latin hypercube designs with controlled correlations and multi dimensional stratification various methods have been proposed to construct latin hypercube designs with small correlations orthogonal arrays have been used to construct latin hypercube designs with multi dimensional stratification to integrate these two ideas we propose a method to construct latin hypercube designs with both controlled correlations and multi dimensional stratification for numerical integration the constructed designs not only filter out lower dimensional variance components as effectively as ordinary orthogonal array based latin hypercube designs but also filter out bilinear terms more effectively the proposed construction method entails no iterative searches sampling properties of the constructed designs are derived examples are given to illustrate the proposed construction method and the theoretical results

variable selection for gaussian process models in computer experiments in many situations simulation of complex phenomena requires a large number of inputs and is computationally expensive identifying the inputs that most impact the system so that these factors can be further investigated can be a critical step in the scientific endeavor in computer experiments it is common to use a gaussian spatial process to model the output of the simulator in this article we introduce a new simple method for identifying active factors in computer screening experiments the approach is bayesian and only requires the generation of a new inert variable in the analysis however in the spirit of frequentist hypothesis testing the posterior distribution of the inert factor is used as a reference distribution against which the importance of the experimental factors can be assessed the methodology is demonstrated on an application in material science a computer experiment from the literature and simulated examples

constructing tables of minimum aberration pn m designs fries and hunter 1980 presented a practical algorithm for selecting standard 2 n m fractional factorial designs based on a criterion they called minimum aberration in this article some simple results are presented that enable the fries hunter algorithm to be used for a wider range of n and m and for designs with factors at p levels where p 2 is prime examples of minimum aberration 2 n m designs with resolution r 4 are given for m n m 9 a matrix is given for generating 3 n m designs with m n m 6 which have or nearly have minimum aberration

choice of optimal blocking schemes in two level and three level designs blocking is commonly used in design of experiments to reduce systematic variation and increase precision of effect estimation for 2n k designs in 2p blocks others have studied the confounding pattern between blocking effects and treatment effects and proposed some criteria to choose optimal blocking schemes we propose alternative criteria that allow estimation of more lower order effects extensions to three level fractional factorial design are considered and tables of useful designs are given

minimum aberration designs with two level and four level factors summary for optimal assignment of factors to columns of a 4 2 n design we consider extensions of the minimum aberration criterion for the 2 level designs minimum aberration 412n and 422n designs in 16 and 32 runs are obtained and tabulated some results on the wordlength patterns and design classification are obtained

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

balanced repeated replications based on orthogonal multi arrays summary to obtain variance estimates in stratified sampling with possibly unequal numbers of primary sampling units per stratum one can either randomly divide the units in each stratum into two groups and apply the balanced half samples method to these groups or use mixed orthogonal arrays to form a set of balanced subsamples with the first technique resulting variance estimates can be very inefficient and with the second technique it can be difficult to construct orthogonal arrays with a small number of replicates for a given stratified design the proposed extension of the orthogonal array method to orthogonal multi arrays retains all of the orthogonal array method s desirable properties but allows greater flexibility in construction and thus can handle more complex stratified designs using fewer replicates

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

blocking schemes for definitive screening designs in earlier work jones and nachtsheim proposed a new class of screening designs called definitive screening designs as originally presented these designs are three level designs for quantitative factors that provide estimates of main effects that are unbiased by any second order effect and require only one more than twice as many runs as there are factors definitive screening designs avoid direct confounding of any pair of second order effects and for designs that have more than five factors project to efficient response surface designs for any two or three factors recently jones and nachtsheim expanded the applicability of these designs by showing how to include any number of two level categorical factors however methods for blocking definitive screening designs have not been addressed in this article we develop orthogonal blocking schemes for definitive screening designs we separately consider the cases where all of the factors are quantitative and where there is a mix of quantitative and tw

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

distributed computation of nash equilibria in linear quadratic stochastic differential games in this paper a class of n person stochastic linear quadratic differential games under multiple probabilistic modeling is studied with each player acquiring a noisy measurement of the initial state conditions for the existence and uniqueness of the nash equilibrium is obtained and a method is provided for an iterative distributed computation of the solution the distributed algorithm involves learning in the policy space and it does not require that each player knows the others perceptions of the probabilistic model underlying the decision process for the finite horizon problem such an iteration converges whenever the length of the time horizon is sufficiently small and the limit in this case is an affine policy for all players if the underlying distributions are jointly gaussian when the horizon is infinite and a discount factor is used in the cost functionals the iteration converges under conditions depending on the magnitude of the discount factor the limiting policies again being affine in

