doubling and projection a method of constructing two level designs of resolution iv given a two level regular fractional factorial design of resolution iv the method of doubling produces another design of resolution iv which doubles both the run size and the number of factors of the initial design on the other hand the projection of a design of resolution iv onto a subset of factors is of resolution iv or higher recent work in the literature of projective geometry essentially determines the structures of all regular designs of resolution iv with n n 4 1 in terms of doubling and projection where n is the run size and n is the number of factors these results imply that for instance all regular designs of resolution iv with 5n 16 n n 2 must be projections of the regular design of resolution iv with n 2 factors we show that for 9n 32 n 5 n 16 all minimum aberration designs are projections of the design with 5n 16 factors which is constructed by repeatedly doubling the 2 5 1 design defined by i abcde to prove this result we also derive some properties of doubling including an identity that relates the wordlength pattern of a design to that of its double and a result that does the same for the alias patterns of two factor interactions

a tight upper bound of the average absolute error in a constant step size sign algorithm a direct performance index of the adaptive filtering sign algorithm sa is the average absolute error aae at the output of the filter adopting this performance index an easy analysis of sa is achieved under a weak assumption it is proved for both deterministic and random inputs to the filter that the aae has a tight upper bound that exceeds the minimum aae by half the product of the step size and power of the filter input the assumption used is existence of average squared and average absolute values of filter input signals a practical interest of the result is that it provides a formula for the biggest step size as a function of tolerable adaptation noise to desired signal ratio

regular fractional factorial designs with minimum aberration and maximum estimation capacity using the approach of finite projective geometry we make a systematic study of estimation capacity a criterion of model robustness under the absence of interactions involving three or more factors some general results providing designs with maximum estimation capacity are obtained in particular for two level factorials it is seen that constructing a design with maximum estimation capacity calls for choosing points from a finite projective geometry such that the number of lines is maximized and the distribution of these lines among the chosen points is as uniform as possible we also explore the connection with minimum aberration designs under which the sizes of the alias sets of two factor interactions which are not aliased with main effects are the most uniform possible

complete enumeration of two level orthogonal arrays of strength d with d 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 2 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

quarter fraction factorial designs constructed via quaternary codes submitted quarter fraction factorial designs constructed via quaternary codes by frederick k h phoa and hongquan xu university of california los angeles the research of developing a general methodology for the con struction of good nonregular designs has been very active in the last decade recent research by xu and wong 2007 suggested a new class of nonregular designs constructed from quaternary codes this paper explores the properties and uses of quaternary codes towards the construction of quarter fraction nonregular designs some theo retical results are obtained regarding the aliasing structure of such designs optimal designs are constructed under the maximum resolu tion minimum aberration and maximum projectivity criteria these designs often have larger generalized resolution and larger projectiv ity than regular designs of the same size it is further shown that some of these designs have generalized minimum aberration and maximum projectivity among all possible designs 1 introduction in many scienti c researches and investigations the interests lie in the study of e ects of many factors simultaneously frac tional factorial designs especially two level fractional factorial designs are the most commonly used experimental plans for this type of investigations designs that can be constructed through de ning relations among factors are called regular designs any two factorial e ects in a regular design are supported in part by nsf grant dms 05 05728 ams 2000 subject classi cations primary 62k15 keywords and phrases aliasing index fractional factorial design generalized minimum aberration generalized resolution nonregular design projectivity

clear two factor interactions and minimum aberration wu and hamada recommend selecting resolution iv designs with the maximum number of clear two factor interactions 2fis called maxc2 designs in this paper we develop a method by using graphical representations combinatorial and group theoretic arguments to prove if a given design is a maxc2 design in particular we show that all known minimum aberration designs with resolution iv are maxc2 designs except in six cases and that the second 2 9 4 2 13 7 2 16 10 and 2 17 11 designs given in wu and hamada are maxc2 designs the method also enables us to identify new maxc2 designs that are too large to be verified by computer search

