The tensor distribution function

Diffusion weighted magnetic resonance imaging is a powerful tool that can be employed to study white matter microstructure by examining the 3D displacement profile of water molecules in brain tissue. By applying diffusion-sensitized gradients along a minimum of six directions, second-order tensors (represented by three-by-three positive definite matrices) can be computed to model dominant diffusion processes. However, conventional DTI is not sufficient to resolve more complicated white matter configurations, e.g., crossing fiber tracts. Recently, a number of high-angular resolution schemes with more than six gradient directions have been employed to address this issue. In this article, we introduce the tensor distribution function (TDF), a probability function defined on the space of symmetric positive definite matrices. Using the calculus of variations, we solve the TDF that optimally describes the observed data. Here, fiber crossing is modeled as an ensemble of Gaussian diffusion processes with weights specified by the TDF. Once this optimal TDF is determined, the orientation distribution function (ODF) can easily be computed by analytic integration of the resulting displacement probability function. Moreover, a tensor orientation distribution function (TOD) may also be derived from the TDF, allowing for the estimation of principal fiber directions and their corresponding eigenvalues.

Virtual countries: Internet domain names and geographical terms

This paper examines the dispute between the Seattle company Virtual Countries Inc. and the Republic of South Africa over the ownership of the domain name address southafrica.com. The first part of the paper deals with the pre-emptive litigation taken by Virtual Countries Inc. in a District Court of the United States. The second part considers the possible arbitration of the dispute under the Uniform Domain Name Dispute Resolution Process of the Internet Corporation for Assigned Names and Numbers (ICANN) and examines the wider implications of this dispute for the jurisdiction and the governance of ICANN. The final section of the paper evaluates the Final Report of the Second WIPO Internet Domain Name Process.

Cord Cutting Anxiety Oversimplifies Distribution Revolution

Cord cutting refers to the act of cable and satellite consumers cancelling their subscriptions and opting instead for non-traditional distribution outlets, like streaming media platforms. The trend has been the subject of much debate in the trade press and a source of much concern for the industry. Yet many questions remain unanswered: Is it really a major trend? Does it save consumers money? Can viewers still find the content they love? How do we even “cut the cord” anyway?