Non-gaussian Spatial Correlations Dramatically Weaken Localization.

We perform variational studies of the interaction-localization problem to describe the interaction-induced renormalizations of the effective (screened) random potential seen by quasiparticles. Here we present results of careful finite-size scaling studies for the conductance of disordered Hubbard chains at half-filling and zero temperature. While our results indicate that quasiparticle wave functions remain exponentially localized even in the presence of moderate to strong repulsive interactions, we show that interactions produce a strong decrease of the characteristic conductance scale g^{*} signaling the crossover to strong localization. This effect, which cannot be captured by a simple renormalization of the disorder strength, instead reflects a peculiar non-Gaussian form of the spatial correlations of the screened disordered potential, a hitherto neglected mechanism to dramatically reduce the impact of Anderson localization (interference) effects.

Spatial correlations and cross sections of clusters in the A + B -> 0 reaction

We consider the distribution of cross sections of clusters and the density-density correlation functions for the A+B¿0 reaction. We solve the reaction-diffusion equations numerically for random initial distributions of reactants. When both reactant species have the same diffusion coefficients the distribution of cross sections and the correlation functions scale with the diffusion length and obey superuniversal laws (independent of dimension). For different diffusion coefficients the correlation functions still scale, but the scaling functions depend on the dimension and on the diffusion coefficients. Furthermore, we display explicitly the peculiarities of the cluster-size distribution in one dimension.

Spatial correlations and cross sections of clusters in the A + B -> 0 reaction

We consider the distribution of cross sections of clusters and the density-density correlation functions for the A+B¿0 reaction. We solve the reaction-diffusion equations numerically for random initial distributions of reactants. When both reactant species have the same diffusion coefficients the distribution of cross sections and the correlation functions scale with the diffusion length and obey superuniversal laws (independent of dimension). For different diffusion coefficients the correlation functions still scale, but the scaling functions depend on the dimension and on the diffusion coefficients. Furthermore, we display explicitly the peculiarities of the cluster-size distribution in one dimension.

Spatial correlations between beta-amyloid (Abeta) deposits and blood vessels in early-onset Alzheimer's disease

In cases of late-onset Alzheimer’s disease (AD), there is a spatial correlation between the classsic ‘cored’ type of Beta-amyloid (Abeta) deposit and the large vertically penetrating arterioles in the cerebral cortex suggesting that blood vessels are involved in the pathogenesis of the classic deposits. In this chapter, the spatial correlations between the diffuse, primitive, and classic Abeta deposits and blood vessels were studied in 10 cases of early-onset AD in the age range 40 – 65 years. Sections of frontal cortex were immunostained with antibodies against Abeta?and with collagen IV to reveal the Abeta deposits and blood vessel profiles. In the early-onset cases as a whole, all types of Abeta? deposit and blood vessel profiles were distributed in clusters. There was a positive spatial correlation between the clusters of the diffuse Abeta deposits and the larger (>10µm) and smaller diameter (<10?m) blood vessel profiles in one and three cases respectively. The primitive and classic Abeta deposits were spatially correlated with larger and smaller blood vessels both in three and four cases respectively. Spatial correlations between the Abeta deposits and blood vessels may be more prevalent in cases expressing amyloid precursor protein (APP) than presenilin 1 (PSEN1) mutations. Apolipoprotein E (Apo E) genotype of the patient did not appear to influence the spatial correlation with blood vessel profiles. The data suggest that the larger diameter blood vessels are less important in the pathogenesis of the classic Abeta deposits in early-onset compared with late-onset AD.

Spatial correlations between the vacuolation, prion protein (PrPsc) deposits and the cerebral blood vessels in sporadic Creutzfeldt-Jakob disease