convergence analysis of a data echo canceller with a stochastic gradient adaptive fir filter using the sign algorithm under the assumption that the errors at the taps are gaussian distributed a new set of recurrence formulae is derived for calculating theoretical convergence process of a data echo canceller equipped with an fir filter that is adaptively controlled by using the stochastic gradient sign algorithm with a binary and white process as the filter input convergence curves for the mean squared residual echo based on the recurrence formulae show an excellent agreement with those obtained by simulation approximate recurrence formulae that yield a useful though less accurate estimation of the residual echo convergence are also proposed furthermore a closed form solution to the approximate recurrence formulae is derived and finally probability density function of the residual echo is depicted as it changes its shape as the echo canceller converges

a bayesian variable selection approach for analyzing designed experiments with complex aliasing experiments using designs with complex aliasing patterns are often performed for example twolevel nongeometric plackett burman designs multilevel and mixed level fractional factorial designs two level fractional factorial designs with hard to control factors and supersaturated designs hamada and wu proposed an iterative guided stepwise regression strategy for analyzing the data from such designs that allows entertainment of interactions their strategy provides a restricted search in a rather large model space however this article provides an efficient methodology based on a bayesian variable selection algorithm for searching the model space more thoroughly we show how the use of hierarchical priors provides a flexible and powerful way to focus the search on a reasonable class of models the proposed methodology is demonstrated with four examples three of which come from actual industrial experiments

analysis of a sign algorithm with delayed data an adaptive filter whose weights are adapted using a sign algorithm with a delayed error signal is analyzed for stationary environments it is proved that the excess average absolute estimation error is bounded for all values of the error signal delay and the algorithm step size for the nonstationary case when the optimal filter weights are time varying the optimum step size which minimizes the excess average absolute error is derived it is shown that the optimum step size does not depend on the additive noise power the analytical results are supported by computer simulations

bayesian prediction of deterministic functions with applications to the design and analysis of computer experiments abstract this article is concerned with prediction of a function y t over a multidimensional domain t given the function values at a set of sites t 1 t 2 t n in t and with the design that is with the selection of those sites the motivating application is the design and analysis of computer experiments where t determines the input to a computer model of a physical or behavioral system and y t is a response that is part of the output or is calculated from it following a bayesian formulation prior uncertainty about the function y is expressed by means of a random function y which is taken here to be a gaussian stochastic process the mean of the posterior process can be used as the prediction function t and the variance can be used as a measure of uncertainty this kind of approach has been used previously in bayesian interpolation and is strongly related to the kriging methods used in geostatistics here emphasis is placed on product linear and product cubic correlation func

some projection properties of orthogonal arrays the definition of an orthogonal array imposes an important geometric property the projection of an oa 2 t 2 k t a 2 t run orthogonal array with k two level factors and strength t onto any t factors consists of copies of the complete 2 t factorial in this article projections of an oa n 2 k t onto t 1 and t 2 factors are considered the projection onto any t 1 factors must be one of three types one or more copies of the complete 2 t 1 factorial one or more copies of a half replicate of 2 t 1 or a combination of both it is also shown that for k t 2 only when n is a multiple of 2 t 1 can the projection onto some t 1 factors be copies of a half replicate of 2 t 1 therefore if n is not a multiple of 2 t 1 then the projection of an oa n 2 k t with k t 2 onto any t 1 factors must contain at least one complete 2 t 1 factorial some properties of projections onto t 2 factors are established and are applied to show that if n is not a multiple of 8 then for any oa n 2 k 2 with k 4 the projection onto any four factors has the property that all the main effects and two factor interactions of these four factors are estimable when the higher order interactions are negligible

indicator function and its application in two level factorial designs a two level factorial design can be uniquely represented by a polynomial indicator function therefore properties of factorial designs can be studied through their indicator functions this paper shows that the indicator function is an effective tool in studying two level factorial designs the indicator function is used to generalize the aberration criterion of a regular two level fractional factorial design to all two level factorial designs an important identity of generalized aberration is proved the connection between a uniformity measure and aberration is also extended to all two level factorial designs

