the volume of gaussian states by information geometry we formulate the problem of determining the volume of the set of gaussian physical states in the framework of information geometry this is done by considering phase space probability distributions parametrized by their covariances and endowing the resulting statistical manifold with the fisher rao metric we then evaluate the volume of classical quantum and quantum entangled states for two mode systems showing chains of strict inclusions

d optimal 0 1 weighing designs for eight objects abstract let g m n max det w t w w m m n 0 1 a matrix w m m n 0 1 with det w t w g m n is called d optimal here we determine g m 8 for m large with the help of a variation of mitchell s detmax algorithm and describe the d optimal examples

notes on d optimal designs abstract the purpose of this paper is to exhibit new infinite families of d optimal 0 1 matrices we show that hadamard designs lead to d optimal matrices of size j mj and j 1 mj for certain integers j 3 mod 4 and all positive integers m for j a power of a prime and j 1 mod 4 supplementary difference sets lead to d optimal matrices of size j 2mj and j 1 2mj for all positive integers m we also show that for a given j and d sufficiently large about half of the entries in each column of a d optimal matrix are ones this leads to a new relationship between d optimality for 0 1 matrices and for 1 matrices known results about d optimal 1 matrices are then used to obtain new d optimal 0 1 matrices

geometry of gaussian quantum states we study the hilbert schmidt measure on the manifold of mixed gaussian states in multi mode continuous variable quantum systems an analytical expression for the hilbert schmidt volume element is derived its corresponding probability measure can be used to study typical properties of gaussian states it turns out that although the manifold of gaussian states is unbounded an ensemble of gaussian states distributed according to this measure still has a normalizable distribution of symplectic eigenvalues from which unitarily invariant properties can be obtained by contrast we find that for an ensemble of one mode gaussian states based on the bures measure the corresponding distribution cannot be normalized as important applications we determine the distribution and the mean value of von neumann entropy and purity for the hilbert schmidt measure

change based inference in attractor nets linear analysis one standard interpretation of networks of cortical neurons is that they form dynamical attractors computations such as stimulus estimation are performed by mapping inputs to points on the networks attractive manifolds these points represent population codes for the stimulus values however this standard interpretation is hard to reconcile with the observation that the firing rates of such neurons constantly change following presentation of stimuli we have recently suggested an alternative interpretation according to which computations are realized by systematic changes in the states of such networks over time this way of performing computations is fast accurate readily learnable and robust to various forms of noise here we analyze the computation of stimulus discrimination in this change based setting relating it directly to the computation of stimulus estimation in the conventional attractor based view we use a common linear approximation to compare the two methods and show that perfect performance at estimation implies chance performance at discrimination

construction of e s 2 optimal supersaturated designs booth and cox proposed the e s 2 criterion for constructing two level supersaturated designs nguyen technometrics 38 1996 69 73 and tang and wu canad j statist 25 1997 191 201 independently derived a lower bound for e s 2 this lower bound can be achieved only when m is a multiple of n 1 where m is the number of factors and n is the run size we present a method that uses difference families to construct designs that satisfy this lower bound we also derive better lower bounds for the case where the nguyen tang wu bound is not achievable our bounds cover more cases than a bound recently obtained by butler mead eskridge and gilmour j r stat soc ser b stat methodol 63 2001 621 632 new e s 2 optimal designs are obtained by using a computer to search for designs that achieve the improved bounds

population coding with correlation and an unfaithful model this study investigates a population decoding paradigm in which the maximum likelihood inference is based on an unfaithful decoding model umli this is usually the case for neural population decoding because the encoding process of the brain is not exactly known or because a simplified decoding model is preferred for saving computational cost we consider an unfaithful decoding model that neglects the pair wise correlation between neuronal activities and prove that umli is asymptotically efficient when the neuronal correlation is uniform or of limited range the performance of umli is compared with that of the maximum likelihood inference based on the faithful model and that of the center of mass decoding method it turns out that umli has advantages of decreasing the computational complexity remarkably and maintaining high level decoding accuracy moreover it can be implemented by a biologically feasible recurrent network pouget zhang deneve latham 1998 the effect of correlation on the decoding accuracy is also discussed

