Analysis Of Spatial Correlations Research Articles

Information Theory for Correlation Analysis and Estimation of Uncertainty Reduction in Maps and Models

The quantification and analysis of uncertainties is important in all cases where maps and models of uncertain properties are the basis for further decisions. Once these uncertainties are identified, the logical next step is to determine how they can be reduced. Information theory provides a framework for the analysis of spatial uncertainties when different subregions are considered as random variables. In the work presented here, joint entropy, conditional entropy, and mutual information are applied for a detailed analysis of spatial uncertainty correlations. The aim is to determine (i) which areas in a spatial analysis share information, and (ii) where, and by how much, additional information would reduce uncertainties. As an illustration, a typical geological example is evaluated: the case of a subsurface layer with uncertain depth, shape and thickness. Mutual information and multivariate conditional entropies are determined based on multiple simulated model realisations. Even for this simple case, the measures not only provide a clear picture of uncertainties and their correlations but also give detailed insights into the potential reduction of uncertainties at each position, given additional information at a different location. The methods are directly applicable to other types of spatial uncertainty evaluations, especially where multiple realisations of a model simulation are analysed. In summary, the application of information theoretic measures opens up the path to a better understanding of spatial uncertainties, and their relationship to information and prior knowledge, for cases where uncertain property distributions are spatially analysed and visualised in maps and models.

Space-time combined correlation integral and earthquake interactions

Scale invariant properties of seismicity argue for the presence of complex triggering mechanisms. We propose a new method, based on the space-time combined generalization of the correlation integral, that leads to a self-consistent visualization and analysis of both spatial and temporal correlations. The analysis has been applied on global medium-high seismicity. Results show that earthquakes do interact even on long distances and are correlated in time within defined spatial ranges varying over elapsed time. On that base we redefine the aftershock concept.

In-vivo investigation of the human cingulum bundle using the optimization of MR diffusion spectrum imaging

Diffusion spectrum imaging (DSI) is a generalization of diffusion tensor imaging to map fibrous structure of white matter and potentially very sensitive to alterations of the cingulum bundles in dementia. In this in-vivo 4T study, DSI parameters especially spatial resolution and diffusion encoding bandwidth were optimized on humans to segment the cingulum bundles for tract level measurements of diffusion. The careful tailoring of the DSI acquisitions in conjunction with fiber tracking provided an optimal DSI setting for a reliable quantification of the cingulum bundle tracts. The optimization of tracking the cingulum bundle was verified using fiber tract quantifications, including coefficients of variability of DSI measurements along the fibers between and within healthy subjects in back-to-back studies and variogram analysis of spatial correlations between diffusion orientation distribution functions (ODF) along the cingulum bundle tracts. The results demonstrate that the identification of the cingulum bundle in human brain is reproducible using an optimized DSI parameter for maximum b-value and high spatial resolution of the DSI acquisition with a feasible acquisition time of whole brain in clinical practice. This optimized DSI setting should be useful for detecting alterations along the cingulum bundle in Alzheimer disease and related neurodegenerative disorders.

Intra- and intermolecular organization of sulfopolystyrene ionomers in solutions: Neutron scattering study

Processes of self-organization of sulfonated PS with a low content of ionogenic groups in the acidic form (SO3H) in chloroform have been studied by cold neutron scattering. An analysis of spatial correlations of macromolecules shows that two factors (electrostatic interactions and hydrogen bonds between SO3H groups) are responsible for the conformational transformation of ionomer chains to hollow structures of the type of spherical micelles with dense packing of SO3H groups in the shell stabilized by hydrogen bonds. At a moderate content of SO3H groups (2.6 mol %), micellar particles of ionomers form chain clusters composed of three to five particles. In solutions of ionomers with a higher content of ionogenic groups (∼4.5 mol %), highly ordered three-dimensional structures appear in the form of fragments of a simple cubic lattice with a constant equal to the diameter of micelles.

