Minimum SNR and acquisition for bias-free estimation of fractional anisotropy in diffusion tensor imaging - a comparison of two analytical techniques and field strengths

Although it is known that low signal-to-noise ratio (SNR) can affect tensor metrics, few studies reporting disease or treatment effects on fractional anisotropy (FA) report SNR; the implicit assumption is that SNR is adequate. However, the level at which low SNR causes bias in FA may vary with tissue FA, field strength and analytical methodology. We determined the SNR thresholds at 1.5 T vs. 3 T in regions of white matter (WM) with different FA and compared FA derived using manual region-of-interest (ROI) analysis to tract-based spatial statistics (TBSS), an operator-independent whole-brain analysis tool. Using ROI analysis, SNR thresholds on our hardware-software magnetic resonance platforms were 25 at 1.5 T and 20 at 3 T in the callosal genu (CG), 40 at 1.5 and 3 T in the anterior corona radiata (ACR), and 50 at 1.5 T and 70 at 3 T in the putamen (PUT). Using TBSS, SNR thresholds were 20 at 1.5 T and 3 T in the CG, and 35 at 1.5 T and 40 at 3 T in the ACR. Below these thresholds, the mean FA increased logarithmically, and the standard deviations widened. Achieving bias-free SNR in the PUT required at least nine acquisitions at 1.5 T and six acquisitions at 3 T. In the CG and ACR, bias-free SNR was achieved with at least three acquisitions at 1.5 T and one acquisition at 3 T. Using diffusion tensor imaging (DTI) to study regions of low FA, e.g., basal ganglia, cerebral cortex, and WM in the abnormal brain, SNR should be documented. SNR thresholds below which FA is biased varied with the analytical technique, inherent tissue FA and field strength. Studies using DTI to study WM injury should document that bias-free SNR has been achieved in the region of the brain being studied as part of quality control.     

Critical entanglement and geometric phase of a two-qubitmodel with Dzyaloshinski--Moriya anisotropic interaction

We consider a two-qubit system described by the Heisenberg XY model with Dzyaloshinski--Moriya (DM) anisotropic interaction in a perpendicular magnetic field to investigate the relation between entanglement, geometric phase and quantum phase transition (QPT). It is shown that the DM interaction has an effect on the critical boundary. The combination of entanglement and geometric phase may characterize QPT completely. Their jumps mean that the occurrence of QPT and inversely the QPT at the critical point at least corresponds to a jump of one of them.     

并联倒锥黑体腔

处于并联态的几个等角倒锥嵌于腔体开口端,其间的细长狭缝几乎能耗尽腔体的入射光能,以此概念模拟黑体得ε=0.99999999的大口径黑体模拟器。     

椭球内反射的几何光学性质

本文讨论椭球的内反射性质。由椭球的一个焦点F_1发射出的光波将在反射过程中与椭球的长轴充分逼近,使焦点F_1所具有的辐射以极狭窄的光束从椭球长轴的一端发射出来。     

航天时间延迟积分CCD相机摆扫成像快速几何校正设计与分析

为实现在轨卫星机动成像条带的快速准确拼接和应用,针对高分辨力卫星在轨推摆扫相结合的机动成像模式,提出了一种光线追迹像移匹配数学建模方法。通过对卫星机动过程中的摆角变化、地球表面面型的影响分析,利用摆扫过程中姿态对地指向不断改变导致的交轨方向速度失配量和成像变形量,补偿相机像面各点处的像移量从而进行快速几何校正。利用小卫星姿态控制系统全物理仿真平台对成像进行了仿真分析。分析结果表明,成像过程中随着扫描角的增加,像面上的像移量增大,成像变形情况也变严重。利用均方误差分析仿真成像与实验成像质量,仿真成像与实验成像相差-0.000011左右,较好地满足地面卫星相机成像仿真需求。对不同扫描角下存在速度失配的图像进行快速几何校正,该校正后图像的均方误差变小。该校正方法具有效率高,便于拼接应用的优点。     

Is Empty Spacetime a Physical Thing?

This article deals with empty spacetime and the question of its physical reality. By “empty spacetime” we mean a collection of bare spacetime points, the remains of ridding spacetime of all matter and fields. We ask whether these geometric objects—themselves intrinsic to the concept of field—might be observable through some physical test. By taking quantum-mechanical notions into account, we challenge the negative conclusion drawn from the diffeomorphism invariance postulate of general relativity, and we propose new foundational ideas regarding the possible observation—as well as conceptual overthrow—of this geometric ether.     

对称性对四体系统结构和内部运动的影响

文中用谐振子乘积基展开法求解了四体系统的Schrdinger方程.通过分析波函数及形状密度函数在多维坐标空间的分布,比较了四体全对称0⁺态,四体金对称0^－态和四体全反对称0⁺态,四体全反对称0^－态的结构和内部运动的差异;讨论了对称性的影响.     

Operating a geometric quantum gate by external controllable parameters

A scheme to perfectly preserve an initial qubit state in geometric quantum computation is proposed for a single-qubit geometric quantum gate in a nuclear magnetic resonance system. At first, by adjusting some magnetic field parameters, one can let the dynamic phase be proportional to the geometric phase. Then, by controlling the azimuthal angle in the initial state, we may realize a geometric quantum gate whose fidelity is equal to one under cyclic evolution. This means that the quantum information is no distortion in the process of geometric quantum computation.     

低聚壳聚糖几何结构和物理化学属性的理论研究

运用密度泛函B3LYP/6-31G+(d)方法对gg构象的低聚壳聚糖进行了结构优化、频率计算和电子结构,并用更高精度的WB97XD/6-311+G(d,p)方法计算了平均结合能及零点能校正,分析了热力学性质.结果表明,由于低聚壳聚糖中的氢键作用,使其形成螺旋结构;聚合度的增加,使平均结合能随之下降,结构的稳定性增强;在降解过程中,均为放热反应,验证了利用降温来提高降解产率的实验的可行性;此外,聚合度的增加,使能隙减小且快速收敛于聚合度为7的6.99 eV,稳定的反应活性与实验相符;HOMO、LUMO的电子密度分布表明,化学活性集中在C2位的氨基、C6位的羟基以及链的两端位置.该结果对低聚壳聚糖模型的建立和低聚壳聚糖降解过程、活性位置以及物理化学属性的尺寸依赖等现象的研究有着指导意义.     

Some Useful Integral Representations for Information-Theoretic Analyses

This work is an extension of our earlier article, where a well-known integral representation of the logarithmic function was explored and was accompanied with demonstrations of its usefulness in obtaining compact, easily-calculable, exact formulas for quantities that involve expectations of the logarithm of a positive random variable. Here, in the same spirit, we derive an exact integral representation (in one or two dimensions) of the moment of a nonnegative random variable, or the sum of such independent random variables, where the moment order is a general positive non-integer real (also known as fractional moments). The proposed formula is applied to a variety of examples with an information-theoretic motivation, and it is shown how it facilitates their numerical evaluations. In particular, when applied to the calculation of a moment of the sum of a large number, n, of nonnegative random variables, it is clear that integration over one or two dimensions, as suggested by our proposed integral representation, is significantly easier than the alternative of integrating over n dimensions, as needed in the direct calculation of the desired moment.