Quantum algorithm for neighborhood preserving embedding

Neighborhood preserving embedding (NPE) is an important linear dimensionality reduction technique that aims at preserving the local manifold structure. NPE contains three steps, i.e., finding the nearest neighbors of each data point, constructing the weight matrix, and obtaining the transformation matrix. Liang et al. proposed a variational quantum algorithm (VQA) for NPE [Phys. Rev. A 101 032323 (2020)]. The algorithm consists of three quantum sub-algorithms, corresponding to the three steps of NPE, and was expected to have an exponential speedup on the dimensionality n. However, the algorithm has two disadvantages: (i) It is not known how to efficiently obtain the input of the third sub-algorithm from the output of the second one. (ii) Its complexity cannot be rigorously analyzed because the third sub-algorithm in it is a VQA. In this paper, we propose a complete quantum algorithm for NPE, in which we redesign the three sub-algorithms and give a rigorous complexity analysis. It is shown that our algorithm can achieve a polynomial speedup on the number of data points m and an exponential speedup on the dimensionality n under certain conditions over the classical NPE algorithm, and achieve a significant speedup compared to Liang et al.'s algorithm even without considering the complexity of the VQA.     

Front face synchronous fluorescence as a tool for the quality assurance of Greek milk

This research focuses on implementing the low cost and rapid front face synchronous fluorescence (SyFS) in order to ensure the quality assurance of Greek milk. Specifically, samples originated from the Greek domestic production of goat, sheep, cow, as well as foreign cow milk samples and adulterated cow milk samples. SyFS spectra were acquired in the excitation area of 250–500 nm with (Δλ)= 100 nm. Greek and foreign cow milk samples were differentiated based on intensity variations at wavelengths 350–515 nm, 540–579 nm, and 580–600 nm. The emissions at these wavelength positions correspond to tryptophan, vitamin A, and riboflavin. The supervised model with 94 samples exhibited p-value = 7,98E-11, RMSEE= 0,29171, RMSEcv= 0,29284 and RMSEP= 0,98013, AUROC for Greek samples= 0,61 and AUROC for foreign= 0,85. We differentiated milk samples according to the animal type with PCA and OPLS-DA models of 107 samples exhibiting RMSEE= 0,225842, RMSEcv= 0,228054 and RMSEP= 0,518635, AUROC for sheep samples= 0,99, AUROC for goat samples= 0,98 and AUROC for cow samples= 0,96. In fact, the emission band 350–591 nm characterized sheep milk and corresponds to aminoacids and fatty acids, cow milk was related to the 350–600 nm emission band related to the b-carotene and to the goat milk the emission bands 350–505 nm and 520–600 nm were attributed to tryptophan, NADH and Rivoflabin. Finally, we investigated whether SyFS coupled with chemometrics may provide preliminary evidence on adulterated cow milk samples. All models were validated with permutation testing, p-values and ROC curves.     

The global weak solution for the shallow water wave model of moderate amplitude

In this paper, we firstly establish the existence theorem of the global weak solutions of the Cauchy problem for the shallow water wave model of moderate amplitude, then following the idea in Xin and Zhang’s work (see Xin and Zhang, 2002), we prove the uniqueness of global weak solutions using the localization analysis in the transport equation theory. Finally, several travelling wave solutions are derived.     

长链支化聚丙烯的非线性流变行为

通过大幅振荡剪切试验方法, 研究了长链支化聚丙烯的非线性流变学行为, 揭示了长链支化结构与非线性黏弹响应的关系. 利用傅里叶变换流变学方法得到试样的三次倍频相对振幅I_3/1与应变的标度关系, 用于界定线性聚丙烯和长链支化聚丙烯非线性流变行为的差异, 并定义了非线性系数来量度长链支化程度. 在高应变下, I_3/1与应变的变化关系可以进一步描述长链支化在非线性流场下的特性, 并得到了长链支化程度与其非线性响应之间的变化关系. 通过应力波的Lissajous曲线分解, 发现了环内和环间黏弹性的差异, 长链支化结构在大应变流场下的非线性黏弹性响应弱于线性结构, 支化程度越高非线性响应越弱.     

在微粗糙平面上滚动的Chaplygin球的稳定性

本文利用文献[1]的结果,继续讨论 Chaplygin 球在微粗糙平面上滚动的稳定性。严格证明了在粘性和库仓两种磨擦条件下球绕最大惯量主轴滚动的一致稳定性,和在粘性摩擦条件及球的最大与中间主惯量矩十分接近的前提下球绕最小惯量主轴滚动的不稳定性。     

Large amplitude oscillatory shear behavior of PEO-PPO-PEO triblock copolymer solutions

Rheological properties of poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) (PEO-PPO-PEO) triblock copolymer solution in both linear and nonlinear regions have been investigated. PEO-PPO-PEO triblock copolymer solution shows a dramatic change in mechanical properties as temperature changes. PEO-PPO-PEO triblock copolymer undergoes a transition from sol to gel with increase of temperature. During this transition the copolymer solution passes through three different stages, namely sol, soft gel, and hard gel. In our previous research (Hyun et al. in J Non-Newtonian Fluid Mech 55:51–65, 2002), large amplitude oscillatory shear (LAOS) behavior was found to be very sensitive to the generated microstructures. In this study, we investigated the relationship between the LAOS type and the microdomain structure. Newtonian behavior is observed in sol region, while there appear two kinds of LAOS types in the soft gel region. One is type I (G′, G′′ decreasing) and the other is a combination of type I and type IV (G′, G′′ increasing followed by decreasing). Type III (G′ decreasing, G′′ increasing followed by decreasing) is observed in the hard gel region. We compared the shape of stress curves, Lissajous pattern, and Fourier transform (FT) rheology of hard gel and soft gel under LAOS, and tried to relate the complex LAOS behavior with the microstructural change. From these investigations, it was found that the LAOS behavior and the stress pattern at large strain are closely related to the microdomain structure of PEO-PPO-PEO triblock copolymer, and provide a lot of useful information on the microstructures induced by large deformation.     

Studying the Effect of the Spatial Frequency and Amplitude of Corrugation on the Stress–Strain State of Cylindrical Shells

An approach developed earlier to solve two-dimensional static problems for noncircular cylindrical shells is used to analyze the effect of the spatial frequency and amplitude of corrugation on the stress–strain state of shells. The results of the analysis are presented in the form of plots and tables     

垂直激励圆柱形容器中的表面波特性研究

利用奇异摄动理论的两时间变量展开法，研究了垂直强迫激励圆柱形容器中的单一水表面驻波模式。假设流体是无粘、不可压且运动是无旋的，在忽略了表面张力的影响下，得到一个具有立方项以及底部驱动项影响的非线性振幅方程。对上述方程进行了数值计算，并研究了特定(3，4)模式的表面驻波结构和特性，如驻波的节点分布及随某些参数的变化规律等，从计算的等高线的图象来看，和以往的实验结果相当吻合。     

弹性非保守压杆的大幅度动力分析

本文讨论弹性非保守压杆的大幅度动力问题。导出了在一般非保守力作用下杆的非线性运动微分方程,并给出与此相应的拟Hamilton变分表达式,具体地分析了悬臂杆在大挠度下的动力特性,当挠度很小其高次项可以略去时,本文所得结论都能近似地退化为线性理论的结果。