Integrative interaction analysis using threshold gradient directed regularization

For many complex business and industry problems, high‐dimensional data collection and modeling have been conducted. It has been shown that interactions may have important implications beyond the main effects. The number of unknown parameters in an interaction analysis can be larger or much larger than the sample size. As such, results generated from analyzing a single data set are often unsatisfactory. Integrative analysis, which jointly analyzes the raw data from multiple independent studies, has been conducted in a series of recent studies and shown to outperform single–data set analysis, meta‐analysis, and other multi–data set analyses. In this study, our goal is to conduct integrative analysis in interaction analysis. For regularized estimation and selection of important interactions (and main effects), we apply a threshold gradient directed regularization approach. Advancing from the existing studies, the threshold gradient directed regularization approach is modified to respect the “main effects, interactions” hierarchy. The proposed approach has an intuitive formulation and is computationally simple and broadly applicable. Simulations and the analyses of financial early warning system data and news‐APP (application) recommendation behavior data demonstrate its satisfactory practical performance.     

The choice of screening design

A screening design is an experimental plan used for identifying the expectedly few active factors from potentially many. In this paper, we compare the performances of 3 experimental plans, a Plackett‐Burman design, a minimum run resolution IV design, and a definitive screening design, all with 12 and 13 runs, when they are used for screening and 3 out of 6 factors are active. The functional relationship between the response and the factors was allowed to be of 2 types, a second‐order model and a model with all main effects and interactions included. D‐efficiencies for the designs ability to estimate parameters in such models were computed, but it turned out that these are not very informative for comparing the screening performances of the 2‐level designs to the definitive screening design. The overall screening performance of the 2‐level designs was quite good, but there exist situations where the definitive screening design, allowing both screening and estimation of second‐order models in the same operation, has a reasonable high probability of being successful.     

2(n1+n2)-(k1+k2)42混合水平裂区设计包含纯净效应的条件

混水平部分因析裂区设计在各类试验中有广泛应用. 在三因子及更高阶交互作用可以忽略这一很弱的假设下, 试验者可以得到纯净主效应或者纯净两因子交互作用成分的无偏估计. 本文给出了含有两个四水平因子和若干二水平因子的混水平裂区设计包含各类纯净主效应或者纯净两因子交互作用成分的条件以及构造相应设计的方法.     

A multi-level Taguchi-factorial two-stage stochastic programming approach for characterization of parameter uncertainties and their interactions: An application to water resources management

This paper presents a multi-level Taguchi-factorial two-stage stochastic programming (MTTSP) approach for supporting water resources management under parameter uncertainties and their interactions. MTTSP is capable of performing uncertainty analysis, policy analysis, factor screening, and interaction detection in a comprehensive and systematic way. A water resources management problem is used to demonstrate the applicability of the proposed approach. The results indicate that interval solutions can be generated for the objective function and decision variables, and a variety of decision alternatives can be obtained under different policy scenarios. The experimental data obtained from the Taguchi’s orthogonal array design are helpful in identifying the significant factors affecting the total net benefit. Then the findings from the multi-level factorial experiment reveal the latent interactions among those important factors and their curvature effects on the model response. Such a sequential strategy of experimental designs is useful in analyzing the interactions for a large number of factors in a computationally efficient manner.     

Properties and Data Analysis of Order of Addition Designs with Conditions

Order of addition designs with conditions are widely used in experiments, but references on this subject are rather primitive. The paper gives the definition of conditional main effect of pair-wise ordering factor, studies the orthogonality of conditional main effects of pair-wise ordering factors, and proposes the model of order of addition designs with conditions. Finally, it gives the methods for data analysis through two examples.     

A modified adaptive Lasso for identifying interactions in the Cox model with the heredity constraint

In many biomedical studies, identifying effects of covariate interactions on survival is a major goal. Important examples are treatment–subgroup interactions in clinical trials, and gene–gene or gene–environment interactions in genomic studies. A common problem when implementing a variable selection algorithm in such settings is the requirement that the model must satisfy the strong heredity constraint, wherein an interaction may be included in the model only if the interaction’s component variables are included as main effects. We propose a modified Lasso method for the Cox regression model that adaptively selects important single covariates and pairwise interactions while enforcing the strong heredity constraint. The proposed method is based on a modified log partial likelihood including two adaptively weighted penalties, one for main effects and one for interactions. A two-dimensional tuning parameter for the penalties is determined by generalized cross-validation. Asymptotic properties are established, including consistency and rate of convergence, and it is shown that the proposed selection procedure has oracle properties, given proper choice of regularization parameters. Simulations illustrate that the proposed method performs reliably across a range of different scenarios.     

