An efficient algorithm for finding the largest chain graph according to a given chain graph

Chain graph (CG) is a general model of graphical Markov models. Some different chain graphs may describe the same conditional independence structure, then we say that these CGs are Markov equivalent. In 1990 Frydenberg showed that every class of Markov equivalent CGs has a CG which is called the largest chain graph with the greatest number of lines. This paper presents an efficient algorithm for finding the largest chain graph of the corresponding Markov equivalent class of a given CG. The computational complexity of the algorithm is O(n3). It is more efficient than the complexity O(n!) of the present algorithms. Also a more intuitive graphical characterization of the largest chain graph is provided based on the algorithm in this paper.     

Differentially Private Precision Matrix Estimation

In this paper, we study the problem of precision matrix estimation when the dataset contains sensitive information. In the differential privacy framework, we develop a differentially private ridge estimator by perturbing the sample covariance matrix. Then we develop a differentially private graphical lasso estimator by using the alternating direction method of multipliers (ADMM) algorithm. Furthermore, we prove theoretical results showing that the differentially private ridge estimator for the precision matrix is consistent under fixed-dimension asymptotic, and establish a convergence rate of differentially private graphical lasso estimator in the Frobenius norm as both data dimension p and sample size n are allowed to grow. The empirical results that show the utility of the proposed methods are also provided.     

Precision Matrix Estimation by Inverse Principal Orthogonal Decomposition

We investigate the structure of a large precision matrix in Gaussian graphical models by decomposing it into a low rank component and a remainder part with sparse precision matrix.Based on the decomposition,we propose to estimate the large precision matrix by inverting a principal orthogonal decomposition(IPOD).The IPOD approach has appealing practical interpretations in conditional graphical models given the low rank component,and it connects to Gaussian graphical models with latent variables.Specifically,we show that the low rank component in the decomposition of the large precision matrix can be viewed as the contribution from the latent variables in a Gaussian graphical model.Compared with existing approaches for latent variable graphical models,the IPOD is conveniently feasible in practice where only inverting a low-dimensional matrix is required.To identify the number of latent variables,which is an objective of its own interest,we investigate and justify an approach by examining the ratios of adjacent eigenvalues of the sample covariance matrix?Theoretical properties,numerical examples,and a real data application demonstrate the merits of the IPOD approach in its convenience,performance,and interpretability.     

Divagations about the periodic table: Boolean hypercube and quantum similarity connections

In this study, several simple aspects associated with the periodic table (PT) of the elements are commented. First, the connection of the PT with the structure of a seven-dimensional Boolean hypercube leads afterward to discuss the nature of those PT elements bearing prime atomic numbers. Second, the use of quantum similarity (QS) to obtain an alternative insight on the PT element relations will be also developed. The foundation of the second part starts admitting that any element of the PT can be attached to a schematic electronic density function, constructed with a single Gaussian function: a Gaussian atomic density function, allowing to consider the PT elements as a set of quantum objects, and permits a straightforward construction of a QS matrix. Such QS scheme can be applied to the whole PT or to any subset of it. Manipulation of the QS matrices attached to any quantum object set allows the evaluation of statistical-like values, acting as coordinates to numerically or graphically represent the chosen PT atomic element sets. © 2019 Wiley Periodicals, Inc.     

Change points in heavy‐tailed multivariate time series: Methods using precision matrices

We propose two robust data‐driven techniques for detecting network structure change points between heavy‐tailed multivariate time series for situations where both the placement and number of change points are unknown. The first technique utilizes the graphical lasso method to estimate the change points, whereas the second technique utilizes the tlasso method. The techniques not only locate the change points but also estimate an undirected graph (or precision matrix) representing the relationship between the time series within each interval created by pairs of adjacent change points. An inference procedure on the edges is used in the graphs to effectively remove false‐positive edges, which are caused by the data deviating from normality. The techniques are compared using simulated multivariate t‐distributed (heavy‐tailed) time series data and the best method is applied to two financial returns data sets of stocks and indices. The results illustrate the method's ability to determine how the dependence structure of the returns changes over time. This information could potentially be used as a tool for portfolio optimization.     