tracking analysis of the sign algorithm in nonstationary environments a tracking analysis of the adaptive filters equipped with the sign algorithm and operating in nonstationary environments is presented under the assumption that the nonstationary can be modeled using a random disturbance it is shown that the long term time average of the mean absolute error is bounded and that there exists an optimal choice of the convergence constant mu which minimizes this quality applying the commonly used independence assumption and under the assumption that the nonstationarity is solely due to the time varying behavior of the optimal coefficients it is shown that the distributions of the successive coefficient misalignment vectors converge to a limiting distribution when the adaptive filter is used in the system identification mode finally under the additional assumption that the signals involved are zero mean and gaussian a set of nonlinear difference equations is derived that characterizes the mean and mean squared behavior of the filter coefficients and the mean squared estimation error during adaptation and tracking results of several experiments that show very good correlation with the theoretical analyses are presented

orthogonal arrays robust to nonnegligible two factor interactions summary 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

stochastic polynomial interpolation for uncertainty quantification with computer experiments multivariate polynomials are increasingly being used to construct emulators of computer models for uncertainty quantification for deterministic computer codes interpolating polynomial metamodels should be used instead of noninterpolating ones for logical consistency and prediction accuracy however available methods for constructing interpolating polynomials only provide point predictions there is no known method that can provide probabilistic statements about the interpolation error furthermore there are few alternatives to grid designs and sparse grids for constructing multivariate interpolating polynomials a significant disadvantage of these designs is the large gaps between allowable design sizes this article proposes a stochastic interpolating polynomial sip that seeks to overcome the problems discussed above a bayesian approach in which interpolation uncertainty is quantified probabilistically through the posterior distribution of the output is employed this allows assessment of the effe

the lms algorithm with delayed coefficient adaptation the behavior of the delayed least mean square dlms algorithm is studied it is found that the step size in the coefficient update plays a key role in the convergence and stability of the algorithm an upper bound for the step size is derived that ensures the stability of the dlms the relationship between the step size and the convergence speed and the effect of the delay on the convergence speed are also studied the analytical results are supported by computer simulations

geometric isomorphism and minimum aberration for factorial designs with quantitative factors factorial designs have broad applications in agricultural engineering and scientific studies in constructing and studying properties of factorial designs traditional design theory treats all factors as nominal however this is not appropriate for experiments that involve quantitative factors for designs with quantitative factors level permutation of one or more factors in a design matrix could result in different geometric structures and thus different design properties in this paper indicator functions are introduced to represent factorial designs a polynomial form of indicator functions is used to characterize the geometric structure of those designs geometric isomorphism is defined for classifying designs with quantitative factors based on indicator functions a new aberration criteria is proposed and some minimum aberration designs are presented

convergence analysis of the sign algorithm without the independence and gaussian assumptions the paper is concerned with rigorous convergence analysis of the sign algorithm sa in the context of adaptive plant identification asymptotic time averaged convergence for the mean absolute weight misalignment is proved for all values of the algorithm step size and initial weight vector the paper has three main contributions with respect to available convergence results of the sa the first is the deletion of the gaussian assumption which is important when covering the case of discrete valued data no assumption about the distribution of the regressor sequence is used except for the usual assumption of positive definite covariance matrix the assumptions used about the noise allow nonexistence unboundedness and vanishing of the noise probability density function for arguments strictly different from zero the second contribution is the deletion of the assumption of independent successive regressors this deletion is important since in applications two successive regressors usually share all their components except two hence they are strongly dependent even for white plant input the case of colored noise is also analyzed finally the third contribution is the extension of the above results to the nonstationary case the used assumptions allow nonstationarity of the plant input plant noise and plant parameters

a graph aided method for planning two level experiments when certain interactions are important in planning a fractional factorial experiment prior knowledge may suggest that some interactions are potentially important and should therefore be estimated free of the main effects in this article we propose a graph aided method to solve this problem for two level experiments first we choose the defining relations for a 2 n k design according to a goodness criterion such as the minimum aberration criterion then we construct all of the nonisomorphic graphs that represent the solutions to the problem of simultaneous estimation of main effects and two factor interactions for the given defining relations in each graph a vertex represents a factor and an edge represents the interaction between the two factors for the experiment planner the job is simple draw a graph representing the specified interactions and compare it with the list of graphs obtained previously our approach is a substantial improvement over taguchi s linear graphs

