Nonorthogonal Designs Research Articles

Permutation Strategies for Inference in ANOVA‐Based Models for Nonorthogonal Designs Including Continuous Covariates

ABSTRACTAnalysis of variance and linear models is undoubtedly one of the most useful statistical contributions to experimental and observational science. With the ability to characterize a system through multivariate responses, these methods have emerged to be general tools regardless of response dimensionality. Contemporary methods for establishing statistical inference, such as ANOVA simultaneous component analysis (ASCA), are based on Monte Carlo sampling; however, a flat uniform resampling scheme may violate the structure of the uncertainty for unbalanced designs as well as for observational data. In this work, we provide permutation strategies for inferential testing for unbalanced designs including interaction models and establish nonuniform randomization based on the concept of propensity score matching. Lastly, we provide a general method for modelling continuous covariates based on kernel smoothers. All methods are characterized on their ability to provide unbiased Type I error results.

PLS for designed experiments

In many emerging new areas of research, for example in -omics sciences, complex data sets are generated implementing well-designed experiments with the aim to study the effects of factors on responses measured by high-through analytical platforms. The data sets are multivariate in their nature and require suitable data analysis techniques to be investigated. Partial Least Squares (PLS) regression has been developed and successfully applied to solve multivariate regression problems where data are correlated, redundant and noisy, but it is not able to take explicitly into account the experimental design used to generate the data. In this study, we adapt PLS to model data generated by crossed factorial designs. A new method based on constrained PLS2 regression and a type III sums of squares-like approach based on PLS2 are developed to treat orthogonal and non-orthogonal designs, respectively. Post-transformation and Procrustes analysis are applied to discover the 'latent’ structure useful to investigate the relationships between factors and responses. The mathematical properties of the data decomposition, the inference process to assess the reliability of the model and some basic tools for model interpretation are presented and discussed. One simulated and two experimental data sets, one generated implementing an orthogonal design and one obtained by a non-orthogonal design, are investigated to show how the methodology works in practice.

Exposing the confounding in experimental designs to understand and evaluate them, and formulating linear mixed models for analyzing the data from a designed experiment.

Comparative experiments involve the allocation of treatments to units, ideally by randomization. This necessarily confounds treatment information with unit information, which we distinguish from the other forms of information blending, in particular aliasing and marginality. We outline a factor-allocation paradigm for describing experimental designs with the aim of (i) exhibiting the confounding in a design, using analysis-of-variance-like tables, so as to understand and evaluate the design and (ii) formulating a linear mixed model based on the factor allocation that the design involves. The approach exhibits the dispersal of treatments information between units sources, allows designers a choice in the strategy that they adopt for including block-treatment interactions, clarifies differences between experiments, accommodates systematic allocation of factors, and provides a consolidated analysis of nonorthogonal designs. It provides insights into the process of designing experiments and issues that commonly arise with designs. The paradigm has pedagogical advantages and is implemented using the R package dae.

Language concatenates perceptual features into representations during comprehension

Although many studies have investigated the activation of perceptual representations during language comprehension, to our knowledge only one previous study has directly tested how perceptual features are combined into representations during comprehension. In their classic study, Potter and Faulconer [(1979). Understanding noun phrases. Journal of Verbal Learning and Verbal Behavior, 18, 509–521.] investigated the perceptual representation of adjective-noun combinations. However, their non-orthogonal design did not allow the differentiation between conjunctive vs. disjunctive representations. Using randomized orthogonal designs, we observe evidence for disjunctive perceptual representations when participants represent feature combinations simultaneously (in several experiments; N = 469), and we observe evidence for conjunctive perceptual representations when participants represent feature combinations sequentially (In several experiments; N = 628). Our findings show that the generation of conjunctive representations during comprehension depends on the concatenation of linguistic cues, and thus suggest the construction of elaborate perceptual representations may critically depend on language.

On the Relationship between ANOVA Main Effects and Average Treatment Effects

We adopt a causal inference perspective to shed light into which ANOVA type of sums of squares (SS) should be used for testing main effects and whether main effects should be considered at all in the presence of interactions. We consider balanced, proportional and nonorthogonal designs, and models with and without interactions. When the design is balanced, we show that the average treatment effect is estimated by the main effects obtained by type I, II, and III sums of squares. In proportional designs, we show that the average treatment effect is estimated by the the type I and type II main effects, whereas type III SS yield biased estimates of the average treatment effect if there are interactions. When the design is nonorthogonal, ANOVA type I is always highly biased and ANOVA type II and III main effects are biased if there are interactions. We include a simulation study to illustrate the magnitude of the bias in estimating the average treatment effect across a variety of conditions, and provide recommendations for applied researchers.

