Knowledge-based spatiotemporal linear abstraction

We present a theoretical framework and a case study for reusing the same conceptual and computational methodology for both temporal abstraction and linear (unidimensional) space abstraction, in a domain (evaluation of traffic-control actions) significantly different from the one (clinical medicine) in which the method was originally used. The method, known as knowledge-based temporal abstraction, abstracts high-level concepts and patterns from time-stamped raw data using a formal theory of domain-specific temporal-abstraction knowledge. We applied this method, originally used to interpret time-oriented clinical data, to the domain of traffic control, in which the monitoring task requires linear pattern matching along both space and time. First, we reused the method for creation of unidimensional spatial abstractions over highways, given sensor measurements along each highway measured at the same time point. Second, we reused the method to create temporal abstractions of the traffic behavior, for the same space segments, but during consecutive time points. We defined the corresponding temporal-abstraction and spatial-abstraction domain-specific knowledge. Our results suggest that (1) the knowledge-based temporal-abstraction method is reusable over time and unidimensional space as well as over significantly different domains; (2) the method can be generalized into a knowledge-based linear-abstraction method, which solves tasks requiring abstraction of data along any linear distance measure; and (3) a spatiotemporal-abstraction method can be assembled from two copies of the generalized method and a spatial-decomposition mechanism, and is applicable to tasks requiring abstraction of time-oriented data into meaningful spatiotemporal patterns over a linear, decomposable space, such as traffic over a set of highways.

Linear latent force models using Gaussian Processes

Purely data-driven approaches for machine learning present difficulties when data are scarce relative to the complexity of the model or when the model is forced to extrapolate. On the other hand, purely mechanistic approaches need to identify and specify all the interactions in the problem at hand (which may not be feasible) and still leave the issue of how to parameterize the system. In this paper, we present a hybrid approach using Gaussian processes and differential equations to combine data-driven modeling with a physical model of the system. We show how different, physically inspired, kernel functions can be developed through sensible, simple, mechanistic assumptions about the underlying system. The versatility of our approach is illustrated with three case studies from motion capture, computational biology, and geostatistics.

Changes in spatial point patterns of pioneer woody plants across a large tropical landslide

We assessed whether the relative importance of positive and negative interactions in early successional communities varied across a large landslide on Casita Volcano (Nicaragua). We tested several hypotheses concerning the signatures of these processes in the spatial patterns of woody pioneer plants, as well as those of mortality and recruitment events, in several zones of the landslide differing in substrate stability and fertility, over a period of two years (2001 and 2002). We identified all woody individuals with a diameter >1 cm and mapped them in 28 plots measuring 10 × 10-m. On these maps, we performed a spatial point pattern analysis using univariate and bivariate pair-correlation functions; g (r) and g12 (r), and pairwise differences of univariate and bivariate functions. Spatial signatures of positive and negative interactions among woody plants were more prevalent in the most and least stressful zones of the landslide, respectively. Natural and human-induced disturbances such as the occurrence of fire, removal of newly colonizing plants through erosion and clearcutting of pioneer trees were also identified as potentially important pattern-creating processes. These results are in agreement with the stress-gradient hypothesis, which states that the relative importance of facilitation and competition varies inversely across gradients of abiotic stress. Our findings also indicate that the assembly of early successional plant communities in large heterogeneous landslides might be driven by a much larger array of processes than previously thought.

Maintaining distances with the engineer: patterns of coexistence in plant communities beyond the patch-bare dichotomy

Two-phase plant communities with an engineer conforming conspicuous patches and affecting the performance and patterns of coexisting species are the norm under stressful conditions. To unveil the mechanisms governing coexistence in these communities at multiple spatial scales, we have developed a new point-raster approach of spatial pattern analysis, which was applied to a Mediterranean high mountain grassland to show how Festuca curvifolia patches affect the local distribution of coexisting species. We recorded 22 111 individuals of 17 plant perennial species. Most coexisting species were negatively associated with F. curvifolia clumps. Nevertheless, bivariate nearest-neighbor analyses revealed that the majority of coexisting species were confined at relatively short distances from F. curvifolia borders (between 0-2 cm and up to 8 cm in some cases). Our study suggests the existence of a fine-scale effect of F. curvifolia for most species promoting coexistence through a mechanism we call 'facilitation in the halo'. Most coexisting species are displaced to an interphase area between patches, where two opposite forces reach equilibrium: attenuated severe conditions by proximity to the F. curvifolia canopy (nutrient-rich islands) and competitive exclusion mitigated by avoiding direct contact with F. curvifolia.