Thickness dependence of mobility in CuPc thin film on amorphous SiO2 substrate

Hole mobility in a copper-phthalocyanine (CuPc)-based top-contact transistor has been studied with various organic layer thicknesses. It is found that the transistor performance depends on the thickness of the CuPc layer, and the mobility increases with the increase in the CuPc layer and saturated at the thickness of 6 ML. The upper layers do not actively contribute to the carrier transport in the organic films. The morphology of the organic layer grown on the bare SiO2/Si substrate is also presented. The analysis of spatial correlations shows that the CuPc films grow on the SiO2 according to the mixed-layer mode.

Spatial Correlations in a Transonic Jet

properties. The data are presented from two separate experiments; one with the light sheet orientated in the streamwise direction (r–x plane) and one with the light sheet perpendicular to the flow direction (r–� plane). The instrument’s characteristics allow for the calculation and subsequent analysis of the two-point spatial correlations which are known to be relevant to the source terms in acoustics analogies where sound production is concerned. An examination of the spatial correlations demonstrates the averaged spatial evolution of the jet’s large-scale turbulent structures throughout the noise producing region. In particular, the (r–x) spatial dependence of the axial and azimuthal normal stresses manifest a oblique structure in the mixing layer regions of the flow, whereas the radial normalstressesevolvemoreuniformlytowardtheendofthepotentialcore.Quadrupolesourcetermsrelevanttothe soundproduction mechanismsare alsocalculated from which their spatial distributions areanalyzed with zerotime delay.Theanalysisofthesesourcetermsatx=D � 4showhowthepeakenergyfortheshear-noisecomponentresides on the high-speed side of the shear layer around r=D � 0:33, whereas the self-noise terms peak along the lip-line at r=D � 0:5,andaremostenergeticforthestreamwiseandazimuthalcomponentsofthevelocity.Tofullyevaluatethe quadrupole sources of noise, the space-time correlations of the full three-dimensional turbulent flowfield are required which are currently not available from experiments.

On the extraction of spectral and spatial information from images

For the analysis of spatial and spectral correlations in RGB, multispectral, or hyperspectral images, different ways of combining Principal Component Analysis and multiresolution analysis are investigated and integrated into a unified framework. The integration of different frameworks is the purpose of this paper since a unified framework is necessary in the situation where the efficient analysis of both spatial and spectral correlations is needed at the same time. This unified framework also provides a remedy for a limitation of multivariate image analysis (MIA), namely the loss of spatial information in the images. The unified framework, multiresolutional multivariate image analysis (MR-MIA), is illustrated visually through the decomposition of a simple color image, and then used in a quantitative manner for color-textured image classification where the extraction of both spatial and spectral information is necessary. The performance of MR-MIA approaches are shown to be equal to or better than that of wavelet texture analysis, while employing a smaller number of features, and maintaining computational complexity at the same level. Wavelet texture analysis is shown to be a limiting case of one form of MR-MIA. The true advantages of MR-MIA will be most evident when analyzing hyperspectral images having a large number of spectral bands.

Dynamical Arrest in Attractive Colloids: The Effect of Long-Range Repulsion

We study gelation in suspensions of model colloidal particles with short-ranged attractive and long-ranged repulsive interactions by means of three-dimensional fluorescence confocal microscopy. At low packing fractions, particles form stable equilibrium clusters. Upon increasing the packing fraction the clusters grow in size and become increasingly anisotropic until finally associating into a fully connected network at gelation. We find a surprising order in the gel structure. Analysis of spatial and orientational correlations reveals that the gel is composed of dense chains of particles constructed from face-sharing tetrahedral clusters. Our findings imply that dynamical arrest occurs via cluster growth and association.

Spatially correlated charge transport in organic thin film transistors.

Hole mobility in organic ultrathin film field-effect transistors is studied as a function of the coverage. For layered sexithienyl films, the charge carrier mobility rapidly increases with increasing coverage and saturates at a coverage of about two monolayers. This shows that the first two molecular layers next to the dielectric interface dominate the charge transport. A quantitative analysis of spatial correlations shows that the second layer is crucial, as it provides efficient percolation pathways for carriers generated in both the first and the second layers. The upper layers do not actively contribute either because their domains are smaller than the ones in the second layer or because the carrier density is negligible.

