patterns by collocating events, objects or their attributes has a long history in surveillance and monitoring, and is particularly applied in environmental contexts, such as ecology or epidemiology. The identification of patterns or structures at some scales can be addressed using spatial statistics, particularly marked point processes methodologies. Classification and regression trees are also related to this goal of finding "patterns" by deducing the hierarchy of influence of variables on a dependent outcome. Such variable selection methods have been applied to spatial data, but, often without explicitly acknowledging the spatial dependence. Many methods routinely used in exploratory point pattern analysis are2nd-order statistics, used in a univariate context, though there is also a wide literature on modelling methods for multivariate point pattern processes. This paper proposes an exploratory approach for multivariate spatial data using higher-order statistics built from co-occurrences of events or marks given by the point processes. A spatial entropy measure, derived from these multinomial distributions of co-occurrences at a given order, constitutes the basis of the proposed exploratory methods. © 2010 Elsevier Ltd.

Higher-order co-occurrences for exploratory point pattern analysis and decision tree clustering on spatial data

Analyzing geographical patterns by collocating events, objects or their attributes has a long history in surveillance and monitoring, and is particularly applied in environmental contexts, such as ecology or epidemiology. The identification of patterns or structures at some scales can be addressed using spatial statistics, particularly marked point processes methodologies. Classification and regression trees are also related to this goal of finding "patterns" by deducing the hierarchy of influence of variables on a dependent outcome. Such variable selection methods have been applied to spatial data, but, often without explicitly acknowledging the spatial dependence. Many methods routinely used in exploratory point pattern analysis are2nd-order statistics, used in a univariate context, though there is also a wide literature on modelling methods for multivariate point pattern processes. This paper proposes an exploratory approach for multivariate spatial data using higher-order statistics built from co-occurrences of events or marks given by the point processes. A spatial entropy measure, derived from these multinomial distributions of co-occurrences at a given order, constitutes the basis of the proposed exploratory methods. © 2010 Elsevier Ltd.

Measuring the spatial arrangement patterns of pathological lesions in histological sections of brain tissue

The development of abnormal protein aggregates in the form of extracellular plaques and intracellular inclusions is a characteristic feature of many neurodegenerative diseases such as Alzheimer's disease (AD), Creutzfeldt-Jakob disease (CJD) and the fronto-temporal dementias (FTD). An important aspect of a pathological protein aggregate is its spatial topography in the tissue. Lesions may not be randomly distributed within a histological section but exhibit spatial pattern, a departure from randomness either towards regularity or clustering. Information on the spatial pattern of a lesion may be useful in elucidating its pathogenesis and in studying the relationships between different lesions. This article reviews the methods that have been used to study the spatial topography of lesions. These include simple tests of whether the distribution of a lesion departs significantly from random using randomized points or sample fields, and more complex methods that employ grids or transects of contiguous fields and which can detect the intensity of aggregation and the sizes, distribution and spacing of the clusters. The usefulness of these methods in elucidating the pathogenesis of protein aggregates in neurodegenerative disease is discussed.

What does the study of the spatial patterns of pathological lesions tell us about the pathogenesis of neurodegenerative disorders?

Discrete pathological lesions, which include extracellular protein deposits, intracellular inclusions and changes in cell morphology, occur in the brain in the majority of neurodegenerative disorders. These lesions are not randomly distributed in the brain but exhibit a spatial pattern, that is, a departure from randomness towards regularity or clustering. The spatial pattern of a lesion may reflect pathological processes affecting particular neuroanatomical structures and, therefore, studies of spatial pattern may help to elucidate the pathogenesis of a lesion and of the disorders themselves. The present article reviews first, the statistical methods used to detect spatial patterns and second, the types of spatial patterns exhibited by pathological lesions in a variety of disorders which include Alzheimer's disease, Down syndrome, dementia with Lewy bodies, Creutzfeldt-Jakob disease, Pick's disease and corticobasal degeneration. These studies suggest that despite the morphological and molecular diversity of brain lesions, they often exhibit a common type of spatial pattern (i.e. aggregation into clusters that are regularly distributed in the tissue). The pathogenic implications of spatial pattern analysis are discussed with reference to the individual disorders and to studies of neurodegeneration as a whole.