Negative density dependence and environmental heterogeneity effects on tree ferns across succession in a tropical montane forest.

Although tree ferns are an important component of temperate and tropical forests, very little is known about their ecology. Their peculiar biology (e.g., dispersal by spores and two-phase life cycle) makes it difficult to extrapolate current knowledge on the ecology of other tree species to tree ferns. In this paper, we studied the effects of negative density dependence (NDD) and environmental heterogeneity on populations of two abundant tree fern species, Cyathea caracasana and Alsophila engelii, and how these effects change across a successional gradient. Species patterns harbor information on processes such as competition that can be easily revealed using point pattern analysis techniques. However, its detection may be difficult due to the confounded effects of habitat heterogeneity. Here, we mapped three forest plots along a successional gradient in the montane forests of Southern Ecuador. We employed homogeneous and inhomogeneous K and pair correlation functions to quantify the change in the spatial pattern of different size classes and a case-control design to study associations between juvenile and adult tree ferns. Using spatial estimates of the biomass of four functional tree types (short- and long-lived pioneer, shade- and partial shade-tolerant) as covariates, we fitted heterogeneous Poisson models to the point pattern of juvenile and adult tree ferns and explored the existence of habitat dependencies on these patterns. Our study revealed NDD effects for C. caracasana and strong environmental filtering underlying the pattern of A. engelii. We found that adult and juvenile populations of both species responded differently to habitat heterogeneity and in most cases this heterogeneity was associated with the spatial distribution of biomass of the four functional tree types. These findings show the effectiveness of factoring out environmental heterogeneity to avoid confounding factors when studying NDD and demonstrate the usefulness of covariate maps derived from mapped communities.

Estudio de los factores que condicionan, a escala local, la presencia de Epidendrum rhopalostele (Orchidaceae): Implicaciones para su conservación

