Involutive Solutions and Commutator Representations of the Dirac Hierarchy

The Dirac hierarchy of isospectral evolution equations associated with the Dirac spectral problem are studied in this paper. The commutator representations of Dirac hierarchy are first presented, and then through the nonlinearization of Lax pair the involutive solutions of Dirac hierarchy are obtained.

The Involutive Solutions of the Representation Equation Associated with the Bargmann System

In this paper, by a nonlinear procedure of a eigenvalue problem, we get a Bargmann system and prove it is a completely in tegrable system in the meanning of Liouville. By the way, the involutive solutio n of the representation equation is given.

EQUATION OF MATHEMATICAL PHYSICS AND OTHER AREAS OF APPLICATION: A CLASSICAL INTEGRABLE SYSTEM AND THE INVOLUTIVE REPRESENTATION OF SOLUTIONS OF THE HIGHER ORDER KAUP-NEWELL EQUATION

Under the constrained condition induced by the eigenfunction expresson of the potential (u, v)T = (-[A2q, q], [A2p, p])T = f (q, p), the spatial part of the Lax pair of the Kaup-Newell equation is non linearized to be a completely integrable system (R2N, Adp AND dq, H = H-1) with the Hamiltonian H-1 = -[A3q, p]-1/2[A2p, p][A2q, q]. while the nonlinearization of the time part leads to its N-involutive system {H(m)}. The involutive solution of the compatible fsystem (H-1), (H(m)) is mapped by into the solution of the higher order Kaup-Newell equation.

THE CONFOCAL INVOLUTIVE SYSTEM AND THE INTEGRABILITY OF THE NONLINEARIZED LAX SYSTEMS FOR AKNS HIERARCHY

The completely integrable Hamiltonian systems generated by the general confocal involutive system are proposed. It is proved that the nonlinearized eigenvalue problem for AKNS hierarchy is such an integrable system and showed that the time evolution equations for n≤3 obtained by nonlinearizing the time parts of Lax systems for AKNS hierarchy are Liouville integrable under the constraint of the spatial part.

Factorization of Functional Operators with Involutive Rotation on the Unit Circle

Following the classical definition of factorization of matrix-functions, we introduce a definition of factorization for functional operators with involutive rotation on the unit circle. Partial indices are defined and their uniqueness is proven. In previous works, the main research method for the study scalar singular integral operators and Riemann boundary value problems with Carlemann shift were operator identities, which allowed to eliminate shift and to reduce scalar problems to matrix problems without shift. In this study, the operator identities were used for the opposite purpose: to transform operators of multiplication by matrix-functions into scalar operators with Carlemann linear-fractional shift.

基于改进YOLOv7-tiny的高空作业人员安防装备检测算法

针对现有高空作业人员安防装备检测算法参数量较大且检测目标相对单一,难以适应复杂的高空作业场景等问题,提出一种基于改进YOLOv7-tiny的高空作业人员安防装备检测算法。首先,将主干网络重新设计为更轻量的YOLOv7-FasterNet,并调整空间金字塔池化结构,实现模型参数量的压缩;其次,在ELAN-L模块中扩展梯度传输路径的分支,解决了模型压缩造成的通道信息缺失问题,提升了特征信息的提取能力;最后,将网络中下采样部分替换为Involution模块,降低参数冗余,增强网络对全局的捕获能力。实验结果表明,改进的YOLOv7-tiny算法能够更好地适应复杂高空作业场景,在开源数据集上具备良好的性能。该算法的平均检测精度达到94.7%,较原模型提升1.5%,参数量较原模型下降11.6%,实验结果验证了算法改进措施的有效性。

Involutive characteristic sets of algebraic partial differential equation systems

This paper presents an algorithm to reduce a nonlinear algebraic partial differential equation system into the involutive characteristic set with respect to an abstract involutive prolongation direction, which covers the existing algorithms based on Riquier method, Thomas method, and Pommaret method. It also provides new algorithms for computing involutive characteristic sets due to the existence of new involutive directions. Experiments show that these new algorithms may be used to significantly reduce the computational steps in Wu-Ritt's characteristic set method for algebraic partial differential equations.

A NEW INVOLUTIVE SYSTEM OF POLYNOMIALS AND ITS CLASSICAL INTEGRABLE SYSTEMS

It is well known that, making use of isospectral technique of Lax, we can obtain involutive integrals of motion for some classical integrable systems. Flaschka first applied this Lax trick to the Toda lattice. Afterwards, Moser gave the Lax pairs corresponding

Application of Isogeometric Analysis Method in Three-Dimensional Gear Contact Analysis

Gears are pivotal in mechanical drives,and gear contact analysis is a typically difficult problem to solve.Emerging isogeometric analysis(IGA)methods have developed new ideas to solve this problem.In this paper,a threedimensional body parametric gear model of IGA is established,and a theoretical formula is derived to realize single-tooth contact analysis.Results were benchmarked against those obtained from commercial software utilizing the finite element analysis(FEA)method to validate the accuracy of our approach.Our findings indicate that the IGA-based contact algorithmsuccessfullymet theHertz contact test.When juxtaposed with the FEA approach,the IGAmethod demonstrated fewer node degrees of freedomand reduced computational units,all whilemaintaining comparable accuracy.Notably,the IGA method appeared to exhibit consistency in analysis accuracy irrespective of computational unit density,and also significantlymitigated non-physical oscillations in contact stress across the tooth width.This underscores the prowess of IGA in contact analysis.In conclusion,IGA emerges as a potent tool for addressing contact analysis challenges and holds significant promise for 3D gear modeling,simulation,and optimization of various mechanical components.

