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.     

Enhanced thermoelectric performance of PEDOT:PSS films via ionic liquid post-treatment

Thermoelectric(TE)energy harvesting can effectively convert waste heat into electricity,which is a crucial technology to solve energy concerns.As a promising candidate for energy conversion,poly(3,4-ethylenedioxythiophene):poly(styrene sulfonate)(PEDOT:PSS)has gained significant attention owing to its easy doping,high transparency,and solution processability.However,the TE performance of PEDOT:PSS still needs to be further enhanced.Herein,different approaches have been applied for tuning the TE properties:(i)direct dipping PEDOT:PSS thin films in ionic liquid;(ii)post-treatment of the films with concentrated sulfuric acid(H₂SO₄),and then dipping in ionic liquid.Besides,the same bis(trifluoromethanesulfonyl)amide(TFSI)anion and different cation salts,including 1-ethyl-3-methylimidazolium(EMIM+)and lithium(Li+),are selected to study the influence of varying cation types on the TE properties of PEDOT:PSS.The Seebeck coefficient and electrical conductivity of the PEDOT:PSS film treated with H2SO4EMIM:TFSI increase simultaneously,and the resulting maximum power factor is 46.7μW·m^-1·K^-2,which may be attributed to the ionic liquid facilitating the rearrangement of the molecular chain of PEDOT.The work provides a reference for the development of organic films with high TE properties.     

Exotic localized waves in the shifted nonlocal multicomponent nonlinear Schrödinger equation

Theoretical and Mathematical Physics - We theoretically calculate general higher-order soliton solutions of the space-shifted parity–time-symmetric nonlocal multicomponent nonlinear...     

光纤基底TiNi形状记忆合金薄膜制备工艺

将TiNi基记忆合金薄膜与光纤相结合可制成智能化、集成化且成本经济的微机电系统和微传感器件.本文采用磁控溅射法在二氧化硅光纤基底上制备TiNi记忆合金薄膜,系统讨论了溅射工艺参数以及后续退火处理对薄膜质量的影响.采用自研制光纤镀膜掩膜装置在直径为125μm的光纤圆周表面上形成均匀薄膜.实验表明:在靶基距、背底真空度、Ar气流量和溅射时间一定的条件下,溅射功率存在最佳值;溅射压强较大时,薄膜沉积速率较低,但薄膜表面粗糙度较小.进行退火处理后,薄膜形成较良好的晶体结构,Ti_49.09Ni_50.91薄膜中马氏体B19′相和奥氏体B2相共存,但以B19′为主.根据本文研究结果,在玻璃光纤基底上制备高质量的TiNi基记忆合金薄膜是可实现的,本工作为下一步研制微机电系统和微型传感器做了基础准备.     

带滩槽地形的连续弯道中纵向流速横向分布解析

本文基于沿水深积分的动量方程,假定二次流项和弯道附加应力项沿横断面呈线性分布,提出了预测弯道垂线平均纵向流速的解析计算方法,进一步提出了河槽区和河滩区垂线平均纵向流速沿断面分布的求解模式,并将其应用于带滩槽地形的反向连续弯道水槽中. 根据实测数据率定计算参数,该模式可计算不同出口水深条件下断面垂线平均纵向流速分布,计算结果与实测数据吻合良好.分析了线性分布假设中参数随水深变化的取值规律和沿横断面分布特点,并对参数进行了敏感性分析,分析表明线性假设中一次项系数分区位置对流速峰值的大小和位置影响较大,常数项根据地形横比降变化进行分区取值,流速计算值对常数项在水平段和斜坡段分区位置较为敏感,并根据参数的敏感度提出了参数沿水槽的均值作为参考值.讨论了动量方程中二次流项和弯道附加应力项沿弯道的横向分布规律,进一步认识线性假设的适用范围,结果表明线性假设在本文试验水槽中适用于弯道沿程.研究成果有助于认识带滩槽地形的连续弯道纵向流速分布特征及其形成机制.      

Examples of compactλ-hypersurfaces in Euclidean spaces

In this paper,we first construct compact embeddedλ-hypersurfaces with the topology of torus which are calledλ-torus in Euclidean spaces?n^+1.Then,we give many compact immersedλ-hypersurfaces in Euclidean spaces?n^+1.     

局部分数阶拉普拉斯算子的狄利克雷问题弱解的细正则性

In this paper, we study the Holder regularity of weak solutions to the Dirichlet problem associated with the regional fractional Laplacian (-△)^αΩ on a bounded open set Ω ■R(N ≥ 2) with C^(1,1) boundary ■Ω. We prove that when f ∈ L^p(Ω), and g ∈ C(Ω), the following problem (-△)^αΩu = f in Ω, u = g on ■Ω, admits a unique weak solution u ∈ W^(α,2)(Ω) ∩ C(Ω),where p >N/2-2α and 1/2< α < 1. To solve this problem, we consider it into two special cases, i.e.,g ≡ 0 on ■Ω and f ≡ 0 in Ω. Finally, taking into account the preceding two cases, the general conclusion is drawn.