Comparing different fractions of a factorial design: a metal cutting case study

Full factorial designs of a significant size are very rarely performed in industry due to the number of trials involved and unavailable time and resources. The data in this paper were obtained from a six‐factor full factorial (2⁶) designed experiment that was conducted to determine the optimum operating conditions for a steel milling operation. Fractional‐factorial designs 2 (one‐eighth) and 2 (one‐fourth, using a fold‐over from the one‐eighth) are compared with the full 2⁶ design. Four of the 2 are de‐aliased by adding four more runs. In addition, two 12‐run Plackett–Burman experiments and their combination into a fold‐over 24‐run experiment are considered. Many of the one‐eighth fractional‐factorial designs reveal some significant effects, but the size of the estimates varies much due to aliasing. Adding four more runs improves the estimation considerably. The one‐quarter fraction designs yield satisfactory results, compared to the full factorial, if the ‘correct’ parameterization is assumed. The Plackett–Burman experiments, estimating all main effects, always perform worse than the equivalent regular designs (which have fewer runs). When considering a reduced model many of the different designs are more or less identical. The paper provides empirical evidence for managers and engineers that the choice of an experimental design is very important and highlights how designs of a minimal size may not always result in productive findings. Copyright © 2006 John Wiley & Sons, Ltd.     

A variable nonlinear splitting algorithm for reaction diffusion systems with self‐ and cross‐ diffusion

Self‐ and cross‐diffusion are important nonlinear spatial derivative terms that are included into biological models of predator–prey interactions. Self‐diffusion models overcrowding effects, while cross‐diffusion incorporates the response of one species in light of the concentration of another. In this paper, a novel nonlinear operator splitting method is presented that directly incorporates both self‐ and cross‐diffusion into a computational efficient design. The numerical analysis guarantees the accuracy and demonstrates appropriate criteria for stability. Numerical experiments display its efficiency and accuracy.     

A two-stage variable selection strategy for supersaturated designs with multiple responses

A supersaturated design (SSD), whose run size is not enough for estimating all the main effects, is commonly used in screening experiments. It offers a potential useful tool to investigate a large number of factors with only a few experimental runs. The associated analysis methods have been proposed by many authors to identify active effects in situations where only one response is considered. However, there are often situations where two or more responses are observed simultaneously in one screening experiment, and the analysis of SSDs with multiple responses is thus needed. In this paper, we propose a two-stage variable selection strategy, called the multivariate partial least squares-stepwise regression (MPLS-SR) method, which uses the multivariate partial least squares regression in conjunction with the stepwise regression procedure to select true active effects in SSDs with multiple responses. Simulation studies show that the MPLS-SR method performs pretty good and is easy to understand and implement.     

Analysis of means approach in advanced designs

Analysis of means (ANOM), similar to Shewhart control chart that exhibits individual mean effects on a graphical display, is an attractive alternative mean testing procedure for the analysis of variance (ANOVA). The procedure is primarily used to analyze experimental data from designs with only fixed effects. Recently introduced, the ANOM procedure based on the q‐distribution (ANOMQ procedure) generalizes the ANOM approach to random effects models. This article reveals that the application of ANOM and ANOMQ procedures in advanced designs such as hierarchically nested and split‐plot designs with fixed, random, and mixed effects enhances the data visualization aspect in graphical testing. Data from two real‐world experiments are used to illustrate the proposed procedure; furthermore, these experiments exhibit the ANOM procedures' visualization ability compared with ANOVA from the point of view of the practitioner.     