Simultispin: A versatile graphical user interface for the simulation of solid-state continuous wave EPR spectra

Solid-state continuous wave (cw) electronic paramagnetic resonance (EPR) spectroscopy is particularly suitable for metal complex analysis. Extracting magnetic parameters by simulation is often necessary to describe the electronic structure of the studied molecular compounds that can have various electronic spin states and characterized by different parameters like g-values, hyperfine coupling or zero field splitting values. Easyspin toolbox on MATLAB is a powerful tool, but for the user, it requires spending time with coding and could discourage nonexperts. Facing this context, we have developed a graphical user interface called Simultispin, dedicated to solid-state cw-EPR spectra simulation. Some examples of experimental spectra of metal complexes (mixture of low spin and high spin Fe^III complexes, dynamic disorder of a Cu^II complex, photogeneration of a Mn^III complex), highlighting specific solid-state functions, are described and analyzed based on simulations performed with Simultispin. We hope that its ergonomy and the ease to set up a complete set of parameters to get reliable simulations could help a large EPR community to improve the efficiency of their interpretations.     

Consistency check on the fundamental and alternative flux operators in loop quantum gravity

There are different constructions of the flux of triad in loop quantum gravity, namely the fundamental and alternative flux operators. In parallel to the consistency check on the two versions of operator by the algebraic calculus in the literature, we check their consistency by the graphical calculus. Our calculation based on the original Brink graphical method is obviously simpler than the algebraic calculation. It turns out that our consistency check fixes the regulating factor κreg of the Ashtekar-Lewandowski volume operator as1/2, which corrects its previous value in the literature.     

基于Matlab的二元共聚物组成与转化率关系曲线的绘制及应用

采用Matlab GUI工具,以单体组成为中间变量,依据共聚物组成方程及单体组成与转化率关系式,开发出一款用于绘制二元共聚合反应共聚物组成与单体转化率关系曲线的图形用户程序。通过对苯乙烯与甲基丙烯酸甲酯、丙烯腈与醋酸乙烯酯等共聚反应的应用表明：该图形用户程序界面友好,交互性强,适用性广,计算便捷,解决了绘制过程中共聚物组成与单体转化率关系式过于复杂而无法找到直接关系的困难,为预测不同竞聚率、不同投料比时共聚物组成与转化率的变化规律,控制共聚物组成,选择控制方法,验证实验,指导生产提供理论依据。     

Mechanistic Explanation versus Deductive-Nomological Explanation

This paper discusses the important paper by Paul Thagard on the pathway version of mechanistic explanation that is currently used in chemical explanation. The author claims that this method of explanation has a respectable pedigree and can be traced back to the Chemical Revolution in the arguments used by the Lavoisier School in their theoretical duels with Richard Kirwan, the proponent of a revised phlogistonian theory. Kirwan believed that complex chemical reactions could be explained by recourse to affinity tables that catalogued the attraction that various simple bodies possessed towards each other. To explain was in effect to make a delayed prediction, it is not enough just to show how a phenomenon fits into the discernible patterns of the world. Lavoisier, Fourcroy and their colleagues used pathway reasoning, although disguising this fact by suggesting that affinities varied when subjected to n-body situations.     

A fuzzy measure identification method by diamond pairwise comparisons and $${\phi_s}$$ transformation

We propose an identification method of fuzzy measures by diamond pairwise comparisons. Right and left side of the diamond means ordinal weights’ comparison and up and down means interaction degrees. From the comparisons, we estimate a hierarchy diagram with interaction degrees and weights of evaluation items using the agglomerative hierarchical clustering method. From the diagram, to identify the fuzzy measure, conversion method is proposed.