Semiclassical statistical mechanics ofv-dimensional fluid mixture of hardv-spheres

The problem of calculating the equilibrium properties ofv-dimensional fluid mixture of hardv-spheres is studied. High temperature expansion for the density independent radial distribution function is derived for a hardv-sphere mixture. The ‘excess’ quantum corrections to the second virial coefficient and the excess free energy are also studied. Significant features are the large increase in ‘excess’ quantum correction with increasing dimensionality.     

文本分类实现技术

文本分类是文本数据挖掘的重要技术.从文本分类实现过程的各个环节,包括建立文档模型、特征提取、维数约简、选择分类策略几个方面分别给出了目前实用的解决方案,同时对各种算法进行了分类和性能上的定性与定量的比较,最后讨论了国内文本分类研究中的一些问题和未来的发展.     

A novel fuzzy set based multifactor dimensionality reduction method for detecting gene–gene interaction

BackgroundGene-gene interaction (GGI) is one of the most popular approaches for finding the missing heritability of common complex traits in genetic association studies. The multifactor dimensionality reduction (MDR) method has been widely studied for detecting GGIs. In order to identify the best interaction model associated with disease susceptibility, MDR compares all possible genotype combinations in terms of their predictability of disease status from a simple binary high(H) and low(L) risk classification. However, this simple binary classification does not reflect the uncertainty of H/L classification.MethodsWe regard classifying H/L as equivalent to defining the degree of membership of two risk groups H/L. By adopting the fuzzy set theory, we propose Fuzzy MDR which takes into account the uncertainty of H/L classification. Fuzzy MDR allows the possibility of partial membership of H/L through a membership function which transforms the degree of uncertainty into a [0,1] scale. The best genotype combinations can be selected which maximizes a new fuzzy set based accuracy measure.ResultsTwo simulation studies are conducted to compare the power of the proposed Fuzzy MDR with that of MDR. Our results show that Fuzzy MDR has higher power than MDR. We illustrate the proposed Fuzzy MDR by analysing bipolar disorder (BD) trait of the WTCCC dataset to detect GGI associated with BD.ConclusionsWe propose a novel Fuzzy MDR method to detect gene–gene interaction by taking into account the uncertainly of H/L classification and show that it has higher power than MDR. Fuzzy MDR can be easily extended to handle continuous phenotypes as well. The program written in R for the proposed Fuzzy MDR is available at https://statgen.snu.ac.kr/software/FuzzyMDR.     

基于伽玛-泊松分布和图正则化的单细胞非负矩阵分解算法

单细胞RNA测序(Single-cell RNA sequencing,scRNA-seq)可以获取单细胞水平的基因表达谱。然而,目前许多基于非负矩阵分解(Non-negative Matrix Factorization,NMF)的降维算法在细胞类型识别中往往忽视了数据概率分布和细胞之间的拓扑关系,无法较好地兼顾数据的全局结构和局部结构。为了克服传统NMF降维算法在处理高维含噪稀疏数据时的不足,本文提出一种改进的单细胞非负矩阵分解算法GPNMF。GPNMF结合了伽玛-泊松(Gamma-Poisson)分布假设和图正则化技术,通过迭代更新因子分解矩阵以最小化重构误差,从而有效地保留数据的局部结构与全局结构。通过引入约束优化并稳定化模型,GPNMF在分解单细胞表达数据时能够提供更为稳健和可靠的结果。最后,利用真实scRNA-seq数据进行实验,验证了GPNMF的有效性,并展示了其在单细胞基因表达数据轨迹推断分析中的潜在应用。     

基于局部线性嵌入的特征融合方法在岩石破裂 状态分类的应用*

为了获取岩石破裂过程有效的声发射信号特征,更好的对岩石破裂状态进行分类,提出一种基于流形学习算法的LLE特征融合方法进行数据降维。以红砂岩为研究对象设计室内单轴压缩实验采集信号,然后对原始声发射信号预处理并对信号进行特征提取,以时域、频域下的特征向量重新组合成一组新的多维特征向量,采用线性主元(PCA)和流形学习LLE算法分别进行降维。比较两种算法降维后融合特征的聚类效果二维和三维分布图,使用LLE算法降维后,四种状态分布相对更近,呈一条水平线趋势,且各状态交叉混叠数目较少,第一状态没有一个样本错判,且四个状态相比于PCA降维后的聚类效果更集中。再比较两种算法降维后融合特征的敏感度之和,LLE算法融合特征敏感度之和远大于PCA算法,说明经过LLE算法降维后得到的融合特征更多地表征了原始信号包含的局部信息同时证明了LLE算法相比PCA算法具有更好的聚类效果。最后经LLE特征融合下的砂岩破裂状态分类实验验证,融合特征后的识别率相对单一的时域特征识别提高了6%。表明该方法能显著提高岩石破裂状态分类的识别率,降维性能相对突出。     

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The additive model is a more flexible nonparametric statistical model which allows a data-analytic transform of the covariates.When the number of covariates is big and grows exponentially with the sample size the urgent issue is to reduce dimensionality from high to a moderate scale. In this paper, we propose and investigate marginal empirical likelihood screening methods in ultra-high dimensional additive models. The proposed nonparametric screening method selects variables by ranking a measure of the marginal empirical likelihood ratio evaluated at zero to differentiate contributions of each covariate given to a response variable. We show that, under some mild technical conditions, the proposed marginal empirical likelihood screening methods have a sure screening property and the extent to which the dimensionality can be reduced is also explicitly quantified. We also propose a data-driven thresholding and an iterative marginal empirical likelihood methods to enhance the finite sample performance for fitting sparse additive models. Simulation results and real data analysis demonstrate the proposed methods work competitively and performs better than competitive methods in error of a heteroscedastic case.     

多标记数据的特征及标记降维方法综述

多标记学习降维方法在实际应用问题中用以处理特征,标记或二者维度较高的数据集,已成为研究热点;针对目前多标记学习降维方法数量众多,种类繁杂而导致缺乏科学分类的问题,从多标记数据降维空间选择的角度,提出将多标记学习降维方法按照特征空间降维,标记空间降维和二者均降维的形式归纳为三类,其中特征空间降维又分为特征降维和特征选择两...     

Ce 基重费米子材料的电子态研究与维度调控

重费米子材料作为一类典型的强关联电子体系,蕴含着非常规超导、奇异金属、量子临界、磁有序、重电子态、关联拓扑态等新奇的量子态,而4f 电子在其中扮演着重要的作用。随着高分辨角分辨光电子能谱和薄膜生长技术的发展,精确探测重费米子材料中4f 电子在能量/动量空间的色散和谱权重成为了可能,这为从微观上理解这类材料中的电子关联效应和新奇量子现象提供了重要的基础。本论文总结了几个典型的重费米子单晶和薄膜体系的电子态研究,包括Ce-115 体系、CeCu2Si2、CeRh6Ge4 以及单晶 Ce 膜等。这些结果为理解重费米子体系中重电子态的形成和温度演化、近藤杂化的能带/动量依赖、重电子能带与超导的关系、近藤效应与磁性和其它量子态的竞争、4f 电子的维度调控等重要物理问题提供了谱学证据。