Dirac算子零化的Clifford值函数称为正则函数,正则函数是全纯函数在高维空间中非交换领域的推广。双正则函数是双变量的正则函数。正则函数的增长性问题是Clifford分析中的重要问题之一。本文研究单位球上双正则函数的增长性问题。借鉴Wiman-Valiron理论,利用双正则函数的Taylor级数,研究双正则函数的增长阶,得到广义Lindelöf-Pringsheim定理,建立增长阶与Taylor级数的联系。The Clifford-valued functions of null-solutions of Dirac operator are called regular functions. A regular function is an extension of holomorphic functions in non-commutative domains in high-dimensional spaces. Biregular functions are regular functions of two variables. The growth problem of regular functions is one of the important problems in Clifford analysis. In this paper, we investigate the growth problem of biregular functions in unit balls. Drawing on Wiman-Valiron theory, the growth order of biregular functions is studied by using the Taylor series of biregular functions, and the generalization of Lindelöf-Pringsheim theorem is obtained. This theorem shows the relation between the growth order of biregular functions and the Taylor series.
分类问题是数据挖掘、机器学习等领域的基础性问题之一,然而多数分类方法仅关注向量值样本的分类问题,而对于实际中广泛存在的集值型数据样本的分类关注较少。本文提出了一种基于Wasserstein距离的无监督聚类算法(Wk-means),利用熵正则最优传输模型度量集值型数据点之间的距离,并结合聚类的思想设计了一个可用于集值型数据的Wk-means聚类方法。为验证方法的有效性,本文首先在几个公开数据集上进行了实验,结果证实了Wk-means在多样本、多类别、多特征的集值型数据中表现优异,并且通过统计检验表明本文算法与其他算法存在显著差异。随后将本文方法实际应用于滏阳河水质数据集,结果同样表明相比传统的数据聚类算法,Wk-means能够更准确地划分水质类别,且运行效率更高。本文提出的Wk-means算法在集值型水质数据的分类任务中表现出色,能够为环境监测和管理提供有价值的决策支持。Classification is one of the basic problems in data mining, machine learning and other fields. However, most classification methods only focus on the vector-valued samples, while paying less attention to the classification of set-valued data samples that are widely existed in practice. This paper proposes an unsupervised clustering algorithm (Wk-means) based on Wasserstein distance. Combined with the idea of clustering, Wk-means can be used for set-valued samples, in which the entropy-regularized optimal transport model is used to measure the distance between set-valued samples. In order to verify the effectiveness of Wk-means, experiments are conducted firstly on several public data sets. The results confirm the excellent performance of Wk-means in set-valued data with multi-sample, multi-category, and multi-feature. Moreover, the statistical test show that Wk-means is significantly different from other algorithms. Wk-means is then applied to the Fuyang River water quality data set. The results also show that Wk-means can classify water quality categories more accurately and effectively than the traditional data clustering algorithm. The Wk-means algorithm proposed in this paper performs well in the classification task of set-valued water quality data and can provide valuable decision support for environmental monitoring and management.
目的:本研究旨在利用深度学习技术分析结直肠癌(CRC)病理切片图像,预测与结直肠癌相关的微生物丰度。方法:研究团队整合了TCGA数据库中的病理图像与微生物数据,开发了MDLR-Mean(Microbe Deep Learning Regression Prediction model Mean...
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目的:本研究旨在利用深度学习技术分析结直肠癌(CRC)病理切片图像,预测与结直肠癌相关的微生物丰度。方法:研究团队整合了TCGA数据库中的病理图像与微生物数据,开发了MDLR-Mean(Microbe Deep Learning Regression Prediction model Mean)模型。该模型融合了TOAD(Tumour Origin Assessment via Deep Learning)的肿瘤起源评估能力和MLP的深度学习特性,通过特征聚合技术提升预测精度,并采用MAE损失函数优化模型表现。结果:实验结果显示,MDLR-Mean模型在微生物丰度预测上表现卓越,在皮尔逊相关系数(PCC)、均方误差(MSE)和平均绝对误差(MAE)评估指标上均表现优异(P<0.05)。尤其是平均PCC相较于现有方法提升了36.5%,验证了模型的高效性和准确性。结论:本研究成功验证了MDLR-Mean模型在预测结直肠癌病理切片图像中微生物丰度方面的高准确性和可靠性,揭示深度学习将在未来结直肠癌诊治中发挥重要作用和助力精准医疗。
基于检索增强生成(RAG)的军事领域知识问答系统已经逐渐成为现代情报人员收集和分析情报的重要工具。针对目前RAG方法的应用策略中的混合检索存在可移植性不强以及非必要使用查询改写容易诱发语义漂移的问题,提出一种多策略检索增强生成(MSRAG)方法。首先,根据用户输入的查询特点自适应地匹配检索模型来召回相关文本;其次,利用文本过滤器提取出能够回答问题的关键文本片段;再次,使用文本过滤器进行内容有效性判断以启动基于同义词拓展的查询改写,并将初始查询与改写后的信息合并输入检索控制器以进行更有针对性的再次检索;最后,合并能够回答问题的关键文本片段和问题,并使用提示工程输入生成答案模型来生成响应返回给用户。实验结果表明,MSRAG方法在军事领域数据集(Military)和Medical数据集的ROUGE-L(Recall-Oriented Understudy for Gisting Evaluation Longest common subsequence)指标上相较于凸线性组合RAG方法分别提高了14.35和5.83个百分点。可见,MSRAG方法具备较强的通用性和可移植性,能够缓解非必要查询改写导致的语义漂移现象,有效帮助大模型生成更准确的答案。
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