Complete enumeration of two-Level orthogonal arrays of strength dd with d+2d+2 constraints

Enumerating nonisomorphic orthogonal arrays is an important, yet very difficult, problem. Although orthogonal arrays with a specified set of parameters have been enumerated in a number of cases, general results are extremely rare. In this paper, we provide a complete solution to enumerating nonisomorphic two-level orthogonal arrays of strength $d$ with $d+2$ constraints for any $d$ and any run size $n=\lambda2^d$. Our results not only give the number of nonisomorphic orthogonal arrays for given $d$ and $n$, but also provide a systematic way of explicitly constructing these arrays. Our approach to the problem is to make use of the recently developed theory of $J$-characteristics for fractional factorial designs. Besides the general theoretical results, the paper presents some results from applications of the theory to orthogonal arrays of strength two, three and four.Comment: Published at http://dx.doi.org/10.1214/009053606000001325 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

A general theory of minimum aberration and its applications

Minimum aberration is an increasingly popular criterion for comparing and assessing fractional factorial designs, and few would question its importance and usefulness nowadays. In the past decade or so, a great deal of work has been done on minimum aberration and its various extensions. This paper develops a general theory of minimum aberration based on a sound statistical principle. Our theory provides a unified framework for minimum aberration and further extends the existing work in the area. More importantly, the theory offers a systematic method that enables experimenters to derive their own aberration criteria. Our general theory also brings together two seemingly separate research areas: one on minimum aberration designs and the other on designs with requirement sets. To facilitate the design construction, we develop a complementary design theory for quite a general class of aberration criteria. As an immediate application, we present some construction results on a weak version of this class of criteria.Comment: Published at http://dx.doi.org/10.1214/009053604000001228 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

A new and flexible method for constructing designs for computer experiments

We develop a new method for constructing "good" designs for computer experiments. The method derives its power from its basic structure that builds large designs using small designs. We specialize the method for the construction of orthogonal Latin hypercubes and obtain many results along the way. In terms of run sizes, the existence problem of orthogonal Latin hypercubes is completely solved. We also present an explicit result showing how large orthogonal Latin hypercubes can be constructed using small orthogonal Latin hypercubes. Another appealing feature of our method is that it can easily be adapted to construct other designs; we examine how to make use of the method to construct nearly orthogonal and cascading Latin hypercubes.Comment: Published in at http://dx.doi.org/10.1214/09-AOS757 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Beyond Dropout: Feature Map Distortion to Regularize Deep Neural Networks

Deep neural networks often consist of a great number of trainable parameters for extracting powerful features from given datasets. On one hand, massive trainable parameters significantly enhance the performance of these deep networks. On the other hand, they bring the problem of over-fitting. To this end, dropout based methods disable some elements in the output feature maps during the training phase for reducing the co-adaptation of neurons. Although the generalization ability of the resulting models can be enhanced by these approaches, the conventional binary dropout is not the optimal solution. Therefore, we investigate the empirical Rademacher complexity related to intermediate layers of deep neural networks and propose a feature distortion method (Disout) for addressing the aforementioned problem. In the training period, randomly selected elements in the feature maps will be replaced with specific values by exploiting the generalization error bound. The superiority of the proposed feature map distortion for producing deep neural network with higher testing performance is analyzed and demonstrated on several benchmark image datasets

Selecting Latin hypercubes using correlation criteria

Abstract: Latin hypercube designs have recently found wide applications both in design of experiments and in numerical integration. An important property of this class of designs is that they achieve uniformity in each univariate margin. In this article we study the use of correlation criteria to select a Latin hypercube. We introduce the polynomial canonical correlation of two vectors and argue that a design which has a small polynomial canonical correlation for each pair of its columns is preferred. An algorithm for reducing polynomial canonical correlations of a Latin hypercube is developed. The implementation of the algorithm is discussed, and its performance investigated. Comparison with Owen's algorithm is also made

Polymer-Based Ion Gels as a Versatile Platform of Solid Electrolytes

University of Minnesota Ph.D. dissertation. July 2018. Major: Material Science and Engineering. Advisors: Carl Frisbie, Timothy Lodge. 1 computer file (PDF); xii, 163 pages.Ion gels are a versatile class of functional materials. Combining the excellent electrical properties such as high ionic conductivity and capacitance of the ionic liquid (IL) and the mechanical integrity of the polymer, the composite materials have led to a variety of applications such as electrolyte-gated transistors (EGTs), electroluminescent, and electrochromic soft materials. This thesis is built up from previous research on the electrical and mechanical properties of the ABA triblock polymer-based ion gels and continues to improve properties of the materials for electrochemical device applications. In the first part of the thesis work, the objective is to improve the existing ABA triblock polymer systems with poly(ethylene oxide) (PEO) or poly(methyl methacrylate) (PMMA) as the IL-solvating midblock by combining the merit of the low Tg from PEO and hydrophobicity from PMMA into one system. As a result, poly(styrene-b-ethyl acrylate-b-styrene) (SEAS) triblock polymer was developed. The ion gels made with SEAS demonstrate similarly high ionic conductivity as the PEO-based ion gels, which are significantly improved from those of the PMMA-based ion gels. By shortening the midblock size of the triblock polymer, a synergistic improvement of both the ionic conductivity and the modulus can be achieved. Additionally, the EGTs made by SEAS-based ion gels demonstrate superior stability under humidity compared with EGTs made by SOS-based ion gels. In the following two projects of the thesis work, the polymer platform changes from petroleum-based polymers with hydrocarbon backbones to renewable aliphatic polyesters with the potential aim of EGTs in biocompatible applications. To achieve the ion gels, both physical and chemical crosslinked-systems have been explored. The physically crosslinked ABA aliphatic polyester triblock ion gels demonstrate good mechanical integrity and can be successfully printed under similar conditions as the previous systems, and demonstrate improved ionic conductivity from the PMMA-based ion gels. In addition, the resulting ion gels also demonstrate efficient hydrolytic degradation under basic condition. In a different approach, chemically crosslinked poly(lactide) (PLA)-based ion gels can be synthesized from a facile one-pot method. Owing to a smaller volume fraction in ion-insulating domain, the ion gel demonstrates an excellent ionic conductivity at low polymer concentration. Meanwhile, the ion gel also possesses a high toughness owing to the chemical crosslinks. The thin chemically crosslinked PLA-ion gels can be laminated onto EGTs via a cut-and-stick method. On the other hand, the bulk ion gel demonstrates a good electromechanical response with high electromechanical sensitivity with the applied strain and a low hysteresis between stretching and unstretching

Orthogonal arrays robust to nonnegligible two-factor interactions

Regular fractional factorial designs with clear two-factor interactions provide a useful class of designs that are robust to nonnegligible two-factor interactions. In this paper, the concept of clear two-factor interactions is generalised to orthogonal arrays. The new concept leads to a much wider class of designs robust to nonnegligible two-factor interactions. We study the existence and construction of such designs. The designs we construct have a structure that render themselves particularly attractive in the robust parameter design setting. We also discuss an interesting connection between designs with clear two-factor interactions and mixed orthogonal arrays. Copyright 2006, Oxford University Press.