Quantitative T(1)(ρ) imaging using phase cycling for B0 and B1 field inhomogeneity compensation

T_1ρ imaging is useful in a number of clinical applications. T_1ρ preparation methods, however, are sensitive to non-uniformities of the B₀ magnetic field and the B₁ RF field. These common system imperfections can result in image artifacts and quantification errors in T_1ρ imaging. We report on a phase-cycling method which can eliminate B₁ RF inhomogeneity effects in T_1ρ imaging. This method does not only correct for image artifacts but also for T_2ρ contamination caused by B₁ RF inhomogeneity. The presence of B₀ magnetic field inhomogeneity can compromise the effectiveness of this method for B₁ RF inhomogeneity correction. We demonstrate that, by combining the spin-locking scheme reported by Dixon et al. (Myocardial suppression in vivo by spin locking with composite pulses. Magn Reson Med 1996; 36:90-94) with phase cycling, we can simultaneously correct B₀ magnetic field inhomogeneity effects and B₁ RF inhomogeneity effects in T_1ρ imaging. Phantom and in vivo data sets are used to demonstrate the proposed methods and to compare them with other existing T_1ρ preparation methods.     

Diffusion-weighted imaging of the brain at 7 T with echo-planar and turbo spin echo sequences: preliminary results

Ultra-high-field clinical MRI scanners (e.g., 7 T and above) are becoming increasingly prevalent and can potentially enhance diagnostic ability through higher contrast, resolution and/or sensitivity. Diffusion-weighted MRI is a highly valued component in today's radiological exam and may benefit from the enhanced signal-to-noise ratio provided by high field with the appropriate imaging strategy. The most common diffusion pulse sequence readout (echo-planar imaging (EPI)) has been widely employed for in vivo human 7 T diffusion tensor imaging (DTI). In this article, we present results of brain DTI at 7 T with two diffusion-weighted imaging pulse sequence readouts: echo-planar imaging (EPI-DTI) and turbo spin echo (TSE-DTI). Results indicate that analogous coverage, quality and resolution typical of lower field (2 mm) can be obtained by properly processed EPI-DTI at 7 T, and, with some reduction in efficiency and sharpness, TSE-DTI at 7 T. Furthermore, 7 T TSE-DTI shows promise in obtaining higher-resolution results in targeted acquisitions of specific brain areas.     

Emergent rotational symmetries in disordered magnetic domain patterns

Uniaxial systems often form labyrinthine domains that exhibit short-range order but are macroscopically isotropic and would not be expected to exhibit precise symmetries. However, their underlying frustration results in a multitude of metastable configurations of comparable energy, and driving such a system externally might lead to pattern formation. We find that soft x-ray speckle diffraction patterns of the labyrinthine domains in CoPd/IrMn heterostructures reveal a diverse array of hidden rotational symmetries about the magnetization axis, thereby suggesting an unusual form of emergent order in an otherwise disordered system. These symmetries depend on applied magnetic field, magnetization history, and scattering wave vector. Maps of rotational symmetry exhibit intriguing structures that can be controlled by manipulating the applied magnetic field in concert with the exchange bias condition.     

Absorption spectrum of CO2 in the 4.82-μm region

The absorption spectrum of CO₂ in the 4.82-μm region has been observed with a high-resolution spectrometer. The (11¹0, 03¹0)_I-00⁰0 transition and the “hot” transitions (12²0, 04²0)_I-01¹0 and (20⁰0, 04⁰0)_I-01¹0 have been calibrated. The effective rotational constants of the upper levels have been deduced with good accuracy.     