In the variant form of Creutzfeldt-Jakob disease (vCJD), 'florid' deposits of the protease resistant form of prion protein (PrP(sc)) were aggregated around the cerebral blood vessels suggesting the possibility that prions may spread into the brain via the cerebral microcirculation. The objective of the present study was to determine whether the pathology was spatially related to blood vessels in cases of sporadic CJD (sCJD), a disease without an iatrogenic etiology, and therefore, less likely to be caused by hematogenous spread. Hence, the spatial correlations between the vacuolation ('spongiform change'), PrP(sc) deposits, and the blood vessels were studied in immunolabelled sections of the cerebral cortex and cerebellum in eleven cases of the common M/M1 subtype of sCJD. Both the vacuolation and the PrP(sc) deposits were spatially correlated with the blood vessels; the PrP(sc) deposits being more focally distributed around the vessels than the vacuoles. The frequency of positive spatial correlations was similar in the different gyri of the cerebral cortex, in the upper and lower cortical laminae, and in the molecular layer of the cerebellum. It is hypothesized that the spatial correlation is attributable to factors associated with the blood vessels which promote the aggregation of PrP(sc) to form deposits rather than representing the hematogenous spread of the disease. The aggregated form of PrP(sc) then enhances cell death and may encourages the development of vacuolation in the vicinity of the blood vessels.

Spatial correlations between the vacuolation, prion protein deposits, and surviving neurons in the cerebral cortex in sporadic Creutzfeldt-Jakob disease

In the cerebral cortex of cases of sporadic Creutzfeldt-Jakob disease (sCJD), the vacuolation (spongiform change) and PrP deposits are aggregated into clusters which are regularly distributed parallel to the pia mater. The objective of the present study was to determine the spatial relationships between the clusters of the vacuoles and PrP deposits and between the pathological changes and variations in the density of surviving neurons. In areas with low densities of pathological change, clusters of vacuoles were spatially correlated with the surviving neurons and not with the PrP deposits. By contrast, in more significantly affected areas, clusters of vacuoles were spatially correlated with those of the PrP deposits and not with the surviving neurons. In addition, areas with a high density of vacuoles and a low density of PrP deposits exhibited no spatial correlations between the variables. These data suggest that the spatial relationships between the vacuolation, PrP deposits and surviving neurons in sCJD depend on the density of lesions present. Differences in the pattern of correlation may reflect the developmental stage of the pathology in particular cortical areas.

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.

Spatial correlations between beta-amyloid (A beta) deposits and blood vessels in familial Alzheimer's disease

In sporadic Alzheimer’s disease (SAD), the classic (‘dense-cored’) ß-amyloid (Aß) deposits are aggregated around the larger blood vessels in the upper laminae of the cerebral cortex. To determine whether a similar relationship exists in familial AD (FAD), the spatial correlations between the diffuse, primitive, and classic ß-amyloid (Aß deposits and blood vessels were studied in ten FAD cases including cases linked to amyloid precursor protein (APP) and presenilin (PSEN) gene mutations and expressing apolipoprotein E (apo E) allele E4. Sections of frontal cortex were immunolabelled with antibodies against Aß and with collagen IV to reveal the Aß deposits and blood vessel profiles. In the FAD cases as a whole, Aßdeposits were distributed in clusters. There was a positive spatial correlation between the clusters of the diffuse Aßdeposits and the larger (>10 µm) and smaller diameter (<10 µm) blood vessels in one and three cases respectively. The primitive Aß deposits were spatially correlated with larger and smaller blood vessels each in four cases and the classic deposits in three and four cases respectively. Apo E genotype of the patient did not influence spatial correlation with blood vessels. Hence, spatial correlations between the classic deposits and larger diameter blood vessels were significantly less frequent in FAD compared with SAD. It was concluded that both Aß deposit morphology and AD subtype determine spatial correlations with blood vessels in AD.

Spatial correlations between the vacuolation, prion protein deposition and surviving neurons in variant Creutzfeldt-Jakob Disease (vCJD)

The histological features of cases of variant Creutzfeldt-Jakob disease (vCJD) are often distributed in the brain in clusters. This study investigated the spatial associations between the clusters of the vacuoles, surviving neurons, and prion protein (PrP) deposits in various brain areas in 11 cases of vCJD. Clusters of vacuoles and surviving neurons were positively correlated in the cerebral cortex but negatively correlated in the dentate gyrus. Clusters of the florid and diffuse type of PrP deposit were not positively correlated with those of either the vacuoles or the surviving neurons although a negative correlation was observed between the florid plaques and surviving neurons in some cortical areas. Clusters of the florid and diffuse deposits were either negatively correlated or uncorrelated. These data suggest: 1) that clusters of vacuoles in the cerebral cortex are associated with the presence of surviving neuronal cell bodies, 2) that the clusters of vacuoles are not spatially related to those of the PrP deposits, and 3) different factors are involved in the pathogenesis of the florid and diffuse PrP deposits.