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

efficient nearly orthogonal and space filling latin hypercubes this article presents an algorithm for constructing orthogonal latin hypercubes given a fixed sample size in more dimensions than previous approaches in addition we detail a method that dramatically improves the space filling properties of the resultant latin hypercubes at the expense of inducing small correlations between the columns in the design matrix although the designs are applicable to many situations they were developed to provide department of defense analysts flexibility in fitting models when exploring high dimensional computer simulations where there is considerable a priori uncertainty about the forms of the response surfaces

a connection between uniformity and aberration in regular fractions of two level factorials summary we show a link between the two apparently unrelated areas of uniformity and minimum aberration with reference to regular fractions of two level factorials we derive an expression for the centred l2 discrepancy measure for uniformity in terms of the word length pattern this result indicates in particular excellent behaviour of minimum aberration designs with regard to uniformity and provides further justification for the popular criterion of minimum aberration

geometry and uncertainty in the context of the wigner weyl phase space formulation of quantum mechanics a version of the uncertainty relations invariant under affine canonical transformations is derived for a fixed wigner distribution function possessing a finite covariance directions of minimal uncertainty are found the geometry of the wigner ellipsoid and its legendre transform the dual wigner ellipsoid both of which are associated with the same covariance is discussed the results obtained are generalizations of the well known fact that for one degree of freedom the area of the wigner ellipse must be of order or larger instead of area which is an invariant only when n 1 these results involve poincare invariants of certain curves and surfaces

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

sliced orthogonal array based latin hypercube designs we propose an approach for constructing a new type of design called a sliced orthogonal array based latin hypercube design this approach exploits a slicing structure of orthogonal arrays with strength two and makes use of sliced random permutations such a design achieves one and two dimensional uniformity and can be divided into smaller latin hypercube designs with one dimensional uniformity sampling properties of the proposed designs are derived examples are given for illustrating the construction method and corroborating the derived theoretical results potential applications of the constructed designs include uncertainty quantification of computer models computer models with qualitative and quantitative factors cross validation and efficient allocation of computing resources supplementary materials for this article are available online

model robust two level designs using coordinate exchange algorithms and a maximin criterion we propose a candidate list free exchange algorithm that facilitates construction of exact model robust two level experiment designs in particular we investigate two model spaces previously considered in the literature the first assumes that all main effects and an unknown subset of two factor interactions are active but that the experimenter knows the number of active interactions the second assumes that an unknown subset of the main effects and all associated two factor interactions are active previous literature uses two criteria for design construction first maximize the number of estimable models then differentiate between designs equivalent in estimability by choosing the design with the highest average efficiency we adopt a similar strategy but 1 do not impose orthogonality or factor level balance constraints resulting in generally equal or larger numbers of estimable models and 2 use a flexible secondary criterion that maximizes the minimum efficiency we provide results fo

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

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

a new class of supersaturated designs supersaturated designs are useful in situations in which the number of active factors is very small compared to the total number of factors being considered in this article a new class of supersaturated designs is constructed using half fractions of hadamard matrices when a hadamard matrix of order n is used such a design can investigate up to n 2 factors in n 2 runs results are given for n 60 extension to larger n is straightforward these designs are superior to other existing supersaturated designs and are easy to construct an example with real data is used to illustrate the ideas

computing with continuous attractors stability and online aspects two issues concerning the application of continuous attractors in neural systems are investigated the computational robustness of continuous attractors with respect to input noises and the implementation of bayesian online decoding in a perfect mathematical model for continuous attractors decoding results for stimuli are highly sensitive to input noises and this sensitivity is the inevitable consequence of the system s neutral stability to overcome this shortcoming we modify the conventional network model by including extra dynamical interactions between neurons these interactions vary according to the biologically plausible hebbian learning rule and have the computational role of memorizing and propagating stimulus information accumulated with time as a result the new network model responds to the history of external inputs over a period of time and hence becomes insensitive to short term fluctuations also since dynamical interactions provide a mechanism to convey the prior knowledge of stimulus that is the information of the stimulus presented previously the network effectively implements online bayesian inference this study also reveals some interesting behavior in neural population coding such as the trade off between decoding stability and the speed of tracking time varying stimuli and the relationship between neural tuning width and the tracking speed

