A Note on Unification of Translational Shape Invariant Potential and Scaling Shape Invariant Potential

This article puts forward a general shape invariant potential, which includes the translational shape invariant potential and scaling shape invariant potential as two particular cases, and derives the set of linear differential equations for obtaining general solutions of the generalized shape invariance condition.

Generation and classification of the translational shape-invariant potentials based on the analytical transfer matrix method

For the conventional translational shape-invariant potentials （TSIPs）, it has demonstrated that the phase contribution devoted by the scattered subwaves in the analytical transfer matrix quantization condition is integrable and independent of n. Based on this fact we propose a novel strategy to generate the whole set of conventional TSIPs and classify them into three types. The generating functions are given explicitly and the Morse potential is taken as an example to illustrate this strategy.

TRANSLATION-INVARIANT BASED ADAPTIVE THRESHOLD DENOISING FOR IMPACT SIGNAL

A translation-invariant based adaptive threshold denoising method formechanical impact signal is proposed. Compared with traditional wavelet denoising methods, itsuppresses pseudo-Gibbs phenomena in the neighborhood of signal discontinuities. To remedy thedrawbacks of conventional threshold functions, a new improved threshold function is introduced. Itpossesses more advantages than others. Moreover, based on utilizing characteristics of signal, aadaptive threshold selection procedure for impact signal is proposed. It is data-driven andlevel-dependent, therefore, it is more rational than other threshold estimation methods. Theproposed method is compared to alternative existing methods, and its superiority is revealed bysimulation and real data examples.

Translation invariant tensor product states in a finite lattice system

We show that the matrix （or more generally tensor） product states in a finite translation invariant system can be accurately constructed from a same set of local matrices （or tensors） that are determined from an infinite lattice system in one or higher dimensions. This provides an efficient approach for studying translation invariant tensor product states in finite lattice systems. Two methods are introduced to determine the size-independent local tensors.

Comparison of MRI Under-Sampling Techniques for Compressed Sensing with Translation Invariant Wavelets Using FastTestCS: A Flexible Simulation Tool

A sparsifying transform for use in Compressed Sensing (CS) is a vital piece of image reconstruction for Magnetic Resonance Imaging (MRI). Previously, Translation Invariant Wavelet Transforms (TIWT) have been shown to perform exceedingly well in CS by reducing repetitive line pattern image artifacts that may be observed when using orthogonal wavelets. To further establish its validity as a good sparsifying transform, the TIWT is comprehensively investigated and compared with Total Variation (TV), using six under-sampling patterns through simulation. Both trajectory and random mask based under-sampling of MRI data are reconstructed to demonstrate a comprehensive coverage of tests. Notably, the TIWT in CS reconstruction performs well for all varieties of under-sampling patterns tested, even for cases where TV does not improve the mean squared error. This improved Image Quality (IQ) gives confidence in applying this transform to more CS applications which will contribute to an even greater speed-up of a CS MRI scan. High vs low resolution time of flight MRI CS re-constructions are also analyzed showing how partial Fourier acquisitions must be carefully addressed in CS to prevent loss of IQ. In the spirit of reproducible research, novel software is introduced here as FastTestCS. It is a helpful tool to quickly develop and perform tests with many CS customizations. Easy integration and testing for the TIWT and TV minimization are exemplified. Simulations of 3D MRI datasets are shown to be efficiently distributed as a scalable solution for large studies. Comparisons in reconstruction computation time are made between the Wavelab toolbox and Gnu Scientific Library in FastTestCS that show a significant time savings factor of 60×. The addition of FastTestCS is proven to be a fast, flexible, portable and reproducible simulation aid for CS research.

Binding Energy, Root Mean Square Radius and Magnetic Dipole Moment of the Triton Nucleus

The basis functions of the translation invariant shell model are used to construct the ground state nuclear wave functions of 3H. The used residual two-body interactions consist of central, tensor, spin orbit and quadratic spin orbit terms with Gaussian radial dependence. The parameters of these interactions are so chosen in such a way that they represent the long-range attraction and the short-range repulsion of the nucleon-nucleon interactions. These parameters are so chosen to reproduce good agreement between the calculated values of the binding energy, the root mean-square radius, the D-state probability, the magnetic dipole moment and the electric quadrupole moment of the deuteron nucleus. The variation method is then used to calculate the binding energy of triton by varying the oscillator parameter which exists in the nuclear wave function. The obtained nuclear wave functions are then used to calculate the root mean-square radius and the magnetic dipole moment of the triton.