Spatial correlations between the neuronal inclusions, swollen achromatic neurons, and glial cells in neuronal intermediate filament inclusion disease (NIFID)

Neuronal intermediate filament (IF) inclusion disease (NIFID) is characterized by neuronal loss, neuronal cytoplasmic IF-positive inclusions (NI), swollen neurons (SN), and a glial cell reaction. We studied the spatial correlations between the clusters of NI, SN, and glial cells in four gyri of the temporal lobe (superior temporal gyrus, inferior temporal gyrus, lateral occipitotemporal gyrus, and parahippocampal gyrus) in four cases of NIFID. The densities of histological features (per 50x250 μ sample field) were as follows: NI (mean = 0.41, range 0.28-0.68), SN (mean = 1.41, range 0.47-2.65), glial cell nuclei (mean = 5.21, range 3.63-8.17). The NI and the SN were positively correlated in half of the brain regions examined, the correlations being present at the smallest field size (50x250 μm). The NI were also positively or negatively correlated with the glial cell nuclei in different areas, the negative correlations being present at the smallest field size. Glial cell nuclei were positively or negatively correlated with the SN in different brain areas, mainly at the larger field sizes (400x250 and 800x250 μm). The spatial correlation between the clusters of NI and SN in the cortex suggests their development within the same columns of cells. At first, the glial cell reaction is also confined to these columns but later becomes more generally distributed across the cortex. © Springer-Verlag 2004.

Spatial and linear correlations between soil and corn

The Technologies setting at Agricultural production system have the main characteristics the vertical productivity, reduced costs, soil physical, chemical and biological improvement to promote production sustainable growth. Thus, the study aimed to determine the variability and the linear and special correlations between the plant and soil attributes in order to select and indicate good representation of soil physical quality for forage productivity. In the growing season of 2006, on the Fazenda Bonança in Pereira Barreto (SP), the productivity of autumn corn forage (FDM) in an irrigated no-tillage system and the soil physical properties were analyzed. The purpose was to study the variability and the linear and spatial correlations between the plant and soil properties, to select an indicator of soil physical quality related to corn forage yield. A geostatistical grid was installed to collect soil and plant data, with 125 sampling points in an area of 2,500 m². The results show that the studied properties did not vary randomly and that data variability was low to very high, with well-defined spatial patterns, ranging from 7.8 to 38.0 m. On the other hand, the linear correlation between the plant and the soil properties was low and highly significant. The pairs forage dry matter versus microporosity and stem diameter versus bulk density were best correlated in the 0-0.10 m layer, while the other pairs - forage dry matter versus macro - and total porosity - were inversely correlated in the same layer. However, from the spatial point of view, there was a high inverse correlation between forage dry matter with microporosity, so that microporosity in the 0-0.10 m layer can be considered a good indicator of soil physical quality, with a view to corn forage yield.

Spatial and linear correlations between soil and corn

O conjunto de tecnologias aplicadas ao sistema de produção agrícola tem como características principais a verticalização da produtividade, diminuição de custos, melhoria nas características físicas, químicas e biológicas do solo para proporcionarem o crescimento sustentável do meio de produção. Desta forma, o trabalho teve como objetivo determinar a variabilidade e as correlações lineares e especiais entre os atributos da planta e do solo, visando selecionar um indicador da qualidade física do solo de boa representatividade para produção de forragem. No ano agrícola de 2006, na Fazenda Bonança, município de Pereira Barreto (SP), foram analisados a produtividade de forragem do milho outonal (FDM) em sistema plantio direto irrigado e os atributos físicos do solo, num Latossolo Vermelho distrófico. O objetivo foi estudar a variabilidade e as correlações lineares e espaciais entre os atributos da planta e os do solo, visando selecionar um indicador da qualidade física do solo de boa representatividade para a produtividade da forragem. Foi instalada a malha geoestatística, para coleta de dados do solo e planta, contendo 125 pontos amostrais, numa área de 2.500 m². Os atributos estudados, além de não terem variado aleatoriamente, apresentaram variabilidade dos dados entre baixa e muito alta e seguiram padrões espaciais bem definidos, com alcances entre 7,8 e 38,0 m. Por outro lado, a correlação linear entre os atributos da planta com o do solo foi baixa e extremamente significativa. Os pares Massa Seca de forragem versus Microporosidade e Diâmetro do colmo versus Densidade do Solo foram melhor correlacionados na camada de 0-0.10m, enquanto os outros pares - Massa Seca de Forragem versus Macroporosidade - e Porosidade Total - apresentaram correlação inversa para a mesma camada. Entretanto, do ponto de vista espacial, houve uma alta correlação inversa entre Massa Seca de Forragem com Microporosidade, de modo que a microporosidade na camada de 0-0.10m pode ser considerada um bom indicador de qualidade física do solo, tendo em vista a produção de forragem de milho.