theory of j characteristics for fractional factorial designs and projection justification of minimum g2 aberration deng tang 1999 introduced the generalised resolution and minimum g aberration criteria for assessing nonregular fractional factorials in tang deng 1999 a relaxed variant of minimum g aberration called minimum g 2 aberration is proposed and studied these criteria are defined using a set of j values called j characteristics in this paper we show that a factorial design is uniquely determined by its j characteristics just as a regular factorial design is uniquely determined by its defining relation the theorem is given through an explicit formula that relates the set of design points to that of j characteristics through this formula projection justification of minimum g 2 aberration is established

robust designs through partially clear two factor interactions summary orthogonal arrays with clear two factor interactions provide a class of designs that are robust to nonnegligible effects if certain prior knowledge is available then robust designs allow additional factors to be studied this is done through partially clear two factor interactions we study the existence and construction of such robust designs and present an upper bound on the maximum number of clear two factor interactions

optimal blocking schemes for 2n and 2n p designs systematic sources of variations in factorial experiments can be effectively reduced without biasing the estimates of the treatment effects by grouping the runs into blocks for full factorial designs optimal blocking schemes are obtained by applying the minimum aberration criterion to the block defining contrast subgroup a related concept of order of estimability is proposed for fractional factorial designs because of the intrinsic difference between treatment factors and block variables the minimum aberration approach has to be modified a concept of admissible blocking schemes is proposed for selecting block designs based on multiple criteria the resulting 2 n and 2 n p designs are shown to have better overall properties for practical experiments than those in the literature

effect of delay on the performance of the leaky lms adaptive algorithm this correspondence studies the effect of a nonzero delay on the performance of the leaky lms algorithm the stability bound on the step size is derived for error convergence it is shown that leakage allows for larger bounds on the step size of the delayed lms algorithm theoretical bounds are verified by simulations

john von neumann s analysis of gaussian elimination and the origins of modern numerical analysis just when modern computers digital electronic and programmable were being invented john von neumann and herman goldstine wrote a paper to illustrate the mathematical analyses that they believed would be needed to use the new machines effectively and to guide the development of still faster computers their foresight and the congruence of historical events made their work the first modern paper in numerical analysis von neumann once remarked that to found a mathematical theory one had to prove the first theorem which he and goldstine did for the accuracy of mechanized gaussian elimination but their paper was about more than that von neumann and goldstine described what they surmized would be the significant questions once computers became available for computational science and they suggested enduring ways to answer them

construction properties and analysis of group orthogonal supersaturated designs in this article we propose a new method for constructing supersaturated designs that is based on the kronecker product of two carefully chosen matrices the construction method leads to a partitio

design selection and classification for hadamard matrices using generalized minimum aberration criteria deng and tang 1999 and tang and deng 1999 proposed and justified two criteria of generalized minimum aberration for general two level fractional factorial designs the criteria are defined using a set of values called j characteristics in this article we examine the practical use of the criteria in design selection specifically we consider the problem of classifying and ranking designs that are based on hadamard matrices a theoretical result on j characteristics is developed to facilitate the computation the issue of design selection is further studied by linking generalized aberration with the criteria of efficiency and estimation capacity our studies reveal that generalized aberration performs quite well under these familiar criteria

analysis of computer experiments using penalized likelihood in gaussian kriging models kriging is a popular analysis approach for computer experiments for the purpose of creating a cheap to compute meta model as a surrogate to a computationally expensive engineering simulation model the maximum likelihood approach is used to estimate the parameters in the kriging model however the likelihood function near the optimum may be flat in some situations which leads to maximum likelihood estimates for the parameters in the covariance matrix that have very large variance to overcome this difficulty a penalized likelihood approach is proposed for the kriging model both theoretical analysis and empirical experience using real world data suggest that the proposed method is particularly important in the context of a computationally intensive simulation model where the number of simulation runs must be kept small because collection of a large sample set is prohibitive the proposed approach is applied to the reduction of piston slap an unwanted engine noise due to piston secondary motion issu

