Visualization for Explanation of Deep Learning-Based Defect Detection Model Using Class Activation Map

Recently,convolutional neural network(CNN)-based visual inspec-tion has been developed to detect defects on building surfaces automatically.The CNN model demonstrates remarkable accuracy in image data analysis;however,the predicted results have uncertainty in providing accurate informa-tion to users because of the“black box”problem in the deep learning model.Therefore,this study proposes a visual explanation method to overcome the uncertainty limitation of CNN-based defect identification.The visual repre-sentative gradient-weights class activation mapping(Grad-CAM)method is adopted to provide visually explainable information.A visualizing evaluation index is proposed to quantitatively analyze visual representations;this index reflects a rough estimate of the concordance rate between the visualized heat map and intended defects.In addition,an ablation study,adopting three-branch combinations with the VGG16,is implemented to identify perfor-mance variations by visualizing predicted results.Experiments reveal that the proposed model,combined with hybrid pooling,batch normalization,and multi-attention modules,achieves the best performance with an accuracy of 97.77%,corresponding to an improvement of 2.49%compared with the baseline model.Consequently,this study demonstrates that reliable results from an automatic defect classification model can be provided to an inspector through the visual representation of the predicted results using CNN models.

Combinations of Right Half-Plane Mappings and Vertical Strip Mappings Convex in the Vertical Direction

In this paper, we explore the linear combinations of right half-plane mappings and vertical strip mappings. We demonstrate that the combinations of these harmonic mappings are convex in the vertical direction provided they are locally univalent and sense-preserving. Furthermore, we extend this analysis to a more general case by setting specific conditions. Additionally, we take some common parameters such as as the dilatation of these harmonic mappings, and prove the sufficient conditions that their combinations are locally univalent and convex in the vertical direction. Several examples are constructed by the Mathematica software to demonstrate our main results.

基于多目标遗传算法的8×8 S盒的优化设计方法

混沌系统具有非线性、伪随机性、初始值敏感等特性,为基于动力系统构造性能良好的S盒提供了基础,进一步保证了分组加密算法安全性.目前,基于混沌构造S盒的方法大多数针对单个性能指标进行优化,难以获得全面的性能提升.针对此问题,结合混沌映射与多目标遗传算法,提出了一种新的S盒设计方法.首先,利用混沌映射的特性产生初始S盒种群;然后,以S盒的非线性度和差分均匀性为优化目标,基于遗传算法框架对上述两指标进行优化.针对S盒的特点,在优化算法中引入了交换操作,设计了新的变异操作以及非支配序集计算,有效提升了S盒的非线性度和差分均匀性.实验结果表明该算法产生的S盒其差分均匀度为6,非线性度值至少为110,有效提升了S盒的综合性能.

面向SAR图像目标分类的CNN模型可视化方法

卷积神经网络(CNN)在合成孔径雷达(SAR)图像目标分类任务中应用广泛。由于网络工作机理不透明,CNN模型难以满足高可靠性实际应用的要求。类激活映射方法常用于可视化CNN模型的决策区域,但现有方法主要基于通道级或空间级类激活权重,且在SAR图像数据集上的应用仍处于起步阶段。基于此,该文从神经元特征提取能力和网络决策依据两个层面出发,提出了一种面向SAR图像的CNN模型可视化方法。首先,基于神经元的激活值,对神经元在其感受野范围内的目标结构学习能力进行可视化,然后提出一种通道-空间混合的类激活映射方法,通过对SAR图像中的重要区域进行定位,为模型的决策过程提供依据。实验结果表明,该方法给出了模型在不同设置下的可解释性分析,有效拓展了卷积神经网络在SAR图像上的可视化应用。

Illite Crystallinity Mapping of Very Low Grade Metamorphism of Triassic Metapelites in the Zoigê Area,Western China

X-ray diffraction methods for estimating the metamorphic grade of diagenetic, anchizone and epizone in metapelites are reviewed and applied to samples from a 7000 m＋ borehole in western China and surface samples from the surrounding Zoige area. Kiibler＇s illite crystallinity （IC） measurements provide more consistent results than calculated values of percentage of illite in the I/S mixed layers and percentage of I/S mixed layers. Down-borehole IC values display a typical burial metamorphic relationship between stratigraphic level and IC. A method for preparing very low grade metamorphic maps is described, and isograds plotted on a regional geological map at selected values of IC, delineating a high temperature diagenetic zone, an anchizone, and an epizone. The map shows that IC values are controlled by stratigraphic level in the north of the study area （i.e. burial metamorphism）, and proximity to an igneous intrusive body in the south （i.e. contact metamorphism）.