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

robustness of optimal designs for correlated random variables abstract suppose that y y i is a normal random vector with mean xb and covariance 2 i n where b is a p dimensional vector b j x x ij is an n p matrix with x ij 1 1 this corresponds to a factorial design with 1 1 representing low or high level respectively or corresponds to a weighing design with 1 1 representing an object j with weight b j placed on the left and right of a chemical balance respectively e optimal designs z are chosen that are robust in the sense that they remain e optimal when the covariance of y i y i is 0 for i i within a smaller class of designs similar results are obtained with respect to a general class of optimality criteria which include the a and d criteria

upper bounds on the number of columns in supersaturated designs we consider two level designs in this paper with the two levels denoted by 1 and 1 the run size n of a supersaturated design does not exceed its number of columns or factors m that is n m in a screening experiment although a large number of factors are studied the number of active factors is usually very small this assumption of effect sparsity box meyer 1986 is the rationale for using supersaturated designs booth cox 1962 was the first paper to consider deterministic construction of supersaturated designs three systematic construction methods were recently proposed and discussed in lin 1993 wu 1993 and tang wu 1997 and computer generation of supersaturated designs was considered by lin 1995 nguyen 1996 and li wu 1997 since n m supersaturated designs cannot be made orthogonal it is therefore desirable to have supersaturated designs which are as close to orthogonal as possible the most commonly used measure of non orthogonality among the columns of a supersaturated design is

comparison of design optimality criteria of reduced models for response surface designs in the hypercube results from the comparison of d g and a efficiencies and the scaled average prediction variance iv criterion are presented for the central composite small composite notz hoke box draper and computer generated designs these design optimality criteria are evaluated over the cuboidal design region for three four and five design variables

peres horodecki separability criterion for continuous variable systems the peres horodecki criterion of positivity under partial transpose is studied in the context of separability of bipartite continuous variable states the partial transpose operation admits in the continuous case a geometric interpretation as mirror reflection in phase space this recognition leads to uncertainty principles stronger than the traditional ones to be obeyed by all separable states for all bipartite gaussian states the peres horodecki criterion turns out to be a necessary and sufficient condition for separability

another look at first order saturated designs the p efficient designs the problem of constructing first order saturated designs that are optimal in some sense has received a great deal of attention in the literature since these saturated designs are frequently used in screening situations the focus will be on the potential projective models rather than the full model this article discusses some practical concerns in choosing a design and presents some first order saturated designs having two desirable properties near equal occurrence and near orthogonality these saturated designs are shown to be reasonably efficient for estimating the parameters of projective submodels and thus are called p efficient designs comparisons with the efficiency of d optimal designs are given for designs for all n from 3 to 30

on the bures volume of separable quantum states we obtain two sided estimates for the bures volume of an arbitrary subset of the set of n n density matrices in terms of the hilbert schmidt volume of that subset for general subsets our results are essentially optimal for large n as applications we derive in particular nontrivial lower and upper bounds for the bures volume of sets of separable states and for sets of states with positive partial transpose

bound entangled gaussian states we discuss the entanglement properties of bipartite states with gaussian wigner functions for the separability and the positivity of the partial transpose we establish explicit necessary and sufficient criteria in terms of the covariance matrix of the state it is shown that for systems composed of a single oscillator for alice and an arbitrary number for bob positivity of the partial transpose implies separability however this implication fails with two oscillators on each side as we show by constructing a five parameter family of bound entangled gaussian states

