Fourier Analysis

傅里叶分析
  • 文章类型: Journal Article
    准确预测沿海水域中的叶绿素a(chl-a)浓度对于沿海经济和生态系统至关重要,因为它是有害藻华的关键指标。尽管强大的机器学习方法在预测chl-a浓度方面取得了长足的进步,在有效建模动态时间模式和处理数据噪声和不可靠性方面仍然存在差距。为了摆脱泥潭,我们引入了一种创新的深度学习预测模型(称为ChloroFormer),将变压器网络与傅立叶分析集成在一个分解架构中,利用来自两个不同研究区域的沿海现场数据。我们提出的模型在捕获chl-a浓度中的短期和中期依赖模式方面表现出卓越的能力,超越其他六个深度学习模型在多步预测准确性方面的性能。特别是在涉及极端和频繁开花的场景中,我们提出的模型显示出卓越的预测性能,特别是在准确预测峰值chl-a浓度方面。通过Kolmogorov-Smirnov检验的进一步验证证明,我们的模型不仅复制了chl-a浓度的实际动态,而且保留了观测数据的分布,展示其鲁棒性和可靠性。提出的深度学习模型解决了准确预测chl-a浓度的关键需求,促进具有复杂动态时间模式的海洋观测探索,从而支持沿海地区的海洋保护和决策。
    The accurate prediction of chlorophyll-a (chl-a) concentration in coastal waters is essential to coastal economies and ecosystems as it serves as the key indicator of harmful algal blooms. Although powerful machine learning methods have made strides in forecasting chl-a concentrations, there remains a gap in effectively modeling the dynamic temporal patterns and dealing with data noise and unreliability. To wiggle out of quagmires, we introduce an innovative deep learning prediction model (termed ChloroFormer) by integrating Transformer networks with Fourier analysis within a decomposition architecture, utilizing coastal in-situ data from two distinct study areas. Our proposed model exhibits superior capabilities in capturing both short-term and middle-term dependency patterns in chl-a concentrations, surpassing the performance of six other deep learning models in multistep-ahead predictive accuracy. Particularly in scenarios involving extreme and frequent blooms, our proposed model shows exceptional predictive performance, especially in accurately forecasting peak chl-a concentrations. Further validation through Kolmogorov-Smirnov tests attests that our model not only replicates the actual dynamics of chl-a concentrations but also preserves the distribution of observation data, showcasing its robustness and reliability. The presented deep learning model addresses the critical need for accurate prediction on chl-a concentrations, facilitating the exploration of marine observations with complex dynamic temporal patterns, thereby supporting marine conservation and policy-making in coastal areas.
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  • 文章类型: Journal Article
    背景:在机器人辅助的微创手术中,外科医生操纵主操纵器时的手震颤会导致从属手术器械的振动。
    方法:这封信通过提出一种改进的增强型带限多线性傅立叶组合器(E-BMFLC)算法来解决这个问题,该算法用于过滤外科医生手的生理震颤信号。所提出的方法使用输入信号的幅度来适应学习速率和针对震颤信号的较高幅度频带的组合器频带的密集划分。
    结果:通过使用提出的改进的E-BMFLC算法,补偿精度可提高4.5%-8.9%,以及小于1毫米的空间位置误差。
    结论:结果表明,在所有过滤方法中,改进的E-BMFLC滤波方法实验成功次数最多,实验时间最少。
    BACKGROUND: During a robot-assisted minimally invasive surgery, hand tremors in a surgeon\'s manipulation of the master manipulator can cause vibrations of the slave surgical instruments.
    METHODS: This letter addresses this problem by proposing an improved Enhanced Band-Limited Multiple Linear Fourier Combiner (E-BMFLC) algorithm for filtering the physiological tremor signals of a surgeon\'s hand. The proposed method uses the amplitude of the input signal to adapt the learning rate and a dense division of the combiner bands for the higher amplitude bands of the tremor signals.
    RESULTS: By using the proposed improved E-BMFLC algorithm, the compensation accuracy can be improved by 4.5%-8.9%, as well as a spatial position error of less than 1 mm.
