A simple procedure for computing improved prediction intervals for autoregressive models

Abstract.  This article concerns the construction of prediction intervals for time series models. The estimative or plug-in solution is usually not entirely adequate, since the (conditional) coverage probability may differ substantially from the nominal value. Prediction intervals with improved (conditional) coverage probability can be defined by adjusting the estimative ones, using rather complicated asymptotic procedures or suitable simulation techniques. This article extends to Markov process models a recent result by Vidoni, which defines a relatively simple predictive distribution function, giving improved prediction limits as quantiles. This new solution is fruitfully considered in the challenging context of prediction for time-series models, with particular regard to AR and ARCH processes.     

RNA‐Cleaving Deoxyribozyme Sensor for Nucleic Acid Analysis: The Limit of Detection

Along with biocompatibility, chemical stability, and simplicity of structural prediction and modification, deoxyribozyme‐based molecular sensors have the potential of an improved detection limit due to their ability to catalytically amplify signal. This study contributes to the understanding of the factors responsible for the limit of detection (LOD) of RNA‐cleaving deoxyribozyme sensors. A new sensor that detects specific DNA/RNA sequences was designed from deoxyribozyme OA‐II [Chiuman, W.; Li, Y. (2006) J. Mol. Biol. 357, 748–754]. The sensor architecture allows for a unique combination of high selectivity, low LOD and the convenience of fluorescent signal monitoring in homogeneous solution. The LOD of the sensor was found to be ～1.6×10^?10 M after 3 h of incubation. An equation that allows estimation of the lowest theoretical LOD using characteristics of parent deoxyribozymes and their fluorogenic substrates was derived and experimentally verified. According to the equation, “catalytically perfect” enzymes can serve as scaffolds for the design of sensors with the LOD not lower than ～2×10^?15 M after 3 h of incubation. A new value termed the detection efficiency (DE) is suggested as a time‐independent characteristic of a sensor's sensitivity. The expressions for the theoretical LOD and DE can be used to evaluate nucleic acid and protein enzymes for their application as biosensing platforms.     

Processability and characterization of poly(vinyl chloride)‐b‐poly(n‐butyl acrylate)‐b‐poly(vinyl chloride) prepared by living radical polymerization of vinyl chloride. Comparison with a flexible commercial resin formulation prepared with PVC and dioctyl phthalate

This work reports the synthesis and processing of a new flexible material based on PVC produced by living radical polymerization. The synthesis was carried out in a two‐step process. In the first step the macroinitiator α, ω‐di(iodo)poly(butyl acrylate) [α, ω‐di(iodo)PBA] was synthesized in water by single electron transfer/degenerative chain transfer mediated living radical polymerization (SET‐DTLRP) catalyzed by Na₂S₂O₄. In the second step this macroinitiator was reinitiated by SET‐DTLRP of vinyl chloride (VC), thereby leading to the formation of the block copolymer poly(vinyl chloride)‐b‐poly(butyl acrylate)‐b‐poly(vinyl chloride) [PVC‐b‐PBA‐b‐PVC]. This new material was processed on a laboratory scale. The DMTA traces showed only a single glass transition temperature, thus indicating that no phase segregation was present. The copolymers were studied with regard to their processing, miscibility, and mechanical properties. The first comparison with commercial formulations made with PVC and dioctyl phthalate (DOP) is presented. J. VINYL ADDIT. TECHNOL., 12:156–165, 2006. © 2006 Society of Plastics Engineers     

Prediction Interval for Autoregressive Time Series via Oracally Efficient Estimation of Multi‐Step‐Ahead Innovation Distribution Function

A kernel distribution estimator (KDE) is proposed for multi‐step‐ahead prediction error distribution of autoregressive time series, based on prediction residuals. Under general assumptions, the KDE is proved to be oracally efficient as the infeasible KDE and the empirical cumulative distribution function (cdf) based on unobserved prediction errors. Quantile estimator is obtained from the oracally efficient KDE, and prediction interval for multi‐step‐ahead future observation is constructed using the estimated quantiles and shown to achieve asymptotically the nominal confidence levels. Simulation examples corroborate the asymptotic theory.     