optimal design with many blocking factors designs for sets of experimental units with many blocking factors are studied it is shown that if the set of blocking factors satisfies a certain simple condition then the information matrix for the design has a simple form in consequence a design is optimal if it is optimal with respect to one particular blocking factor and regular with respect to all the rest in a sense which is made precise in the paper this encompasses several previous results for optimal designs with more than one blocking factor and applications to many other situations are given

strong orthogonal arrays and associated latin hypercubes for computer experiments this paper introduces constructs and studies a new class of arrays called strong orthogonal arrays as suitable designs for computer experiments a strong orthogonal array of strength t enjoys better space filling properties than a comparable orthogonal array in all dimensions lower than t while retaining the space filling properties of the latter in t dimensions latin hypercubes based on strong orthogonal arrays of strength t are more space filling than comparable orthogonal array based latin hypercubes in all g dimensions for any 2 g t 1 copyright 2013 oxford university press

a robust criterion for experimental designs for serially correlated observations a new robust criterion for experimental designs is proposed for a given design the criterion is to minimize over all possible run orders the absolute value of the change of the variance function due to possible correlation between the observations the resulting design is robust against possible auto correlation among the observations in the sense that confidence interval coverage levels are maintained accurately applications are given for 2k factorial designs and one mixed level fractional experiment and robust runs are obtained computational strategies are also discussed and a simulated annealing algorithm is developed to search for robust designs

analysis of censored data from fractionated experiments a bayesian approach abstract censored data arise naturally in industrial experiments whose observations are failure times or measurements with mixed continuous categorical outcomes when censored data are observed from a fractionated experiment likelihood based estimates quite often do not exist especially when the opportunity for improvement is great to circumvent this problem we propose a bayesian analysis strategy that has a straightforward implementation using the data augmentation and monte carlo em algorithms for nonregular designs with complex aliasing patterns a modified analysis strategy is proposed that substantially reduces the computation needed for model selection the proposed strategy is illustrated using data from three real industrial experiments for these data sets the analysis results are fairly insensitive to the specification of the prior

main effect plans orthogonal through the block factor many industrial experiments require different number of levels for different factors orthogonal main effect plans omeps for such asymmetrical experiments often require large run size if blocking is needed then run size usually becomes even larger in this article we show that there are situations when use of blocks may in fact be helpful in finding an omep with small run size explicitly we obtained saturated omeps for a 33n 23n experiment in 3n blocks of size 4 each for each hadamard number n in each of these plans the three level factors are nonorthogonal to the block factor but are pairwise orthogonal through the block factor the two level factors are orthogonal to the block factor the data analysis for such a plan is illustrated with the help of examples this article has supplementary material online

using blocked fractional factorial designs to construct discrete choice experiments for healthcare studies discrete choice experiments dces are increasingly used for studying and quantifying subjects preferences in a wide variety of healthcare applications they provide a rich source of data to assess real life decision making processes which involve trade offs between desirable characteristics pertaining to health and healthcare and identification of key attributes affecting healthcare the choice of the design for a dce is critical because it determines which attributes effects and their interactions are identifiable we apply blocked fractional factorial designs to construct dces and address some identification issues by utilizing the known structure of blocked fractional factorial designs our design techniques can be applied to several situations including dces where attributes have different number of levels we demonstrate our design methodology using two healthcare studies to evaluate i asthma patients preferences for symptom based outcome measures and ii patient preference for breast screening services copyright 2016 john wiley sons ltd

generalized resolution for orthogonal arrays the generalized word length pattern of an orthogonal array allows a ranking of orthogonal arrays in terms of the generalized minimum aberration criterion xu and wu 2001 we provide a statistical interpretation for the number of shortest words of an orthogonal array in terms of sums of r values based on orthogonal coding or sums of squared canonical correlations based on arbitrary coding directly related to these results we derive two versions of generalized resolution for qualitative factors both of which are generalizations of the generalized resolution by deng and tang 1999 and tang and deng 1999 we provide a sufficient condition for one of these to attain its upper bound and we provide explicit upper bounds for two classes of symmetric designs factor wise generalized resolution values provide useful additional detail

