Registering spherical navigators with spherical harmonic expansions to measure three-dimensional rotations in magnetic resonance imaging

Subject motion remains a challenging problem to overcome in clinical and research applications of magnetic resonance imaging (MRI). Subject motion degrades the quality of MR images and the integrity of experimental data. A promising method to correct for subject motion in MRI is the spherical navigator (SNAV) echo. Spherical navigators acquire k-space data on the surface of a sphere in order to measure three-dimensional (3D) rigid-body motion. Analysis begins by registering the magnitude of two SNAVs to determine the 3D rotation between them. Several different methods to register SNAV data exist, each with specific capabilities and limitations. In this study, we assessed the accuracy, precision and computational requirements of measuring rotations about all three coordinate axes by correlating the spherical harmonic expansions of SNAV data. We compare the results of this technique to previous SNAV studies and show that, although computationally expensive, the spherical harmonic technique is a highly accurate, precise and robust method to register SNAVs and detect 3D rotations in MRI. A key advantage to the spherical harmonic technique is the ability to optimize the accuracy, precision, processing time and memory requirements by adjusting parameters used in the registration. While present developments are aimed at improving the programming efficiency and memory handling of the algorithm, this registration technique is currently well suited for retrospective motion correction applications, such as removing motion-related image artifacts and aligning slices within a high-resolution 3D volume.     

Dynamics of Rational Surface Automorphisms: Linear Fractional Recurrences

We consider the family f _a,b (x,y)=(y,(y+a)/(x+b)) of birational maps of the plane and the parameter values (a,b) for which f _a,b gives an automorphism of a rational surface. In particular, we find values for which f _a,b is an automorphism of positive entropy but no invariant curve. The Main Theorem: If f _a,b is an automorphism with an invariant curve and positive entropy, then either (1) (a,b) is real, and the restriction of f to the real points has maximal entropy, or (2) f _a,b has a rotation (Siegel) domain. Research supported in part by the NSF.     

Conjugations between circle maps with a single break point

Consider two circle homeomorphisms fi∈C2+α(S?{bi}), α>0, i=1,2 with a single break point bi i.e. a discontinuity in the derivative Dfi, and identical irrational rotation number ρ. Suppose the jump ratios and do not coincide. Then the map ψ conjugating f₁ and f₂ is a singular function i.e. it is continuous on S¹ and Dψ(x)=0 a.e. with respect to Lebesgue measure.     

On homogeneous rotation symmetric bent functions

In this paper, we present partial results towards the conjectured nonexistence of homogeneous rotation symmetric bent functions having degree > 2.     

非分辨空间目标光谱双向反射分布函数的实验室平行测量

为了克服非分辨空间目标识别研究中外场观测和计算机仿真手段的局限性,采用实验方法模拟了天基光照场景,用仪器和技术平行类比望远镜观测时光源-目标-探测器方位,并测量了某高保真卫星模型的光谱双向反射分布函数.分析了空间目标光谱散射模型、实验场旋转轴系和环境模拟设备布局.根据在轨卫星的轨道和姿态建立了外场观测几何到室内5轴旋转系统的角度映射关系.利用该关系控制旋转系统实现了对某卫星过境观测的平行模拟,并对目标混合光谱进行了测量和定标.实验结果发表明:目标光谱数据中存在"闪光"和峰值波长迁移现象;旋转系统各轴定位精度为0.5°,光谱数据相对测量误差为0.018%.该方法能实现空间目标观测的全角度平行模拟,测量结果为非分辨目标外形、材料、旋转等特性的识别提供参考.     

远程控制原子的纠缠特性

考虑初始处于GHZ态的三个二能级原子,将其中两个原子同时注入处于真空态的单模腔中,并与光场发生共振相互作用的情况.利用全量子理论和采用数值计算方法,研究了腔内原子的纠缠性质.通过对是否进行腔外原子态选择性测量和腔外原子旋转操作情况下,腔内原子间的纠缠性质的比较,讨论了对腔外原子的旋转操作和测量对腔内原子间纠缠性质的影响.研究结果表明：若没有对腔外原子进行旋转操作,腔内两原子是分离的|若对腔外原子进行旋转操作和选择性测量,腔内两原子是纠缠的.另一方面,腔内两原子间的纠缠性质随旋转角的变化具有对称性,其对称轴为θ=π/2,可通过控制旋转角度的大小来控制腔内原子间的纠缠度.     

Unidirectional transport in the inertial ratchet

In this article, the unidirectional transport of the inertial ratchet is presented. We observe that in the ratchet, there is positive, negative or even no current. Moreover, the structure of staircases of the ratchet is argued and we observe that it becomes more regular as the damping coefficient is increased.     

An Efficient Synthesis of Stable Phosphorus Ylides Derived from Hydantoin and 5,5-dialkylhydantoins

Stable crystalline phosphorus ylides are obtained in excellent yields from the 1:1:1 addition reaction between triphenylphosphine and dialkyl acetylenedicarboxylates in the presence of strong NH-acids, such as hydantoin and 5,5-dialkylhydantoins. These stable ylides exist in solution as a mixture of two geometrical isomers as a result of restricted rotation around the carbon-carbon partial double bond resulting from conjugation of the ylide moiety with the adjacent carbonyl group.