Research on disruptive design pre-identification in the preliminary design phase of aero engine flow pass multidisciplinary optimization

In aero engine design, determining whether the preliminary design will have disruptive effects on the detailed design is the key to multidisciplinary design optimization in the preliminary design stage. In order to adapt to the non-orthogonal parameter value range caused by the self-constrained parametric modeling method, a non-orthogonal space mapping method that maps the optimal Latin hypercube sampling points of the traditional orthogonal design space to the non-orthogonal design space is proposed. Based on the logical regression method in machine learning field, a kind of feasible domain boundary identification method is employed to identify whether the sample spatial response meets the relevant criteria. The method proposed in this paper is used to identify and analyze the key technologies of the high-pressure turbine mortise joint structure. It is found that the preliminary design of the aero engine may lead to the failure to obtain a mortise joint structure meeting the design requirements in the detailed design stage. The mortise joint structure needs to be pre-optimized in the preliminary design stage.

Optimizing compressive load capacity for differing tensegrity geometries

Tensegrity structures present new possibilities to the field of structural engineering, owing to their ability to efficiently distribute compressive loads associated with their non-orthogonal design. Previous research has shown that when pretensioned, tensegrities exhibit higher resistance to compressive loading. However, over-tensioning can have adverse effects, reducing the tensegrities overall resistance to compressive loading. The geometry of a tensegrity affects how the structure reacts to loading, and the prestress and loading can concurrently affect geometry. This paper uses genetic algorithms to optimize the pretension loads in the cables of a tensegrity to deliver the highest overall vertical load capacity. The results are applied to determine the ultimate load-carrying capacity of tensegrities under a compressive load and determine the optimal aspect ratio at which this is achieved. By optimizing the pretension, the tensegrity can withstand compressive loads up to six times those that have been previously reported in literature.

Millimeter Wave Communications with OMA and NOMA Schemes for Future Communication Systems

Millimeter-wave (mm Wave) communications had been considered widely in recent past due to its largely available bandwidth. This paper describes a detailed survey of mm Wave communications with orthogonal multiple access (OMA), non-orthogonal multiple access (NOMA) schemes, physical design and security for future communication networks. mm Wave provides super-speed connectivity, more reliability, and higher data rate and spectral efficiency. However, communications occurring at mm Wave frequencies can easily get affected by interference and path loss. Various schemes such as small cells, heterogeneous network and hybrid beamforming are used to overcome interferences and highlight the prominence of mm Wave in future communications systems.

Coordinate Rotation–Amplification in the Uncertainty and Bias in Non-orthogonal Sonic Anemometer Vertical Wind Speeds

Recent research indicates that non-orthogonal sonic anemometers underestimate vertical wind velocity and consequently eddy-covariance fluxes of mass and energy. Whether this is a general problem among all non-orthogonal sonic anemometers, including those calibrated for flow-shadowing effects, is unknown. To investigate this, we test two sonic anemometer designs, orthogonal (3Vx-probe, Applied Technologies, Inc.) and non-orthogonal (R3-50, Gill Instruments, Ltd.), in a series of field manipulation experiments featuring replicate instruments mounted in various orientations, and use a Bayesian analysis to determine the most likely posterior correction to produce equivalent measurements. The 3Vx-probe experiment was conducted on a 24-m scaffold at the Glacier Lakes Ecosystem Experiments Site (GLEES), Wyoming, USA AmeriFlux site while R3-50 anemometer experiments were conducted at the GLEES field site and on a 2.9-m scaffold at the Pawnee National Grassland, Colorado, USA. Without applying a shadowing correction to the 3Vx-probe, the posterior correction significantly increases the standard deviation of the horizontal velocity component by 5–15% (95% Bayesian credible interval) but without a significant change in the horizontal temperature flux; with the shadowing correction applied neither of these have significant changes. Similarly, for the R3-50 GLEES experiment, the standard deviation of the vertical velocity and vertical temperature flux significantly increase by 13–18% and 6–10% (95% credible intervals); results from the Pawnee experiment are contradictory and inconclusive. The reason for the underestimated vertical velocity is undetermined, though a mathematical by-product of the non-orthogonal geometry is that small systematic measurement biases can become large uncertainties in the vertical velocity. This could affect all non-orthogonal designs.

Compressed Sensing Based Non-Orthogonal Pilot Designs for Multi-Antenna Grant-Free Access Systems

Grant-free access is an attractive approach to enable spectrum-efficient low-latency access for systems with massive number of users. Pilot design plays a crucial role for grant-free access as it needs to provide a large number of access codes with fast collision detection capability and good channel estimation performance. Recently, pilot designs with fast collision detection capability have been proposed for compressed sensing (CS) based channel estimation. But the existing designs are not optimized for the estimation of highly sparse and block-sparse channels. In this paper, we present several propositions related to the performances of the CS based sparse and block-sparse channel estimation. Utilizing these propositions, we develop a novel non-orthogonal pilot design with fast collision detection capability for grant-free access in block-sparse channels. We also propose two methods to optimize the Peak-to-Average Power Ratio (PAPR) of the proposed non-orthogonal pilot codes. The simulation results illustrate that the proposed design provides similar or better channel estimation and collision detection performances with much better pilot resource efficiency when compared to the existing designs. Finally, we investigate the trade-offs among different design parameters and the channel estimation performances to facilitate better design choices.