INVOLUTIVE BASES UNDER COMPOSITION

In this paper, the behaviors of involutive bases under composition operation are studied. For two kinds of involutive bases, i.e., Pommaret bases, Janet bases, we study their behavior problems under composition. Some further problems are also proposed.

A NEW POLYNOMIAL INVOLUTIVE SYSTEM AND A CLASSICAL COMPLETELY INTEGRABLE SYSTEM

Under the constrained condition induced by the eigenfunctions and the potentials, the Laxsystems of nonlinear evolution equations in relation to a matris eigenvalue problem are nonlin-earized to be a completely integrable system (R^(zN),dp∧dq, H), while the time part of it isnonlinearized to be its N-involutive system {F_m}. The involutive solution of the compatiblesystem (F_0), (F_m) is transformed into the solution of the m-th nonlinear evolution equation.

Free involutive Hom-semigroups and Hom-associative algebras

We construct free Hom-semigroups when its unary operation is multiplicative and is an involution. Our method of construction is by bracketed words. As a consequence , we obtain free Horn-associative algebras generated by a set under the same conditions for the unary operation.

基于改进SSD的钢材表面缺陷检测

工业生产过程中,钢材表面缺陷的检测对于钢材的质量控制发挥着十分重要的作用,针对钢材表面缺陷检测中存在的检测精度低、检测速度慢等问题,提出了一种钢材表面缺陷检测的改进SSD算法。在所提算法中,采用Transformer多头注意力机制模块代替原SSD结构中的Conv5_1层,以提高小目标检测的能力;原SSD结构中的Conv7操作替换为Involution算子操作,以减少运算的参数量;对网络结构进行特征融合处理,以更全面地检测特征图中所包含的信息。利用NEU-DET数据集进行实验,实验结果表明改进后的SSD算法是有效的,可以高效检测到钢材表面的小目标缺陷,相比改进前平均检测精度提高了4.5%,检测速度提高了13.6%。

一种基于Involution卷积的三维人体重建方法

针对从视频中恢复三维人体模型运动序列时,由于图像特征提取能力有限而导致三维人体模型运动序列重建效果不佳的问题,提出了一种基于Involution卷积的三维人体重建方法。首先为了引入自注意力机制,在ResNet50网络结构中加入Involution算子,获取视频图像帧的特征向量,然后使用姿态估计网络和形状估计网络获取人体姿势以及形状参数,最后使用蒙皮多人线性模型(skinned multi-person linear model, SMPL)生成三维人体模型的运动序列。在三维姿态户外数据集(3D pose in the wild, 3DPW)上与视频人体姿态形状估计推理(video inference for body pose and shape estimation, VIBE)方法以及时间一致性网格恢复(temporally consistent mesh recovery, TCMR)方法进行对比实验,平均精度相比于VIBE、TCMR分别提升了3.1%、0.7%,能够为运动捕捉、三维人体动画制作等工作提供更为准确的三维人体模型。

基于弱监督数据集的猪只图像实例分割

在智慧养殖研究中,基于深度学习的猪只图像实例分割方法,是猪只个体识别、体重估测、行为识别等下游任务的关键。为解决模型训练需要大量的逐像素标注图像,以及大量的人力和时间成本的问题,采用弱监督猪只分割策略,制作弱监督数据集,提出一种新的特征提取骨干网络RdsiNet:首先在ResNet-50残差模块基础上引入第2代可变形卷积,扩大网络感受野;其次,使用空间注意力机制,强化网络对重要特征的权重值;最后引入involution算子,借助其空间特异性和通道共享性,实现加强深层空间信息、将特征映射同语义信息连接的功能。通过消融实验和对比实验证明了RdsiNet对于弱监督数据集的有效性,实验结果表明其在Mask R-CNN模型下分割的mAP_(Semg)达到88.6%,高于ResNet-50、GCNet等一系列骨干网络;在BoxInst模型下mAP_(Semg)达到95.2%,同样高于ResNet-50骨干网络的76.7%。而在分割图像对比中,使用RdsiNet骨干网络的分割模型同样具有更好的分割效果:在图像中猪只堆叠情况下,能更好地分辨猪只个体;使用BoxInst训练的模型,测试图像中掩码具有更高的精细度,这更有利于开展下游分析。