Radial distribution function analysis of spatial atomic correlations in carbon nanotubes

This paper reports on structural characterisation of single and multi-wall carbon nanotubes, synthesised by catalytic decomposition of methane and acetylene, by wide-angle pulsed neutron scattering, extended up to a maximum scattering vector of Q max=60 Å −1. The intensity data were converted to real space via the Fourier transform yielding the radial distribution functions (RDFs) with the resolution of approximately 0.1 Å. The structural parameters defining the interatomic distances, their standard deviations and the coordination numbers have been derived from the experimental data by a curve-fitting method based on a least-squares algorithm. The nearest-neighbour carbon–carbon distance 1.41 Å is practically the same as that of graphite and clearly shorter than the value of 1.44 Å found for fullerenes. The results provide experimental evidence for the hexagonal structure within a single tubule and turbostratic stacking of successive tubules. The derived RDFs can be fitted using a model based on a hexagonal network with disorder increasing with square root of the interatomic distance.

Radial distribution function analysis of spatial atomic correlations in carbon nanotubes

This paper reports on structural characterisation of single and multi-wall carbon nanotubes, synthesised by catalytic decomposition of methane and acetylene, by wide-angle pulsed neutron scattering, extended up to a maximum scattering vector of Qmax=60 Å−1. The intensity data were converted to real space via the Fourier transform yielding the radial distribution functions (RDFs) with the resolution of approximately 0.1 Å. The structural parameters defining the interatomic distances, their standard deviations and the coordination numbers have been derived from the experimental data by a curve-fitting method based on a least-squares algorithm. The nearest-neighbour carbon–carbon distance 1.41 Å is practically the same as that of graphite and clearly shorter than the value of 1.44 Å found for fullerenes. The results provide experimental evidence for the hexagonal structure within a single tubule and turbostratic stacking of successive tubules. The derived RDFs can be fitted using a model based on a hexagonal network with disorder increasing with square root of the interatomic distance.

GenomeInspector: Basic Software Tools for Analysis of Spatial Correlations between Genomic Structures within Megabase Sequences

The speed of acquisition of genomic sequence data exceeds the evaluation of function of the sequences by a vast margin. Most software available for the prediction of individual features does not assess the correlation of different motifs (level 1 methods). Here, we present a second-level software package called GenomeInspector (GI) for further analysis of results obtained with level 1 methods. Our approach does not require anya prioriknowledge about motif organization and was designed as a modular package with a graphical user interface. Three examples for GI application are presented.

On the interpretation of solute induced solvent structure

Computer simulation results in which a water molecule is considered, formally, as a solute in liquid water are examined in order to clarify the role played by solution geometry in the interpretation of solvation structure. An analysis of spatial correlations and intermolecular hydrogen bonding in the solvation ’’shell’’ is used to show that solvent molecular packing around the solute can substantially distort the quantitative measures of structure and that this must be considered carefully in their interpretation. (AIP)

Transverse Correlation and Transverse Mode in Simple Liquid

Properties of the transverse correlation and transverse modes in the dynamical region in a simple liquid are studied on the basis of the generalized Langevin equation. Under the assumption of Gaussian decay of the time correlation of the random forces, the molecular expressions for the transverse current correlation function and the transverse response function are obtained. Numerical calculations are made for the liquid argon at T =84.25 K. The analysis of spatial correlations shows that the local correlations in a liquid may conveniently be described by two parts, the radial and the angular parts. The damping of the correlation Δ ( k ) shows a very weak dependence on the wave number k . The dispersion relation of the transverse mode is obtained from the maximum of the correlation function. The analytical properties of the pole of the response function shows the possibility of the propagation of the transverse mode in the case where G / Δ 2 >0.294, G being related with the modulus of rigidity.