Oligonucleotide synthesis onto poly(N‐acryloylmorpholine‐co‐N‐acryloxysuccinimide): Assessment of the resulting conjugates in a DNA sandwich hybridization test

A water‐soluble statistical poly(N‐acryloylmorpholine‐co‐N‐acryloxysuccinimide) [poly(NAM/NAS)] copolymer was studied for polymer–oligonucleotide (ODN) conjugate elaboration and for further use in diagnostic applications. Three different copolymers were first prepared by free‐radical solution polymerization with different N‐acryloylmorpholine (NAM) and N‐acryloxysuccinimide (NAS) molar ratios (80/20, 70/30, and 60/40). Their number‐average molecular weights ranged from 98,000 to 120,000 g/mol, as determined by aqueous size exclusion chromatography with an online light‐scattering detector. Then, polymer–ODN conjugates were obtained via a strategy consisting of the direct synthesis of ODNs onto polymer chains previously grafted onto a controlled pore glass support. Before the grafting of the polymer onto the solid support, a preliminary step was performed to bind a nucleotide starter along the polymer chain (via the reactive NAS units) to initiate automated DNA synthesis. To multiply the number of ODNs growing from starters, a branched phosphoramidite synthon [bearing two O‐dimethoxytrityl groups] was introduced at the first step of ODN elongation as a short sequence of four branched synthons alternated with three thymidine residues. Conjugates were assessed in a DNA sandwich hybridization test developed for hepatitis B virus detection. Sensitivity limits were evaluated and compared to those obtained with an other polymer, poly(maleic anhydride‐alt‐methyl vinyl ether) [poly(MA/MVE)]. A sensitivity limit of 2.6 × 10⁷ DNA copies/mL was reached with the poly(MA/MVE)–ODN conjugate at the capture phase and with the poly(NAM/NAS)–branched ODN conjugate at the detection phase of the test. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 92: 3784–3795, 2004     

Dynamic spatial Bayesian models for radioactivity deposition

Dynamic spatial Bayesian (DSB) models are proposed for the analytical modelling of radioactivity deposition after a nuclear accident. The proposed models are extensions of the multi‐variate time‐series dynamic linear models of West and Harrison (1997) to Markov random field processes. They combine the outputs from a long‐range atmospheric dispersal model with measured data (and prior information) to provide improved deposition prediction in space and time. Two versions of a Gaussian DSB model were applied to the radioactivity deposition in Bavaria over a 15 days period during the Chernobyl nuclear accident. One version had fixed functional forms for its spatial variances and covariances while the other allowed those to adapt and ‘learn’ from data in the conjugate Bayesian paradigm. There were two main sources of information for radioactivity deposition in our application: radioactivity measurements at a sparse set of 13 monitoring stations, and the numerical deposition evaluation of the atmospheric dispersal K‐model for the points of a 64 × 64 regular grid. We have analysed the temporal predictions (one‐step‐ahead forecasting) of those DSB models to show that the dispersal K‐model tended in general to underestimate the deposition levels at all times while the DSB models corrected for that although with different degrees of adjustment.     

Improved prediction limits for a general class of Gaussian models

In this article we consider the problem of prediction for a general class of Gaussian models, which includes, among others, autoregressive moving average time‐series models, linear Gaussian state space models and Gaussian Markov random fields. Using an idea presented in Sjöstedt‐De Luna and Young (2003) , in the context of spatial statistics, we discuss a method for obtaining prediction limits for a future random variable of interest, taking into account the uncertainty introduced by estimating the unknown parameters. The proposed prediction limits can be viewed as a modification of the estimative prediction limit, with unconditional, and eventually conditional, coverage error of smaller asymptotic order. The modifying term has a quite simple form and it involves the bias and the mean square error of the plug‐in estimators for the conditional expectation and the conditional variance of the future observation. Applications of the results to Gaussian time‐series models are presented.     

Online prediction of subcutaneous glucose concentration for type 1 diabetes using empirical models and frequency‐band separation

Online glucose prediction which can be used to provide important information of future glucose status is a key step to facilitate proactive management before glucose reaches undesirable concentrations. Based on frequency‐band separation (FS) and empirical modeling approaches, this article considers several important aspects of on‐line glucose prediction for subjects with type 1 diabetes mellitus. Three issues are of particular interest: (1) Can a global (or universal) model be developed from glucose data for a single subject and then used to make suitably accurate on‐line glucose predictions for other subjects? (2) Does a new FS approach based on data filtering provide more accurate models than standard modeling methods? (3) Does a new latent variable modeling method result in more accurate models than standard modeling methods? These and related issues are investigated by developing autoregressive models and autoregressive models with exogenous inputs based on clinical data for two groups of subjects. The alternative modeling approaches are evaluated with respect to on‐line short‐term prediction accuracy for prediction horizons of 30 and 60 min, using independent test data. © 2013 American Institute of Chemical Engineers AIChE J 60: 574–584, 2014     