asymmetric nested lattice samples we propose an approach for constructing a new class of space filling designs called asymmetric nested lattice samples as a stepping stone to the proposed approach we introduce two methods for generating asymmetric nested orthogonal arrays we then present an elaborate randomization method to shuffle the levels of an asymmetric nested orthogonal array to produce a pair of asymmetric nested lattice samples the constructed designs have a desirable nested structure possess attractive space filling properties and allow different axes to be divided at different scales of fineness for multifidelity computer experiments sequential evaluations and multistep functional fitting and linking parameters the asymmetric feature is appealing for situations where some factors are believed to be more important or deserve more attention than others the proposed designs are also useful in problems where different factors by nature require dividing their axes at different levels of fineness

indicator functions and the algebra of the linear quadratic parameterization indicator functions are constructed under the linear quadratic parameterization for contrasts and applied to the study of partial aliasing properties for three level fractional factorial designs an algebraic operation is introduced for the calculation of indicator function coefficients this operation connects design construction methods to the analysis under the linear quadratic system and helps establish simple conditions for the estimability of interactions

mixed orthogonal arrays for variance estimation with unequal numbers of primary selections per stratum summary for estimating the variance of nonlinear statistics in large scale complex surveys the method of balanced repeated replications has received special attention the method at present is useful in stratified clustered designs with equal number of primary selections from each stratum this paper extends the method to general sample designs with arbitrary number of selections from each stratum it is shown that mixed orthogonal arrays of strength two or equivalently equal frequency orthogonal main effect plans for asymmetrical factorials give a set of balanced subsamples useful in variance estimation

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

space filling fractional factorial designs fractional factorial designs are widely used in various scientific investigations and industrial applications level permutation of factors could alter their geometrical structures and statistical properties this article studies space filling properties of fractional factorial designs under two commonly used space filling measures discrepancy and maximin distance when all possible level permutations are considered the average discrepancy is expressed as a linear combination of generalized word length pattern for fractional factorial designs with any number of levels and any discrepancy defined by a reproducing kernel generalized minimum aberration designs are shown to have good space filling properties on average in terms of both discrepancy and distance several novel relationships between distance distribution and generalized word length pattern are derived it is also shown that level permutations can improve space filling properties for many existing saturated designs a two step construction pro

distributed algorithms for the computation of noncooperative equilibria abstract in this paper a general class of nonquadratic convex nash games is studied from the points of view of existence stability and iterative computation of noncooperative equilibria conditions for contraction of general nonlinear operators are obtained which are then used in the stability study of such games these lead to existence and uniqueness conditions for stable nash equilibrium solutions under both global and local analysis also convergence of an algorithm which employs inaccurate search techniques is verified it is shown in the context of a fish war example that the algorithm given is in some aspects superior to various algorithms found in the literature and is furthermore more meaningful for real world implementation

a variational inequality approach for the determination of oligopolistic market equilibrium this paper presents an alternative approach to that by murphy sherali and soyster 13 for computing market equilibria with mathematical programming methods this approach is based upon a variational inequality representation of the problem and the use of a diagonalization relaxation algorithm

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

decentralized method for computing pareto solutions in multiparty negotiations this paper presents a decentralized method for computing pareto optimal solutions in multiparty negotiations over continuous issues the method is based on the well known weighting method which is decomposed by introducing an own decision variable for each decision maker and by applying the dual decomposition method to the resulting problem the method offers a systematic way for generating some or all pareto optimal solutions so that decision makers do not have to know each others value functions under the assumption of quasilinear value function the requirement that a decision maker knows the explicit form for his value function can be relaxed in that case the decision maker is asked to solve a series of multiobjective programming problems where an additional artificial decision variable is introduced

nearly orthogonal arrays with mixed levels and small runs in running a factorial experiment it may be desirable to use an orthogonal array with different mixed numbers of factor levels because of the orthogonality requirement such arrays may have a large run size by slightly sacrificing the orthogonality requirement we can obtain nearly orthogonal arrays with economic run size some general methods for constructing such arrays are given for 12 18 20 and 24 runs many orthogonal arrays and nearly orthogonal arrays with mixed levels are constructed and tabulated effects of near orthogonality on estimation efficiency and analysis are studied

some theory for constructing minimum aberration fractional factorial designs summary minimum aberration is the most established criterion for selecting a regular fractional factorial design of maximum resolution minimum aberration designs for n runs and n 2 m n factors have previously been constructed using the novel idea of complementary designs in this paper an alternative method of construction is developed by relating the wordlength pattern of designs to the so called confounding between experimental runs this allows minimum aberration designs to be constructed for n runs and 5n 16 m n 2 factors as well as for n 2 m n

