基于迭代p阈值投影算法的压缩感知磁共振成像

针对迭代软阈值投影算法中的软阈值函数收缩功能较差的问题，提出了迭代p阈值投影算法。用p阈值函数替换迭代软阈值投影算法中的软阈值函数，对小系数的惩罚更大，对大系数产生更小的偏置，以抑制噪声，减少重建误差。为加快算法速度，利用Nesterov梯度加速技术，设计了快速迭代p阈值投影算法，用于磁共振图像重建。在紧标架为平移不变离散小波变换和轮廓波下，将快速迭代p阈值投影算法用于压缩感知磁共振成像。与光滑化的快速迭代软阈值算法、迭代软阈值投影算法和交替方向乘子法进行仿真对比分析的结果表明，快速迭代p阈值投影算法提高了磁共振成像的重建速度和重建质量。分析了p值对算法性能的影响，给出了适合的p值选择方法，以获得较好的收敛速度、减小重构误差。     

结构约束下的生成对抗深度图修复

不同于纹理图像，深度图像中的像素点代表采集设备到场景各点的距离，直接使用通用图像修复方法并不能有效恢复深度图像中缺失区域的场景结构，本文提出一个两阶段编解码结构的生成对抗网络以解决深度图像修复问题。与常见生成对抗网络（Generative adversarial networks，GAN）模型不同，本文的生成器网络包括深度生成G1和深度修复G2两个模块。G1模块从RGB图像得到预测深度，替换待修复深度图像缺失区域，保证修复区域局部结构一致性。G2模块引入RGB图像边缘结构，保证全局结构一致性。针对现有图像修复方法没有考虑到修复区域间的一致性问题，设计结构一致注意力模块（Structure coherent attention，SCA）加入到G2中改善修复效果。本文提出的深度图像修复模型在主流数据集上进行了验证，利用结构约束并经过两阶段的生成器模型和判别器模型的共同作用，有效改善了深度图像修复效果。     

基于上下文共指实体依赖的文档级关系抽取

文档级关系提取（Document relationship extraction，DRE）旨在多条句子中识别实体间的关系，而实体可能对应于跨越句子边界的多次提及，其中代词实体提及是因句子之间连接而普遍存在的语法现象，也是影响句子推理的一个重要因素。然而，以往的研究大多侧重于普通实体提及之间的关系，却很少关注代词实体提及的共指和关系捕获。本文提出了基于上下文共指实体依赖（Contextual coreference entity dependency，CCED）的文档级关系抽取模型，即通过融合普通实体和代词实体表示来构建共指实体依赖关系的上下文图结构，并在图上进行实体对间的全局交互推理，从而对实体关系的相互依赖进行建模。分别在公共数据集DocRED、DialogRE和MPDD上对CCED模型进行评估，结果显示在DocRED数据集上，与表现最好的基线模型DocuNet-BERT相比，CCED模型在测试集上的Ign F1性能提高0.55%，F1性能提高0.35%。在DialogRE和MPDD数据集上，与表现最好的基线模型COLN相比，CCED模型在DialogRE测试集上的F1性能提高1.02%，在MPDD测试集上的ACC性能提高1.19%。实验结果验证了新模型对于文档级关系抽取的有效性。     

基于传染病模型的突发事件网民情感演变分析

突发事件发生后，准确地分析网民的情感状态，实现对网民情感状态演变的引导，对管控突发事件舆情、维护社会稳定有重大的现实意义。依据网民对突发事件的评论特性构建了网民情感状态的完备集，并从突发事件利益相关者和突发事件本身两个角度建立不同情绪集。依据传染病模型的传播方式，建立了基于SIS（Susceptible-infectious-susceptible）传染病模型的网民情感状态演变模型EP-SIS和EO-SIS。利用网民对“新型肺炎病毒”的微博评论对模型进行了实证研究，获取影响因子的权重，模型对网民负面情感转换率为0.72。本文构建的突发事件网民情感演变模型可以从不同角度干预，使突发事件中网民负面情感状态发生演变。     