Mean shift testing in correlated data

Several tests for detecting mean shifts at an unknown time in stationary time series have been proposed, including cumulative sum (CUSUM), Gaussian likelihood ratio (LR), maximum of F(F_max) and extreme value statistics. This article reviews these tests, connects them with theoretical results, and compares their finite sample performance via simulation. We propose an adjusted CUSUM statistic which is closely related to the LR test and which links all tests. We find that tests based on CUSUMing estimated one‐step‐ahead prediction residuals from a fitted autoregressive moving average perform well in general and that the LR and F_max tests (which induce substantial computational complexities) offer only a slight increase in power over the adjusted CUSUM test. We also conclude that CUSUM procedures work slightly better when the changepoint time is located near the centre of the data, but the adjusted CUSUM methods are preferable when the changepoint lies closer to the beginning or end of the data record. Finally, an application is presented to demonstrate the importance of the choice of method.     

A review of the operating limits in slot die coating processes

Slot die coating is a pre‐metered process commonly used for producing thin and uniform films. It is an important film fabrication method for applications where precise coating is required. A major concern in slot die coating processes is how to determine the operating limits to set the appropriate range of operating parameters, including coating speed, flow rate, vacuum pressure, coating gap, liquid viscosity and surface tension, etc. Operating limits directly determine the effectiveness and efficiency of the process. In this article, the current state of academic research on operating limits in slot die coating processes is reviewed. Specifically, the theories, mechanisms, and empirical conclusions related to the limits on vacuum pressure, the low‐flow limit, the limit of wet thickness for zero‐vacuum‐pressure cases, the limit of dynamic wetting failure, and the limits of coating speed for a specific flow rate are reviewed. The article concludes with some recommendations for future work. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2508–2524, 2016     

Estimation of Parameters in the NLAR(p) Model

Abstract. In this article, we study a new Laplace autoregressive model of order p– NLAR(p). Conditional least squares, weighted conditional least squares and maximum quasi‐likelihood are used to estimate the model parameters. Comparisons among these estimates of the NLAR(2) model are given via simulation studies.     

Empirical likelihood inference for random coefficient INAR(p) process

In this article, we study the empirical likelihood (EL) method for the pth‐order random coefficient integer‐valued autoregressive process. In particular, the limiting distribution of the log EL ratio statistic is established and the confidence regions for the parameter of interest are derived. Also a simulation study is conducted for the evaluation of the developed approach.     

Random environment integer‐valued autoregressive process

An r states random environment integer‐valued autoregressive process of order 1, RrINAR(1), is introduced. Also, a random environment process is separately defined as a selection mechanism of differently parameterized geometric distributions, thus ensuring the non‐stationary nature of the RrNGINAR(1) model based on the negative binomial thinning. The distributional and correlation properties of this model are discussed, and the k‐step‐ahead conditional expectation and variance are derived. Yule–Walker estimators of model parameters are presented and their strong consistency is proved. The RrNGINAR(1) model motivation is justified on simulated samples and by its application to specific real‐life counting data.     

Equation‐oriented optimization of process flowsheets with dividing‐wall columns

We present a new modeling approach for dividing‐wall columns (DWCs) that is amenable to equation‐oriented flowsheet simulation and optimization. The material, equilibrium, summation, and heat (MESH) equations describing a DWC are highly coupled and nonlinear, making DWC‐based process flowsheets challenging to simulate. Design optimization poses further challenges, typically requiring integer variables to select the number of column stages. To address these difficulties, we represent DWCs as networks of pseudo‐transient (differential‐algebraic) subunit models. We show that these networks have the same steady‐state solution as the original (algebraic) MESH equations, but present significant numerical benefits. We then embed these models in a previously developed pseudo‐transient flowsheet modeling and optimization framework. We further reformulate the models to require only continuous decision variables when selecting the optimal number of stages during design optimization. To illustrate these concepts, we discuss the DWC‐based intensification of the dimethyl ether process. © 2015 American Institute of Chemical Engineers AIChE J, 62: 704–716, 2016     

Improving the antifouling property of poly(vinyl chloride) membranes by poly(vinyl chloride)‐g‐poly(methacrylic acid) as the additive

To improve the antifouling property of poly(vinyl chloride) (PVC) membranes, a series of poly(methacrylic acid) grafted PVC copolymers (PVC‐g‐PMAA) with different grafting degree were synthesized via one‐step atom transfer radical polymerization process utilizing the labile chlorines on PVC backbones followed by one‐step hydrolysis reaction. PVC/PVC‐g‐PMAA blend membranes with different grafting degree and copolymer content were prepared by nonsolvent induced phase separation method. The surface chemical composition, surface charge, membrane structures, wettability, permeability, separation performances and the fouling resistance of blend membranes were carefully investigated. The results indicated that the PMAA chains were segregated towards the surface and the membranes were endowed with negative charge. The hydrophilicity and permeability of the blend membranes were obviously improved. Furthermore, the antifouling ability especially at neutral or alkaline environments was also significantly increased. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015 , 132, 42745.     