El análisis de los factores que determinan el establecimiento y supervivencia de orquídeas epífitas, incluyen: a) las condiciones microambientales de los bosques que las mantienen, b) preferencias por las características de los hospederos donde crecen, c) limitación en la dispersión de semillas, d) interacciones planta-planta, y e) asociaciones micorrízicas para la germinación y resultan esenciales para el desarrollo de estrategias para la conservación y manejo de este grupo de plantas. Este trabajo ha evaluado la importancia de estos factores en Epidendrum rhopalostele, orquídea epífita del bosque de niebla montano, a través de los análisis de los patrones espaciales de los árboles que la portan y de la propia orquídea, a escala de población, estudios de asociación y métodos moleculares. Estos últimos han consistido en el uso de marcadores AFLP para el análisis de la estructura genética de la orquídea y en la secuenciación-clonación de la región ITS para la identificación de los hongos micorrízicos asociados. El objetivo de esta tesis es, por tanto, una mejor comprensión de los factores que condicionan la presencia de orquídeas epífitas en los remanentes de bosque de niebla montano y una evaluación de las implicaciones para la conservación y mantenimiento de sus hábitats y la permanencia de sus poblaciones. El estudio fue realizado en un fragmento de bosque de niebla montano de sucesión secundaria situado al este de la Cordillera Real, en los Andes del sur de Ecuador, a 2250 m.s.n.m y caracterizado por una pendiente marcada, temperatura media anual de 20.8°C y precipitación anual de 2193 mm. En este fragmento se mapearon, identificaron y caracterizaron todos los árboles presentes con DBH > 1 cm y todos los individuos de Epidendrum rhopalostele. Así mismo se tomaron muestras de hoja para obtener ADN de todas las orquídeas registradas y muestras de raíces de individuos con flor de E. rhopalostele, uno por cada forófito, para el análisis filogenético de micorrizas. Análisis espaciales de patrones de puntos basados en la K de Ripley y la distancia al vecino más cercano fueron usados para los árboles, forófitos y la población de E. rhopalostele. Se observó que la distribución espacial de árboles y forófitos de E. rhopalostele no es aleatoria, ya que se ajusta a un proceso agregado de Poisson. De ahí se infiere una limitación en la dispersión de las semillas en el fragmento estudiado y en el establecimiento de la orquídea. El patrón de distribución de la población de E. rhopalostele en el fragmento muestra un agrupamiento a pequeña escala sugiriendo una preferencia por micro-sitios para el establecimiento de la orquídea con un kernel de dispersión de las semillas estimado de 0.4 m. Las características preferentes del micro-sitio como tipos de árboles (Clusia alata y árboles muertos), tolerancia a la sombra, corteza rugosa, distribución en los dos primeros metros sugieren una tendencia a distribuirse en el sotobosque. La existencia de una segregación espacial entre adultos y juveniles sugiere una competencia por recursos limitados condicionada por la preferencia de micro-sitio. La estructura genética de la población de E. rhopalostele analizada a través de Structure y PCoA evidencia la presencia de dos grupos genéticos coexistiendo en el fragmento y en los mismos forófitos, posiblemente por eventos de hibridización entre especies de Epidendrum simpátricas. Los resultados del análisis de autocorrelación espacial efectuados en GenAlex confirman una estructura genético-espacial a pequeña escala que es compatible con un mecanismo de dispersión de semillas a corta distancia ocasionada por gravedad o pequeñas escorrentías, frente a la dispersión a larga distancia promovida por el viento generalmente atribuida a las orquídeas. Para la identificación de los micobiontes se amplificó la región ITS1-5.8S-ITS2, y 47 secuencias fueron usadas para el análisis filogenético basado en neighborjoining, análisis bayesiano y máximum-likelihood que determinó que Epidendrum rhopalostele establece asociaciones micorrízicas con al menos dos especies diferentes de Tulasnella. Se registraron plantas que estaban asociadas con los dos clados de hongos encontrados, sugiriendo ausencia de limitación en la distribución del hongo. Con relación a las implicaciones para la conservación in situ resultado de este trabajo se recomienda la preservación de todo el fragmento de bosque así como de las interacciones existentes (polinizadores, micorrizas) a fin de conservar la diversidad genética de esta orquídea epífita. Si fuere necesaria una reintroducción se deben contemplar distancias entre los individuos en cada forófito dentro de un rango de 0.4 m. Para promover el reclutamiento y regeneración de E. rhopalostele, se recomienda que los forófitos correspondan preferentemente a árboles muertos o caídos y a especies, como Clusia alata, que posean además corteza rugosa, sean tolerantes a la sombra, y en el área del sotobosque con menor luminosidad. Además es conveniente que las orquídeas en su distribución vertical estén ubicadas en los primeros metros. En conclusión, la limitación en la dispersión, las características del micro-sitio, las interacciones intraespecíficas y con especies congenéricas simpátricas y las preferencias micorrízicas condicionan la presencia de esta orquídea epífita en este tipo de bosque. ABSTRACT The analysis of factors that determine the establishment and survival of epiphytic depends on factors such as a) microenvironmental conditions of forest, b) preference for host characteristics where orchids grow, c) seed dispersal limitation, d) plant-plant interaction, e) priority mycorrhizal associations for germination, are essential for the development of strategies for management and conservation. This work evaluated the importance of these factors in Epidendrum rhopalostele, an epiphytic orchid of montane cloud forest through the analysis of spatial patterns of host trees and the orchid, in a more specific scale, with association studies and molecular methods, including AFLPs for orchid population genetic structure and the sequencing of the ITS region for associated mycorrhizal fungi. The aim of this thesis is to understand the factors that condition the presence of epiphytic orchids in the remnants of montane cloud forest and to assess the implications for the conservation and preservation of their habitats and the persistence of the orchid populations. The study was carried out in a fragment of montane cloud forest of secondary succession on the eastern slope of Cordillera Real in the Andes of southern Ecuador, located at 2250 m a.s.l. characterized by a steep slope, mean annual temperature of 20.8°C and annual precipitation of 2193 mm. All trees with DBH > 1 cm were mapped, characterized and identified. All E. rhopalostele individuals present were counted, marked, characterized and mapped. Leaf samples of all orchid individuals were collected for DNA analysis. Root samples of flowering E. rhopalostele individuals were collected for phylogenetic analysis of mycorrhizae, one per phorophyte. Spatial point pattern analysis based on Ripley`s K function and nearest neighbor function was used for trees, phorophytes and orchid population. We observed that spatial distribution of trees and phorophytes is not random, as it adjusts to a Poisson cluster process. This suggests a limitation for seed dispersal in the study fragment that is affecting orchid establishment. Furthermore, the small-scale spatial pattern of E. rhopalostele evidences a clustering that suggests a microsite preference for orchid establishment with a dispersal kernel of 0.4 m. Microsite features such as types of trees (dead trees or Clusia alata), shade tolerance trees, rough bark, distribution in the first meters suggest a tendency to prefer the understory for their establishment. Regarding plant-plant interaction a spatial segregation between adults and juveniles was present suggesting competition for limited resources conditioned for a microsite preference. Analysis of genetic structure of E. rhopalostele population through Structure and PCoA shows two genetic groups coexisting in this fragment and in the same phorophyte, possibly as a result of hybridization between sympatric species of Epidendrum. Our results of spatial autocorrelation analysis develop in GenAlex confirm a small-scale spatial-genetic structure within the genetic groups that is compatible with a short-distance dispersal mechanism caused by gravity or water run-off, instead of the long-distance seed dispersal promoted by wind generally attributed to orchids. For mycobionts identification ITS1-5.8S-ITS2 rDNA region was amplified. Phylogenetic analysis was performed with neighborjoining, Bayesian likelihood and maximum-likelihood for 47 sequences yielded two Tulasnella clades. This orchid establishes mycorrhizal associations with at least two different Tulasnella species. In some cases both fungi clades were present in same root, suggesting no limitation in fungal distribution. Concerning the implications for in situ conservation resulting from this work, the preservation of all forest fragment and their interactions (pollinators, mycorrhiza) is recommended to conserve the genetic diversity of this species. If a reintroduction were necessary, distances between individuals in each phorophyte within a range of 0.4 m, are recommended. To promote recruitment and regeneration of E. rhopalostele it is recommended that phorophytes correspond to dead or fallen trees or species, such as Clusia alata. Trees that have rough bark and are shade tolerant are also recommended. Furthermore, regarding vertical distribution, it is also convenient that orchids are located in the first meter (in understory, area with less light). In conclusion, limitation on seed dispersal, microsite characteristics, plant-plant interactions or interaction with cogeneric sympatric species and mycorrhizal preferences conditioned the presence of this epiphytic orchid in this fragment forest.