blocking in regular fractional factorials a projective geometric approach a projective geometric characterization is given of the existence of any regular main effect s n k design in s blocks it leads to a constructive method for finding a maximal blocking scheme for any given fractional factorial design a useful sufficient condition for admissible block designs is given in terms of the minimum aberration property of a certain unblocked design

optimization of adaptive identification for time varying filters adaptive identification in a time varying context is studied when controlled by the lms algorithm with constant gain under the assumption of correlated successive input vectors it is well known by experience that the tracking mean square error mse epsilon mu results from the tradeoff between the gradient part which is increasing and the lag contribution which is decreasing in this note we clarify the relative roles of the gradient and lag errors by proving their decoupled character this property relies upon independence between the additive noise at the output of the plant to be identified and the information vector at the plant input convergence of the mse is established rather than assumed quantitative evaluations of upper and lower bounds allow an approximate optimization of the gain in two important cases the optimum is exact one of these cases is slow variations it is defined in a quantitative manner thanks to the ratio of the variation noise to the output additive noise

a bayesian approach to the design and analysis of fractionated experiments specifying a prior distribution for the large number of parameters in the statistical model is a critical step in a bayesian approach to the design and analysis of experiments this article shows that the prior distribution can be induced from a functional prior on the underlying transfer function the functional prior requires specification of only a few hyperparameters and thus can be easily implemented in practice the usefulness of the approach is demonstrated through the analysis of some experiments the article also proposes a new class of design criteria and establishes their connections with the minimum aberration criterion

designs of variable resolution prior information or background knowledge may suggest that interactions arise only within certain factors when such knowledge is available we propose using a new class of designs designs of variable resolution several constructions are presented statistical justifications for using such designs from minimum g 2 aberration and design efficiency perspectives are provided copyright 2012 oxford university press

variable selection with the strong heredity constraint and its oracle property in this paper we extend the lasso method tibshirani 1996 for simultaneously fitting a regression model and identifying important interaction terms unlike most of the existing variable selection methods our method automatically enforces the heredity constraint that is an interaction term can be included in the model only if the corresponding main terms are also included in the model furthermore we extend our method to generalized linear models and show that it performs as well as if the true model were given in advance that is the oracle property as in fan and li 2001 and fan and peng 2004 the proof of the oracle property is given in online supplemental materials numerical results on both simulation data and real data indicate that our method tends to remove irrelevant variables more effectively and provide better prediction performance than previous work yuan joseph and lin 2007 and zhao rocha and yu 2009 as well as the classical lasso method

minimum aberration and model robustness for two level fractional factorial designs summary the performance of minimum aberration two level fractional factorial designs is studied under two criteria of model robustness simple sufficient conditions for a design to dominate another design with respect to each of these two criteria are derived it is also shown that a minimum aberration design of resolution ilil or higher maximizes the number of two factor interactions which are not aliases of main effects and subject to that condition minimizes the sum of squares of the sizes of alias sets of two factor interactions this roughly says that minimum aberration designs tend to make the sizes of the alias sets very uniform it follows that minimum aberration is a good surrogate for the two criteria of model robustness that are studied here examples are given to show that minimum aberration designs are indeed highly efficient

functionally induced priors for the analysis of experiments this work develops the idea of using functional priors for the design and analysis of three level and higher level experiments developing a prior distribution for model parameters is challenging because a factor can be qualitative or quantitative we propose appropriate correlation functions and coding schemes so that the prior distribution is simple and the results are interpretable the prior incorporates well known principles such as effect hierarchy and effect heredity which helps resolve the aliasing problems in fractional designs almost automatically the usefulness of the new approach is illustrated through the analysis of some real experiments

orthogonal and nearly orthogonal designs for computer experiments we introduce a method for constructing a rich class of designs that are suitable for use in computer experiments the designs include latin hypercube designs and two level fractional factorial designs as special cases and fill the vast vacuum between these two familiar classes of designs the basic construction method is simple building a series of larger designs based on a given small design if the base design is orthogonal the resulting designs are orthogonal likewise if the base design is nearly orthogonal the resulting designs are nearly orthogonal we present two generalizations of our basic construction method the first generalization improves the projection properties of the basic method the second generalization gives rise to designs that have smaller correlations sample constructions are presented and properties of these designs are discussed