Existence of Two Limit Cycles in Zeeman’s Class 30 for 3D Lotka-Volterra Competitive System

Gyllenberg and Yan(Discrete Contin Dyn Syst Ser B 11(2):347–352,2009)presented a system in Zeeman’s class 30 of 3-dimensional Lotka-Volterra(3D LV)competitive systems to admit at least two limit cycles,one of which is generated by the Hopf bifurcation and the other is obtained by the Poincaré-Bendixson theorem.Yu et al.(J Math Anal Appl 436:521–555,2016,Sect.3.4)recalculated the first Liapunov coefficient of Gyllenberg and Yan’s system to be positive,rather than negative as in Gyllenberg and Yan(2009),and pointed out that the Poincaré-Bendixson theorem is not applicable for that system.Jiang et al.(J Differ Equ 284:183–218,2021,p.213)proposed an open question:“whether Zeeman’s class 30 can be rigorously proved to admit at least two limit cycles by the Hopf theorem and the Poincaré-Bendixson theorem?”This paper provides four systems in Zeeman’s class 30 to admit at least two limit cycles by the Hopf theorem and the Poincaré-Bendixson theorem and gives an answer to the above question.

Likely Limit Sets of a Class of p-order Feigenbaum's Maps

A continuous map from a closed interval into itself is called a p-order Feigenbaum＇s map if it is a solution of the Feigenbaum＇s equation fP（λx）=λf（x）. In this paper, we estimate Hausdorff dimensions of likely limit sets of some p-order Feigenbaum＇s maps. As an application, it is proved that for any 0 〈 t 〈 1, there always exists a p-order Feigenbaum＇s map which has a likely limit set with Hausdorff dimension t. This generalizes some known results in the special case of p =2.

Isolation and Identification of a Specific cDNA Mapping to the Bam HI-I2 and -LFragments within the Inverted Repeats ofUnique Long Re-gion (IRL) in the Genom e ofMarek′s Disease Herpesvirus (MDV) Oncogenic Strain Beijing-1

Objective\ To understand the transcription of BamHI L DNA fragment from genome of strong virulent GA strain of Marek′s disease herpesvirus (MDV) in lymphoblastoid tumor tissue induced by oncogenic strain Beijing 1 (a specific local strain in China) of MDV. Methods\ Two oligonucleotide primers were synthesized according to the reported sequence of \%meq\% gene an ideal oncogenic candidate and our previously determined sequence of BamHI L fragment of Marek′s disease herpesvirus (MDV), respectively. Reverse transcriptase PCR(RT PCR) assay was performed by using these primers and the mRNA as a template which was isolated from visceral lymphoblastoid tumors obtained from chickens artificially infected with strain Beijing 1 of oncogenic MDV. Southern blot molecular hybridization was further carried out to detect the product of RT PCR with digoxigenin labeled nucleotide probe from BamHI I2 and L fragment in the gene library of MDV strain GA, respectively. Results\ Two probes could simultaneously hybridize this cDNA amplified by RT PCR with a length of about 730 bp. Conclusion\ It is suggested that \%meq\% transcription could extend from the right hand end of BamHI I2 to the adjacent BamHI L, and the BamHI L region was likely to be transcribed in MDV induced lymphoblastoid tumors.

STOCHASTIC FLOWS OF MAPPINGS

In this paper, the stochastic flow of mappings generated by a Feller convolution semigroup on a compact metric space is studied. This kind of flow is the generalization of superprocesses of stochastic flows and stochastic diffeomorphism induced by the strong solutions of stochastic differential equations.