    CONCLUSIONS: The results show that among all filtering methods, the improved E-BMFLC filtering method has the highest number of successful experiments and the lowest experimental time.
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  • 文章类型: Journal Article
    当低温EM数据集不完整时,低温电子显微镜(cryo-EM)的重建图表现出畸变,通常由不均匀分布的方向引起。先前已尝试使用倾斜收集策略和对网格或空气-水界面的修改来解决此首选方向问题。然而,这些方法通常需要耗时的实验,效果总是依赖于蛋白质。这里,我们开发了一种包含去除未对齐粒子的程序,以及一种基于傅立叶分量信噪比的迭代重建方法,通过使用纯计算算法恢复丢失的数据来纠正这种失真。此过程称为信噪比迭代重建方法(SIRM),适用于各种蛋白质的不完整数据集,以修复低温EM图中的失真并获得更各向同性的分辨率。此外,SIRM为进一步的重建改进提供了更好的参考图,导致改进的对齐,这最终提高了地图质量和效益模型构建。
    Reconstruction maps of cryo-electron microscopy (cryo-EM) exhibit distortion when the cryo-EM dataset is incomplete, usually caused by unevenly distributed orientations. Prior efforts had been attempted to address this preferred orientation problem using tilt-collection strategy and modifications to grids or to air-water interfaces. However, these approaches often require time-consuming experiments, and the effect was always protein dependent. Here, we developed a procedure containing removing misaligned particles and an iterative reconstruction method based on signal-to-noise ratio of Fourier component to correct this distortion by recovering missing data using a purely computational algorithm. This procedure called signal-to-noise ratio iterative reconstruction method (SIRM) was applied on incomplete datasets of various proteins to fix distortion in cryo-EM maps and to a more isotropic resolution. In addition, SIRM provides a better reference map for further reconstruction refinements, resulting in an improved alignment, which ultimately improves map quality and benefits model building.
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  • 文章类型: Journal Article
    图像相位一致性(IPC)的概念深深植根于人类视觉系统解释和处理空间频率信息的方式。它在视觉感知中起着重要的作用,影响我们识别物体的能力,识别纹理,破译我们环境中的空间关系。IPC对照明的变化是强大的,对比,以及其他可能改变光波振幅的变量,但它们的相对相位不变。此特性对于感知任务至关重要,因为它可以确保对特征的一致检测,而无需考虑照明或其他环境因素的波动。它还可以影响认知和情绪反应;跨元素的内聚阶段信息促进了对统一或和谐的感知,而不一致会产生不和谐或紧张感。在这次调查中,我们首先研究了生物视觉研究的证据,这些证据表明IPC被人类感知系统所采用。我们继续概述IPC的典型数学表示和不同计算方法。然后,我们总结了IPC在计算机视觉中的广泛应用,包括去噪,图像质量评估,特征检测和描述,图像分割,图像配准,图像融合,和物体检测,在其他用途中,并用一些例子说明它的优点。最后,我们讨论了当前与IPC的实际应用相关的挑战以及潜在的增强途径。
    The concept of Image Phase Congruency (IPC) is deeply rooted in the way the human visual system interprets and processes spatial frequency information. It plays an important role in visual perception, influencing our capacity to identify objects, recognize textures, and decipher spatial relationships in our environments. IPC is robust to changes in lighting, contrast, and other variables that might modify the amplitude of light waves yet leave their relative phase unchanged. This characteristic is vital for perceptual tasks as it ensures the consistent detection of features regardless of fluctuations in illumination or other environmental factors. It can also impact cognitive and emotional responses; cohesive phase information across elements fosters a perception of unity or harmony, while inconsistencies can engender a sense of discord or tension. In this survey, we begin by examining the evidence from biological vision studies suggesting that IPC is employed by the human perceptual system. We proceed to outline the typical mathematical representation and different computational approaches to IPC. We then summarize the extensive applications of IPC in computer vision, including denoise, image quality assessment, feature detection and description, image segmentation, image registration, image fusion, and object detection, among other uses, and illustrate its advantages with a number of examples. Finally, we discuss the current challenges associated with the practical applications of IPC and potential avenues for enhancement.