Arrangements on Parametric Surfaces II: Concretizations and Applications

We describe the algorithms and implementation details involved in the concretizations of a generic framework that enables exact construction, maintenance, and manipulation of arrangements embedded on certain two-dimensional orientable parametric surfaces in three-dimensional space. The fundamentals of the framework are described in a companion paper. Our work covers arrangements embedded on elliptic quadrics and cyclides induced by intersections with other algebraic surfaces, and a specialized case of arrangements induced by arcs of great circles embedded on the sphere. We also demonstrate how such arrangements can be used to accomplish various geometric tasks efficiently, such as computing the Minkowski sums of polytopes, the envelope of surfaces, and Voronoi diagrams embedded on parametric surfaces. We do not assume general position. Namely, we handle degenerate input, and produce exact results in all cases. Our implementation is realized using Cgal and, in particular, the package that provides the underlying framework. We have conducted experiments on various data sets, and documented the practical efficiency of our approach.     

A modified functional delta method and its application to the estimation of risk functionals

The classical functional delta method (FDM) provides a convenient tool for deriving the asymptotic distribution of statistical functionals from the weak convergence of the respective empirical processes. However, for many interesting functionals depending on the tails of the underlying distribution this FDM cannot be applied since the method typically relies on Hadamard differentiability w.r.t. the uniform sup-norm. In this article, we present a version of the FDM which is suitable also for nonuniform sup-norms, with the outcome that the range of application of the FDM enlarges essentially. On one hand, our FDM, which we shall call the modified FDM, works for functionals that are “differentiable” in a weaker sense than Hadamard differentiability. On the other hand, it requires weak convergence of the empirical process w.r.t. a nonuniform sup-norm. The latter is not problematic since there exist strong respective results on weighted empirical processes obtained by Shorack and Wellner (1986) [25], Shao and Yu (1996) [23], Wu (2008) [32], and others. We illustrate the gain of the modified FDM by deriving the asymptotic distribution of plug-in estimates of popular risk measures that cannot be treated with the classical FDM.     

The Renormalization Group and Its Finite Lattice Approximations

We investigate finite lattice approximations to the Wilson renormalization group in models of unconstrained spins. We discuss first the properties of the renormalization group transformation (RGT) that control the accuracy of this type of approximation and explain different methods and techniques to practically identify them. We also discuss how to determine the anomalous dimension of the field. We apply our considerations to a linear sigma model in two dimensions in the domain of attraction of the Ising fixed point using a Bell–Wilson RGT. We are able to identify optimal RGTs which allow accurate computations of quantities such as critical exponents, fixed-point couplings and eigenvectors with modest statistics. We finally discuss the advantages and limitations of this type of approach.     

InGaAs/GaAs multiple-quantum-well modulators and switches

The design, fabrication and characterization of electrooptical modulators and switches based on pseudomorphic InGaAs/GaAs multiple-quantum-well (MQW) structures is presented. The absorption and refractive index changes (, n) of In_0.2Ga_0.8As/GaAs MQW structures due to the quantum-confined Stark effect are examined in detail. The figures of merit /₀ and n/₀ give information on the design of modulation and switching devices. Based on these results, we develop two types of efficient and high-speed modulators, vertical and waveguide modulators, and for the first time an InGaAs/GaAs intersectional X-type switch. Recent experimental results for each device are presented.     

Homoclinic orbits on compact hypersufaces in 293-1293-1293-1, of restricted contact type

Consider a smooth Hamiltonian system in ^2N , , the energy surface ={x/H(x)=H(0)} being compact, and 0 being a hyperbolic equilibrium. We assume, moreover, that {0} is of restricted contact type. These conditions are symplectically invariant. By a variational method, we prove the existence of an orbit homoclinic, i.e. non-constant and doubly asymptotic, to 0.     

The coherent-constructible correspondence and Fourier-Mukai transforms

As evidence for his conjecture in birational log geometry, Kawamata constructed a family of derived equivalences between toric orbifolds. In a previous paper, the authors showed that the derived category of a toric orbifold is naturally identified with a category of polyhedrally-constructible sheaves on ℝ ⁿ . In this paper we investigate and reprove some of Kawamata’s results from this perspective.