generalized minimum aberration for asymmetrical fractional factorial designs by studying treatment contrasts and anova models we propose a generalized minimum aberration criterion for comparing asymmetrical fractional factorial designs the criterion is independent of the choice of treatment contrasts and thus model free it works for symmetrical and asymmetrical designs regular and nonregular designs in particular it reduces to the minimum aberration criterion for regular designs and the minimum g 2 aberration criterion for two level nonregular designs in addition by exploring the connection between factorial design theory and coding theory we develop a complementary design theory for general symmetrical designs which covers many existing results as special cases

nonregular designs with desirable projection properties in many industrial applications the experimenter is interested in estimating some of the main effects and two factor interactions in this article we rank two level orthogonal designs based on the number of estimable models containing a subset of main effects and their associated two factor interactions by ranking designs in this way the experimenter can directly assess the usefulness of the experimental plan for the purpose in mind we apply the new ranking criterion to the class of all non isomorphic two level orthogonal designs with 16 and 20 runs and introduce a computationally efficient algorithm based on two theoretical results which will aid in finding designs with larger run sizes catalogs of useful designs with 16 20 24 and 28 runs are presented

adaptive filtering with binary reinforcement recently there has been increased interest in high speed adaptive filtering where the usual stochastic gradient or least mean square lms algorithm is replaced with the simpler algorithm where adaptation is guided only by the polarity of the error signal in this paper the convergence of this binary reinforcement br algorithm is proved under the usual independence assumption and the surprising observation is made that unlike the lms algorithm convergence occurs for any positive value of the step size parameter while the stochastic gradient algorithm attempts to minimize a mean square error cost function the binary reinforcement algorithm in fact attempts to minimize a mean absolute error cost function it is proved for the binary reinforcement algorithm that the tap weight vector converges in distribution to a random vector that is suitably concentrated about the optimal value based on a least mean absolute error cost function for a sufficiently small step size the expected cost of the asymptotic weight vector can be made as close as desired to thc minimum cost attain ed by the optimum weight vector

comparison of the convergence of two algorithms for adaptive fir digital filters the convergence properties of two different algorithms for the updating of the coefficients of an adaptive fir digital filter are investigated and compared with one another these algorithms are the stochastic iteration algorithm and the sign algorithm in this latter algorithm a one bit gradient estimation is used which makes its implementation very simple the convergence is characterized by the residual echo variance after convergence and a parameter that indicates the speed of the convergence it is shown that the convergence of the sign algorithm can always be assured but is much slower than that of the stochastic iteration algorithm if the same variance of the residual echo is to be obtained

universality in two dimensional cellular structures evolving by cell division and disappearance the dynamics of two dimensional cellular networks is written in terms of coupled population equations which describe how the population of s sided cells is affected by cell division and disappearance in these equations the effect of the rest of the foam on the disappearing or dividing cell is treated as a local mean field under not too restrictive conditions the equilibrium distribution p s of cells satisfies a linear difference equation of order two or higher the population equations are asymptotically integrable the asymptotic integrability implies a universal distribution p s approximately cs kzs for large values of s which is also the boltzmann distribution associated with the maximum entropy inference asymptotic integrability of the population equations is absent in a global mean field approximation the importance of short range topological information to control the evolution of foams is thus confirmed

a trigonometric approach to quaternary code designs with application to one eighth and one sixteenth fractions the study of good nonregular fractional factorial designs has received significant attention over the last two decades recent research indicates that designs constructed from quaternary codes qc are very promising in this regard the present paper shows how a trigonometric approach can facilitate a systematic understanding of such qc designs and lead to new theoretical results covering hitherto unexplored situations we focus attention on one eighth and one sixteenth fractions of two level factorials and show that optimal qc designs often have larger generalized resolution and projectivity than comparable regular designs moreover some of these designs are found to have maximum projectivity among all designs