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  • 文章类型: Journal Article
    背景:这项研究评估了使用科伦坡人工晶状体(IOL)2和IOLMaster700测量的近视患者的眼部参数的一致性。
    方法:80例患者(男性,22岁;平均年龄,2023年5月,这项研究包括29.14±7.36岁)的近视(159眼)。参与者的轴向长度(AXL),中央角膜厚度(CCT),透镜厚度(LT),白到白距离(WTW),前平板(K1),陡峭(K2),平均(Km)角膜角化术,散光(Astig),J0矢量,和J45载体使用IOLMaster700和ColomboIOL2进行测量。使用广义估计方程比较了两种设备的测量结果,相关分析,还有Bland-Altman的阴谋.
    结果:对于科伦坡IOL2,K2和J0的值较低(比值比[OR]=0.587,p=0.033;OR=0.779,p<0.0001),和较大的WTW值,Astig,和J45(OR=1.277,OR=1.482,OR=1.1,均p<0.0001)。两种仪器的所有眼部测量均显示出正相关,与AXL的相关性最强(r=0.9996,p<0.0001)。两种仪器测量的AXL和CCT的组内相关系数分别为0.999和0.988(均p<0.0001),Bland-Altman图显示95%的一致性极限(LoA)为-0.078至0.11mm和-9.989至13.486μm,分别。LT的最大绝对95%LoA,WTW,K1、K2和J0相对较高,达到0.829毫米,0.717mm,0.983D,0.948D,和0.632D,分别。
    结论:在年轻的近视患者中,使用ColomboIOL2和IOLMaster700获得的CCT和AXL测量值具有可比性。然而,WTW,LT,角膜屈光力,和散光值在临床实践中不能互换使用.
    BACKGROUND: This study assessed the agreement of ocular parameters of patients with myopia measured using Colombo intraocular lens (IOL) 2 and IOLMaster 700.
    METHODS: Eighty patients (male, 22; average age, 29.14 ± 7.36 years) with myopia (159 eyes) were included in this study in May 2023. The participants\' axial length (AXL), central corneal thickness (CCT), lens thickness (LT), white-to-white distance (WTW), front flat (K1), steep (K2), mean (Km) corneal keratometry, astigmatism (Astig), J0 vector, and J45 vector were measured using the IOLMaster 700 and Colombo IOL 2. The measurements from both devices were compared using the generalized estimating equation, correlation analysis, and Bland-Altman plots.
    RESULTS: With the Colombo IOL 2, lower values for K2 and J0 (odds ratio [OR] = 0.587, p = 0.033; OR = 0.779, p < 0.0001, respectively), and larger values for WTW, Astig, and J45 (OR = 1.277, OR = 1.482, OR = 1.1, all p < 0.0001) were obtained. All ocular measurements by both instruments showed positive correlations, with AXL demonstrating the strongest correlation (r = 0.9996, p < 0.0001). The intraclass correlation coefficients for AXL and CCT measured by both instruments was 0.999 and 0.988 (both p < 0.0001), and Bland-Altman plot showed 95% limits of agreement (LoA) of -0.078 to 0.11 mm and - 9.989 to 13.486 μm, respectively. The maximum absolute 95% LoA for LT, WTW, K1, K2, and J0 were relatively high, achieving 0.829 mm, 0.717 mm, 0.983 D, 0.948 D, and 0.632 D, respectively.
    CONCLUSIONS: In young patients with myopia, CCT and AXL measurements obtained with the Colombo IOL 2 and IOLMaster 700 were comparable. However, WTW, LT, corneal refractive power, and astigmatism values could not be used interchangeably in clinical practice.
