3D MRI of non-Gaussian (3)He gas diffusion in the rat lung

In (3)He magnetic resonance images of pulmonary air spaces, the confining architecture of the parenchymal tissue results in a non-Gaussian distribution of signal phase that non-exponentially attenuates image intensity as diffusion weighting is increased. Here, two approaches previously used for the analysis of non-Gaussian effects in the lung are compared and related using diffusion-weighted (3)He MR images of mechanically ventilated rats. One approach is model-based and was presented by Yablonskiy et al., while the other approach utilizes the second order decay contribution that is predicted from the cumulant expansion theorem. Total lung coverage is achieved using a hybrid 3D pulse sequence that combines conventional phase encoding with sparse radial sampling for efficient gas usage. This enables the acquisition of nine 3D images using a total of only approximately 1 L of hyperpolarized (3)He gas. Diffusion weighting ranges from 0 s/cm(2) to 40 s/cm(2). Results show that the non-Gaussian effects of (3)He gas diffusion in healthy rat lungs are directly attributed to the anisotropic geometry of lung microstructure as predicted by the Yablonskiy model, and that quantitative analysis over the entire lung can be reliably repeated in time-course studies of the same animal.     

Adaptive discretization for signal detection in statistical inverse problems

We discuss statistical tests in inverse problems when the original equation is replaced by a discretized one, i.e. a linear system of equations. Previous studies revealed that using the discretization level as regularizing procedure is possible, but its application is limited unless discretization is restricted to the singular value decomposition, see C. Marteau and P. Mathé, General regularization schemes for signal detection in inverse problems, 2013. General linear regularization may circumvent this, and we propose a regularization of the discretized equations. The discretization level may be chosen adaptively, which may save computational budget. This results in tests which are known to yield the optimal separation rate up to some constant in many cases.     

光栅投影相位法系统模型及标定方法

本文针对传统投影光栅相位法的光学三角法模型进行了改进,采用直入射光路并配合使用一种简便易行的标定方法,只需使用相移公式求取相位差,而不会引入与系统几何位置关系有关的量,简化了求取高度矩阵的要求。实验结果表明,新系统模型精度良好,测量误差为0.107 mm。采用该模型和标定方法可以克服传统方法系统模型的局限性,最大限度减少误差源并提高抗干扰性。     

Reception pattern influence on magnetoacoustic tomography with magnetic induction

Based on the acoustic radiation theory of a dipole source,the influence of the transducer reception pattern is studied for magnetoacoustic tomography with magnetic induction(MAT-MI).Numerical studies are conducted to simulate acoustic pressures,waveforms,and reconstructed images with unidirectional,omnidirectional,and strong directional transducers.With the analyses of equivalent and projection sources,the influences of the model dimension and the layer effect are qualitatively analyzed to evaluate the performance of MAT-MI.Three-dimensional simulation studies show that the strong directional transducer with a large radius can reduce the influences of equivalent sources,projection sources,and the layer effect effectively,resulting in enhanced pressure and improved image contrast,which is beneficial for boundary pressure extraction in conductivity reconstruction.The reconstructed conductivity contrast images present the conductivity boundaries as stripes with different contrasts and polarities,representing the values and directions of the conductivity changes of the scanned layer.The favorable results provide solid evidence for transducer selection and suggest potential practical applications of MAT-MI in biomedical imaging.     

Higher‐Dimensional Unification with continuous and fuzzy coset spaces as extra dimensions

We first review the Coset Space Dimensional Reduction (CSDR) programme and present the best model constructed so far based on the , 10‐dimensional E₈ gauge theory reduced over the nearly‐Kähler manifold with the additional use of the Wilson flux mechanism. Then we present the corresponding programme in the case that the extra dimensions are considered to be fuzzy coset spaces and the best model that has been constructed in this framework too. In both cases the best model appears to be the trinification GUT .     

LOBSTER: Local orbital projections,atomic charges,and chemical-bonding analysis from projector-augmented-wave-based density-functional theory

We present an update on recently developed methodology and functionality in the computer program Local Orbital Basis Suite Toward Electronic-Structure Reconstruction (LOBSTER) for chemical-bonding analysis in periodic systems. LOBSTER is based on an analytic projection from projector-augmented wave (PAW) density-functional theory (DFT) computations (Maintz et al., J. Comput. Chem. 2013 , 34, 2557), reconstructing chemical information in terms of local, auxiliary atomic orbitals and thereby opening the output of PAW-based DFT codes to chemical interpretation. We demonstrate how LOBSTER has been improved by taking into account time-reversal symmetry, thereby speeding up the DFT and LOBSTER calculations by a factor of 2. Over the recent years, the functionalities have also been continually expanded, including accurate projected densities of states (DOSs), crystal orbital Hamilton population (COHP) analysis, atomic and orbital charges, gross populations, and the recently introduced k -dependent COHP. The software is offered free-of-charge for non-commercial research.     

A mathematical discussion of Pons Viver's implementation of Löwdin's spin projection operator

Recently, the molecular electronic structure theories for efficiently treating static (or strong) correlation in a black-box manner have attracted much attention. In these theories, a spin projection operator is used to recover the spin symmetry of a broken-symmetry Slater determinant. Very recently, Pons Viver proposed the practical and exact implementation of Löwdin's spin projection operator (Int. J. Quantum Chem. 2019, 119, e25770). In the present study, we attempt to supply mathematical proofs to Pons Viver's proposals and show a condition for establishing Pons Viver's implementation. Moreover, we explicitly derive the (spin projected) extended Hartree-Fock (EHF) equations on the basis of the model of common orbitals (ie, closed-shell orbitals used in the restricted open-shell Hartree-Fock (ROHF) method), which was combined by Pons Viver with the EHF method.     

严格渐进伪压缩映象之修正型Mann迭代算法的强收敛性

本文利用CQ方法获得了k-严格渐进伪压缩映象修正型迭代算法的强收敛结果.此结果推广并改进了T.H.Kim和徐洪坤2006年获得的相应的一主要结果.即,从渐进非扩张映象推广到k-严格渐进伪压缩映象,并且去掉了闭凸子集C的有界性假设条件.     

Solving stochastic convex feasibility problems in hilbert spaces

In a stochastic convex feasibility problem connected with a complete probability space (Ω,A,μ) and a family of closed convex sets (C_ω)_ωεΩ in a real Hilbert space H, one wants to find a point that belongs to C_ω for μ almost all ω ε Ω. We present a projection based method where the variable relaxation parameter is defined by a geometrical condition, leading to an iteration sequence that is always weakly convergent to a μ almost common point. We then give a general condition assuring norm convergence of this equation to that μ almost common point     

Normalized intensity correlation function of single-mode laser system driven by colored cross-correlation noises

Considering a single-mode laser system with cross-correlated additive colored noise and multiplicative colored noise, we study the effects of correlation among noises on the normalized intensity correlation function C(s).C(s) is derived by means of the projection operator method.