how often do simple dynamical processes have infinitely many coexisting sinks this work concerns the nature of chaotic dynamical processes sheldon newhouse wrote on dynamical processes depending on a parameter xx 1 t xn wherex is in the plane such as might arise when studying poincare return maps for autonomous differential equations in ir3 he proved that if the system is chaotic there will very often be existing parameter values for which there are infinitely many periodic attractors coexisting in a bounded region of the plane and that such parameter values would be dense in some interval the fact that infinitely many coexisting sinks can occur brings into question the very nature of the foundations of chaotic dynamical processes we prove for an apparently typical situation that newhouse s construction yields only a set of parameter values of measure zero

columnwise pairwise algorithms with applications to the construction of supersaturated designs motivated by the construction of supersaturated designs we develop a class of algorithms called columnwise pairwise exchange algorithms they differ from the k exchange algorithms in two respects 1 they exchange columns instead of rows of the design matrix and 2 they employ a pairwise adjustment in the search for a better column the proposed algorithms perform very well in the construction of supersaturated designs both for a single criterion and for multiple criteria they are also applicable to the construction of designs that are not supersaturated

the decomposition of treatment degrees of freedom in quantitative factorial experiments summary in an experiment in which every treatment factor has the same number p of levels where p is prime there is a classical breakdown of the treatment degrees of freedom into components such as ab ab2 ab2 c each of p 1 degrees of freedom the disadvantages of this system are i the lack of canonical single degrees of freedom and ii the fact that the breakdown bears no relation to the contrasts typically of interest if all treatment factors are quantitative in this note we decompose the treatment degrees of freedom into single degrees of freedom and use these to show how appropriate choice of levels of quantitative factors enables quantitative contrasts to be completely unconfounded in classical designs

k circulant supersaturated designs a class of supersaturated designs called k circulant designs is explored these designs are constructed from cyclic generators by cycling k elements at a time the class of designs includes many es2 optimal designs some of which are already known and some of which are more efficient than known designs for model estimation under factor sparsity generators for the most efficient designs are listed and projection properties of some of the designs are explored we also illustrate that some k circulant supersaturated designs can be augmented with interaction columns to produce efficient designs for a larger number of factors or for estimating interactions

analysis of the constraint proposal method for two party negotiations abstract in the constraint proposal method a mediator locates points at which the two decision makers have joint tangent hyperplanes we give conditions under which these points are pareto optimal and we prove that under these conditions the mediator s problem has a solution in practice the mediator adjusts a hyperplane going through a reference point until the decision makers most preferred alternatives on the hyperplane coincide we give local convergence conditions for fixed point iteration as an adjustment process we also discuss the relationship of exchange economies and the constraint proposal method and the possible ways of using the method

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

on the existence of saturated and nearly saturated asymmetrical orthogonal arrays we develop a combinatorial condition necessary for the existence of a saturated asymmetrical orthogonal array of strength 2 this condition limits the choice of integral solutions to the system of equations in the bose bush approach and can thus strengthen considerably the bose bush approach as applied to a symmetrical part of such an array as a consequence several nonexistence results follow for saturated and nearly saturated orthogonal arrays of strength 2 one of these leads to a partial settlement of an issue left open in a paper by wu zhang and wang nonexistence of a class of saturated asymmetrical orthogonal arrays of strength 4 is briefly discussed

construction of nested space filling designs new types of designs called nested space filling designs have been proposed for conducting multiple computer experiments with different levels of accuracy in this article we develop several approaches to constructing such designs the development of these methods also leads to the introduction of several new discrete mathematics concepts including nested orthogonal arrays and nested difference matrices

2n l designs with weak minimum aberration since not all 2 n l fractional factorial designs with maximum resolution are equally good fries and hunter introduced the minimum aberration criterion for selecting good 2 n l fractional factorial designs with the same resolution we modify the concept of minimum aberration and define weak minimum aberration and show the usefulness of this new design concept using some techniques from finite geometry we construct 2 n l fractional factorial designs of resolution iii with weak minimum aberration further several families of 2 n l fractional factorial designs of resolution iii and iv with minimum aberration are obtained

iterative techniques for the nash solution in quadratic games with unknown parameters we study adaptive schemes for repeated quadratic nash games in a deterministic and a stochastic framework the convergence of the schemes is demonstrated under certain conditions