Nuevas herramientas para el estudio de la interacción entre especies en el espacio y en el tiempo

Las funciones de segundo orden son cada vez más empleadas en el análisis de procesos ecológicos. En este trabajo presentamos dos funciones de 2º orden desarrolladas recientemente que permiten analizar la interacción espacio-temporal entre dos especies o tipos funcionales de individuos. Estas funciones han sido desarrolladas para el estudio de interacciones entre especies en masas forestales a partir de la actual distribución diamétrica de los árboles. La primera de ellas es la función bivariante para procesos de puntos con marca Krsmm, que permite analizar la correlación espacial de una variable entre los individuos pertenecientes a dos especies en función de la distancia. La segunda es la función de reemplazo , que permite analizar la asociación entre los individuos pertenecientes a dos especies en función de la diferencia entre sus diámetros u otra variable asociada a dichos individuos. Para mostrar el comportamiento de ambas funciones en el análisis de sistemas forestales en los que operan diferentes procesos ecológicos se presentan tres casos de estudio: una masa mixta de Pinus pinea L. y Pinus pinaster Ait. en la Meseta Norte, un bosque de niebla de la Región Tropical Andina y el ecotono entre las masas de Quercus pyrenaica Willd. y Pinus sylvestris L. en el Sistema Central, en los que tanto la función Krsmm como la función r se utilizan para analizar la dinámica forestal a partir de parcelas experimentales con todos los árboles localizados y de parcelas de inventario.