fractional factorial designs with admissible sets of clear two factor interactions we consider the problem of selecting two level fractional factorial designs that allow joint estimation of all main effects and some specified two factor interactions 2fi s without aliasing from other 2fi s this problem is to find among all 2 m p designs with given m and p those resolution iv designs whose sets of clear 2fi s contain the specified 2fi s as subsets we use a linear graph to represent the set of clear 2fi s for a resolution iv design where each line connecting two vertexes represents a clear 2fi between the factors represented by the two vertexes we call a 2 m p resolution iv design admissible if its graph is not isomorphic to any proper subgraph of the graph of any other 2 m p resolution iv design we show that all even resolution iv designs are inadmissible we then use a classical subgraph isomorphism algorithm to determine all admissible designs of 32 64 and 128 runs this leads to a concise catalog of all admissible designs of 32 and 64 runs and a lengthy but substantially re

an efficient variable selection approach for analyzing designed experiments the analysis of experiments in which numerous potential variables are examined is driven by the principles of effect sparsity effect hierarchy and effect heredity we propose an efficient variable selection strategy to specifically address the unique challenges faced by such analysis the proposed methods are natural extensions of the lars general purpose variable selection algorithm they can be computed very rapidly and can find sparse models that better satisfy the goals of experiments simulations and real examples are used to illustrate the wide applicability of the proposed methods

bayesian inspired minimum aberration two and four level designs summary motivated by a bayesian framework we propose a new minimum aberration type criterion for designing experiments with two and four level factors the bayesian approach helps in overcoming the ad hoc nature of effect ordering in the existing minimum aberration type criteria the approach is also capable of distinguishing between qualitative and quantitative factors numerous examples are given to demonstrate its advantages

bayes optimal designs for two and three level factorial experiments abstract two and three level factorial designs are often used for exploratory experiments with many independent variables the purpose of such experiments is to estimate the effects of all active independent variables and their interactions for reasons of economy or other constraints only a fraction of the full number of experimental settings of the independent variables may be run precluding the separate data based estimation of all the effects in this situation of relatively sparse data and many unknown parameters the benefits of reliable prior information used in the estimation and experimental design can be especially significant in this article exact bayes optimal designs of two and three level fractional factorial experiments and of blocked two and three level factorial experiments are derived the optimality criteria used in this process are versions of the bayes criterion introduced by duncan and degroot it is shown that the classical fractional factorial designs for the 2k experime

the stability of adaptive minimum mean square error equalizers using delayed adjustment the necessary and sufficient conditions for the stability and convergence of adaptive minimum mean square error equalizers are developed the analysis includes the effect of delays in the adjustment path as occur for instance when the decoder in a data transmission system delays its output decisions

some identities on q sp n m designs with application to minimum aberration designs chen and hedayat and tang and wu studied and characterized minimum aberration 2 n m designs in terms of their complemetary designs based on a new and more powerful approach we extend the study to identify minimum aberration q n m designs through their complementary designs by using macwilliams identities and krawtchouk polynomials in coding theory we obtain some general and explicit relationships between the wordlength pattern of a q n m design and that of its complementary design these identities provide a powerful tool for characterizing minimum aberration q n m designs the case of q 3 is studied in more details

optimum step size of sign algorithm for nonstationary adaptive filtering the adaptive filtering sign algorithm is analyzed in the case of nonstationary and correlated data the excess time average absolute estimation error eaae is used as a performance index of the algorithm it is proved that the eaae is the sum of two terms one proportional to the algorithm step size mu and the other proportional to 1 mu the optimum step size that minimizes the eaae is found equal to square root q p with q being the power of fluctuations of the optimal filter weights and p being the power of filter input this formula is derived under the assumption that increments of optimal filter weights are white computer simulations are used to examine the validity of the formula for other models of variation of the optimal filter simulation results show a good fit with the obtained optimum step size formula

minimum aberration construction results for nonregular two level fractional factorial designs summary nonregular two level fractional factorial designs are designs which cannot be specified in terms of a set of defining contrasts the aliasing properties of nonregular designs can be compared by using a generalisation of the minimum aberration criterion called minimum g2 aberration until now the only nontrivial designs that are known to have minimum g2 aberration are designs for n runs and m n 5 factors in this paper a number of construction results are presented which allow minimum g2 aberration designs to be found for many of the cases with n 16 24 32 48 64 and 96 runs and m n 2 2 factors