Efficiency measure,modelling and estimation in combined array designs

In off‐line quality control, the settings that minimize the variance of a quality characteristic are unknown and must be determined based on an estimated dual response model of mean and variance. The present paper proposes a direct measure of the efficiency of any given design‐estimation procedure for variance minimization. This not only facilitates the comparison of different design‐estimation procedures, but may also provide a guideline for choosing a better solution when the estimated dual response model suggests multiple solutions. Motivated by the analysis of an industrial experiment on spray painting, the present paper also applies a class of link functions to model process variances in off‐line quality control. For model fitting, a parametric distribution is employed in updating the variance estimates used in an iteratively weighted least squares procedure for mean estimation. In analysing combined array experiments, Engel and Huele (Technometrics, 1996; 39:365) used log‐link to model process variances and considered an iteratively weighted least squares leading to the pseudo‐likelihood estimates of variances as discussed in Carroll and Ruppert (Transformation and Weighting in Regression, Chapman & Hall: New York). Their method is a special case of the approach considered in this paper. It is seen for the spray paint data that the log‐link may not be satisfactory and the class of link functions considered here improves substantially the fit to process variances. This conclusion is reached with a suggested method of comparing ‘empirical variances’ with the ‘theoretical variances’ based on the assumed model. Copyright © 2003 John Wiley & Sons, Ltd.     

Weak and Strong Interactions between Internal Solitary Waves

The interaction of weakly nonlinear long internal gravity waves is studied. Weak interactions occur when the wave phase speeds are unequal; this case includes that of a head-on collision. It is shown that each wave satisfies a Korteweg-de Vries equation, and the main effect of the interaction is described by a phase shift. Strong interactions occur when the wave phase speeds are nearly equal although the waves belong to different modes. This case is described by a pair of coupled Korteweg-de Vries equations, for which some preliminary numerical results are presented.     

Optimisation of the vibrational response of ultrasonic cutting systems

^** Email: m.cartmell{at}mech.gla.ac.uk This paper provides an account of an investigation into possibledynamic interactions between two coupled non-linear sub-systems,each possessing opposing non-linear overhang characteristicsin the frequency domain in terms of positive and negative cubicstiffnesses. This system is a two-degree-of-freedom Duffingoscillator in which certain non-linear effects can be advantageouslyneutralised under specific conditions. This theoretical vehiclehas been used as a preliminary methodology for understandingthe interactive behaviour within typical industrial ultrasoniccutting components. Ultrasonic energy is generated within apiezoelectric exciter, which is inherently non-linear, and whichis coupled to a bar- or block-horn, and to one or more materialcutting blades, for example. The horn/blade configurations arealso non-linear, and within the whole system there are responsefeatures which are strongly reminiscent of positive and negativecubic stiffness effects. The two-degree-of-freedom model isanalysed and it is shown that a practically useful mitigatingeffect on the overall non-linear response of the system canbe created under certain conditions when one of the cubic stiffnessesis varied. It has also been shown experimentally that couplingof ultrasonic components with different non-linear characteristicscan strongly influence the performance of the system and thatthe general behaviour of the hypothetical theoretical modelis indeed borne out in practice. Further experiments have shownthat a multiple horn/blade configuration can, under certaincircumstances, display autoparametric responses based on theforced response of the desired longitudinal mode parametricallyexciting an undesired lateral mode. Typical autoparametric responsephenomena have been observed and are presented at the end ofthe paper.     

On designing experiments for a dynamic response modeled by regression splines

Dynamic response systems are often found in science, engineering, and medical applications, but the discussion on experimental design for such a system is relatively rare in literature. For an experimenter, designing such experiments requires making decisions on (1) when or where to take response measurements along the dynamic variable and (2) how to choose the combination of experimental factors and their levels. The first consideration is unique for such experiments, especially when the measurement cost is high. In this paper, we present a design approach through the mixed‐effect linear model, which is based on a hierarchical B‐spline function for the dynamic response. We develop several theorems that can assist in finding a statistically efficient sampling plan and propose an algorithm for searching the D‐optimal design of a dynamic response system.     

Bayesian analysis of definitive screening designs when the response is nonnormal

Definitive screening designs (DSDs) are a class of experimental designs that allow the estimation of linear, quadratic, and interaction effects with little experimental effort if there is effect sparsity. The number of experimental runs is twice the number of factors of interest plus one. Many industrial experiments involve nonnormal responses. Generalized linear models (GLMs) are a useful alternative for analyzing these kind of data. The analysis of GLMs is based on asymptotic theory, something very debatable, for example, in the case of the DSD with only 13 experimental runs. So far, analysis of DSDs considers a normal response. In this work, we show a five‐step strategy that makes use of tools coming from the Bayesian approach to analyze this kind of experiment when the response is nonnormal. We consider the case of binomial, gamma, and Poisson responses without having to resort to asymptotic approximations. We use posterior odds that effects are active and posterior probability intervals for the effects and use them to evaluate the significance of the effects. We also combine the results of the Bayesian procedure with the lasso estimation procedure to enhance the scope of the method. Copyright © 2016 John Wiley & Sons, Ltd.     

