Nonparametric tests of structure for high angular resolution diffusion imaging in Q-space

High angular resolution diffusion imaging data is the observed characteristic function for the local diffusion of water molecules in tissue. This data is used to infer structural information in brain imaging. Nonparametric scalar measures are proposed to summarize such data, and to locally characterize spatial features of the diffusion probability density function (PDF), relying on the geometry of the characteristic function. Summary statistics are defined so that their distributions are, to first-order, both independent of nuisance parameters and also analytically tractable. The dominant direction of the diffusion at a spatial location (voxel) is determined, and a new set of axes are introduced in Fourier space. Variation quantified in these axes determines the local spatial properties of the diffusion density. Nonparametric hypothesis tests for determining whether the diffusion is unimodal, isotropic or multi-modal are proposed. More subtle characteristics of white-matter microstructure, such as the degree of anisotropy of the PDF and symmetry compared with a variety of asymmetric PDF alternatives, may be ascertained directly in the Fourier domain without parametric assumptions on the form of the diffusion PDF. We simulate a set of diffusion processes and characterize their local properties using the newly introduced summaries. We show how complex white-matter structures across multiple voxels exhibit clear ellipsoidal and asymmetric structure in simulation, and assess the performance of the statistics in clinically-acquired magnetic resonance imaging data.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS441 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Beyond the black box

We describe the role the open-source software community plays in fixing bugs through a case study of a problem with integer determinant computations in SageMath.Comment: Extended version of article to appear in the Notices of the AM

Ethnic differences in adiposity and diabetes risk – insights from genetic studies

Type 2 diabetes is more common in non-Europeans and starts at a younger age and at lower BMI cut-offs. This review discusses the insights from genetic studies about pathophysiological mechanisms which determine risk of disease with a focus on the role of adiposity and body fat distribution in ethnic disparity in risk of type 2 diabetes. During the past decade, genome-wide association studies (GWAS) have identified more than 400 genetic variants associated with the risk of type 2 diabetes. The Eurocentric nature of these genetic studies have made them less effective in identifying mechanisms that make non-Europeans more susceptible to higher risk of disease. One possible mechanism suggested by epidemiological studies is the role of ethnic difference in body fat distribution. Using genetic variants associated with an ability to store extra fat in a safe place, which is subcutaneous adipose tissue, we discuss how different ethnic groups could be genetically less susceptible to type 2 diabetes by developing a more favourable fat distribution

Open Content in Open Context

This article presents the challenges and rewards of sharing research content through a discussion of Open Context, a new open access data publication system for field sciences and museum collections. Open Context is the first data repository of its kind, allowing self-publication of research data, community commentary through tagging, and clear citation and stable hyperlinks, and Creative Commons licenses that make reusing content legal and easy.The Nov-Dec 2007 issue of Educational Technology magazine is an entire special issue dedicated to "Opening Educational Resources." A series of articles in this issue highlight open educational models, including OpenCourseWare, Connexions and this piece on Open Context, co-authored by Sarah Whitcher Kansa and Eric Kansa

Information flow between volatilities across time scales

Conventional time series analysis, focusing exclusively on a time series at a given scale, lacks the ability to explain the nature of the data generating process. A process equation that successfully explains daily price changes, for example, is unable to characterize the nature of hourly price changes. On the other hand, statistical properties of monthly price changes are often not fully covered by a model based on daily price changes. In this paper, we simultaneously model regimes of volatilities at multiple time scales through wavelet-domain hidden Markov models. We establish an important stylized property of volatility across different time scales. We call this property asymmetric vertical dependence. It is asymmetric in the sense that a low volatility state (regime) at a long time horizon is most likely followed by low volatility states at shorter time horizons. On the other hand, a high volatility state at long time horizons does not necessarily imply a high volatility state at shorter time horizons. Our analysis provides evidence that volatility is a mixture of high and low volatility regimes, resulting in a distribution that is non-Gaussian. This result has important implications regarding the scaling behavior of volatility, and consequently, the calculation of risk at different time scales.Discrete wavelet transform, wavelet-domain hidden Markov trees, foreign exchange markets; stock markets; multiresolution analysis; scaling

Enhancing Humanities Research Productivity in a Collaborative Data Sharing Environment

This project represents a multi-organizational, interdisciplinary effort to enhance collaborative research in cultural heritage fields by exploring user experience with Web-based technologies. The objective of this project is to document user needs around online systems for sharing primary data and documentation of cultural heritage collections. To this end, we will draw upon the experience and insights of representatives from different stakeholder groups in three broad arenas: academic researchers, heritage managers, and specialist communities. Investigations undertaken in this study will result in best-practice guidelines to guide humanities computing efforts on how to best meet the diverse user needs in future online data sharing systems. Using an iterative cycle of development, deployment, and evaluation, this project will enhance Open Context, a collaborative, open-access data sharing system already in use for archaeology and related disciplines

Confidence Interval

A poem about estimating probabilities

Hypergeometric decomposition of symmetric K3 quartic pencils

We study the hypergeometric functions associated to five one-parameter deformations of Delsarte K3 quartic hypersurfaces in projective space. We compute all of their Picard--Fuchs differential equations; we count points using Gauss sums and rewrite this in terms of finite field hypergeometric sums; then we match up each differential equation to a factor of the zeta function, and we write this in terms of global L-functions. This computation gives a complete, explicit description of the motives for these pencils in terms of hypergeometric motives.Comment: 70 pages, minor revision, to appear in Research in the Mathematical Science