Clustering of Pick bodies in the dentate gyrus in Pick's disease

In patients with Pick's disease (PD), high densities of tau positive Pick bodies (PB) have been observed within the granule cell layer of the dentate gyrus. This study investigated the spatial patterns of PB along the granule cell layer in coronal sections of the hippocampus in eight patients with PD. In all patients, there was evidence of clustering of PB within the granule cell layer; however, there was considerable variation in the pattern of clustering. In five patients, the clusters of PB were regularly distributed along the dentate gyms, and in two of these patients, the smaller clusters were aggregated into larger superclusters. In three patients, a single large cluster of PB, more than 1200 μm in diameter, was present. Clustering of PB may reflect a primary degenerative process within the granule cells or the degeneration of pathways that project to the dentate gyrus.

Clustering and periodicity of neurofibrillary tangles in the upper and lower cortical laminae in Alzheimer's disease

In Alzheimer's disease (AD), neurofibrillary tangles (NFT) occur within neurons in both the upper and lower cortical laminae. Using a statistical method that estimates the size and spacing of NFT clusters along the cortex parallel to the pia mater, two hypotheses were tested: 1) that the cluster size and distribution of the NFT in gyri of the temporal lobe reflect degeneration of the feedforward (FF) and feedback (FB) cortico-cortical pathways, and 2) that there is a spatial relationship between the clusters of NFT in the upper and lower laminae. In 16 temporal lobe gyri from 10 cases of sporadic AD, NFT were present in both the upper and lower laminae in 11/16 (69%) gyri and in either the upper or lower laminae in 5/16 (31%) gyri. Clustering of the NFT was observed in all gyri. A significant peak-to-peak distance was observed in the upper laminae in 13/15 (87%) gyri and in the lower laminae in 8/ 12 (67%) gyri, suggesting a regularly repeating pattern of NFT clusters along the cortex. The regularly distributed clusters of NFT were between 500 and 800 μm in size, the estimated size of the cells of origin of the FF and FB cortico-cortical projections, in the upper laminae of 6/13 (46%) gyri and in the lower laminae of 2/8 (25%) gyri. Clusters of NFT in the upper laminae were spatially correlated (in phase) with those in the lower laminae in 5/16 (31%) gyri. The clustering patterns of the NFT are consistent with their formation in relation to the FF and FB cortico-cortical pathways. In most gyri, NFT clusters appeared to develop independently in the upper and lower laminae.

Spatial patterns of the pathological changes in the temporal lobe of patients with neuronal intermediate filament inclusion disease

Neuronal intermediate filament inclusion disease (NIFID) is a new neurodegenerative disease characterized histologically by the presence of neuronal cytoplasmic inclusions (NI) immunopositive for intermediate filament proteins, neuronal loss, swollen achromatic neurons (SN), and gliosis. We studied the spatial patterns of these pathological changes parallel to the pia mater in gyri of the temporal lobe in four cases of NIFID. Both the NI and SN occurred in clusters that were regularly distributed parallel to the pia mater, the cluster sizes of the SN being significantly greater than those of the NI. In a significant proportion of areas studied, there was a spatial correlation between the clusters of NI and those of the SN and with the density of the surviving neurons. In addition, the clusters of surviving neurons were negatively correlated (out of phase) with the clusters of glial cell nuclei. The pattern of clustering of these histological features suggests that there is degeneration of the cortico-cortical projections in NIFID leading to the formation of NI and SN within the same vertical columns of cells. The glial cell reaction may be a response to the loss of neurons rather than to the appearance of the NI or SN.

Spatial patterns of the pathological changes in the cerebellar cortex in sporadic Creutzfeldt-Jakob disease (sCJD)

The spatial patterns of the vacuolation ("spongiform change"), surviving cells, and prion protein (PrP) deposition were studied in the various cell laminae of the cerebellar cortex in 11 cases of sporadic Creutzfeldt-Jakob disease (sCJD). Clustering of the histological features, with the clusters regularly distributed along the folia, was evident in all cell laminae. In the molecular layer, clusters of vacuoles coincided with the surviving Purkinje cells. In the granule cell layer, however, the spatial relationship between the vacuoles and surviving cells was more complex and varied between cases. PrP deposition was not spatially correlated with either the vacuoles or the surviving cells in any of the cerebellar laminae in the majority of cases. In some cases, there were spatial relationships between th histological features in the molecular and granule cell layers. The data suggest that degeneration of the cerebellar cortex in sCJD may occur in a topographic pattern consistent with the spread of prion pathology along anatomical pathways. The development of the vacuolation may be an early stage of the pathology in the cerebellum preceding the appearance of the PrP deposits. In addition, there is evidence that the pathological changes may spread across the different laminae of the cerebellar cortex.