Synthesis of pH‐responsive crosslinked poly[styrene‐co‐(maleic sodium anhydride)] and cellulose composite hydrogel nanofibers by electrospinning

BACKGROUND: Stimuli‐sensitive materials show enormous potential in the development of drug delivery systems. But the low response rate of most stimuli‐sensitive materials limits their wider application. We propose that electrospinning, a technique for the preparation of ultrafine fibrous materials with ultrafine diameters, may be used to prepare materials with a fast response to stimuli. RESULTS: Poly[styrene‐co‐(maleic sodium anhydride)] and cellulose (SMA‐Na/cellulose) hydrogel nanofibers were prepared through hydrolysis of precursor electrospun poly[styrene‐co‐(maleic anhydride)]/cellulose acetate (SMA/CA) nanofibers. In the presence of diethylene glycol, the SMA/CA composite nanofibers were crosslinked by esterification at 145 °C, and then hydrolyzed to yield crosslinked SMA‐Na/cellulose hydrogel nanofibers. These nanofibers showed better mechanical strengths and were pH responsive. Their water swelling ratio showed a characteristic two‐step increase at pH = 5.0 and 8.2, with the water swelling ratio reaching a maximum of 27.6 g g^?1 at pH = 9.1. CONCLUSION: The crosslinked SMA‐Na hydrogel nanofibers supported on cellulose showed improved dimensional stability upon immersion in aqueous solutions. They were pH responsive. This new type of hydrogel nanofiber is a potential material for biomedical applications. Copyright © 2009 Society of Chemical Industry     

Thermal properties,adhesive strength,and optical transparency of cyclolinear poly(aryloxycyclotriphosphazenes)

Four cyclolinear poly(aryloxycyclotriphosphazenes) derived from poly[4,4′‐(isopropoylidene)diphenoxytetrachlorocyclotriphosphazene] and poly[4,4′‐(hexafluoroisopropylidene)diphenoxytetrachlorocyclotriphosphazene] were synthesized from the reaction of hexachlorocyclotriphosphazene (HCP) with 4,4′‐(isopropylidene)diphenol (bisphenol A) or 4,4′‐(hexafluoroisopropylidene)diphenol (bisphenol AF) in molar ratio 1 : 1 via a one‐step condensation polymerization. Subsequent reaction of the resulted chlorine‐bound polymers with adequate amount of the sodium salts of 4‐methoxycarbonylphenoxide or 4‐propoxycarbonylphenoxide yielded the corresponding chlorine‐free polymers, [poly(tetra‐4‐methoxycarbonylphenoxy)‐4,4′‐(isopropoylidene)diphenoxy cyclotriphosphazene] (MBACP), [poly(tetra‐4‐propoxycarbonylphenoxy)‐4,4′‐(isopropoylidene)diphenoxycyclotriphosphazene] (PBACP), [poly(tetra‐4‐methoxycarbonylphenoxy)‐4,4′‐(hexafluoroisopropylidene)diphenoxycyclotriphosphazene] (MBAFCP), [poly(tetra‐4‐propoxycarbonylphenoxy)‐4,4′‐(hexafluoroisopropylidene)diphenoxycyclotriphosphazene] (PBAFCP), respectively. The chemical structures were characterized by Fourier transformer infrared, ¹H, and ¹³C‐NMR. Thermal properties of polymers were investigated using DSC and TGA analysis. The obtained polymers were thermoplastic, having moderate T_g values in the range of 26–78°C and good thermal stability up to 350°C in N₂ and O₂ gases. The thermal decomposition of the isopropylidene‐containing polymers is a one‐step process, while that of hexafluoroisopropylidene‐containing polymers is a two‐step process. However, presence of the latter group in the polymers backbone showed negligible effects on the thermo‐oxidative stability. The adhesive strength was measured by lap‐shear strength test on glass–glass bonded joint and found to be in the range of 1.78–2.62 MPa, this property may be attributed to the physical interactions between glass–glass interfaces and the polar‐pendant units present at the polymers backbone. The products showed high optical transparency when they applied between two glass surfaces, the adhesive layers were colorless, with the UV cut‐off wavelength of 300–302 nm, and the maximum transparency of about 90% was observed within the wavelengths range of 400–700 nm. Because of their properties, the cyclolinear poly(aryloxycyclotriphosphazenes) synthesized in this study are recommended as potential candidates for high thermally stable, transparent adhesives required in industrial applications. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011.     

