Statistical Network Analysis for Functional MRI: Summary Networks and Group Comparisons

Comparing weighted networks in neuroscience is hard, because the topological properties of a given network are necessarily dependent on the number of edges of that network. This problem arises in the analysis of both weighted and unweighted networks. The term density is often used in this context, in order to refer to the mean edge weight of a weighted network, or to the number of edges in an unweighted one. Comparing families of networks is therefore statistically difficult because differences in topology are necessarily associated with differences in density. In this review paper, we consider this problem from two different perspectives, which include (i) the construction of summary networks, such as how to compute and visualize the mean network from a sample of network-valued data points; and (ii) how to test for topological differences, when two families of networks also exhibit significant differences in density. In the first instance, we show that the issue of summarizing a family of networks can be conducted by adopting a mass-univariate approach, which produces a statistical parametric network (SPN). In the second part of this review, we then highlight the inherent problems associated with the comparison of topological functions of families of networks that differ in density. In particular, we show that a wide range of topological summaries, such as global efficiency and network modularity are highly sensitive to differences in density. Moreover, these problems are not restricted to unweighted metrics, as we demonstrate that the same issues remain present when considering the weighted versions of these metrics. We conclude by encouraging caution, when reporting such statistical comparisons, and by emphasizing the importance of constructing summary networks.Comment: 16 pages, 5 figure

Weighted Frechet Means as Convex Combinations in Metric Spaces: Properties and Generalized Median Inequalities

In this short note, we study the properties of the weighted Frechet mean as a convex combination operator on an arbitrary metric space, (Y,d). We show that this binary operator is commutative, non-associative, idempotent, invariant to multiplication by a constant weight and possesses an identity element. We also treat the properties of the weighted cumulative Frechet mean. These tools allow us to derive several types of median inequalities for abstract metric spaces that hold for both negative and positive Alexandrov spaces. In particular, we show through an example that these bounds cannot be improved upon in general metric spaces. For weighted Frechet means, however, such inequalities can solely be derived for weights equal or greater than one. This latter limitation highlights the inherent difficulties associated with working with abstract-valued random variables.Comment: 7 pages, 1 figure. Submitted to Probability and Statistics Letter

Use of flowable fill as a backfill material around buried pipes

The objective of this research work was to study the performance of flowable fill as a backfill material around buried plastic corrugated pipes. The flowable fill materials used in this study contained varying proportions of fly ash, bottom ash, river sand, waste foundry sand, and cement. The relationships between flowability and compressive strength were investigated for different mixtures by using ASTM test methods in order to design suitable mixtures that meet WVDOT materials specifications. The second phase of the research was to design and construct a laboratory-scale pipe testing apparatus. The final phase was to find the pipe-soil interactions under several variable laboratory conditions using the constructed pipe testing apparatus and different backfill materials. These variables included: trench width, pipe diameter, in-situ soil strength, backfill strength, and surcharge loading. The results of these experiments show that the fly ash based flowable fill materials can be successfully used as a backfill around buried pipes even with narrow trench widths

Alluvial Sedimentation Associated with Logging in Low Gradient Watersheds in DeSoto National Forest, Mississippi

Forestry and related businesses are an important factor of Mississippi’s economy, contributing between $11 and$14 billion annually (Mississippi Forestry Commission, 2006). The timber industry is not only important in Mississippi but is an important sector of the economy throughout the Gulf Coast region. While providing positive economic benefits to the region, the forestry industry can also negatively affect soil properties, hillslope stability, and increase sedimentation rates in local streams and rivers. The aim of this research is to determine if forestry removal causes an increase of soil erosion and how it affects floodplain sedimentation in the low gradient watershed Whiskey Creek, located in DeSoto National Forest. Using the Revised Universal Soil Loss Equation (RUSLE) to model and predict sediment erosion, and the use of historical aerial photographs to determine exact locations of forestry removals, the RUSLE model predicted 10 times more erosion during periods of logging compared to natural conditions. Radiometrically dated sediment was used to determine the sediment accumulation rates of Whiskey Creek and was compared to a predicted sedimentation rate produced by three different land clearance scenarios using the RUSLE model. Of the three scenarios suggested, the most severe model provided the best results when compared to the measured sediment accumulation rate

International Workshop on Nutrient Balances for Sustainable Agricultural Production and Natural Resource Management in Southeast Asia, Bangkok, Thailand, 20-22 February 2001: selected papers and presentations

Soil management / Soil properties / Soil fertility / Soil degradation / Crop production / Farmers / Agricultural extension / Farming systems / Sustainability / Rice / Cassava / Vegetables / Maize / Fertilizers / Decision support tools / Economic aspects

Segmentation of neuroanatomy in magnetic resonance images

Segmentation in neurological Magnetic Resonance Imaging (MRI) is necessary for volume measurement, feature extraction and for the three-dimensional display of neuroanatomy. This thesis proposes several automated and semi-automated methods which offer considerable advantages over manual methods because of their lack of subjectivity, their data reduction capabilities, and the time savings they give. Work has concentrated on the use of dual echo multi-slice spin-echo data sets in order to take advantage of the intrinsically multi-parametric nature of MRI. Such data is widely acquired clinically and segmentation therefore does not require additional scans. The literature has been reviewed. Factors affecting image non-uniformity for a modem 1.5 Tesla imager have been investigated. These investigations demonstrate that a robust, fast, automatic three-dimensional non-uniformity correction may be applied to data as a pre-processing step. The merit of using an anisotropic smoothing method for noisy data has been demonstrated. Several approaches to neurological MRI segmentation have been developed. Edge-based processing is used to identify the skin (the major outer contour) and the eyes. Edge-focusing, two threshold based techniques and a fast radial CSF identification approach are proposed to identify the intracranial region contour in each slice of the data set. Once isolated, the intracranial region is further processed to identify CSF, and, depending upon the MRI pulse sequence used, the brain itself may be sub-divided into grey matter and white matter using semiautomatic contrast enhancement and clustering methods. The segmentation of Multiple Sclerosis (MS) plaques has also been considered. The utility of the stack, a data driven multi-resolution approach to segmentation, has been investigated, and several improvements to the method suggested. The factors affecting the intrinsic accuracy of neurological volume measurement in MRI have been studied and their magnitudes determined for spin-echo imaging. Geometric distortion - both object dependent and object independent - has been considered, as well as slice warp, slice profile, slice position and the partial volume effect. Finally, the accuracy of the approaches to segmentation developed in this thesis have been evaluated. Intracranial volume measurements are within 5% of expert observers' measurements, white matter volumes within 10%, and CSF volumes consistently lower than the expert observers' measurements due to the observers' inability to take the partial volume effect into account