轻量化篮球裁判手势识别算法

针对一般手势识别算法的参数量、计算量和精度难以平衡的问题,提出一种轻量化篮球裁判手势识别算法。该算法在YOLOV5s(You Only Look Once Version 5s)算法的基础上进行重构:首先,用Involution算子替代CSP1_1的卷积算子,以扩大上下文信息捕获范围并减少核冗余;其次,在C3模块后加入协同注意力(CA)机制,以得到更强的手势特征提取能力;然后,用轻量化内容感知上采样算子改进原始上采样模块,并将采样点集中在目标区域而忽略背景部分;最后,利用以SiLU作为激活函数的Ghost-Net进行轻量化剪枝。在自制的篮球裁判手势数据集上的实验结果表明,该轻量化篮球裁判手势识别算法的计算量、参数量和模型大小分别为3.3 GFLOPs、4.0×10^(6)和8.5 MB,与YOLOV5s算法相比,分别减少了79%、44%和40%,mAP@0.5为91.7%,在分辨率为1920×1280的比赛视频上的检测帧率达到89.3 frame/s,证明该算法能满足低误差、高帧率和轻量化的要求。

改进人脸特征矫正网络的遮挡人脸识别方法

现有人脸识别模型受口罩等遮挡因素影响导致准确率无法提升。当前主流研究方法将有无遮挡场景分开训练后,整合应用于多场景。针对遮挡人脸识别模型的局限性,提出一种改进人脸特征矫正网络(FFR-Net)模型。该模型可同时用于有无遮挡人脸识别并应用于口罩与眼镜遮挡两种识别场景中。人脸特征矫正网络模型提出了一种人脸特征矫正模块,为保证充分利用无遮挡区域特征信息,在该模块中的空间分支引入involution算子扩大图像信息交互区域,增强在空间范围内面部特征信息;在通道分支引入坐标注意力机制,捕获跨通道信息以增强特征表示,利于模型准确地定位识别目标区域;将Meta-ACON作为该模块新的动态激活函数,通过动态调整线性或非线性程度以提高模型泛化能力和计算准确度。最后,利用改进的人脸特征矫正网络模型在CASIA-Webface经处理的有无口罩遮挡人脸数据集上进行训练,其在LFW经处理的有无口罩遮挡数据集、Meglass数据集上的测试结果准确率分别达到了82.50%和89.75%,优于现有算法,验证了所提方法的有效性。

双线性内卷神经网络用于眼底疾病图像分类

由于眼底图像具有复杂程度高、个体差异弱、类间距离短等特点,纯卷积神经网络(CNN)和基于注意力的网络并不能在眼底疾病图像分类任务上达到令人满意的精度。因此,采用involution算子实现了注意力双线性内卷神经网络(ABINN)模型用于眼底疾病图像分类。ABINN模型的参数量仅是传统双线性卷积神经网络(BCNN)模型的11%,并提取了眼底图像的底层语义信息和空间结构信息进行二阶特征融合,是CNN和注意力方法的有效并联。此外,提出了两种基于involution算子实现注意力计算的实例化方法:基于图块的注意力子网络(AST)和基于像素的注意力子网络(ASX),这两种方法可以在CNN的基础结构内完成注意力的计算,从而使双线性子网络能在同一个架构下训练并进行特征融合。在公开眼底图像数据集OIA-ODIR上进行实验,结果显示ABINN模型的精度为85%,比通用BCNN模型提高了15.8个百分点,比TransEye模型提高了0.9个百分点。

GRU和Involution改进的深度伪造视频检测方法

近年来深度伪造视频在网络上广泛传播,造成了负面影响。针对现有检测模型准确率低和信息提取不够充分和全面的问题,提出了一种GRU(gated recurrent unit)和Involution改进的深度伪造视频检测方法。首先使用VGG19作为主干网络提取空间特征,并将Involution算子嵌入主干网络,从空间和通道信息两方面加强了人脸图像的空间建模能力。然后通过主胶囊层关注特征的位置信息和使用GRU提取帧间的时序特征。最后在训练模型阶段使用focalloss作为损失函数来平衡样本。在Deepfakes、FaceSwap和Celeb-DF数据集中进行测试,实验结果表明该方法优于主流检测方法,改进对比实验进一步证明了检测方法的有效性。

注意力机制与Involution算子改进的人脸表情识别

针对复杂人脸表情识别面临背景干扰、空间信息分布不均匀等问题,提出一种注意力机制和Involution算子改进的人脸表情识别方法,该方法以VGG19为基线网络,前端引入注意力机制提取表情强相关特征,抑制背景干扰,并利用联合正则化策略平衡和改善特征数据分布,提高模型训练质量;后端采用密集连接加强有效特征复用,提取高层语义信息。所提方法在CK+、FER2013、RAF-DB等3个公开数据集上进行了验证,准确率均取得显著提高,且优于当前诸多先进方法。此外,为提高网络处理复杂条件下的数据集,在其后端引入Involution算子替代部分卷积层,提高了空间多样性信息学习能力。实验结果表明,所提模型可有效提高RAF-DB等复杂数据集的人脸表情识别准确率。