uniform design theory and application a uniform design ud seeks design points that are uniformly scattered on the domain it has been popular since 1980 a survey of ud is given in the first portion the fundamental idea and construction method are presented and discussed and examples are given for illustration it is shown that ud s have many desirable properties for a wide variety of applications furthermore we use the global optimization algorithm threshold accepting to generate ud s with low discrepancy the relationship between uniformity and orthogonality is investigated it turns out that most ud s obtained here are indeed orthogonal

majorization framework for balanced lattice designs this paper aims to generalize and unify classical criteria for comparisons of balanced lattice designs including fractional factorial designs supersaturated designs and uniform designs we present a general majorization framework for assessing designs which includes a stringent criterion of majorization via pairwise coincidences and flexible surrogates via convex functions classical orthogonality aberration and uniformity criteria are unified by choosing combinatorial and exponential kernels a construction method is also sketched out

approximate model spaces for model robust experiment design optimal designs depend upon a prespecified model form a popular and effective model robust alternative is to design with respect to a set of models instead of just one however model spaces associated with experiments of interest are often prohibitively large and so algorithmically generated designs are infeasible here we present a simple method that largely eliminates this problem by choosing a small set of models that approximates the full set and finding designs that are explicitly robust for this small set we build our procedure on a restricted columnwise pairwise algorithm and explore its effectiveness for two model spaces in the literature for smaller full model spaces we find that the designs constructed with the new method compare favorably with robust designs that use the full model space with construction times reduced by orders of magnitude we also construct designs that heretofore have been unobtainable due to the size of their model spaces supplementary material available online

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

dualistic differential geometry of positive definite matrices and its applications to related problems abstract analysis on the set of positive definite matrices is involved in many engineering problems we develop a differential geometric theory of the set of positive definite matrices by means of a specific class of connections introduced into it consequently various dualistic aspects of the set are elucidated next using the theory we derive new results and interesting geometrical interpretations for matrix approximation positive definite matrix completion and linear matrix inequality problems

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

largest j simplices in d cubes some relatives of the hadamard maximum determinant problem abstract this paper studies the computationally difficult problem of finding a largest j dimensional simplex in a given d dimensional cube the case in which j d is of special interest for it is equivalent to the hadamard maximum determinant problem it has been solved for infinitely many values of d but not for d 14 the subcase in which j d 3 mod 4 subsumes the famous problem on the existence of hadamard matrices the known results for the case j d are here summarized and used but the main focus is on fixed small values of j when j 1 the problem is trivial and when j 2 or j 3 it is here solved completely i e for all d beyond that the results are fragmentary but numerous and they lead to several attractive conjectures some other problems involving simplices in cubes are mentioned and the relationship of largest simplices to d optimal weighing designs is discussed

a general criterion for factorial designs under model uncertainty motivated by two industrial experiments in which rather extreme prior knowledge was used to choose the design we show that the qb criterion which aims to improve the estimation in as many models as possible by incorporating experimenters prior knowledge along with an approximation to the as criterion is more general and has a better statistical interpretation than many standard criteria the generalization and application of the criterion to different types of designs are presented the relationships between qb and other criteria for different situations are explored it is shown that the e s2 criterion is a special case of qb and several aberration type criteria are limiting cases of our criterion so that qb provides a bridge between alphabetic optimality and aberration the two case studies illustrate the potential benefits of the qb criterion r programs for calculating qb are available online as supplemental materials

better subset regression this paper studies the relationship between model fitting and screening performance to find efficient screening methods for high dimensional linear regression models under a sparsity assumption we show in a general asymptotic setting that a subset that includes the true submodel always yields a smaller residual sum of squares than those that do not to seek such a subset we consider the optimization problem associated with best subset regression an em algorithm known as orthogonalizing subset screening and its accelerated version are proposed for searching for the best subset although the algorithms do not always find the best subset their monotonicity makes the subset fit the data better than initial subsets and thus the subset can have better screening performance asymptotically simulation results show that our methods are very competitive

generating systematic supersaturated designs practitioners are routinely faced with distinguishing between factors that have real effects and those whose apparent effects are due to random error when there are many factors the usual advice given is to run so called main effect designs resolution iii designs in the orthogonal case that require at least k 1 runs for investigating k factors this may be wasteful however if the goal is only to detect those active factors this is particularly true when the number of factors is large in such situations a supersaturated design can often save considerable cost a supersaturated design is a fraction of a factorial design composed of n observations where n k 1 when such a design is used the abandonment of orthogonality is inevitable this article examines the maximum number of factors that can be accommodated when the degree of the nonorthogonality is specified furthermore interesting properties of systematic supersaturated designs are revealed for example such a design may be adequate