Multiphase experiments with at least one later laboratory phase. II. Nonorthogonal designs

SummaryPrinciples and laws that apply to nonorthogonal multiphase experiments are developed and illustrated using examples that are nonorthogonal but structure‐balanced, not structure, but first‐order, balanced or unbalanced, thus exposing the differences between the different design types. The design of such experiments using standard designs, a catalogue of designs and computer searches is exemplified. Factor–allocation diagrams are employed to depict the allocations in the examples, and used in producing the anatomies of designs or, when possible, the related skeleton‐analysis‐of‐variance tables, to assess the properties of designs. The formulation of mixed models based on them is also described. Tools used for structure‐balanced experiments are also shown to be applicable to those experiments that are not.

Uplink Non-Orthogonal Multiple Access With Finite-Alphabet Inputs

This paper focuses on the non-orthogonal multiple access (NOMA) design for a classical two-user multiple access channel (MAC) with finite-alphabet inputs. In contrast to most of the existing NOMA designs using continuous Gaussian input distributions, we consider practical quadrature amplitude modulation (QAM) constellations at both transmitters, the sizes of which are assumed to be not necessarily identical. We propose maximizing the minimum Euclidean distance of the received sum constellation with a maximum likelihood (ML) detector by adjusting the scaling factors (i.e., instantaneous transmitted powers and phases) of both users. The formulated problem is a mixed continuous–discrete optimization problem, which is nontrivial to resolve in general. By carefully observing the structure of the objective function, we define a new type of Farey sequence, termed punched Farey sequence to tackle the formulated problem. Based on this, we manage to achieve a closed-form optimal solution to the original problem by first dividing the entire feasible region into a finite number of Farey intervals and then taking the maximum over all possible intervals. The resulting sum constellation is proved to be a regular QAM constellation of a larger size, and hence, a simple quantization receiver can be implemented as the ML detector for the demodulation. Moreover, the superiority of NOMA over time-division multiple access in terms of minimum Euclidean distance is rigorously proved. We subsequently address how to extend our design framework intended for the two-user MAC to systems with multiple users and multiple antennas. Finally, simulation results are provided to verify our theoretical analysis and demonstrate the merits of the proposed NOMA over existing orthogonal and non-orthogonal designs.

A Survey on NoSQL Stores

Recent demands for storing and querying big data have revealed various shortcomings of traditional relational database systems. This, in turn, has led to the emergence of a new kind of complementary nonrelational data store, named as NoSQL. This survey mainly aims at elucidating the design decisions of NoSQL stores with regard to the four nonorthogonal design principles of distributed database systems: data model, consistency model, data partitioning, and the CAP theorem. For each principle, its available strategies and corresponding features, strengths, and drawbacks are explained. Furthermore, various implementations of each strategy are exemplified and crystallized through a collection of representative academic and industrial NoSQL technologies. Finally, we disclose some existing challenges in developing effective NoSQL stores, which need attention of the research community, application designers, and architects.

Generating Improved Experimental Designs with Spatially and Genetically Correlated Observations Using Mixed Models

The aim of this study was to generate and evaluate the efficiency of improved field experiments while simultaneously accounting for spatial correlations and different levels of genetic relatedness using a mixed models framework for orthogonal and non-orthogonal designs. Optimality criteria and a search algorithm were implemented to generate randomized complete block (RCB), incomplete block (IB), augmented block (AB) and unequally replicated (UR) designs. Several conditions were evaluated including size of the experiment, levels of heritability, and optimality criteria. For RCB designs with half-sib or full-sib families, the optimization procedure yielded important improvements under the presence of mild to strong spatial correlation levels and relatively low heritability values. Also, for these designs, improvements in terms of overall design efficiency (ODE%) reached values of up to 8.7%, but these gains varied depending on the evaluated conditions. In general, for all evaluated designs, higher ODE% values were achieved from genetically unrelated individuals compared to experiments with half-sib and full-sib families. As expected, accuracy of prediction of genetic values improved as levels of heritability and spatial correlations increased. This study has demonstrated that important improvements in design efficiency and prediction accuracies can be achieved by optimizing how the levels of a treatment are assigned to the experimental units.

