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.

Developments of the total entropy utility function for the dual purpose of model discrimination and parameter estimation in Bayesian design

The total entropy utility function is considered for the dual purpose of Bayesian design for model discrimination and parameter estimation. A sequential design setting is proposed where it is shown how to efficiently estimate the total entropy utility for a wide variety of data types. Utility estimation relies on forming particle approximations to a number of intractable integrals which is afforded by the use of the sequential Monte Carlo algorithm for Bayesian inference. A number of motivating examples are considered for demonstrating the performance of total entropy in comparison to utilities for model discrimination and parameter estimation. The results suggest that the total entropy utility selects designs which are efficient under both experimental goals with little compromise in achieving either goal. As such, the total entropy utility is advocated as a general utility for Bayesian design in the presence of model uncertainty.

Defining the light emitting area for displays in the unipolar regime of highly efficient light emitting transistors

Light-emitting field effect transistors (LEFETs) are an emerging class of multifunctional optoelectronic devices. It combines the light emitting function of an OLED with the switching function of a transistor in a single device architecture the dual functionality of LEFETs has the potential applications in active matrix displays. However, the key problem of existing LEFETs thus far has been their low EQEs at high brightness, poor ON/OFF and poorly defined light emitting area-a thin emissive zone at the edge of the electrodes. Here we report heterostructure LEFETs based on solution processed unipolar charge transport and an emissive polymer that have an EQE of up to 1% at a brightness of 1350a €...cd/m 2, ON/OFF ratio > 10 4 and a well-defined light emitting zone suitable for display pixel design. We show that a non-planar hole-injecting electrode combined with a semi-transparent electron-injecting electrode enables to achieve high EQE at high brightness and high ON/OFF ratio. Furthermore, we demonstrate that heterostructure LEFETs have a better frequency response (f cut-off = 2.6a €...kHz) compared to single layer LEFETs the results presented here therefore are a major step along the pathway towards the realization of LEFETs for display applications.