A NEW ITERATIVE METHOD FOR FINDING COMMON SOLUTIONS OF GENERALIZED EQUILIBRIUM PROBLEM,FIXED POINT PROBLEM OF INFINITE k-STRICT PSEUDO-CONTRACTIVE MAPPINGS,AND QUASI-VARIATIONAL INCLUSION PROBLEM

In this article, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a generalized equilibrium problems, the set of common fixed point for a family of infinite k-strict pseudo-contractive mappings, and the set of solutions of the variational inclusion problem with multi-valued maximal monotone mappings and inverse-strongly monotone mappings in Hilbert space. Under suitable conditions, some strong convergence theorems are proved. Our results extends the recent results in G.L.Acedo and H.K.Xu [2], Zhang, Lee and Chan [8], Wakahashi and Toyoda [9], Takahashi and Takahashi [I0] and S. S. Chang, H. W. Joseph Lee and C. K. Chan [II], S.Takahashi and W.Takahashi [12]. Moreover, the method of proof adopted in this article is different from those of [4] and [12].

More on Fixed Point Theorem of {a, b, c}-Generalized Nonexpansive Mappings in Normed Spaces

Let X be a weakly Cauchy normed space in which the parallelogram law holds, C be a bounded closed convex subset of X with one contracting point and T be an {a,b,c}-generalized-nonexpansive mapping from C into C. We prove that the infimum of the set {‖x-T（x）‖} on C is zero, study some facts concerning the {a,b,c}-generalized-nonexpansive mapping and prove that the asymptotic center of any bounded sequence with respect to C is singleton. Depending on the fact that the {a,b,0}-generalized-nonexpansive mapping from C into C has fixed points, accord- ingly, another version of the Browder＇s strong convergence theorem for mappings is given.

具有稚虫迁徙机制的S型自适应混沌蜉蝣算法

针对蜉蝣优化算法(MA)全局搜索能力较弱,对子代优秀个体有效信息利用不够充分的缺点,以及在计算中后期易陷入局部收敛,进而影响优化效果的问题,提出一种具有稚虫迁徙机制的S型自适应混沌蜉蝣优化算法(S-AMA)。S-AMA算法首先采用Logistic混沌映射产生蜉蝣种群,增加算法初期种群的多样性;随后,将蜉蝣生命周期进行数学建模,并引入S型生命系数替换原有的重力惯性系数,动态调整算法探索能力和开发能力间的平衡性;最后,根据蜉蝣在缺氧环境下的种群活动,引入稚虫迁徙机制强化子代优秀个体摆脱局部最优的能力,进而更加充分地搜索最优解附近的区域,以增强算法的收敛精度。实验部分将S-AMA应用于标准函数测试集,并分别进行优化对比实验、Wilcoxon秩和检验。结果表明:与对比算法相比,S-AMA算法具有更好的寻优能力、收敛速度及鲁棒性。

DRSTN:深度残差软阈值化网络

在采用深度残差等神经网络模型解决图像分类任务时,特征提取过程损失的一些重要特征会影响模型的分类性能。神经网络“端到端”的学习模式带来的黑盒问题,也会限制其在诸多领域的应用和发展。另外,神经网络模型往往需要较长的训练时间。为了提高深度残差网络模型的分类效果和训练效率,引入了模型迁移方法和软阈值化方法,提出了DRSTN(Deep Residual Soft Thresholding Network)网络,并对此网络结构进行微调,生成了不同版本的DRSTN网络。DRSTN网络的性能得益于3个方面的有机整合:1)通过梯度加权类激活映射(Gradients-weighted Class Activation Mapping,Grad-CAM)方法对网络的特征提取进行可视化,根据可视化结果挑选进一步优化的模型;2)基于模型迁移,研究人员不必全新地搭建模型,可以直接在已有的模型上进行优化,能够节省大量训练时间;3)软阈值化作为非线性变换层嵌入到深度残差网络体系结构中,以消除样本中不相关的特征。实验结果表明,在相同训练条件下,DRSTN_KS(3*3)_RB(2:2:2)网络在CIFAR-10数据集上的分类精度相比SKNet-18,ResNet18和ConvNeXt_tiny网络分别提高了15.5%,8.8%和10.9%;该网络也具有一定的泛化性,在MNIST和Fashion MNIST数据集上能够达到快速的迁移效果,分类精度分别达到99.06%和93.15%。

Research into the Application of Mind Map in English Intensive Reading Classes

Mind map has been widely recognized as an effective teaching and learning tool in all levels of education. This paper, based on the writer’s teaching practice, aimed to investigate the potential use of mind map in English intensive reading classes of college students, and found that it could help students to understand and memorize the main ideas and important details of reading materials in a systematical way.

