Applications of Markov Chains in Particulate Process Engineering: A Review

Processes involving particles, are known to exhibit extremely unpredictable behaviour, mainly due to the mesoscopic nature of granular media. Understanding particulate processes, not only for intellectual satisfaction, but also for process design and operation, basically requires a systems approach in modelling. Because they combine simplicity and flexibility, the stochastic models based on the Markov chain theory are very valuable mathematical tools to this respect. However, they are still largely ignored by the whole core of chemical engineering researchers. This motivates the existence of this review paper, in which we examine the three traditional issues: mixing and transport, separation and transformation.     

Conditional Heteroskedasticity Driven by Hidden Markov Chains

We consider a generalized autoregressive conditionally heteroskedastic (GARCH) equation where the coefficients depend on the state of a nonobserved Markov chain. Necessary and sufficient conditions ensuring the existence of a stationary solution are given. In the case of ARCH regimes, the maximum likelihood estimates are shown to be consistent. The identification problem is also considered. This is illustrated by means of real and simulated data sets.     

Moving Average Representations for Multivariate Stationary Processes

Abstract. Backward and forward moving average (MA) representations are established for multivariate stationary processes. It is observed that in the multivariate case, in contrast to the univariate case, the backward and forward MA coefficients correspondingly, in general, are different. A method is presented to adopt the known techniques in deriving the backward MA to obtain the forward ones.     

Testing for Stationarity in Multivariate Locally Stationary Processes

In this article, we propose a nonparametric procedure for validating the assumption of stationarity in multivariate locally stationary time series models. We develop a bootstrap‐assisted test based on a Kolmogorov–Smirnov‐type statistic, which tracks the deviation of the time‐varying spectral density from its best stationary approximation. In contrast to all other nonparametric approaches, which have been proposed in the literature so far, the test statistic does not depend on any regularization parameters like smoothing bandwidths or a window length, which is usually required in a segmentation of the data. We additionally show how our new procedure can be used to identify the components where non‐stationarities occur and indicate possible extensions of this innovative approach. We conclude with an extensive simulation study, which shows finite‐sample properties of the new method and contains a comparison with existing approaches.     

汕头市基于改进Markov链的空气质量预报模型的研究

为了更有效的对汕头市空气质量进行预测,我们将基于Markov链理论的空气质量的统计预报模型进行了改进,加入了气象因素对模型进行修正,并作实例验证其可行性及准确率检验。证明了该模型具有较好的短期预测正确率,有一定的实用价值。     

On White Noises Driven by Hidden Markov Chains

We consider a time series model where the variance of the underlying process depends on the state of a non-observed Markov chain. Maximum likelihood estimates are shown to be consistent. Estimators with asymptotic Gaussian distribution are proposed. Prediction and identification are also mentioned. This is illustrated by means of real and simulated data sets     

振荡流反应器的物料停留时间分布模型研究

提出了一个基于马尔柯夫链（Markov chains）的考虑腔室间返混的振荡流反应器物料停留时间分布模型。通过对在内径50mm,长1．95m的振荡流反应器进行的理想脉冲示踪试验数据的统计分析,给出了模型的唯一参数回流比R的经验计算公式。发现在试验条件下,存在一个与最小回流比R相对应的振荡条件。这振荡条件可表示为振荡流雷诺数（Reo）与净流雷诺数（Ren）的比值ζ,其范围为1．6〈ζ〈2．5。     

超声法提取甘草蔓籽油的研究

采用超声法提取甘草蔓籽油,通过单因素试验和正交试验,以甘草蔓籽油提取率为考察指标,对超声法提取甘草蔓籽油的工艺进行了优化。结果表明:选用石油醚作为萃取溶剂,料液比为1∶8(质量/体积)、超声功率为400W、温度为50℃、超声时间为30min,此条件下甘草蔓籽油的得率达35.37%,为进一步开发甘草蔓籽油提供了科学依据。     

Collective dynamics modeling of polydisperse particulate systems via Markov chains

This paper develops an efficient approach to modeling and analyzing the overall dynamics of polydisperse particulate systems, exemplified using a rotating drum with horizontal axis, under both constant and time-varying operating conditions. This approach captures the collective dynamics using stochastic models in the form of Markov chains. The characteristics of such dynamics can be obtained from the Markov chains operator. It provides a systematic way to the analysis of collective dynamical features of particle movements. The obtained operators are used to estimate the spatial particle distribution and the degree of particulate mixing as examples of collective dynamic features of polydisperse particulate systems. In this paper, Markov chains models were developed from discrete element method simulation results to show the effectiveness of the proposed approach.     

Simulation of Real Discrete Time Gaussian Multivariate Stationary Processes with Given Spectral Densities

In this article we establish a simulation procedure to generate values for a real discrete time multivariate stationary process, based on a factor of spectral density matrix. We prove the convergence of the simulator, at each time epoch, to the actual process, and provide the corresponding rate of convergence. We merely assume that the spectral density matrix is continuous and of bounded variation. By using the positive root factor, we provide an extended version for the Sun and Chaika ( 1997 ) simulator, for real univariate stationary processes.     

Stationary Phases for Complexation Gas Chromatography and Microextraction Methods

The main goal of this review is to provide an overview of the trends in the technological development of complexation gas chromatography. This kind of chromatography, despite the passage of years, continues to offer new opportunities. The authors would like to show how complexation gas chromatography evolved over the years, due to the variety of stationary phases with complexation properties, their ability to separate, very specifically, the structures of the molecules and chemical compounds, improving the quality of the obtained results, and continuously lowering the detection limits of the analysed compounds in very complex matrices, including environmental and medical samples. The work is dedicated to the memory of Professor E. Gil-Av, whose scientific achievements were the inspiration for the improvement and widening of the research on the use of complexing metal ions and coordination metal compounds for selective separation in gas chromatography.     