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

new e s2 optimal supersaturated designs constructed from incomplete block designs we present a method for constructing two level supersaturated designs ssds from incomplete block designs a lower bound of e s2 that also covers the case of odd run sizes is given this bound is attained by ssds constructed from balanced incomplete block designs we study ssds that can be constructed from regular graph designs when balanced incomplete block designs do not exist a computer search is conducted to find ssds with 5 n 50 and n m 2n that can be constructed from regular graph designs where m is the number of factors and n is the run size many ssds derived from regular graph designs are optimal the best e s2 optimal ssds with respect to additional optimality criteria are tabulated some notes on the construction of saturated designs also are given

projective three level main effects designs robust to model uncertainty this paper is concerned with designing experiments under the assumption that an analysis strategy is used that considers interactions in addition to main effects a criterion which averages an approximation to as efficiency over lower dimensional projections of the design is introduced to compare designs a columnwise design procedure is used to construct three level designs for six factors in 18 runs the projection efficiencies of these designs are explored and compared with designs obtained from the l 18 orthogonal array results are also given for designs with 14 and 17 runs

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

optimal supersaturated designs we consider screening experiments where an investigator wishes to study many factors using fewer observations our focus is on experiments with two level factors and a main effects model with intercept since the number of parameters is larger than the number of observations traditional methods of inference and design are unavailable in 1959 box suggested the use of supersaturated designs and in 1962 booth and cox introduced measures for efficiency of these designs including e s2 which is the average of squares of the off diagonal entries of the information matrix ignoring the intercept for a design to be e s2 optimal the main effect of every factor must be orthogonal to the intercept factors are balanced and among all designs that satisfy this condition it should minimize e s2 this is a natural approach since it identifies the most nearly orthogonal design and orthogonal designs enjoy many desirable properties including efficient parameter estimation factor balance in an e s2 optimal d

robustness of a optimal designs abstract suppose that y y i is a normal random vector with mean xb and covariance 2 i n where b is a p dimensional vector b j x x ij is an n p matrix a optimal designs x are chosen from the traditional set d of a optimal designs for 0 such that x is still a optimal in d when the components y i are dependent i e for i i the covariance of y i y i is with 0 such designs depend on the sign of the general results are applied to x x ij where x ij 1 1 this corresponds to a factorial design with 1 1 representing low level or high level respectively or corresponds to a weighing design with 1 1 representing an object j with weight b j being weighed on the left and right of a chemical balance respectively

hidden projection properties of some nonregular fractional factorial designs and their applications in factor screening often only a few factors among a large pool of potential factors are active under such assumption of effect sparsity in choosing a design for factor screening it is important to consider projections of the design onto small subsets of factors cheng showed that as long as the run size of a two level orthogonal array of strength two is not a multiple of 8 its projection onto any four factors allows the estimation of all the main effects and two factor interactions when the higher order interactions are negligible this result applies for example to all plackett burman designs whose run sizes are not multiples of 8 it is shown here that the same hidden projection property also holds for paley designs of sizes greater than 8 even when their run sizes are multiples of 8 a key result is that such designs do not have defining words of length three or four applications of this result to the construction of e s 2 optimal supersaturated designs are also discussed in particular certain designs constructed by using wu s method are shown to be e s 2 optimal the article concludes with some three level designs with good projection properties