Common Fixed Point Theorems of Single-valued and Set-valued Mappings in Complete,Convex Metric Spaces

Under the conditions of compatility or sub -c ompatility between a sigle-valued mapping and set-valued mapping, this paper d iscusses the existence of common fixed points for two set-valued mappings and a single-valued mapping in complete, convex matric spaces. We extend and develop the main results.

On the Equivalence of Implicit Kirk-Type Fixed Point Iteration Schemes for a General Class of Maps

In this paper, a modified implicit Kirk-multistep iteration scheme and a strong convergence result for a general class of maps in a normed linear space was established. It was also shown that the convergence of this iteration scheme is equivalent to the convergency of some other implicit Kirk-type iteration (implicit Kirk-Noor, implicit Kirk-Ishikawa and implicit Kirk-Mann iterations) for the same class of maps. Some numerical examples were considered to show that the equivalence of convergence results to the fixed point is true. The results unify most equivalence results in literature.

Preoperative functional MRI localization of language areas in Chinese patients with brain tumors Validation with intraoperative electrocortical mapping

Ten Chinese patients with brain tumors involving language regions were selected. Preoperative functional MRI was performed to locate Broca＇s or Wernicke＇s area, and the cortex that was essential for language function was determined by electrocortical mapping. A site-by-site comparison between functional MRI and electrocortical mapping was performed with the aid of a neuronavigation device. Results showed that the sensitivity and specificity of preoperative functional MRI were 80.0% and 85.0% in Broca＇s area and 66.6% and 85.2% in Wemicke＇s area, respectively. These experimental findings indicate that functional MRI is an accurate, reliable technique with which to identify the location of Wernicke＇s area or Broca＇s area in patients with brain tumors.

Characterization of FeCo Nanoparticles Reinforced Natural Rubber using Nanomechanical Mapping

The morphology, nanomechanical properties and interfacial regions of natural rubber（NR） and FeCo nanoparticles composite were determined by AFM nanomechanical mapping. The results showed that the size of FeCo particles was mostly from 40 to 100 nm and the FeCo nanoparticles were homogeneously dispersed in the NR bulk. The strength of NR composite increased with the FeCo nanoparticles loading. Young＇s modulus of NR region, FeCo region and interfacial region was measured by AFM nanomechanical tapping as 1.6 ± 0.6, 16.7 ±4.2 and 5.8 ± 1.5 MPa, respectively. The width of the interface for NR5, NR10 and NR15 was determined to be 15±8.1, 26±14.3 and 32±16.4 nm, respectively.

Fractional Snow/Non-Snow Cover Mapping through Incorporation of Thermal Band in Snow Index Design

Substantial development has been achieved in snow cover delineations through binary mapping techniques. Continuous efforts for development and institution of methodologies in fractional snow cover mapping are steadily conducted by the research communities. In this work, the attempts are driven towards the attainment of the same. MODIS (Moderate Resolution Imaging Spectroradiometer) images are worked upon Landsat 8 images under multivariate polynomial regression schemes utilizing corresponding count of pixels in a test region of Himachal Pradesh. 11.00 μm centered waveband is employed to develop a scheme for snow mapping followed by a qualitative and quantitative comparison with NDSI and S3 snow index where the values of correlation coefficient between fractional snow cover and index values have been obtained as 77.04%, 78.82% and 85.15% for NDSI, S3 and our scheme respectively. Exponential empirical relationships have been tried to be employed to attain improvements in prediction of snow cover followed by a test of correlation between true and theoretical fractional snow cover values. An improvement in degree of correlation is obtained over the conventional methodologies which serves for the verification of scheme employed and empirical relationship defined, collectively. The results provide a scope for improvements and investigations in the subject of fractional snow cover mapping.

ON AN EQUATION CHARACTERIZING MULTI-CAUCHY-JENSEN MAPPINGS AND ITS HYERS-ULAM STABILITY

In this paper, we give two characterizations of multi-Cauchy-Jensen mappings. One of them reduces the system of n equations defining these mappings to a single functional equation. We also prove, using the fixed point method, the generalized Hyers-Ulam stability of this equation. Our results generalize some known outcomes.