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  • 文章类型: Journal Article
    灵敏地检测危险和可疑的生物气溶胶对于保障公众健康至关重要。花粉对通过荧光光谱识别细菌物种的潜在影响不容忽视。在分析之前,光谱经过预处理步骤,包括规范化,多元散射校正,和Savitzky-Golay平滑。此外,使用差异转换光谱,标准正态变量,和快速傅里叶变换技术。采用随机森林算法对31种不同类型的样本进行分类和识别。快速傅里叶变换将样品激发-发射矩阵荧光光谱数据的分类精度提高了9.2%,结果准确率为89.24%。有害物质,包括金黄色葡萄球菌,蓖麻毒素,β-银环蛇毒素,和葡萄球菌肠毒素B,被明确区分。光谱数据变换和分类算法有效地消除了花粉对其他成分的干扰。此外,建立了基于光谱特征变换的分类识别模型,在检测有害物质和保护公众健康方面具有出色的应用潜力。本研究为有害生物气溶胶快速检测方法的应用奠定了坚实的基础。
    Sensitively detecting hazardous and suspected bioaerosols is crucial for safeguarding public health. The potential impact of pollen on identifying bacterial species through fluorescence spectra should not be overlooked. Before the analysis, the spectrum underwent preprocessing steps, including normalization, multivariate scattering correction, and Savitzky-Golay smoothing. Additionally, the spectrum was transformed using difference, standard normal variable, and fast Fourier transform techniques. A random forest algorithm was employed for the classification and identification of 31 different types of samples. The fast Fourier transform improved the classification accuracy of the sample excitation-emission matrix fluorescence spectrum data by 9.2%, resulting in an accuracy of 89.24%. The harmful substances, including Staphylococcus aureus, ricin, beta-bungarotoxin, and Staphylococcal enterotoxin B, were clearly distinguished. The spectral data transformation and classification algorithm effectively eliminated the interference of pollen on other components. Furthermore, a classification and recognition model based on spectral feature transformation was established, demonstrating excellent application potential in detecting hazardous substances and protecting public health. This study provided a solid foundation for the application of rapid detection methods for harmful bioaerosols.
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  • 文章类型: Journal Article
    砷(As)是全球关注的地下水污染物。溶解有机物(DOM)的降解可以为As释放提供还原环境。然而,DOM与当地微生物群落的相互作用以及DOM的不同来源和类型如何影响含水层中As的生物转化是不确定的。这项研究使用了光谱学,傅里叶变换离子回旋共振质谱(FT-ICRMS),宏基因组学,和结构方程模型(SEM)来演示如何促进含水层中As的生物转化。结果表明,高砷地下水中的DOM主要是高度不饱和的低氧(O)化合物,这些化合物具有良好的腐殖质和稳定性。宏基因组学分析显示不动杆菌,假黄单胞菌,和假单胞菌在高砷环境中占主导地位;这些属都包含As解毒基因,并且是同一门(Proteobacteria)的成员。SEM分析表明,变形杆菌的存在与地下水中高度不饱和的低O化合物和促进亚砷酸盐释放的条件呈正相关。结果表明,地下水系统中As的生物地球化学转化如何受到来自不同来源和不同特征的DOM的影响。
    Arsenic (As) is a groundwater contaminant of global concern. The degradation of dissolved organic matter (DOM) can provide a reducing environment for As release. However, the interaction of DOM with local microbial communities and how different sources and types of DOM influence the biotransformation of As in aquifers is uncertain. This study used optical spectroscopy, Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS), metagenomics, and structural equation modeling (SEM) to demonstrate the how the biotransformation of As in aquifers is promoted. The results indicated that the DOM in high-As groundwater is dominated by highly unsaturated low-oxygen(O) compounds that are quite humic and stable. Metagenomics analysis indicated Acinetobacter, Pseudoxanthomonas, and Pseudomonas predominate in high-As environments; these genera all contain As detoxification genes and are members of the same phylum (Proteobacteria). SEM analyses indicated the presence of Proteobacteria is positively related to highly unsaturated low-O compounds in the groundwater and conditions that promote arsenite release. The results illustrate how the biogeochemical transformation of As in groundwater systems is affected by DOM from different sources and with different characteristics.
