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.     

Perturbation theory for thermodynamic properties of a ν-dimensional square-well fluid

The Barker-Henderson perturbation theory is used for a ν-dimensional fluid with square-well potential. Analytic expressions are given for the equation of state, excess free energy per particle and internal energy. The numerical results are discussed. A significant feature is the increase of the thermodynamic properties with increasing dimensionality.     

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.     

Gearbox failure diagnosis based on vector autoregressive modelling of vibration data and dynamic principal component analysis

Email: mgt.liu{at}utoronto.ca Email: makis{at}mie.utoronto.ca Received on 4 August 2006. Accepted on 14 December 2006. An effective gearbox failure diagnosis helps prevent catastrophicgearbox failure and can contribute to significant economic benefits.This paper proposes a gear failure diagnosis method based onvector autoregressive modelling of high-frequency vibrationdata, dimensionality reduction applying dynamic principal componentanalysis (PCA) and condition monitoring using a multivariatecontrol chart. After extracting useful information from thevibration data obtained from distinct directions via dynamicPCA, a failure diagnosis scheme is implemented and tested usingreal gearbox vibration data. It is shown that the failure diagnosisscheme can indicate the gear teeth failure pattern when thegear is damaged, which has not been demonstrated in the previousstudies. For a comparison, PCA is applied to the same data set.The results show that the advantages of dynamic PCA over PCAfor failure diagnosis using vibration data consist not onlyin indicating more accurately the occurrence of incipient faultand the actual gear condition, but also in a much lower falsealarm rate.     

Gene association study with SVM, MLP and cross validation for diagnosis of diseases

Gene association study is one of the major challenges of biochip technology both for gene diagnosis where only a gene subset is responsible for some diseases, and for the treatment of the curse of dimensionality which occurs especially in DNA microarray datasets where there are more than thousands of genes and only a few number of experiments （samples）. This paper presents a gene selection method by training linear support vector machine （SVM）/nonlinear MLP （multilayer perceptron） classifiers and testing them with cross-validation for finding a gene subset which is optimal/suboptimal for the diagnosis of binary/multiple disease types. Genes are selected with linear SVM classifier for the diagnosis of each binary disease types pair and tested by leave-one-out cross-validation; then, genes in the gene subset initialized by the union of them are deleted one by one by removing the gene which brings the greatest decrease of the generalization power, for samples, on the gene subset after removal, where generalization is measured by training MLPs with leaveone-out and leave-four-out cross-validations. The proposed method was tested with experiments on real DNA microarray MIT data and NCI data. The result shows that it outperforms conventional SNR method in the separability of the data with expression levels on selected genes. For real DNA microarray MIT/NCI data, which is composed of 7129/2308 effective genes with only 72/64 labeled samples belonging to 2/4 disease classes, only 11/6 genes are selected to be diagnostic genes. The selected genes are tested by the classification of samples on these genes with SVM/MLP with leave-one-out/both leave-one-out and leave-four-out cross-validations. The result of no misclassification indicates that the selected genes can be really considered as diagnostic genes for the diagnosis of the corresponding diseases.     

一种求解MMC的快速算法

最大间距准则(Maximum Margin Criterion,MMC)能够有效地克服线性鉴别分析(Linear Discriminant Analysis,LDA)算法所面临的小样本问题.但是,原有的MMC求解算法复杂度较高,为了提高MMC算法的计算效率,本文提出了一种新的快速的MMC求解算法.在理论上,新的MMC求解算法和原有算法等价,但计算复杂度比原算法要低的多.在人脸库上的实验表明,新的MMC求解算法的计算速度远比现有的MMC求解算法要快,但是其识别率与现有求解算法相同.     

Assessing the statistical validity of proteomics based biomarkers

A strategy is presented for the statistical validation of discrimination models in proteomics studies. Several existing tools are combined to form a solid statistical basis for biomarker discovery that should precede a biochemical validation of any biomarker. These tools consist of permutation tests, single and double cross-validation. The cross-validation steps can simply be combined with a new variable selection method, called rank products. The strategy is especially suited for the low-samples-to-variables-ratio (undersampling) case, as is often encountered in proteomics and metabolomics studies. As a classification method, principal component discriminant analysis is used; however, the methodology can be used with any classifier. A dataset containing serum samples from Gaucher patients and healthy controls serves as a test case. Double cross-validation shows that the sensitivity of the model is 89% and the specificity 90%. Potential putative biomarkers are identified using the novel variable selection method. Results from permutation tests support the choice of double cross-validation as the tool for determining error rates when the modelling procedure involves a tuneable parameter. This shows that even cross-validation does not guarantee unbiased results. The validation of discrimination models with a combination of permutation tests and double cross-validation helps to avoid erroneous results which may result from the undersampling.     

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。     

Refined semi-empirical formula for liquid–vapour critical point exponent δ and its relevance to the random field Ising model

Recent work in D.J. Klein and N.H. March, Phys. Lett. A 372, 5052 (2008) has considered, by a semi-empirical approach, the critical exponent δ at the liquid–vapour critical point as a function of dimensionality D. Here we first refine δ(d′), again semi-empirically, but with better results for other critical exponents, especially η(d′). The resulting form of δ(d′) is then utilised to discuss the random field Ising model. Systems with random fields are expected to exhibit drastically modified critical properties. We discuss the relation between a d-dimensional spin system in a random field with a d′-dimensional spin assembly in a zero magnetic field. A further matter focused in here concerns effective reduced dimensionality and hyperscaling relations. We conclude by assessing the way in which the available experimental results relate to the issues raised above.