Clustering of neuronal inclusions in "dementia with neurofilament inclusions"

Dementia with neurofilament inclusions (DNI) is a new disorder characterized clinically by early-onset dementia and histologically by the presence of intraneural inclusions immunopositive for neurofilament antigens but lacking tau and α-synuclein reactivity. We studied the clustering patterns of the neurofilament inclusions (NI) in regions of the temporal lobe in three cases of DNI to determine whether they have the same spatial patterns as inclusions in the tauopathies and α-synucleinopathies. The NI exhibited a clustered distribution (mean size of clusters 400 μm, range 50-800 μm, SD 687.8) in 24/28 of the areas studied. In 22 of these areas, the clusters exhibited a regular distribution along the tissue parallel to the pia mater or alveus. In 3 cortical areas, there was evidence of a more complex pattern in which the NI clusters were aggregated into larger superclusters. In 6 cortical areas, the size of the clusters approximated to those of the cells of origin of the cortico-cortical pathways but in the remaining areas cluster size was smaller than 400 μm. Despite the unique molecular profile of the NI, their spatial patterns are similar to those shown by filamentous neuronal inclusions in the tauopathies and α-synucleinopathies.

The spatial patterns of prion protein deposits in cases of variant Creutzfeldt-Jakob disease

The spatial patterns of the prion protein (PrP) deposits were studied in immunostained sections of areas of the cerebral cortex, hippocampus, dentate gyrus, and the molecular layer of the cerebellum in 11 cases of variant Creutzfeldt-Jakob disease (vCJD). Clustering of PrP deposits, with a regular distribution of the clusters parallel to the tissue boundary, was the most common spatial pattern observed. Two morphological types of PrP deposit were recognised, those consisting of a condensed core (florid deposits) and those deposits lacking a condensed core (non-florid deposits). The florid and non-florid PrP deposits exhibited a different profile of spatial patterns. First, the florid deposits exhibited a regularly distributed pattern of clusters more frequently than the non-florid deposits. Second, the florid deposits formed larger clusters (greater than1,600 µm in diameter) less frequently than the non-florid deposits. In the areas of the cerebral cortex that exhibited a regular distribution of PrP deposit clusters, the cluster size of the deposits approximated that of the groups of cells of the cortico-cortical pathway origin in only 12% of analyses. No significant differences in the frequency of the different types of spatial pattern were observed in different brain regions, or in the cerebral cortex between the upper and lower laminae. It was concluded that the spatial patterns of the PrP deposits in the cerebral cortex in vCJD are unlikely to reflect the degeneration of the cortico-cortical pathways as has been reported in sporadic CJD (sCJD). In addition, different factors could be involved in the development of the deposits with and without a condensed core.

Correlations between the clustering patterns of the pathological changes in sporadic Creutzfeldt-Jakob disease

Correlations between the clustering patterns of the vacuolation ('spongiform change'), prion protein (PrP) deposits, and surviving neurons were studied in the cerebral cortex, hippocampus, and cerebellum in 11 cases of sporadic Creutzfeldt-Jakob disease (sCJD). Differences in the sizes of the clusters of vacuoles were observed between brain regions and in the cerebral cortex, between the upper and lower laminae. With the exception of the parietal cortex, mean cluster size of the vacuoles was similar to that of the PrP deposits in each brain area. Clusters of the vacuoles were spatially correlated with the density of surviving neurons and with the clusters of PrP deposits in 47% and 53% of cortical areas analysed respectively but there were few spatial correlation between the PrP deposits and the density of surviving neurons. The data suggest that the pathology of sCJD may spread through the brain via specific anatomical pathways. Development of the clusters of vacuoles is spatially related to surviving neurons while the appearance of clusters of PrP deposits is related to the development of the vacuolation.