基于惩罚逻辑回归的乳腺癌预测

本文采用惩罚逻辑回归方法,利用威斯康星大学的乳腺癌数据对乳腺肿瘤进行预测。首先选取与乳腺癌相关的10个指标作为自变量,接着采用逻辑回归、LASSO惩罚逻辑回归、L2惩罚逻辑回归和弹性网惩罚逻辑回归作为分类器,利用75%的数据集作为训练集建立模型,最后利用25%的测试集、混淆矩阵和ROC曲线评估不同模型的预测精度。结果表明,LASSO惩罚逻辑回归的预测表现最好,预测精度达到97.18%;弹性网惩罚逻辑回归的预测表现随着α的增大发生变化,特别当α=0.9时,预测精度达到97.18%,与LASSO惩罚逻辑回归的预测表现一样好;L2惩罚逻辑回归的预测表现排第3,逻辑回归表现最差。因此,在乳腺肿瘤诊断中可借助LASSO惩罚逻辑回归和弹性网惩罚逻辑回归提高诊断精度。     

基于局部相似性学习的鲁棒非负矩阵分解

现有的非负矩阵分解方法往往聚焦于数据全局结构信息的学习，在很多情况下忽略了对数据局部信息的学习，而局部学习的方法也通常局限于流行学习，存在一些缺陷。为解决这一问题，提出了一种基于数据局部相似性学习的鲁棒非负矩阵分解算法（Robust nonnegative matrix factorization with local similarity learning， RLS-NMF）。采用一种新的数据局部相似性学习方法，它与流形方法存在显著区别，能够同时学习数据的全局结构信息，从而能挖掘数据类内相似和类间相离的性质。同时，考虑到现实应用中的数据存在异常值和噪声，该算法还使用l2,1范数拟合特征残差，过滤冗余的噪声信息，保证了算法的鲁棒性。多个基准数据集上的实验结果显示了该算法的最优性能，进一步证明了该算法的有效性。     

基于改进SOA-VMD的磁声发射信号去噪算法

磁声发射（MAE）是铁磁性材料磁化过程中产生的声发射信号，在构件应力检测和微观损伤检测中有着广泛的应用。针对MAE信号非稳态、复杂性、衰减性等特点，提出海鸥算法结合变分模态分解（SOA-VMD）的去噪方法，为克服海鸥算法求解过程中易陷入局部最优解问题，利用柯西变异算子产生随机迭代过程，使改进算法即柯西变异海欧算法（CVSOA）跳出早熟收敛。采用以幅值谱熵为适应度函数，优化VMD算法中分解模态个数K和二次惩戒因子α两个参数，将含噪声的MAE信号进行VMD分解重构。经仿真信号和实际检测信号分析表明，改进后的CVSOA-VMD算法全局寻优能力和去噪性能优于传统的SOA-VMD算法，降噪后的MAE信号特征值对于不同应力下均方根、偏斜度特征值的重复性更好，可靠性更高。     

低硬件成本256点FFT处理器的IP核设计

设计了一种基于现场可编程门阵列（Field programmable gate array， FPGA）的低硬件成本256点快速傅里叶变换（Fast Fourier transform， FFT）处理器的IP核。采用按频率抽取的基-2⁴算法和单路延迟负反馈（Single-path delay feedback， SDF）流水线架构用于减少旋转因子的复数乘法运算复杂度。为了降低硬件成本，提出了一种串接正则有符号数（Canonical signed digit， CSD）常数乘法器取代常用的布斯乘法器用来完成旋转因子W256i与对应序列的复数乘法运算，同时这种乘法器还能够移除存储旋转因子系数的只读存储器（Read only memory， ROM）。该处理器IP核基于QUARTUS PRIME平台进行综合，在Cyclone 10LP FPGA上实现。结果显示，该FFT处理器最高工作频率为100 MHz，对于24位符号数FFT运算，逻辑单元（Logic elements， LEs）使用量与记忆体位（Memory bits， MBs）使用量仅为3 978 LEs和6 456 MBs。     