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  • 文章类型: Journal Article
    CNN在EEG信号检测方面表现出卓越的性能,然而,它仍然面临着全球认知方面的限制。此外,由于脑电信号的个体差异,癫痫检测模型的泛化能力为周。为了解决这个问题,本文提出了一种利用多头自我注意机制的跨患者癫痫检测方法。该方法首先利用短时傅里叶变换(STFT)将原始脑电信号转换为时频特征,然后使用卷积神经网络(CNN)对本地信息进行建模,随后使用Transformer的多头自注意机制捕获特征之间的全局依赖关系,最后使用这些特征进行癫痫检测。同时,该模型采用了具有交替结构的轻型多头注意机制模块,可以综合提取多尺度特征,同时显著降低计算成本。在CHB-MIT数据集上的实验结果表明,所提出的模型具有较高的准确性,灵敏度,特异性,F1得分,AUC为92.89%,96.17%,92.99%,94.41%,96.77%,分别。与现有方法相比,本文提出的方法具有较好的性能和较好的推广性。
    CNN has demonstrated remarkable performance in EEG signal detection, yet it still faces limitations in terms of global perception. Additionally, due to individual differences in EEG signals, the generalization ability of epilepsy detection models is week. To address this issue, this paper presents a cross-patient epilepsy detection method utilizing a multi-head self-attention mechanism. This method first utilizes Short-Time Fourier Transform (STFT) to transform the original EEG signals into time-frequency features, then models local information using Convolutional Neural Network (CNN), subsequently captures global dependency relationships between features using the multi-head self-attention mechanism of Transformer, and finally performs epilepsy detection using these features. Meanwhile, this model employs a light multi-head attention mechanism module with an alternating structure, which can comprehensively extract multi-scale features while significantly reducing computational costs. Experimental results on the CHB-MIT dataset show that the proposed model achieves accuracy, sensitivity, specificity, F1 score, and AUC of 92.89%, 96.17%, 92.99%, 94.41%, and 96.77%, respectively. Compared to the existing methods, the method proposed in this paper obtains better performance along with better generalization.
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  • 文章类型: Journal Article
    药物引起的心脏毒性的鉴定仍然是一个具有深远的临床和经济影响的紧迫挑战。经常导致患者伤害和资源密集型药物召回。目前的方法,包括体内和体外模型,在准确鉴定心脏毒性物质方面有严重的局限性。开创了这些传统技术的范式转变,我们的研究提出了两个基于深度学习的框架,STFT-CNN和SST-CNN,以显著提高的准确性和可靠性评估心脏毒性。利用诱导多能干细胞衍生的心肌细胞(iPSC-CM)的力量作为更人类相关的细胞模型,我们通过阻抗测量记录机械跳动信号。这些时间信号通过先进的变换技术转换成丰富的二维表示,特别是短时傅里叶变换(STFT)和同步压缩变换(SST)。这些转换后的数据被输入到拟议的框架中进行综合分析,包括药物类型分类,浓度分类,心脏毒性分类,和新药鉴定。与递归神经网络(RNN)和一维卷积神经网络(1D-CNN)等传统模型相比,SST-CNN在药物类型分类方面提供了98.55%的令人印象深刻的测试准确性,在区分心脏毒性和非心脏毒性药物方面提供了99%的准确性。它的可行性进一步强调了恒星的98.5%的平均精度用于各种浓度的分类,我们提出的框架的优越性强调了它们在彻底改变药物安全性评估方面的前景。具有可扩展性的潜力,它们代表了药物安全性评估的重大飞跃,提供了一条通往更强大的道路,高效,和人类相关的心脏毒性评估。
    The identification of drug-induced cardiotoxicity remains a pressing challenge with far-reaching clinical and economic ramifications, often leading to patient harm and resource-intensive drug recalls. Current methodologies, including in vivo and in vitro models, have severe limitations in accurate identification of cardiotoxic substances. Pioneering a paradigm shift from these conventional techniques, our study presents two deep learning-based frameworks, STFT-CNN and SST-CNN, to assess cardiotoxicity with markedly improved accuracy and reliability. Leveraging the power of induced pluripotent stem cell-derived cardiomyocytes (iPSC-CMs) as a more human-relevant cell model, we record mechanical beating signals through impedance measurements. These temporal signals were converted into enriched two-dimensional representations through advanced transformation techniques, specifically short-time Fourier transform (STFT) and synchro-squeezing transform (SST). These transformed data are fed into the proposed frameworks for comprehensive analysis, including drug type classification, concentration classification, cardiotoxicity classification, and new drug identification. Compared to traditional models like recurrent neural network (RNN) and 1-dimensional convolutional neural network (1D-CNN), SST-CNN delivered an impressive test accuracy of 98.55% in drug type classification and 99% in distinguishing cardiotoxic and noncardiotoxic drugs. Its feasibility is further highlighted with a stellar 98.5% average accuracy for classification of various concentrations, and the superiority of our proposed frameworks underscores their promise in revolutionizing drug safety assessments. With a potential for scalability, they represent a major leap in drug safety assessments, offering a pathway to more robust, efficient, and human-relevant cardiotoxicity evaluations.
