On Regression Methods for Virtual Metrology in Semiconductor Manufacturing

Virtual metrology (VM) aims to predict metrology values using sensor data from production equipment and physical metrology values of preceding samples. VM is a promising technology for the semiconductor manufacturing industry as it can reduce the frequency of in-line metrology operations and provide supportive information for other operations such as fault detection, predictive maintenance and run-to-run control. The prediction models for VM can be from a large variety of linear and nonlinear regression methods and the selection of a proper regression method for a specific VM problem is not straightforward, especially when the candidate predictor set is of high dimension, correlated and noisy. Using process data from a benchmark semiconductor manufacturing process, this paper evaluates the performance of four typical regression methods for VM: multiple linear regression (MLR), least absolute shrinkage and selection operator (LASSO), neural networks (NN) and Gaussian process regression (GPR). It is observed that GPR performs the best among the four methods and that, remarkably, the performance of linear regression approaches that of GPR as the subset of selected input variables is increased. The observed competitiveness of high-dimensional linear regression models, which does not hold true in general, is explained in the context of extreme learning machines and functional link neural networks.

Tiotropium and olodaterol fixed-dose combination versus mono-components in COPD (GOLD 2-4)

Efficacy and safety of tiotropium+olodaterol fixed-dose combination (FDC) compared with the mono-components was evaluated in patients with moderate to very severe chronic obstructive pulmonary disease (COPD) in two replicate, randomised, double-blind, parallel-group, multicentre, phase III trials. Patients received tiotropium+olodaterol FDC 2.5/5 μg or 5/5 μg, tiotropium 2.5 μg or 5 μg, or olodaterol 5 μg delivered once-daily via Respimat inhaler over 52 weeks. Primary end points were forced expiratory volume in 1 s (FEV1) area under the curve from 0 to 3 h (AUC0-3) response, trough FEV1 response and St George's Respiratory Questionnaire (SGRQ) total score at 24 weeks. In total, 5162 patients (2624 in Study 1237.5 and 2538 in Study 1237.6) received treatment. Both FDCs significantly improved FEV1 AUC0-3 and trough FEV1 response versus the mono-components in both studies. Statistically significant improvements in SGRQ total score versus the mono-components were only seen for tiotropium+olodaterol FDC 5/5 μg. Incidence of adverse events was comparable between the FDCs and the mono-components. These studies demonstrated significant improvements in lung function and health-related quality of life with once-daily tiotropium+olodaterol FDC versus mono-components over 1 year in patients with moderate to very severe COPD.

AfterImage:for baroque flute and fixed media

Commissioned by Sonic Arts Network and Huddersfield Contemporary Music Festival with funds from ACGB for Eleanor Dawson (flute)

Novel Panel Cointegration Tests Emending for Cross-Section Dependence with N Fixed

In this paper, we propose new cointegration tests for single equations and panels. Inboth cases, the asymptotic distributions of the tests, which are derived with N fixed andT → ∞, are shown to be standard normals. The effects of serial correlation and crosssectionaldependence are mopped out via long-run variances. An effective bias correctionis derived which is shown to work well in finite samples; particularly when N is smallerthan T. Our panel tests are robust to possible cointegration across units.

Design of a Dissolving Microneedle Platform for Transdermal Delivery of a Fixed-Dose Combination of Cardiovascular Drugs

Microneedles (MNs) are a minimally invasive drug delivery platform, designed to enhance transdermal drug delivery by breaching the stratum corneum. For the first time, this study describes the simultaneous delivery of a combination of three drugs using a dissolving polymeric MN system. In the present study, aspirin, lisinopril dihydrate, and atorvastatin calcium trihydrate were used as exemplar cardiovascular drugs and formulated into MN arrays using two biocompatible polymers, poly(vinylpyrrollidone) and poly(methylvinylether/maleic acid). Following fabrication, dissolution, mechanical testing, and determination of drug recovery from the MN arrays, in vitro drug delivery studies were undertaken, followed by HPLC analysis. All three drugs were successfully delivered in vitro across neonatal porcine skin, with similar permeation profiles achieved from both polymer formulations. An average of 126.3 ± 18.1 μg of atorvastatin calcium trihydrate was delivered, notably lower than the 687.9 ± 101.3 μg of lisinopril and 3924 ± 1011 μg of aspirin, because of the hydrophobic nature of the atorvastatin molecule and hence poor dissolution from the array. Polymer deposition into the skin may be an issue with repeat application of such a MN array, hence future work will consider more appropriate MN systems for continuous use, alongside tailoring delivery to less hydrophilic compounds.

Forward and backward least angle regression for nonlinear system identification

A forward and backward least angle regression (LAR) algorithm is proposed to construct the nonlinear autoregressive model with exogenous inputs (NARX) that is widely used to describe a large class of nonlinear dynamic systems. The main objective of this paper is to improve model sparsity and generalization performance of the original forward LAR algorithm. This is achieved by introducing a replacement scheme using an additional backward LAR stage. The backward stage replaces insignificant model terms selected by forward LAR with more significant ones, leading to an improved model in terms of the model compactness and performance. A numerical example to construct four types of NARX models, namely polynomials, radial basis function (RBF) networks, neuro fuzzy and wavelet networks, is presented to illustrate the effectiveness of the proposed technique in comparison with some popular methods.

Supervised Aggregative Feature Extraction for Big Data Time Series Regression

In many applications, and especially those where batch processes are involved, a target scalar output of interest is often dependent on one or more time series of data. With the exponential growth in data logging in modern industries such time series are increasingly available for statistical modeling in soft sensing applications. In order to exploit time series data for predictive modelling, it is necessary to summarise the information they contain as a set of features to use as model regressors. Typically this is done in an unsupervised fashion using simple techniques such as computing statistical moments, principal components or wavelet decompositions, often leading to significant information loss and hence suboptimal predictive models. In this paper, a functional learning paradigm is exploited in a supervised fashion to derive continuous, smooth estimates of time series data (yielding aggregated local information), while simultaneously estimating a continuous shape function yielding optimal predictions. The proposed Supervised Aggregative Feature Extraction (SAFE) methodology can be extended to support nonlinear predictive models by embedding the functional learning framework in a Reproducing Kernel Hilbert Spaces setting. SAFE has a number of attractive features including closed form solution and the ability to explicitly incorporate first and second order derivative information. Using simulation studies and a practical semiconductor manufacturing case study we highlight the strengths of the new methodology with respect to standard unsupervised feature extraction approaches.