Structure‐Based Design of Microsomal Prostaglandin E2 Synthase‐1 (mPGES‐1) Inhibitors using a Virtual Fragment Growing Optimization Scheme

A small library of 2,3‐dihydroxybenzamide‐ and N‐(2,3‐dihydroxyphenyl)‐4‐sulfonamide‐based microsomal prostaglandin E₂ synthase‐1 (mPGES‐1) inhibitors was identified following a step‐by‐step optimization of small aromatic fragments selected to interact in focused regions in the active site of mPGES‐1. During the virtual optimization process, the 2,3‐dihydroxybenzamide moiety was first selected as a backbone of the proposed new chemical entities; the identified compounds were then synthesized and biologically evaluated, identifying derivatives with very promising inhibitory activities in the micromolar range. Subsequent structure‐guided replacement of the 2,3‐dihydroxybenzamide by the N‐(2,3‐dihydroxyphenyl)sulfonamide moiety led to the identification of N‐(2,3‐dihydroxyphenyl)‐4‐biphenylsulfonamide ( 6 ), the most potent small molecule of the series (IC₅₀=0.53±0.04 μm ). The simple synthetic procedure and the possibility of enhancing the potency of this class of inhibitors through additional structural modifications pave the way for further development of new molecules with mPGES‐1‐inhibitory activity, with potential application as anti‐inflammatory and anticancer agents.     

Equation‐oriented flowsheet simulation and optimization using pseudo‐transient models

Tight integration through material and energy recycling is essential to the energy efficiency and economic viability of process and energy systems. Equation‐oriented (EO) steady‐state process simulation and optimization are key enablers in the optimal design of integrated processes. A new process modeling and simulation concept based on pseudo‐transient continuation is introduced. An algorithm for reformulating the steady‐state models of process unit operations as differential‐algebraic equation systems that are statically equivalent with the original model is presented. These pseudo‐transient models improve the convergence of EO process flowsheet simulations by expanding the convergence basin. This concept is used to build a library of pseudo‐transient models for common process unit operations, and this modeling concept seamlessly integrates with a previously developed time‐relaxation optimization algorithm. Two design case studies are presented to validate the proposed framework. © 2014 American Institute of Chemical Engineers AIChE J 60: 4104–4123, 2014     

Synthesis and characterization of poly(L‐lactide‐co‐ϵ‐caprolactone)‐b‐poly(L‐lactide) biodegradable diblock copolyesters: Effect of the block lengths on their thermal properties

Poly(L ‐lactide‐co‐ε‐caprolactone)‐b‐poly(L ‐lactide) [P(LL‐co‐CL)‐b‐PLL] diblock copolyesters were synthesized in a two‐step process with 1‐dodecanol (DDC) and stannous octoate as the initiating system. In the first‐step reaction, a 50:50 mol % amorphous poly(L ‐lactide‐co‐ε‐caprolactone) [P(LL‐co‐CL)] copolyester was synthesized via the bulk copolymerization of L ‐lactide and ε‐caprolactone, which was followed by the polymerization of the PLL crystalline block at the end chain in the second‐step reaction. The yielded copolyesters were characterized with dilute‐solution viscometry, gel permeation chromatography, ¹H‐ and ¹³C‐NMR, and differential scanning calorimetry methods. The molecular weights of the P(LL‐co‐CL) copolyesters from the first‐step reaction were controlled by the DDC concentrations, whereas in the second‐step reaction, the molecular weights of the P(LL‐co‐CL)‐b‐PLL diblock copolyesters depended on the starting P(LL‐co‐CL) copolyester molecular weights and L ‐lactide/prepolymer molar ratios. The starting P(LL‐co‐CL) copolyester molecular weights and PLL block lengths seemed to be the main factors affecting specific thermal properties, including the melting temperature (T_m), heat of melting (ΔH_m), crystallizing temperature (T_c), and heat of crystallizing (ΔH_c), of the final P(LL‐co‐CL)‐b‐PLL diblock copolyester products. T_m, ΔH_m, T_c, and ΔH_c increased when the PLL block lengths increased. However, these thermal properties of the diblock copolyesters also decreased when the P(LL‐co‐CL) block lengths increased. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci, 2007