approximate representation of the pareto frontier in multiparty negotiations decentralized methods and privacy preservation abstract multiparty negotiations have drawn much research attention in recent years and an important problem is how to find a pareto optimal solution or the entire pareto frontier in a decentralized way privacy preservation is also important in negotiation analysis the main aim of this paper is to find an approximate representation of the pareto frontier in a decentralized manner and meanwhile all parties privacy can be effectively protected in this paper we propose a decentralized discrete time algorithm based on a weight sum method and the well known subgradient optimization algorithm where a mediator works as a coordinator to help negotiators the proposed algorithm is easily executable and it only requires the mediator to compute a weighted average of the noisy estimates received from negotiators and negotiators to follow a subgradient optimization iteration at this weighted average the proposed algorithm can generate an approximate pareto optimal solution for one particular weight vector and an approximate representation of the pareto frontier by varying appropriately weight vectors the approximation error between the obtained approximate representation and the pareto frontier can be controlled by the number of iterations and the step size moreover it also reveals that the proposed algorithm is privacy preserving as a result of the random disturbance technique and the weighted average scheme used in this algorithm

an approach to the construction of asymmetrical orthogonal arrays abstract use of asymmetrical orthogonal arrays oa s for planning industrial experiments with mixed levels has become increasingly popular in addition to applications to experimental investigations in many disciplines they can also be used in the balanced repeated replications method of inference from general stratified survey samples in this article we propose a general approach to the construction of asymmetrical oa s with economic run size and flexibility in the choice of factor levels as applications of this approach we construct several general classes of arrays that include numerous existing classes of arrays as special cases a large number of known asymmetrical oa s can be reproduced by our approach in a unified and simple manner many new arrays are obtained a list of asymmetrical oa s with moderate run size is given our approach consists of three steps we first construct an oa as the generalized kronecker sum of an oa and some difference matrices we then add to the constructed oa co

the idle column method design construction properties and comparisons taguchi s idle column method for constructing arrays is investigated and generalized a general construction method is proposed via a necessary and sufficient condition on two level orthogonal arrays to which the method is applicable a method is developed for identifying the idle column and pairs of columns in the arrays mixed two and three level idle column arrays with 64 or fewer runs are tabulated some guidelines are offered on when the idle column arrays should be used and when they should be replaced by orthogonal main effect plans or d optimal designs

optimal projective three level designs for factor screening and interaction detection orthogonal arrays oas are widely used in industrial experiments for factor screening suppose that only a few of the factors in the experiments turn out to be important an oa can be used not only for screening factors but also for detecting interactions among a subset of active factors in this article a set of optimality criteria is proposed to assess the performance of designs for factor screening projection and interaction detection and a three step approach is proposed to search for optimal designs combinatorial and algorithmic construction methods are proposed for generating new designs permutations of levels are used for improving the eligibility and estimation efficiency of the projected designs the techniques are then applied to search for best three level designs with 18 and 27 runs many new efficient and practically useful nonregular designs are found and their properties are discussed

homoclinic orbits in a parametrized saddle focus system abstract we consider a parametrized dynamical system with a saddle focus equilibrium point and which for one value of the parameter has a homoclinic orbit conditions on the eigenvalues for the equilibrium point together with transversality conditions imply the existence of an infinite discrete set of parameter values for which the system has a homoclinic orbit such systems arise in the study of nerve axon equations where a homoclinic orbit corresponds to a finite train of nerve impulses traveling at a velocity identified by the associated parameter value

permuting regular fractional factorial designs for screening quantitative factors fractional factorial designs are widely used in screening experiments they are often chosen by the minimum aberration criterion which regards factor levels as symbols for designs with quantitative factors however permuting the levels for one or more factors could alter their geometrical structures and statistical properties we provide a justification of the minimum aberration criterion for quantitative factors and study level permutations for regular fractional factorial designs in order to improve their efficiency for screening quantitative factors we show how regular designs can be linearly permuted to reduce contamination of nonnegligible interactions on the estimation of linear effects without increasing the run size we further show that such linear permutations are unique under the minimum aberration criterion and the best level permutations can be determined without an exhaustive search we establish additional theoretical results for three level designs and obtain the best level permutations for regular designs with 27 and 81 runs we illustrate the practical benefits of level permutation with an antiviral drug combination experiment

existence and construction of randomization defining contrast subspaces for regular factorial designs regular factorial designs with randomization restrictions are widely used in practice this paper provides a unified approach to the construction of such designs using randomization defining contrast subspaces for the representation of randomization restrictions we use finite projective geometry to determine the existence of designs with the required structure and develop a systematic approach for their construction an attractive feature is that commonly used factorial designs with randomization restrictions are special cases of this general representation issues related to the use of these designs for particular factorial experiments are also addressed

a distributed computation algorithm for solving portfolio problems with integer variables a portfolio problem with integer variables can facilitate the use of complex models including models containing discrete asset values transaction costs and logical constraints this study proposes a distributed algorithm for solving a portfolio program to obtain a global optimum for a portfolio problem with n integer variables the objective function first is converted into an ellipse function containing n separated quadratic terms next the problem is decomposed into m equal size separable programming problems solvable by a distributed computation system composed of m personal computers linked via the internet the numerical examples illustrate that the proposed method can obtain the global optimum effectively for large scale portfolio problems involving integral variables