SPATIAL CORRELATION BETWEEN PHYSICAL PROPERTIES OF SOIL AND WEEDS IN TWO MANAGEMENT SYSTEMS

The spatial correlation between soil properties and weeds is relevant in agronomic and environmental terms. The analysis of this correlation is crucial for the interpretation of its meaning, for influencing factors such as dispersal mechanisms, seed production and survival, and the range of influence of soil management techniques. This study aimed to evaluate the spatial correlation between the physical properties of soil and weeds in no-tillage (NT) and conventional tillage (CT) systems. The following physical properties of soil and weeds were analyzed: soil bulk density, macroporosity, microporosity, total porosity, aeration capacity of soil matrix, soil water content at field capacity, weed shoot biomass, weed density, Commelina benghalensis density, and Bidens pilosa density. Generally, the ranges of the spatial correlations were higher in NT than in CT. The cross-variograms showed that many variables have a structure of combined spatial variation and can therefore be mapped from one another by co-kriging. This combined variation also allows inferences about the physical and biological meanings of the study variables. Results also showed that soil management systems influence the spatial dependence structure significantly.

SPATIAL DEPENDENCE OF ELECTRICAL CONDUCTIVITY AND CHEMICAL PROPERTIES OF THE SOIL BY ELECTROMAGNETIC INDUCTION

Brazilian soils have natural high chemical variability; thus, apparent electrical conductivity (ECa) can assist interpretation of crop yield variations. We aimed to select soil chemical properties with the best linear and spatial correlations to explain ECa variation in the soil using a Profiler sensor (EMP-400). The study was carried out in Sidrolândia, MS, Brazil. We analyzed the following variables: electrical conductivity - EC (2, 7, and 15 kHz), organic matter, available K, base saturation, and cation exchange capacity (CEC). Soil ECa was measured with the aid of an all-terrain vehicle, which crossed the entire area in strips spaced at 0.45 m. Soil samples were collected at the 0-20 cm depth with a total of 36 samples within about 70 ha. Classical descriptive analysis was applied to each property via SAS software, and GS+ for spatial dependence analysis. The equipment was able to simultaneously detect ECa at the different frequencies. It was also possible to establish site-specific management zones through analysis of correlation with chemical properties. We observed that CEC was the property that had the best correlation with ECa at 15 kHz.

Correlations of control variables in variational data assimilation

Variational data assimilation systems for numerical weather prediction rely on a transformation of model variables to a set of control variables that are assumed to be uncorrelated. Most implementations of this transformation are based on the assumption that the balanced part of the flow can be represented by the vorticity. However, this assumption is likely to break down in dynamical regimes characterized by low Burger number. It has recently been proposed that a variable transformation based on potential vorticity should lead to control variables that are uncorrelated over a wider range of regimes. In this paper we test the assumption that a transform based on vorticity and one based on potential vorticity produce an uncorrelated set of control variables. Using a shallow-water model we calculate the correlations between the transformed variables in the different methods. We show that the control variables resulting from a vorticity-based transformation may retain large correlations in some dynamical regimes, whereas a potential vorticity based transformation successfully produces a set of uncorrelated control variables. Calculations of spatial correlations show that the benefit of the potential vorticity transformation is linked to its ability to capture more accurately the balanced component of the flow.