融合深浅特征和动态选择机制的行人检测研究

针对无人驾驶场景下行人多尺度、小尺度造成漏检率升高，检测精度下降的问题，本文提出一种融合深浅层特征和级联动态选择机制的行人检测方法。首先，在YOLO v3-tiny的基础上基于密集连接的卷积神经网络改进特征提取部分，融合行人的深层特征和浅层特征加强网络对行人的识别能力；其次，在改进的主干网络上级联具有动态选择机制的注意力模块，使检测网络更加适应动态的行人尺度变化；最后，本文选择BDD 100K数据集和Caltech加州理工学院行人数据集进行实验，在保证实时性的前提下（25 ms/张），本文模型在BDD 100K数据集行人漏检率降低11.4%，平均检测精度提高11.7%，在Caltech行人漏检率降低10.1%，平均检测精度提高6.7%，适用于无人驾驶行人检测领域。     

基于同步性静息态脑网络的原发性失眠诊断

全球有约1/3的人口曾受到失眠的困扰，研究表明脑电的高度觉醒是失眠的一个重要原因，表现在高频脑电活动的增强。然而，由于存在较大的干扰因素，日常静息态条件下评判困难。因此本文提取原发性失眠患者和健康对照的脑电图（Electroencephalogram，EEG）高频频带（Beta、Gamma频带），使用更适合EEG这种非线性、非平稳信号的相位锁相值（Phase locking value， PLV）方法来构建静息态功能脑网络，使用自适应阈值技术进行二值化处理。为了提升失眠症脑网络特征评价的可靠性，综合了各脑网络特征，提出了用于失眠症检测的脑网络综合度量指标。且发现在Gamma频带上，综合指标在原发性失眠患者组与健康对照组之间存在显著性差异（p=0.044）。应用支持向量机（Support vector machine， SVM）进行自动分类，在Beta频带上的正确率达77.7%，灵敏度达90.7%，相较于原始网络特征正确率提高了9.4%，灵敏度提高了20.7%；同时与现有研究对比，本文提出的脑网络综合度量指标的正确率提升了19.4%，灵敏度提升了20.7%。此外，发现Beta频带的综合度量指标分类效果更好，对于失眠症患者的日常诊断具有潜在的应用价值。     

The N-soliton solution and localized wave interaction solutions of the (2+1)-dimensional generalized Hirota-Satsuma-Ito equation

In this paper, the $N$-soliton solution is constructed for the ($2+1$)-dimensional generalized Hirota–Satsuma–Ito equation, from which some localized waves such as line solitons, lumps, periodic solitons and their interactions are obtained by choosing special parameters. Especially, by selecting appropriate parameters on the multi-soliton solutions, the two soliton can reduce to a periodic soliton or a lump soliton, the three soliton can reduce to the elastic interaction solution between a line soliton and a periodic soliton or the elastic interaction between a line soliton and a lump soliton, while the four soliton can reduce to elastic interaction solutions among two line solitons and a periodic soliton or the elastic interaction ones between two periodic solitons. Detailed behaviours of such solutions are illustrated analytically and graphically by analysing the influence of parameters. Finally, an inelastic interaction solution between a lump soliton and a line soliton is constructed via the ansatz method, and the relevant interaction and propagation characteristics are discussed graphically. The results obtained in this paper may be helpful for understanding the interaction phenomena of localized nonlinear waves in two-dimensional nonlinear wave equations.     

On multi-soliton solutions for the (2+1)-dimensional breaking soliton equation with variable coefficients in a graded-index waveguide

In this work, we construct multi-soliton solutions of the $(2+1)$-dimensional breaking soliton equation with variable coefficients by using the generalized unified method. We employ this method to obtain double- and triple-soliton solutions. Furthermore, we study the nonlinear interactions between these solutions in a graded-index waveguide. The physical insight and the movement role of the waves are discussed and analyzed graphically for different choices of the arbitrary functions in the obtained solutions. The interactions between the solitons are elastic whether the coefficients of the equation are constants or variables.     