Human CD4- CD8- Invariant Natural Killer T Cells Promote IgG Secretion from B Cells Stimulated by Cross-Linking of Their Antigen Receptors

Immunoglobulin (Ig) M production can be induced by the interaction of thymus-independent type-2 (TI-2) antigen (Ag) with B cell Ag receptors (BCRs) without the involvement of conventional T cells;for IgG production through the same process, however, a second signal is required. Previous studies have reported that invariant natural killer T (iNKT) cells may be responsible for the second signal involved in IgG production. In the present study, we addressed whether human iNKT cells could participate in the production of Ig against TI-2 Ag in vitro. Two major distinct subsets of human iNKT cells, CD4+ CD8β- (CD4) and CD4- CD8β- [double negative (DN)] cells, were generated from peripheral blood monocytes from a healthy volunteer. BCR engagement, triggered by anti-IgM antibody stimulation, examined here as a model of BCR engagement triggered by TI-2 Ag, induced abundant IgM production by B cells. Both CD4 and DN iNKT cells reduced IgM production and conversely enhanced IgG production in a dose-dependent manner. In addition, IgG production by CD19+CD27- (naïve) and CD19+CD27+ (memory) B cells was predominantly promoted by DNiNKT cells rather than CD4 iNKT cells;nevertheless, IgM production by both B cell subsets was similarly reduced by either subset of iNKT cells. These results suggest that the DN iNKT subsets may preferentially promote Ig class switching by B cells upon stimulation with TI-2 Ag.

轻小型SAR卫星平飞模式设计

对于轻小型合成孔径雷达(SAR)卫星在轨使用时对重点区域多目标观测效能提升的需求,提出轻小型SAR卫星平飞模式设计方法。介绍了卫星平飞模式设计方法,提出载荷平面相控阵天线距离维大角度扫描能力设计;针对区域多目标,提出条件触发方式目标决策策略,以及星上雷达工作参数计算策略;基于建立的目标决策和任务规划模型,分别针对卫星左侧视、在侧视、平飞、左右机动侧视等4种工作模式下进行多目标观测效能评估仿真分析。结果表明:相比于卫星斜飞模式下,平飞模式目标观测效能可提升至41%;相比于卫星左右机动侧视模式下,平飞模式目标观测效能可提升至73%。因此,设计的卫星平飞模式可有效提升面向区域多目标的观测效能。

改进阈值的TI小波去噪法在MT去噪中的应用

在测量电场和磁场分量的过程中,由于地质因素、工频、人文干扰和其他外界因素以及观测系统所造成的干扰等,常常会使实际数据含有噪声,从而影响到视电阻率和相位的计算以及后续的正反演工作。为提高处理效果,在已有快速算法的基础上,将改进阈值的TI小波去噪法应用在大地电磁信号去噪中。利用该方法对大地电磁信号去噪,可以达到既有效去除噪声又较大程度地维持原始信号形态的目的。在对实测大地电磁数据进行去噪处理后的结果显示,该去噪方法使信号数据的突变现象得到有效的控制和减少,并使时间序列、视电阻率曲线和相位曲线的质量都有了明显的改善,因而具有较好的去噪效果。

基于边界约束最优投影梯度NMF的TINST域图像融合方法

针对多模态图像的融合问题,提出一种平移不变不可分离剪切波结合边界约束最优投影梯度非负矩阵分解的图像融合方法,解决了已有融合方法中融合精度较低的问题.该方法利用平移不变不可分离剪切波对源图像进行分解;将低频子带系数视为原始观测数据,采用边界约束最优投影梯度非负矩阵分解算法得到包含特征基的融合低频子带系数,将高频方向子带系数作为脉冲耦合神经网络的外部输入激励,边缘强度作为链接强度,经点火处理和判决选择运算,得到融合高频方向子带系数;最后对融合子带进行平移不变不可分离剪切波逆变换得到融合图像.为了验证该融合方法的有效性,对几组不同模态的图像进行对比融合实验.融合图像的主观与客观评价结果表明,该融合方法优于目前已有的典型多尺度图像融合方法.

基于项目相关度的STI新群体冷启动推荐方法

针对推荐系统中相似偏好用户数量较少情况下的一类新群体冷启动问题开展研究,基于多元相关分析,对传统的尺度与平移不变(Scale and Translation Invariant,STI)的协同过滤推荐方法进行改进,提出一种基于项目相关度的STI推荐方法,以应对推荐系统中的新群体冷启动问题.在此基础上,基于Movie Lens数据集对所提出的方法进行了性能分析,结果表明,所提出的方法较Pearson方法及ST1N1方法在解决新群体冷启动推荐的过程中具有更高的推荐准确率.

High-visibility ghost imaging with phase-controlled discrete classical light sources

We take phase modulation to create discrete phase-controlled sources and realize the super-bunching effect by a phasecorrelated method. From theoretical and numerical simulations, we find the space translation invariance of the bunching effect is a key point for the ghost imaging realization. Experimentally, we create the orderly phase-correlated discrete sources which can realize high-visibility second-order ghost imaging than the result with chaotic sources. Moreover, some factors affecting the visibility of ghost image are discussed in detail.