A Clearer Picture of Total Variation Blind Deconvolution

Blind deconvolution is the problem of recovering a sharp image and a blur kernel from a noisy blurry image. Recently, there has been a significant effort on understanding the basic mechanisms to solve blind deconvolution. While this effort resulted in the deployment of effective algorithms, the theoretical findings generated contrasting views on why these approaches worked. On the one hand, one could observe experimentally that alternating energy minimization algorithms converge to the desired solution. On the other hand, it has been shown that such alternating minimization algorithms should fail to converge and one should instead use a so-called Variational Bayes approach. To clarify this conundrum, recent work showed that a good image and blur prior is instead what makes a blind deconvolution algorithm work. Unfortunately, this analysis did not apply to algorithms based on total variation regularization. In this manuscript, we provide both analysis and experiments to get a clearer picture of blind deconvolution. Our analysis reveals the very reason why an algorithm based on total variation works. We also introduce an implementation of this algorithm and show that, in spite of its extreme simplicity, it is very robust and achieves a performance comparable to the top performing algorithms.

Global adaptation of spring bread and durum wheat lines near-isogenic for major reduced height genes

The effect of major dwarfing genes, Rht-B1 and Rht-D1, in bread (Triticum aestivum L.) and durum (Triticum turgidum L. var. durum) wheats varies with environment. Six reduced-height near-isogenic spring wheat lines, included in the International Adaptation Trial (IAT), were grown in 81 trials around the world. Of the 56 IAT trials yielding > 3 Mg ha(-1), the mean yield of semidwarfs was significantly greater than tails in 54% of trials; in the 27 trials yielding < 3 Mg ha-1, semidwarfs were superior in only 24%. Sixteen pairs of semidwarf-tall near-isolines were grown in six managed drought environment trials (DETs) in northwestern Mexico. In these trials, semidwarfs outyielded talls in all but the most droughted environment (2.5 Mg ha(-1)). The effect of the height alleles varied with genetic background and environment. For both yield and height, variance components for allele and environment by allele interaction were larger than those for genetic background and genetic background by environment. Pattern analysis showed that tall and semidwarf lines had similar adaptation to stressed environments (< 2.8 Mg ha(-1), low rainfall), while semidwarfs yielded more in less stressed environments (> 4.3 Mg ha(-1), high rainfall). The best adapted near-isogenic pair had a Kauz background, where the tall was only 16% taller than the dwarf. In the Kauz-derived pair, the semidwarf outyielded the tall in only 13% of trials with no differences in low yielding trials. This supports the idea that '' short talls '' may be useful in marginal environments (yield < 3 Mg ha(-1)).

Using generative models for handwritten digit recognition

We describe a method of recognizing handwritten digits by fitting generative models that are built from deformable B-splines with Gaussian ``ink generators'' spaced along the length of the spline. The splines are adjusted using a novel elastic matching procedure based on the Expectation Maximization (EM) algorithm that maximizes the likelihood of the model generating the data. This approach has many advantages. (1) After identifying the model most likely to have generated the data, the system not only produces a classification of the digit but also a rich description of the instantiation parameters which can yield information such as the writing style. (2) During the process of explaining the image, generative models can perform recognition driven segmentation. (3) The method involves a relatively small number of parameters and hence training is relatively easy and fast. (4) Unlike many other recognition schemes it does not rely on some form of pre-normalization of input images, but can handle arbitrary scalings, translations and a limited degree of image rotation. We have demonstrated our method of fitting models to images does not get trapped in poor local minima. The main disadvantage of the method is it requires much more computation than more standard OCR techniques.

A hierarchical latent variable model for data visualization

Visualization has proven to be a powerful and widely-applicable tool the analysis and interpretation of data. Most visualization algorithms aim to find a projection from the data space down to a two-dimensional visualization space. However, for complex data sets living in a high-dimensional space it is unlikely that a single two-dimensional projection can reveal all of the interesting structure. We therefore introduce a hierarchical visualization algorithm which allows the complete data set to be visualized at the top level, with clusters and sub-clusters of data points visualized at deeper levels. The algorithm is based on a hierarchical mixture of latent variable models, whose parameters are estimated using the expectation-maximization algorithm. We demonstrate the principle of the approach first on a toy data set, and then apply the algorithm to the visualization of a synthetic data set in 12 dimensions obtained from a simulation of multi-phase flows in oil pipelines and to data in 36 dimensions derived from satellite images.