Bayesian Variable Selection and Estimation Based on Global-Local Shrinkage Priors

We consider in this paper simultaneous Bayesian variable selection and estimation for linear regression models with global-local shrinkage priors on the regression coefficients. We propose a variable selection procedure that selects a variable if the ratio of the posterior mean of its regression coefficient to the corresponding ordinary least square estimate is greater than a half. The regression coefficient is estimated by the posterior mean or zero depending on whether the corresponding variable is selected or not. Under the assumption of orthogonal designs, we prove that if the local parameters have polynomial-tailed priors, the proposed method enjoys the oracle property in the sense that it can achieve variable selection consistency and optimal estimation rate at the same time. However, if, instead, an exponential-tailed prior is used for the local parameters, the proposed method has variable selection consistency but not the optimal estimation rate. We show via simulation and real data examples that our proposed selection mechanism works for nonorthogonal designs as well.

Design and Performance Analysis of Multiuser CPM With Single User Detection

This paper focuses on the design and performance analysis of single user detectable multiuser systems based upon continuous phase modulation. This problem is formulated as a special application of mismatched receiver theory, where a closed-form expression for achievable Euclidean distance can be derived. This expression inspires the constructions of two classes of spectrally efficient multiuser designs: nonorthogonal and orthogonal designs. They are both confirmed to offer strong robustness against nonlinear hardware impairment in downlink and uplink transmissions, but differ in spectral efficiency, complexity and achievable minimum Euclidean distance. Moreover, the proposed designs are able to reduce the convergence threshold in serially concatenated multiuser systems. As a general approach to constructing orthogonal and near-orthogonal signals, the proposed techniques find potential applications in multiantenna systems, and full-duplex communications. Compared with existing continuous phase modulated multiuser designs, the proposed techniques offer improved spectral efficiency and significantly reduced detection complexity.

Roger Mead, 1938–2015

Roger Mead, 1938–2015

Application of permutation genetic algorithm for sequential model building–model validation design of experiments

The work presented in this paper is motivated by a complex multivariate engineering problem associated with engine mapping experiments, which require efficient design of experiments (DoE) strategies to minimise expensive testing. The paper describes the development and evaluation of a Permutation Genetic Algorithm (PermGA) to enable an exploration-based sequential DoE strategy for complex real-life engineering problems. A known PermGA was implemented to generate uniform OLH DoEs, and substantially extended to support generation of model building---model validation (MB---MV) sequences, by generating optimal infill sets of test points as OLH DoEs that preserve good space-filling and projection properties for the merged MB + MV test plan. The algorithm was further extended to address issues with non-orthogonal design spaces, which is a common problem in engineering applications. The effectiveness of the PermGA algorithm for the MB---MV OLH DoE sequence was evaluated through a theoretical benchmark problem based on the Six-Hump-Camel-Back function, as well as the Gasoline Direct Injection engine steady-state engine mapping problem that motivated this research. The case studies show that the algorithm is effective in delivering quasi-orthogonal space-filling DoEs with good properties even after several MB---MV iterations, while the improvement in model adequacy and accuracy can be monitored by the engineering analyst. The practical importance of this work, demonstrated through the engine case study, is that significant reduction in the effort and cost of testing can be achieved.

Sensors based on zirconia-modified perfluorinated sulfonic acid membranes sensitive to organic anions in multiionic aqueous solutions

The effect of modification of perfluorinated sulfonic acid membranes with zirconia on their conducting properties and electrode-active properties for potentiometric sensors whose analytical signal is the Donnan potential (DP) has been studied. It has been found that the incorporation of ZrO2 particles into the membrane matrix results in an increase in the ionic conductivity, as compared with unmodified membranes, and the proton diffusion coefficient changes nonmonotonically. Membranes with a gradient dopant distribution along the sample length provide for a partial decrease in the cation-exchange function of DP sensors because of a decrease in the concentration of fixed cation-exchange groups and due to the sorption of coions. This results in an increase in the sensor sensitivity to organic and sulfur-containing anions in multiionic aqueous solutions. Multivariate calibration methods with a nonorthogonal experimental design were used to evaluate the effects of the concentrations and nature of counterions and coions and pH in the test solutions on the characteristics of DP sensors.

On the construction of optimal designs

Two strategies for specifying additional data to be included with the data of a non-orthogonal design are presented. The additional data increase the magnitude of the information matrix X′X and the orthogonality of the design matrix. Sequentially, the new points are augmented to the original design, such that each new point optimally increases the smallest eigenvalue of X′X. The new runs are created in a predefined spherical region and a rectangular region. Optimum number of additional observations is presented in order to orthogonalize the design matrix X and optimize some functions of the information matrix X′X. Comparisons of the results acquired with the proposed methods versus the most commonly used procedures for data augmentation are carried out. In addition, the advantages of the use of our techniques over the studied methods to solve the augmenting data problems are discussed.