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

tableaux a frequences marginales d ordre 2 proportionnelles abstract we study conditions for existence and we introduce methods of construction of some combinatorial configurations called proportional frequency arrays these arrays are used for planning factorial experiments when all interactions among the factors are supposed negligible and they provide orthogonal fractional factorial designs we are concerned here with constructing minimal or nearly minimal designs it is shown that only orthogonal arrays of strength 2 are of minimal size some conditions for existence are given for designs which are balanced arrays with one more run than the minimum several balanced arrays with two symbols providing designs of reduced size n 100 are also constructed

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

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

moment aberration projection for nonregular fractional factorial designs nonregular fractional factorial designs such as plackett burman designs are widely used in industrial experiments for run size economy and flexibility a novel criterion called moment aberration projection is proposed to rank and classify nonregular designs it measures the goodness of a design through moments of the number of coincidences between the rows of its projection designs the new criterion is used to rank and classify designs of 16 20 and 27 runs examples are given to illustrate that the ranking of designs is supported by other design criteria

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

blocked regular fractional factorial designs with minimum aberration this paper considers the construction of minimum aberration ma blocked factorial designs based on coding theory the concept of minimum moment aberration due to xu 2003 for unblocked designs is extended to blocked designs the coding theory approach studies designs in a row wise fashion and therefore links blocked designs with nonregular and supersaturated designs a lower bound on blocked wordlength pattern is established it is shown that a blocked design has ma if it originates from an unblocked ma design and achieves the lower bound it is also shown that a regular design can be partitioned into maximal blocks if and only if it contains a row without zeros sufficient conditions are given for constructing ma blocked designs from unblocked ma designs the theory is then applied to construct ma blocked designs for all 32 runs 64 runs up to 32 factors and all 81 runs with respect to four combined wordlength patterns

existence and stability of multiple impulse solutions of a nerve equation a piecewise linear partial differential equation which models the propagation of a nerve impulse along an axon is studied for the equation parameters used there are two solutions which represent solitary impulses traveling with fixed form one with a slower velocity c s1 than the velocity c f1 of the other we show that near these velocities there exist multiple impulse solutions and exhibit four such solutions each of which has two pulses the local stability of these solutions is analyzed the two solutions whose velocities are near c s1 demonstrate instabilities which indicate growth or decay of the separate pulses for one of the multiple impulse solutions with velocity near c s1 and for one of those with velocity near c f1 the second pulse deomonstrates an instability which indicates a change in the spacing between the two pulses the other solution with velocity near c f1 is stable

bifurcations of systems with structurally unstable homoclinic orbits and moduli of ω equivalence abstract bifurcations of both two dimensional diffeomorphisms with a homoclinic tangency and three dimensional flows with a homoclinic loop of an equilibrium state of saddle focus type are studied in one and two parameter families due to the well known impossibility of a complete study of such bifurcations the problem is restricted to the study of the bifurcations of the so called low round periodic orbits in this connection the idea of taking moduli continuous invariants of the topological conjugacy on the nonwandering set as the main control parameters together with the standard splitting parameter is proposed on this way new bifurcational effects are found which do not occur at a one parameter analysis in particular the density of cusp bifurcations is revealed