Hierarchical GTM: constructing localized non-linear projection manifolds in a principled way

It has been argued that a single two-dimensional visualization plot may not be sufficient to capture all of the interesting aspects of complex data sets, and therefore a hierarchical visualization system is desirable. In this paper we extend an existing locally linear hierarchical visualization system PhiVis ¸iteBishop98a in several directions: bf(1) We allow for em non-linear projection manifolds. The basic building block is the Generative Topographic Mapping (GTM). bf(2) We introduce a general formulation of hierarchical probabilistic models consisting of local probabilistic models organized in a hierarchical tree. General training equations are derived, regardless of the position of the model in the tree. bf(3) Using tools from differential geometry we derive expressions for local directional curvatures of the projection manifold. Like PhiVis, our system is statistically principled and is built interactively in a top-down fashion using the EM algorithm. It enables the user to interactively highlight those data in the ancestor visualization plots which are captured by a child model. We also incorporate into our system a hierarchical, locally selective representation of magnification factors and directional curvatures of the projection manifolds. Such information is important for further refinement of the hierarchical visualization plot, as well as for controlling the amount of regularization imposed on the local models. We demonstrate the principle of the approach on a toy data set and apply our system to two more complex 12- and 18-dimensional data sets.

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.

Hippocampal pathology in progressive supranuclear palsy (PSP): a quantitative study of 8 cases

Objective: To quantify the neuronal and glial cell pathology in the hippocampus and the parahippocampal gyrus (PHG) of 8 cases of progressive supranuclear palsy (PSP). Material: tau-immunolabeled sections of the temporal lobe of 8 diagnosed cases of PSP. Method: The densities of lesions were measured in the PHG, CA sectors of the hippocampus and the dentate gyrus (DG) and studied using spatial pattern analysis. Results: Neurofibrillary tangles (NFT) and abnormally enlarged neurons (EN) were most frequent in the PHG and in sector CA1 of the hippocampus, oligodendroglial inclusions (“coiled bodies”) (GI) in the PHG, subiculum, sectors CA1 and CA2, and neuritic plaques (NP) in sectors CA2 and CA4. The DG was the least affected region. Vacuolation and GI were observed in the alveus. No tufted astrocytes (TA) were observed. Pathological changes exhibited clustering, the lesions often exhibiting a regular distribution of the clusters parallel to the tissue boundary. There was a positive correlation between the degree of vacuolation in the alveus and the densities of NFT in CA1 and GI in CA1 and CA2. Conclusion: The pathology most significantly affected the output pathways of the hippocampus, lesions were topographically distributed, and hippocampal pathology may be one factor contributing to cognitive decline in PSP.

A quantitative study of the pathological changes in the cerebellum in 15 cases of variant Creutzfeldt–Jakob disease (vCJD)

Aims: To determine in the cerebellum in variant Creutzfeldt–Jakob disease (vCJD): (i) whether the pathology affected all laminae; (ii) the spatial topography of the pathology along the folia; (iii) spatial correlations between the pathological changes; and (iv) whether the pathology was similar to that of the common methionine/methionine Type 1 subtype of sporadic CJD. Methods: Sequential cerebellar sections of 15 cases of vCJD were stained with haematoxylin and eosin, or immunolabelled with monoclonal antibody 12F10 against prion protein (PrP) and studied using spatial pattern analysis. Results: Loss of Purkinje cells was evident compared with control cases. Densities of the vacuolation and the protease-resistant form of prion protein (PrPSc) (diffuse and florid plaques) were greater in the granule cell layer (GL) than the molecular layer (ML). In the ML, vacuoles and PrPSc plaques occurred in clusters regularly distributed along the folia with larger clusters of vacuoles and diffuse plaques in the GL. There was a negative spatial correlation between the vacuoles and the surviving Purkinje cells in the ML. There was a positive spatial correlation between the vacuoles and diffuse PrPSc plaques in the ML and GL. Conclusions: (i) all laminae were affected by the pathology, the GL more severely than the ML; (ii) the pathology was topographically distributed along the folia especially in the Purkinje cell layer and ML; (iii) pathological spread may occur in relation to the loop of anatomical connections involving the cerebellum, thalamus, cerebral cortex and pons; and (iv) there were pathological differences compared with methionine/methionine Type 1 sporadic CJD.