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  • 文章类型: Journal Article
    这项研究的重点是通过将门控递归单元(GRU)集成到图神经网络(GNN)中来提高流行病时间序列数据预测的精度,形成GRGNN。通过与七种常用的预测方法进行比较,验证了引入GRU(门控递归单元)的GNN(图形神经网络)网络的准确性。
    GRGNN方法涉及使用通过GRU(门控递归单位)的积分改进的GNN(图形神经网络)网络的多变量时间序列预测。此外,介绍了图形傅里叶变换(GFT)和离散傅里叶变换(DFT)。GFT捕获频谱域中的序列间相关性,而DFT将数据从时域转换到频域,揭示时间节点相关性。在GFT和DFT之后,疫情数据通过频域中的一维卷积和门控线性回归进行预测,频谱域中的图卷积,和时域中的GRU(门控递归单位)。采用GFT和DFT的逆变换,并在通过全连接层后获得最终预测。对三个数据集进行评估:38个非洲国家和42个欧洲国家的COVID-19数据集,和来自Kaggle的20个匈牙利地区的水痘数据集。度量包括平均均方根误差(ARMSE)和平均平均绝对误差(AMAE)。
    对于非洲COVID-19数据集和匈牙利水痘数据集,在各种预测步长上,GRGNN始终优于ARMSE和AMAE中的其他方法。即使在扩展的预测步骤中,也可以获得最佳结果,突出模型的健壮性。
    GRGNN被证明在预测流行病时间序列数据方面具有很高的准确性,展示其在流行病监测和预警应用中的潜力。然而,需要进一步的讨论和研究,以完善其应用和判断方法,强调在这一领域进行探索和研究的持续需要。
    UNASSIGNED: This study focuses on enhancing the precision of epidemic time series data prediction by integrating Gated Recurrent Unit (GRU) into a Graph Neural Network (GNN), forming the GRGNN. The accuracy of the GNN (Graph Neural Network) network with introduced GRU (Gated Recurrent Units) is validated by comparing it with seven commonly used prediction methods.
    UNASSIGNED: The GRGNN methodology involves multivariate time series prediction using a GNN (Graph Neural Network) network improved by the integration of GRU (Gated Recurrent Units). Additionally, Graphical Fourier Transform (GFT) and Discrete Fourier Transform (DFT) are introduced. GFT captures inter-sequence correlations in the spectral domain, while DFT transforms data from the time domain to the frequency domain, revealing temporal node correlations. Following GFT and DFT, outbreak data are predicted through one-dimensional convolution and gated linear regression in the frequency domain, graph convolution in the spectral domain, and GRU (Gated Recurrent Units) in the time domain. The inverse transformation of GFT and DFT is employed, and final predictions are obtained after passing through a fully connected layer. Evaluation is conducted on three datasets: the COVID-19 datasets of 38 African countries and 42 European countries from worldometers, and the chickenpox dataset of 20 Hungarian regions from Kaggle. Metrics include Average Root Mean Square Error (ARMSE) and Average Mean Absolute Error (AMAE).
    UNASSIGNED: For African COVID-19 dataset and Hungarian Chickenpox dataset, GRGNN consistently outperforms other methods in ARMSE and AMAE across various prediction step lengths. Optimal results are achieved even at extended prediction steps, highlighting the model\'s robustness.
    UNASSIGNED: GRGNN proves effective in predicting epidemic time series data with high accuracy, demonstrating its potential in epidemic surveillance and early warning applications. However, further discussions and studies are warranted to refine its application and judgment methods, emphasizing the ongoing need for exploration and research in this domain.
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