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

balanced repeated replications based on mixed orthogonal arrays summary for stratified samples with arbitrary numbers of primary sampling units per stratum one can divide the units in the stratum into two groups and then apply the balanced half samples method to the two groups thus formed the efficiency loss of the grouped balanced half samples variance estimator can be substantial use of a mixed orthogonal array whose numbers of symbols correspond to the numbers of units per stratum gives a set of balanced subsamples unlike that of gupta nigam 1987 the proposed method of analysis gives a consistent variance estimator and bias reduction for nonlinear statistics to further reduce the number of replicates use of nearly orthogonal arrays is considered the balanced half samples method mccarthy 1966 1969 is commonly used for estimating the variance of nonlinear statistics from stratified samples with two primary sampling units per stratum these samples arise naturally if deep stratification is desired as in some large scale surveys the method is extended gurney jewett 1975 to the case of p primary sampling units per stratum for prime p this extension for p 2 is not adopted in common practice since it requires a much larger number of replicates also in many survey designs the numbers of primary sampling units are unequal a common practice is to divide the units in the stratum into two groups and then to apply the balanced half samples method to the two groups thus formed this has gained popularity because the software for obtaining balanced half samples is readily available and the number of replicates required is more economical as shown in 2 the resulting variance estimators can be quite inefficient and their bias based on a conditional analysis can be considerable the conditional analysis also suggests a method of grouping to reduce the bias the degree of grouping depends on the tradeoff between computational economy and statistical efficiency if the efficiency loss from grouping is not justifiable one may draw replicates by using mixed orthogonal arrays with variable numbers of symbols to accommodate the different numbers of units or groups of units in the strata as long as an orthogonal array is used for drawing replicates we call the method balanced repeated replications in 3 we show that the analysis method of gupta nigam 1987 based on mixed orthogonal arrays leads to an inconsistent variance estimator for nonlinear statistics and propose a method that is valid for variance estimation and bias reduction

characterization of minimum aberration 2 sp n k designs in terms of their complementary designs a general result is obtained that relates the word length pattern of a 2 n k design to that of its complementary design by applying this result and using group isomorphism we are able to characterize minimum aberration 2 n k designs in terms of properties of their complementary designs the approach is quite powerful for small values of 2 n k n 1 in particular we obtain minimum aberration 2 n k designs with 2 n k n 1 1 to 11 for any n and k

orthogonal array based latin hypercubes abstract in this article we use orthogonal arrays oa s to construct latin hypercubes besides preserving the univariate stratification properties of latin hypercubes these strength r oa based latin hypercubes also stratify each r dimensional margin therefore such oa based latin hypercubes provide more suitable designs for computer experiments and numerical integration than do general latin hypercubes we prove that when used for integration the sampling scheme with oa based latin hypercubes offers a substantial improvement over latin hypercube sampling

topology of vibro impact systems in the neighborhood of grazing abstract the grazing bifurcation is considered for the newtonian model of vibro impact systems a brief review on the conditions sufficient for the existence of a grazing family of periodic solutions is given the properties of these periodic solutions are discussed a plenty of results on the topological structure of attractors of vibro impact systems is known however since the considered system is strongly nonlinear these attractors must be very sensitive to changes of parameters of the system on the other hand they are observed in experiments and numerical simulations we offer theorem 2 an approach which allows to explain this contradiction and give a new robust mathematical model of the non hyperbolic dynamics in a neighborhood of grazing

on the construction of asymmetrical orthogonal arrays general techniques for the construction of asymmetrical orthogonal arrays of strength 2 are presented these are then applied to special cases to obtain new families of such arrays among these are saturated main effect plans based on s m runs with factors at s nu i levels i 0 1 ldots r where m geq v r v 0 1 v i 1 divides v i i 1 2 ldots r and s is a prime power

construction of optimal multi level supersaturated designs author s xu hongquan wu cfj abstract a supersaturated design is a design whose run size is not large enough for estimating all the main effects the goodness of multi level supersaturated designs can be judged by the generalized minimum aberration criterion proposed by xu and wu 2001 optimal supersaturated designs are shown to have a periodic property and general methods for constructing optimal multilevel supersaturated designs are proposed inspired by the addelman kempthorne construction of orthogonal arrays optimal multi level supersaturated designs are given in an explicit form columns are labeled with linear or quadratic polynomials and rows are points over a finite field additive characters are used to study the properties of resulting designs some small optimal supersaturated designs of 3 4 and 5 levels are listed with their properties

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

distributed computation of pareto solutions in n player games the problem of computing pareto optimal solutions with distributed algorithms is considered inn player games we shall first formulate a new geometric problem for finding pareto solutions it involves solving joint tangents for the players objective functions this problem can then be solved with distributed iterative methods and two such methods are presented the principal results are related to the analysis of the geometric problem we give conditions under which its solutions are pareto optimal characterize the solutions and prove an existence theorem there are two important reasons for the interest in distributed algorithms first they can carry computational advantages over centralized schemes second they can be used in situations where the players do not know each others objective functions

