From micro-correlations to macro-correlations

Random vectors with a symmetric correlation structure share a common value of pair-wise correlation between their different components. The symmetric correlation structure appears in a multitude of settings, e.g. mixture models. In a mixture model the components of the random vector are drawn independently from a general probability distribution that is determined by an underlying parameter, and the parameter itself is randomized. In this paper we study the overall correlation of high-dimensional random vectors with a symmetric correlation structure. Considering such a random vector, and terming its pair-wise correlation “micro-correlation”, we use an asymptotic analysis to derive the random vector’s “macro-correlation” : a score that takes values in the unit interval, and that quantifies the random vector’s overall correlation. The method of obtaining macro-correlations from micro-correlations is then applied to a diverse collection of frameworks that demonstrate the method’s wide applicability.     

A Marginal Sampler for σ-Stable Poisson–Kingman Mixture Models

We investigate the class of σ-stable Poisson–Kingman random probability measures (RPMs) in the context of Bayesian nonparametric mixture modeling. This is a large class of discrete RPMs, which encompasses most of the popular discrete RPMs used in Bayesian nonparametrics, such as the Dirichlet process, Pitman–Yor process, the normalized inverse Gaussian process, and the normalized generalized Gamma process. We show how certain sampling properties and marginal characterizations of σ-stable Poisson–Kingman RPMs can be usefully exploited for devising a Markov chain Monte Carlo (MCMC) algorithm for performing posterior inference with a Bayesian nonparametric mixture model. Specifically, we introduce a novel and efficient MCMC sampling scheme in an augmented space that has a small number of auxiliary variables per iteration. We apply our sampling scheme to a density estimation and clustering tasks with unidimensional and multidimensional datasets, and compare it against competing MCMC sampling schemes. Supplementary materials for this article are available online.     

Boiling Temperature Measurements on the Binary Mixtures of m-Xylene with some Aliphatic Alcohols

Boiling temperatures at 95 kPa, over the entire composition range are measured for the four binary systems formed by m-xylene with n-butanol, iso -butanol, sec -butanol and tert -butanol. A Swietoslawski-type ebulliometer was used for the measurements. The composition versus temperature measurements are well represented by the Wilson model.     

基于逆检索-非负最小二乘法的拉曼混合物分析方法研究

拉曼光谱因它可以提供非常丰富的结构信息而被看作是一项"指纹"技术,因此拉曼光谱可以被用作物质的定性识别。并且拉曼光谱具有制样简单,不破坏样品,在几乎所有的环境下都可以采集。通常认为拉曼光谱只能提供纯物质的结构信息,故利用拉曼光谱分析混合物的成分是有难度的。在便携式拉曼光谱仪、光谱数据库和化学计量学的基础上,开发了一种快速的混合物鉴别方法。根据基于小波域的自动精确峰值检测拉曼光谱的特点,对经典的逆搜索过程进行了改进。匹配质量可以用计算混合物和数据库中相减光谱中的负比率(按最小比例计算反向匹配峰的比值),提出一种基于改进的逆搜索和非负最小二乘法(Reverse searching and non-negative least squares,RSearch-NNLS),用于混合物分析。方法包括以下步骤:1)通过Whittaker平滑、ariPLS基线校正以及连续小波变换建立纯物质的拉曼光谱库;2)通过逆检索法对采集到的混合物拉曼光谱进行定性分析;3)根据第2步的结果,使用非负最小二乘法对候选化合物进行比例估算。方法是一种鉴别混合物的方法,具有一定的应用前景。     

分枝定界算法用于有机混合物的同时定性定量分析

分枝定界法用于多组分同时定性定量分析，只需解析一份试样测得的数据，即可同时得到待测样品中所含组分的种类、数目及含量，具有简单、快速、准确等优点。此文对分枝定界法在判据应用方面进行了改进，应用四个判据，解决了最佳子集难判断的问题。建立了精蒽中不经分离同时测定蒽、菲和咔唑的方法。     

Use and abuse of chemometrics in chromatography

This article presents a selection of the relevant issues that emerge at the interface between chromatography and chemometrics. In the first part, we present advantages and drawbacks of applying signal-enhancement, warping and mixture-analysis methods. In the second part, we discuss typical examples of misuse and abuse of chemometrics that can occur with those less familiar with the data-processing approaches. Finally, we conclude that close collaboration between the communities of chromatographers and chemometricians will allow a deeper insight into the chromatographic systems being analyzed and permit new chromatographic problems to be solved in an efficient, elegant manner.     

Carbon dioxide-methane mixture adsorption on activated carbon

In this work, we report new experimental data of pure and binary adsorption equilibria of carbon dioxide and methane on the activated carbon RB2 at 273 and 298 K. The pressure range studied were 0–3.5 MPa for pure gases and 0–0.1 MPa for mixtures. The combination of the generalized Dubinin model to describe the pure CO₂ and CH₄ isotherms with the IAST (Ideal Adsorbed Solution Theory) for the mixtures provide a method for the calculation of the binary adsorption equilibria. This formulation predicts with acceptable accuracy the binary adsorption data and can easily be integrated in general dynamic simulation of PSA (pressure swing adsorption process) adsorption columns. It involves only three parameters, independent of the temperature, and directly determined with only one adsorption isotherm of CO₂.     

Influence of common ions during ultrafiltration of mixtures: Part I. Common anions mixtures

A lot of experiments were investigated to show the behaviour of an ultrafiltration membrane during the filtration of pure salt solutions. What happens when the filtered solution contains several ions?

In this paper, results are given concerning the filtration of mixtures of two salts solutions, salts with a common anion: NaCl + CaCl₂ and Na₂SO₄ + CaSO₄.

The surface charge of the membrane is characterized by streaming potential measurements and rejection rates by means of chromatography. These results confirm the adsorption of divalent ions on the surface and a good selectivity for divalent cations.     

The constrained Fisher scoring method for maximum likelihood computation of a nonparametric mixing distribution

This paper proposes a new method for computing the nonparametric maximum likelihood estimate of a mixing distribution. It uses the Fisher scoring quadratic approximation to the log-likelihood function of the mixing proportions. At each iteration, new candidate support points are found and included, as guided by the gradient function, and bad support points are discarded, after being found redundant by optimizing the quadratic approximation. Numerical studies show that the CFS method is generally competitive with the fast and stable constrained Newton method; it may even have an advantage over the latter when the initial estimate is badly chosen.     

A theory of the adaptive growth of biological materials

Summary In this paper, a new theory of the adaptive growth of biological materials is presented. The theory is derived from the basic laws of continuum mechanics. The material is described as a classical mixture of solid material and fluid. It will be shown that several well-known models of the adaptive growth are embedded in this more general theory. In addition, it is clarified on which material assumptions these models are based. Finally, a solution procedure for the new theory is developed, and several examples are given. Received 31 March 1999; accepted for publication 1 June 1999