catching homologies by geometric entropy abstract a geometric entropy is defined in terms of the riemannian volume of the parameter space of a statistical manifold associated with a given network as such it can be a good candidate for measuring networks complexity here we investigate its ability to single out topological features of networks proceeding in a bottom up manner first we consider small size networks by analytical methods and then large size networks by numerical techniques two different classes of networks the random graphs and the scale free networks are investigated computing their betti numbers and then showing the capability of geometric entropy of detecting homologies

a general method of constructing e s2 optimal supersaturated designs there has been much recent interest in supersaturated designs and their application in factor screening experiments supersaturated designs have mainly been constructed by using the e s 2 optimality criterion originally proposed by booth and cox in 1962 however until now e s 2 optimal designs have only been established with certainty for n experimental runs when the number of factors m is a multiple of n 1 and in adjacent cases where m q n 1 r r 2 q an integer a method of constructing e s 2 optimal designs is presented which allows a reasonably complete solution to be found for various numbers of runs n including n 8 12 16 20 24 32 40 48 64

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

maximum likelihood estimation of models for residual covariance in spatial regression we describe the maximum likelihood method for fitting the linear model when residuals are correlated and when the covariance among the residuals is determined by a parametric model containing unknown parameters observations are assumed to be gaussian we give conditions which ensure consistency and asymptotic normality of the estimators our main concern is with the analysis of spatial data and in this context we describe some simulation experiments to assess the small sample behaviour of estimators we also discuss an application of the spectral approximation to the likelihood for processes on a lattice

construction of supersaturated designs through partially aliased interactions summary an n x n hadamard matrix can be used to construct a saturated 2 n 1 design with n runs furthermore if an interaction column for two of the columns of the matrix is not fully aliased with any column of the matrix this interaction column can be used as a supplementary column for studying an additional factor for some small hadamard matrices studied by plackett burman 1946 the number of such interaction columns is very large thus allowing the construction of supersaturated designs whose number of factors far exceeds the number of runs a general method of construction along these lines is proposed the efficiency of the constructed designs is studied by using three criteria

quantifying networks complexity from information geometry viewpoint we consider a gaussian statistical model whose parameter space is given by the variances of random variables underlying this model we identify networks by interpreting random variables as sitting on vertices and their correlations as weighted edges among vertices we then associate to the parameter space a statistical manifold endowed with a riemannian metric structure that of fisher rao going on in analogy with the microcanonical definition of entropy in statistical mechanics we introduce an entropic measure of networks complexity we prove that it is invariant under networks isomorphism above all considering networks as simplicial complexes we evaluate this entropy on simplexes and find that it monotonically increases with their dimension

blocking in compound dispersion experiments in quality design a dispersion experiment attempts to estimate the effects of control factors on the dispersion introduced by error factors that is the effect of product design on the stability of the performance of the product as its operating environment changes in conducting a dispersion experiment it is important to distinguish the sources of dispersion that one wishes to control from extraneous sources of dispersion so blocking is often necessary this is especially true when the quality or utility of a product is appraised subjectively as in conjoint analysis compound designs for dispersion experiments are orthogonal array designs that generalize taguchi s direct product designs compared to direct product designs compound designs are often stronger for a given size or smaller for a given strength this article discusses blocked compound dispersion experiments providing that blocks form an orthogonal array of strength 1 for the error factors dispersion within blocks may be pooled to estima

a general theory of minimum aberration and its applications minimum aberration is an increasingly popular criterion for comparing and assessing fractional factorial designs and few would question its importance and usefulness nowadays in the past decade or so a great deal of work has been done on minimum aberration and its various extensions this paper develops a general theory of minimum aberration based on a sound statistical principle our theory provides a unified framework for minimum aberration and further extends the existing work in the area more importantly the theory offers a systematic method that enables experimenters to derive their own aberration criteria our general theory also brings together two seemingly separate research areas one on minimum aberration designs and the other on designs with requirement sets to facilitate the design construction we develop a complementary design theory for quite a general class of aberration criteria as an immediate application we present some construction results on a weak version of this class of criteria

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