connections between two level designs of resolutions iii and v resolution iii designs are resolution iii designs in which no two factor interactions are confounded with one another they arise naturally in the search for small composite designs and were first suggested by hartley 1959 new results given here link resolution iii designs to resolution v designs enabling passage between the two types of designs to be made this means that previously untabulated resolution iii designs can be derived directly from known resolution v designs for example a hartley type composite design can be based on a 27 1 iii design derived from a 26 1 v design the usual composite design is based on a 27 1 v design double the number of factorial runs the resolution iii designs can also be usefully modified for specific industrial applications box and jones 1989 moreover the maximum number of factors it is possible to accommodate in a resolution iii design of a given size can be obtained directly from the known maximum for resolution v designs of the same size

generating pareto solutions in a two party setting constraint proposal methods this paper presents a class of methods called constraint proposal methods for generating pareto optimal solutions in two party negotiations in these methods joint tangents of the decision makers value functions are searched by adjusting an artificial plane constraint the problem of generating pareto optimal solutions decomposes into ordinary multiple criteria decision making problems for the individual decision makers and into a coordination problem for an assisting mediator depending on the numerical iteration scheme used to solve the coordination problem different constraint proposal methods are obtained we analyze and illustrate the behaviour of some iteration schemes by numerical examples using both precise and imprecise answers from decision makers an example of a method belonging to the class under study is the ramona method that has been previously described from a practical point of view we present the underlying theory for it by describing it as a constraint proposal method and include some applications

constraint proposal method for computing pareto solutions in multi party negotiations abstract the constraint proposal method for computing pareto optimal solutions is extended to multi party negotiations in the method a neutral coordinator assists decision makers in finding pareto optimal solutions so that the elicitation of the decision makers value functions is not required during the procedure the decision makers have to indicate their most preferred points on different sets of linear constraints the method can be used to generate either one pareto optimal solution dominating the status quo solution of the negotiation or an approximation to the pareto frontier in the latter case a distributive negotiation among the efficient agreements can be carried out afterwards

minimum aberration two level split plot designs the treatment design portion of fractionated two level split plot designs is associated with a subset of the 2 n k fractional factorial designs the concept of aberration is then extended to these splitplot designs to compare designs two methods are presented for constructing two level minimumaberration split plot designs along with examples an extensive catalog of such designs is tabulated extensions to prime level designs and relations to inner outer arrays are also presented

optimal fractions of two level factorials under a baseline parameterization two level fractional factorial designs are considered under a baseline parameterization the criterion of minimum aberration is formulated in this context and optimal designs under this criterion are investigated the underlying theory and the concept of isomorphism turn out to be significantly different from their counterparts under orthogonal parameterization and this is reflected in the optimal designs obtained copyright 2012 oxford university press

fractional resolution and minimum aberration in blocked 2 n k designs systematic sources of variation can be reduced in fractional factorial experiments by grouping the runs into blocks this is accomplished through the use of blocking factors the concepts of resolution and minimum aberration design optimization criteria ordinarily used to rank unblocked fractional factorial designs are extended to such blocked fractional factorial designs by treating the treatment and blocking factors differently in terms of their contribution to word length in the defining contrast subgroup some limited theoretical results are derived and tables of minimumaberration blocked two level fractional factorial designs are presented and considered the relationship between clear effects effects that are estimable when higher order effects are assumed negligible and minimum aberration in the presence of blocking is discussed

construction of 2 m4 n designs via a grouping scheme on developpe une methode pour grouper les 2 k 1 effets factoriels dans un plan factoriel a deux niveaux dans des ensembles disjoints mutuellement s t st ou st est l interaction generalisee des effets s et t comme application on construit des tableaux orthogonaux oa 2 k 2 m 4 n 2 de taille 2 k m contraintes avec 2 niveaux et n contraintes avec 4 niveaux satisfaisant m 3n 2 k 1 et de puissance 2 le nombre maximum de contraintes avec 4 niveaux dans la construction ne peut plus etre ameliore dans ce sens le schema de groupement qu on donne est optimal on discute les avantages de la presente approche par rapport a d autres methodes de construction

on models with non rough poincare homoclinic curves abstract the possibility of an a priori complete description of finite parameter models including systems with structurally unstable poincare homoclinic curves is studied the main result reported here is that systems having a countable set of moduli of equivalence and systems having infinitely many degenerate periodic and homoclinic orbits are dense in the newhouse regions of non stability we discuss the question of correctly setting a problem for the analysis of models of such type

on the construction of minimal partially replicated orthogonal main effect plans in this article several methods are given for constructing orthogonal main effect plans that require a minimal number of runs and yet have a maximal number of repeated observations these designs yield an unbiased estimate of pure error and provide a means of testing the assumption of no interactions among main effects