Optimal estimation of the diffusion coefficient from non-averaged and averaged noisy magnitude data

The magnitude operation changes the signal distribution in MRI images from Gaussian to Rician. This introduces a bias that must be taken into account when estimating the apparent diffusion coefficient. Several estimators are known in the literature. In the present paper, two novel schemes are proposed. Both are based on simple least squares fitting of the measured signal, either to the median (MD) or to the maximum probability (MP) value of the Probability Density Function (PDF). Fitting to the mean (MN) or a high signal-to-noise ratio approximation to the mean (HS) is also possible. Special attention is paid to the case of averaged magnitude images. The PDF, which cannot be expressed in closed form, is analyzed numerically. A scheme for performing maximum likelihood (ML) estimation from averaged magnitude images is proposed. The performance of several estimators is evaluated by Monte Carlo (MC) simulations. We focus on typical clinical situations, where the number of acquisitions is limited. For non-averaged data the optimal choice is found to be MP or HS, whereas uncorrected schemes and the power image (PI) method should be avoided. For averaged data MD and ML perform equally well, whereas uncorrected schemes and HS are inadequate. MD provides easier implementation and higher computational efficiency than ML. Unbiased estimation of the diffusion coefficient allows high resolution diffusion tensor imaging (DTI) and may therefore help solving the problem of crossing fibers encountered in white matter tractography.     

Generalized excluded volume and the diffusivity and viscosity of supercooled liquids and glasses over the entire fragility spectrum

Transport properties of glass-formers near glass transition reflect the varying degrees of the sensitivity of the solid-like dynamics and structures with respect to temperature, depending on their fragility. Notably, however, most glasses resume Arrehenius transport behavior upon onset of vitrification. To address this phenomenon a theory of the self-diffusion coefficient and viscosity is developed on the basis of a model constructed for the generalized excluded volume of glass-formers described by the generic van der Waals equation of state. The molecular clustering behavior of a glass-former is exploited in terms of an order parameter that measures the concentration of glassy, clustered molecules, which is then related to the excluded volume. The formulas arrived therefrom are shown to excellently account for the self-diffusion coefficient and viscosity of various glass-formers over the entire fragility spectrum studied experimentally: e.g., _GeO2${\mathrm{GeO}}_2$, silica, ethanol, glycerol, diopside, propylene carbonate, o$o$-terphenyl, tris-napthylbenzene, toluene, and so on. The excluded volume effect thus investigated is shown to essentially characterize the fragility of the glass-formers. The resulting theory not only predicts for fragile glass-formers to resume Arrehenius transport behavior upon the onset of the glass transition, but also explains a crossover between strong and fragile glass-formers in their diffusivity and viscosity profiles as vitrification sets in.     

Diffusion-direction-dependent imaging: a novel MRI approach for peripheral nerve imaging

A novel magnetic resonance imaging approach, called diffusion-direction-dependent imaging (DDI), is introduced. Due to inherent anisotropic diffusion properties, peripheral nerves can be visualized on diffusion tensor imaging (DTI). The largest signal attenuation on DTI correlates with the direction of a nerve fiber, and the least signal attenuation correlates with the direction perpendicular to the nerve fiber. Since low signal-to-noise ratio is a concern in peripheral nerve DTI, we explored a new approach focusing on the perpendicular diffusion direction. A 36-gradient diffusion direction scheme was used. A mean expected curve specific for peripheral nerves was calculated based on the sciatic nerve and its division into the common peroneal nerve and the tibial nerve in three healthy volunteers. By a simple postprocessing method, a comparison of the mean expected curve and the measured curve was made voxel by voxel, and the sciatic nerve and its division were reconstructed, excluding other tissues. More studies are needed to investigate whether other postprocessing methods or other diffusion direction schemes are more suited for peripheral nerve imaging with DDI. Further studies may also be of interest to investigate whether DDI can be a complementary method to conventional T(1)-weighted and T(2)-weighted sequences in the imaging of peripheral nerve pathology or even in the visualization of other tissues, possibly with different diffusion direction schemes.     

