应用图论分析与最优化理论来数据挖掘大规模水牛普里昂蛋白结构数据

图论、最优化理论显然在蛋白质结构的研究中大有用场. 首先, 调查/回顾了研究蛋白质结构的所有图论模型. 其后, 建立了一个图论模型: 让蛋白质的侧链来作为图的顶点, 应用图论的诸如团、 $k$-团、 社群、 枢纽、聚类等概念来建立图的边. 然后, 应用数学最优化的现代摩登数据挖掘算法/方法来分析水牛普里昂蛋白结构的大数据. 成功与令人耳目一新的数值结果将展示给朋友们.     

On the vanishing of homology in random Čech complexes

We compute the homology of random ?ech complexes over a homogeneous Poisson process on the d‐dimensional torus, and show that there are, coarsely, two phase transitions. The first transition is analogous to the Erd?s ‐Rényi phase transition, where the ?ech complex becomes connected. The second transition is where all the other homology groups are computed correctly (almost simultaneously). Our calculations also suggest a finer measurement of scales, where there is a further refinement to this picture and separation between different homology groups. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 51, 14–51, 2017     

Sufficient Dimension Reduction and Variable Selection for Large-p-Small-n Data With Highly Correlated Predictors

Sufficient dimension reduction (SDR) is a paradigm for reducing the dimension of the predictors without losing regression information. Most SDR methods require inverting the covariance matrix of the predictors. This hinders their use in the analysis of contemporary datasets where the number of predictors exceeds the available sample size and the predictors are highly correlated. To this end, by incorporating the seeded SDR idea and the sequential dimension-reduction framework, we propose a SDR method for high-dimensional data with correlated predictors. The performance of the proposed method is studied via extensive simulations. To demonstrate its use, an application to microarray gene expression data where the response is the production rate of riboflavin (vitamin B₂) is presented.     

Efficient Data Augmentation for Fitting Stochastic Epidemic Models to Prevalence Data

Stochastic epidemic models describe the dynamics of an epidemic as a disease spreads through a population. Typically, only a fraction of cases are observed at a set of discrete times. The absence of complete information about the time evolution of an epidemic gives rise to a complicated latent variable problem in which the state space size of the epidemic grows large as the population size increases. This makes analytically integrating over the missing data infeasible for populations of even moderate size. We present a data augmentation Markov chain Monte Carlo (MCMC) framework for Bayesian estimation of stochastic epidemic model parameters, in which measurements are augmented with subject-level disease histories. In our MCMC algorithm, we propose each new subject-level path, conditional on the data, using a time-inhomogenous continuous-time Markov process with rates determined by the infection histories of other individuals. The method is general, and may be applied to a broad class of epidemic models with only minimal modifications to the model dynamics and/or emission distribution. We present our algorithm in the context of multiple stochastic epidemic models in which the data are binomially sampled prevalence counts, and apply our method to data from an outbreak of influenza in a British boarding school. Supplementary material for this article is available online.     

Tensor Decomposition With Generalized Lasso Penalties

We present an approach for penalized tensor decomposition (PTD) that estimates smoothly varying latent factors in multiway data. This generalizes existing work on sparse tensor decomposition and penalized matrix decompositions, in a manner parallel to the generalized lasso for regression and smoothing problems. Our approach presents many nontrivial challenges at the intersection of modeling and computation, which are studied in detail. An efficient coordinate-wise optimization algorithm for PTD is presented, and its convergence properties are characterized. The method is applied both to simulated data and real data on flu hospitalizations in Texas and motion-capture data from video cameras. These results show that our penalized tensor decomposition can offer major improvements on existing methods for analyzing multiway data that exhibit smooth spatial or temporal features.     

Semiparametric Bayesian inference for mean-covariance regression models

In this paper, we propose a Bayesian semiparametric mean-covariance regression model with known covariance structures. A mixture model is used to describe the potential non-normal distribution of the regression errors. Moreover, an empirical likelihood adjusted mixture of Dirichlet process model is constructed to produce distributions with given mean and variance constraints. We illustrate through simulation studies that the proposed method provides better estimations in some non-normal cases. We also demonstrate the implementation of our method by analyzing the data set from a sleep deprivation study.     

Phase II monitoring of changes in mean from high‐dimensional data

The generalized T² chart (GT‐chart), which is composed of the T² statistic based on a small number of principal components and the remaining components, is a popular alternative to the traditional Hotelling's T² control chart. However, the application of the GT‐chart to high‐dimensional data, which are now ubiquitous, encounters difficulties from high dimensionality similar to other multivariate procedures. The sample principal components and their eigenvalues do not consistently estimate the population values, and the GT‐chart relying on them is also inconsistent in estimating the control limits. In this paper, we investigate the effects of high dimensionality on the GT‐chart and then propose a corrected GT‐chart using the recent results of random matrix theory for the spiked covariance model. We numerically show that the corrected GT‐chart exhibits superior performance compared to the existing methods, including the GT‐chart and Hotelling's T² control chart, under various high‐dimensional cases. Finally, we apply the proposed corrected GT‐chart to monitor chemical processes introduced in the literature.     

Panel‐based stratified cluster sampling and analysis for photovoltaic outdoor measurements

We study a stratified multisite cluster‐sampling panel time series approach in order to analyse and evaluate the quality and reliability of produced items, motivated by the problem to sample and analyse multisite outdoor measurements from photovoltaic systems. The specific stratified sampling in spatial clusters reduces sampling costs and allows for heterogeneity as well as for the analysis of spatial correlations due to defects and damages that tend to occur in clusters. The analysis is based on weighted least squares using data‐dependent weights. We show that this does not affect consistency and asymptotic normality of the least squares estimator under the proposed sampling design under general conditions. The estimation of the relevant variance–covariance matrices is discussed in detail for various models including nested designs and random effects. The strata corresponding to damages or manufacturers are modelled via a quality feature by means of a threshold approach. The analysis of outdoor electroluminescence images shows that spatial correlations and local clusters may arise in such photovoltaic data. Further, relevant statistics such as the mean pixel intensity cannot be assumed to follow a Gaussian law. We investigate the proposed inferential tools in detail by simulations in order to assess the influence of spatial cluster correlations and serial correlations on the test's size and power. ©2016 The Authors. Applied Stochastic Models in Business and Industry published by John Wiley & Sons, Ltd.     

Optimization of Vacuum-Microwave-Assisted Extraction of Natural Polyphenols and Flavonoids from Raw Solid Waste of the Orange Juice Producing Industry at Industrial Scale

Orange pomace (OP) is a solid waste produced in bulk as a byproduct of the orange juice industry and accounts for approximately 50% of the quantity of the fruits processed into juice. In numerous literature references there is information about diverse uses of orange pomace for the production of high-added-value products including production of natural antioxidant and antimicrobial extracts rich in polyphenols and flavonoids which can substitute the hazardous chemical antioxidants/antimicrobials used in agro-food and cosmetics sectors. In this work and for the first time, according to our knowledge, the eco-friendly aqueous vacuum microwave assisted extraction of orange pomace was investigated and optimized at real industrial scale in order to produce aqueous antioxidant/antimicrobial extracts. A Response Surface Optimization methodology with a multipoint historical data experimental design was employed to obtain the optimal values of the process parameters in order to achieve the maximum rates of extraction of OP total polyphenols and/or total flavonoids for economically optimum production at industrial scale. The three factors used for the optimization were: (a) microwave power (b) water to raw pomace ratio and (c) extraction time. Moreover, the effectiveness and statistical soundness of the derived cubic polynomial predictive models were verified by ANOVA.