Soliton Interactions for the Three‐Coupled Discrete Nonlinear Schrödinger Equations in the Alpha Helical Proteins

Three‐coupled discrete nonlinear Schrödinger equations, which describe the dynamics of the three hydrogen bonding spines in the alpha helical proteins with the interspine coupling at the discrete level, are investigated. Binary Bell polynomials are applied to construct the bilinear forms and bilinear Bäcklund transformation of those equations. Propagation characteristics and interactions of the bound‐state solitons are discussed. Bound states of two and three bright solitons arise when all of them propagate in parallel. Elastic interaction between the bound‐state solitons and one bright soliton is given. Increase of the dipole‐dipole interaction energy can lead to the increase of the soliton velocity, that is, the one‐interaction period becomes shorter.     

Multiple Penalty Regression: Fitting and Extrapolating a Discrete Incomplete Multi-way Layout

The d iscrete multi-way layout is an abstract data type associated with regression, experimental designs, digital images or videos, spatial statistics, gene or protein chips, and more. The factors influencing response can be nominal or ordinal. The observed factor level combinations are finitely discrete and often incomplete or irregularly spaced. This paper develops low risk biased estimators of the means at the observed factor level combinations; and extrapolates the estimated means to larger discrete complete layouts. Candidate penalized least squares (PLS) estimators with multiple quadratic penalties express competing conjectures about each of the main effects and interactions in the analysis of variance decomposition of the means. The candidate PLS estimator with smallest estimated quadratic risk attains, asymptotically, the smallest risk over all candidate PLS estimators. In the theoretical analysis, the dimension of the regression space tends to infinity. No assumptions are made about the unknown means or about replication.     

The smoothing effect of a simultaneous directions parallel method as applied to Poisson problems

By using local Fourier analysis, a simultaneous directions parallel method, which is a particular instance of the parallel fractional step algorithm, is shown to possess smoothing effects when applied to Poisson problems. The specific smoothing factor is determined and the expected factor values are found to be consistent with those obtained. The simultaneous directions approach is an advantageous alternative to other existing smoothers in the multigrid environment. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

Simulation of particle ejecta effects from the surface under impulse action

This paper presents research results of ejecta due to plane shock wave arrival at a free smooth surface of a homogeneous pattern in the cluster dynamics (CD) simulation. Provided are 3D simulation results illustrating that ejecta effect is not only due to the physical reasons but also due to the side computation effects. One-dimensional model is developed to study the problems of cluster motion. This model was used to analyze the cluster behavior when a shock wave arrives at the boundary of the pattern. The oscillation character of the near-boundary clusters was analyzed as well as the impact of the interaction potential anharmonicity. It is shown that the most high-frequency mode of oscillations of the cluster lattice defined by potential anharmonicity (with neighbors moving in opposite phase) plays an important role in side ejecta effects. Hence, the criteria was developed to define the threshold loading velocity associated with ejecta in 3D problems.The method is suggested to eliminate the ejecta computation effects using the modification of cluster motion equations. The efficiency of this method is verified in a number of 3D simulations. It is shown that the suggested approach eliminates the side ejecta effects and keeps the fundamental physical regularities of loading and further motion of the pattern.     

Circadian synchrony in networks of protein rhythm driven neurons

The interaction between gene activation and cellular activity has recently emerged as a critical aspect of brain behavior, but the dynamics of networks incorporating these interactions are poorly understood. An interesting phenomena arises when the genetic activation oscillates endogenously and a network of such cells synchronize to a coherent rhythm, such as is the case with the suprachiasmatic nucleus. To explain this synchronization, we propose a model in which a mRNA/protein expression cycle drives neurons electrical activity, and synaptic activation shifts the phase of the protein rhythm. Using lattice networks, we demonstrate that these interactions are sufficient to generate coherent oscillation. © 2006 Wiley Periodicals, Inc. Complexity 12: 67–72, 2006