Walsh Fourier Transform of Locally Stationary Time Series

A new time-frequency model and a method to classify time series data are proposed in this article. By viewing the observed signals as realizations of locally dyadic stationary (LDS) processes, a LDS model can be used to provide a time-frequency decomposition of the signals, under which the evolutionary Walsh spectrum and related statistics can be defined and estimated. The classification procedure is as follows. First choose a training data set that comprises two groups of time series with a known group. Then compute the time frequency feature (the energy) using the training data set, and use a best tree method to maximize the discrepancy of this feature between the two groups. Finally, choose the testing data set with the unknown group as validation data, and use a discriminant statistic to classify the validation data to one of the groups. The classification method is illustrated via an electroencephalographic dataset and the Ericsson B transaction time dataset. The proposed classification method performs better for integer-valued time series in terms of classification error rates in both simulations and real-life applications.     

气相色谱固定液硼酸酯的合成及应用研究

用脂肪酸和二乙醇胺反应合成烷醇酰胺。烷醇酰胺与硼酸反应生成硼酸酯类表面活性剂脂肪酸二乙醇胺硼酸酯。脂肪酸二乙醇胺硼酸酯的结构用红外光谱进行了表征。该表面活性剂作为气相色谱固定液,制成色谱柱。测定了此固定液的最高使用温度280℃、相对极性61．2和对苯、甲苯和二甲苯以及乙酸乙酯和乙酸丁酯组成的混合物有明显的分离效果。     

Finding the Right Heavy Chains for Immunostimulatory Antibodies

For twelve years, the oncology field has been revolutionized by antibodies targeting immune checkpoints. They must be considered as a heterogenous family of immunostimulatory antibodies displaying very different mechanisms of action, not only depending on the target or on the cells expressing it, but also on the IgG subclass or IgG variant that has been chosen. To dissect this complex landscape, the clinical experience has been confronted with a precise analysis of the heavy chain isotypes, referred as new Ge nomenclature. For antibodies targeting inhibitory receptors, anti-CTLA-4 antibodies (whose main effect is to kill regulatory T cells) will be distinguished from anti-PD-1 antibodies and other true antagonistic antibodies. Antibodies targeting ligands of inhibitory receptors (PD-L1, CD47) represent another different category, due to the antigen expression on tumors and a possible beneficial killing effect. The case of agonistic antibodies targeting lymphocyte activatory receptors, such as CD40 or 4-1BB, is still another “under construction” category because these products are less advanced in their clinical development. Altogether, it appears that choosing the right heavy chain is crucial to obtain the desired pharmacological effect in patients.     

拟除虫菊酯类农药在高压液相色谱的手性固定相上的分离研究进展

本文综述了近20年来拟除虫菊酯类农药及其酸、醇部分和一些衍生物在高压液相色谱手性固定相上的分离研究进展,引用文献46篇。     

侧链含有环糊精的聚合物的研究进展

聚合物侧链可通过化学键及分子间力与环糊精相互作用。当聚合物侧链通过化学键与环糊精作用时,环糊精空腔一般为空,可与小分子包合,对不同立体结构的分子具有选择性,在分析化学方面具有潜在的应用。当聚合物侧链与环糊精包合时,环糊精空腔与一定结构的侧链包合,形成侧链型多聚(准)轮烷。侧链型环糊精基多聚(准)轮烷的结构、性能独特,在许多领域具有潜在的应用。本文介绍了国内外文献中关于侧链含有环糊精的聚合物的研究进展,包括合成方法以及在各领域的应用等。     

Parameter Estimation for Periodically Stationary Time Series

Abstract. The innovations algorithm can be used to obtain parameter estimates for periodically stationary time series models. In this paper, we compute the asymptotic distribution for these estimates in the case, where the innovations have a finite fourth moment. These asymptotic results are useful to determine which model parameters are significant. In the process, we also develop asymptotics for the Yule–Walker estimates.     

Stochastic molecular descriptors for polymers. 2. Spherical truncation of electrostatic interactions on entropy based polymers 3D-QSAR

The spherical truncation of electrostatic field with different functions break down long-range interactions at a given cutoff distance (r_off) resulting in short-range ones. Consequently, a Markov Chain model may approach to the entropies of spatial distribution of charges within the polymer backbone. These entropies can be used to predict polymers properties [González-Díaz H, Molina RR, Uriarte E. Polymer 2004; 45: 3845 [53]]. Herein, we explore the effect of abrupt, shifting, force shifting, and switching truncation functions on QSAR models classifying 26 proteins with different function: lysozymes, dihydrofolate reductases, and alcohol dehydrogenases. Almost all methods have shown overall accuracies higher than 85% instead of 80.8% for models based on physicochemical parameters. The present result points to a acceptable robustness of the Markov model for different truncation schemes and r_off values. The results of best accuracy 92.3% with abrupt truncation coincides with our recent communication [Bioorg Med Chem Lett 2004; 14: 4691-4695]. Nonetheless, the simpler model with three variables and high accuracy (88%) was derived with a shifting function and r_off=10 Å.     

A Nonparametric Model for Stationary Time Series

Stationary processes are a natural choice as statistical models for time series data, owing to their good estimating properties. In practice, however, alternative models are often proposed that sacrifice stationarity in favour of the greater modelling flexibility required by many real‐life applications. We present a family of time‐homogeneous Markov processes with nonparametric stationary densities, which retain the desirable statistical properties for inference, while achieving substantial modelling flexibility, matching those achievable with certain non‐stationary models. A latent extension of the model enables exact inference through a trans‐dimensional Markov chain Monte Carlo method. Numerical illustrations are presented.