簸箕型流道泵站水泵振动信号消噪方法研究

为解决水泵信号振源复杂、含噪量大,难以在信号内获得有效数据的问题,研究一种基于改进平移不变量小波阈值的振动信号消噪方法。将水泵振动信号划分为信号高频区域和低频区域,选取对应合适的小波范围,在小波分解层数作用下正交变换含噪信号。利用阈值限制小波系数完成滤波,通过设定噪声标准偏差值,求得振动信号小波系数中间值,实现信号重构。将振动信号含噪部分在时域空间完成循环平移,填补信号不连续缺陷部位,平移去噪后计算振动信号平均值,得到最终消噪振动信号。仿真分析结果显示:该方法在平移不变量的辅助下,可填补信号不连续缺陷点,从噪声中恢复出原始振动信号,波形的失真较小,信号信噪比较高,鲁棒性好,可完整地保存信号的轮廓和特征。为分析簸箕型进水流道内部流态提供新思路,保证水泵整体工作可靠性。

基于TI-DWT-MSSNF的谱光滑与评价

提出了基于平移不变离散小波变换(Translation Invariant Discrete Wavelet Transform,TI-DWT)小波模极大值空间选择性滤波(Translation Invariant Discrete Wavelet Transform Wavelet Modulus Maxima Spatial Selectivity Filter,TI-DWT-MSSNF)的能谱平滑算法,并构建了光滑效果评价指标。分别使用α谱仪和γ谱仪获取了239Pu、241Am的α能谱和137Cs的γ能谱,将5点3次多项式最小二乘法、传统的小波模极大值法和TI-DWT-MSSNF分别用于α和γ谱平滑处理。结果表明:相比较5点3次多项式最小二乘法和传统的小波模极大值法,TI-DWT-MSSNF消除统计涨落更加彻底,特征信息保留更好,峰形畸变更小,是一种更优的方法。

算子代数上Hermitian双线性泛函表示

在紧支集无穷次可微函数空间，或急速下降无穷次可微函数空间上，给出取值算子代数中的Ｈｅｒｍｉｔｉａｎ双线性泛函的表示，为算子代数上的广义函数提供有用的工具．

Rotation Scaling and Translation Invariants of 3D Radial Shifted Legendre Moments

This paper proposes a new set of 3D rotation scaling and translation invariants of 3D radially shifted Legendre moments. We aim to develop two kinds of transformed shifted Legendre moments： a 3D substituted radial shifted Legendre moments （3DSRSLMs） and a 3D weighted radial one （3DWRSLMs）. Both are centered on two types of polynomials. In the first case, a new 3D ra- dial complex moment is proposed. In the second case, new 3D substituted/weighted radial shifted Legendremoments （3DSRSLMs/3DWRSLMs） are introduced using a spherical representation of volumetric image. 3D invariants as derived from the sug- gested 3D radial shifted Legendre moments will appear in the third case. To confirm the proposed approach, we have resolved three is- sues. To confirm the proposed approach, we have resolved three issues： rotation, scaling and translation invariants. The result of experi- ments shows that the 3DSRSLMs and 3DWRSLMs have done better than the 3D radial complex moments with and without noise. Sim- ultaneously, the reconstruction converges rapidly to the original image using 3D radial 3DSRSLMs and 3DWRSLMs, and the test of 3D images are clearly recognized from a set of images that are available in Princeton shape benchmark （PSB） database for 3D image.

A GENERALIZATION OF LEBESGUE DIFFERENTIAL THEOREM AND ITS APPLICATION

The author generalizes the classical Lebesgue differential theorem to the case of rather general metrics. Then. the author applies it to the subelliptic metric to check the integral characterization of Holder continuous functions related to the metric.

The Properties of Expected Scattering and Averaged Scattering and Their Applications to Texture Classification

In order to further improve the effectiveness of image processing,it is necessary that an efficient invariant representation is stable to deformation applied to images.This motivates the study of image representations defining an Euclidean metric stable to these deformation.This paper mainly focuses on two aspects.On the one hand,in this paper,two properties of expected scattering and averaged scattering,i.e.,Lipschitz continuity and translation invariance,are proved in detail.These properties support that excepted scattering and averaged scattering are invariant,stable and informative representations.On the other hand,the issue of texture classification based on expected scattering and averaged scattering has been analyzed respectively in this study.Energy features,which are based on expected scattering and averaged scattering,are calculated and used for classification.Experimental results show that starting with the seventh feature,the two approaches can achieve good performance in texture image classification.

Towards Translational Invariance of Total Energywith Finite Element Methods for Kohn-Sham Equation

Numerical oscillation of the total energy can be observed when the Kohn-Sham equation is solved by real-space methods to simulate the translational move of an electronic system.Effectively remove or reduce the unphysical oscillation is crucial not only for the optimization of the geometry of the electronic structure,but also for the study of molecular dynamics.In this paper,we study such unphysical oscillation based on the numerical framework in[G.Bao,G.H.Hu,and D.Liu,An h-adaptive fi-nite element solver for the calculations of the electronic structures,Journal of Computational Physics,Volume 231,Issue 14,Pages 4967-4979,2012],and deliver some numerical methods to constrain such unphysical effect for both pseudopotential and all-electron calculations,including a stabilized cubature strategy for Hamiltonian operator,and an a posteriori error estimator of the finite element methods for Kohn-Sham equation.The numerical results demonstrate the effectiveness of our method on restraining unphysical oscillation of the total energies.