The heterogeneous distribution of the liquid phase in partially filled porous glasses and its effect on self-diffusion

The spatial distribution of the liquid phase in a typical, partially filled, porous glass (VitraPor #5) has been examined with the aid of magnetic resonance microscopy and field gradient nuclear magnetic resonance diffusometry techniques. The correlation length of the material turned out to be long enough to permit the visualization of the microscopic heterogeneity of the material by magnetic resonance imaging. Contrasts are dominated by transverse relaxation depending on local filling degree, which in turn depends on local microstructure. The bimodal heterogeneity of the latter was also visualized by scanning electron microscopy. The effect of heterogeneity on an effective diffusion coefficient has been examined for polar (water) and nonpolar (cyclohexane) molecules.     

基于ROI编码的干涉超光谱图像近无损压缩

针对干涉超光谱成像仪所成图像的特点,提出了一种基于ROI（Region of Interest,感兴趣区域）编码的干涉超光谱图像序列压缩方法.利用帧内差值变换,结合矩形ROI编码,在提高遥感图像压缩比的同时,使压缩后的重建图像质量达到近无损的技术要求.实验结果表明,这种压缩方法在干涉超光谱图像压缩中当相对光谱二次误差为2.04％时,干涉图像的压缩比达到9.66∶1.     

Properties of RhP predicted by first-principles

Using density functional theory combined with a global crystal structure search with the particle swarm optimization method, we propose three stable three-dimensional (3D) metallic RhP structures, namely, the Cmcm (RhP-I), P6/mmm (RhP-II), and P6₃mc (RhP-III) phases. All these structures are found to be dynamically stable through vibrational normal mode calculations, indicating that they could be successfully synthesized in experiments. We show that the RhP-I phase has a relatively high thermodynamic stability and high mechanical strength in comparison with the others. The RhP-II and RhP-III phases have porous structures which could accommodate small atoms or molecules. However their thermodynamics are poor, especially the RhP-III phase. The RhP-II structure is stable at 500 K, but the RhP-III fails to survive even at the freezing point of water. Importantly, all these materials have one dimensional conducting channels corresponding to ultrahigh Fermi velocities. Moreover, the porous hexagonal RhP-II and III structures exhibit excellent ability to trap lithium, hydrogen, oxygen, and boron atoms. The RhP-II structure could be especially useful for directly dissociating the hydrogen molecule into two atoms without an energy barrier. In the present study, we identify three new metallic structures to the family of RhP structures, and anticipate their potential for technological applications.     

First-Principle Calculations of the Adsorption, Dissociation and Diffusion of Hydrogen on the Mg(0001) Surface

First-principle pseudopotential plane wave calculations and the Nudged Elastic Band method based on density functional theory (DFT) have been used in this article to study the dissociation of molecular hydrogen on a Mg(0001) surface and the subsequent diffusion of atomic hydrogen into the magnesium substrate. First, the dissociation pathway of H2 and the relative barrier were investigated. It was shown that physical adsorption rather than chemisorption of molecular hydrogen was observed in the calculation of the dissociation process of molecular hydrogen. Also, the diffusion process of atomic hydrogen on Mg(0001) was presented. The surface effect, which affected the diffusion of hydrogen obviously, was observed. Finally, comparing the values of the activation energies for the steps of dissociation, diffusion, and desorption, our calculation further showed that the dissociation of H2 and the desorption of hydride were the rate-limiting steps.     

工件的释放时间和加工时间具有一致性的单机在线排序问题研究

工件的释放时间和加工时间具有一致性, 是指释放时间大的工件其加工时间不小于释放时间小的工件的加工时间, 即若$r_{i}\geq r_{j}$, 则$p_{i}\geq p_{j}$。本文在该一致性约束下, 研究最小化最大加权完工时间单机在线排序问题, 和最小化总加权完工时间单机在线排序问题, 并分别设计出$\frac{\sqrt{5}+1}{2}$-竞争的最好可能在线算法。     

A tensor norm preserving unconditionality for -spaces

We show that, for each , there is an -tensor norm (in the sense of Grothendieck) with the surprising property that the -tensor product has local unconditional structure for each choice of arbitrary -spaces . In fact, is the tensor norm associated to the ideal of multiple -summing -linear forms on Banach spaces.