Lump solutions to a (2+1)-dimensional extended KP equation

With the aid of a computer algebra system, we present lump solutions to a ($2+1$)-dimensional extended Kadomtsev–Petviashvili equation (eKP) and give the sufficient and necessary conditions to guarantee analyticity and rational localization of the solutions. We plot a few solutions for some specific values of the free parameters involved and finally derive one of the lump solutions of the Kadomtsev–Petviashvili (KP) equations from the lump solutions of the eKP equation.     

A variable exponent nonlocal p(x)-Laplacian equation for image restoration

In this paper, we focus on the mathematical and numerical study of a variable exponent nonlocal $p\left(X\right)$-Laplacian equation for image denoising. Based on the Semigroup Theory, we prove the existence and uniqueness of solution for the proposed model. To illustrate the efficiency and effectiveness of our model, we provide the denoising experimental results as well we compare it with some existing models in the literature.     

Visual Servo Control Achieving Nanometer Resolution in $X$ –$Y$–$Z$

This paper presents a three-axis vision motion sensor and its applications to visual servo control. The vision sensor is integrated with a three-axis piezo stage to form a visual servo control system that achieves nanometer resolution in all three $x$– $y$–$z$ motion axes. Motion measurement is achieved using a single interferometer-equipped optical microscope. A real-time image-processing algorithm that processes interference fringe patterns and that achieves nanometer out-of-plane resolution is presented. Furthermore, a feedback-control scheme is introduced to control the sensor plane using an Objective-Z-Positioner to enable automatic tracking of moving objects. It expands the out-of-plane measurement range of the vision sensor beyond its inherent depth of field of several micrometers to 100 $mu$m and beyond. An integrated visual servo system is implemented and experimental results are shown.      

$K$ Constrained Shortest Path Problem

Motivated by a real project for a sophisticated automated storage and retrieval system (AS/RS), we study the problem of generating K shortest paths that are required to satisfy a set of constraints. We propose a structural branching procedure that decomposes the problem into at most K|N| subproblems, where |N| is the number of nodes in the network. By using a Network Modification procedure, each subproblem can be transformed into a constrained shortest path problem (CSP). When these constraints satisfy a so called separable property, the subproblem can be further simplified. Based on this branching procedure, we propose a specific algorithm for an application where resource and loopless constraints have to be respected. Numerical results show that our algorithm is very efficient and robust.     

An LP-rounding 22-approximation for restricted maximum acyclic subgraph

In the classical Maximum Acyclic Subgraph problem (MAS), given a directed-edge weighted graph, we are required to find an ordering of the nodes that maximizes the total weight of forward-directed edges. MAS admits a 2-approximation, and this approximation is optimal under the Unique Game Conjecture.     

C1 continuous h-adaptive least-squares spectral element method for phase-field models

To describe the interfacial dynamics between two phases using the phase-field method, the interfacial region needs to be close enough to a sharp interface so as to reproduce the correct physics. Due to the high gradients of the solution within the interfacial region and consequent high computational cost, the use of the phase-field method has been limited to the small-scale problems whose characteristic length is similar to the interfacial thickness. By using finer mesh at the interface and coarser mesh in the rest of computational domain, the phase-field methods can handle larger scale of problems with realistic interface thicknesses. In this work, a $C^1$ continuous $h$-adaptive mesh refinement technique with the least-squares spectral element method is presented. It is applied to the Navier–Stokes-Cahn–Hilliard (NSCH) system and the isothermal Navier–Stokes–Korteweg (NSK) system. Hermite polynomials are used to give global differentiability in the approximated solution, and a space–time coupled formulation and the element-by-element technique are implemented. Two refinement strategies based on the solution gradient and the local error estimators are suggested, and they are compared in two numerical examples.