a work time optimal algorithm for computing all string covers abstract in recent study of repetitive structures of strings generalized notions of periods have been introduced a typical regularity the period u of a given string x grasps the repetitiveness of x since x is a prefix of a string constructed by concatenations of u a substring w of x is called a cover of x if x can be constructed by concatenations and superpositions of w the notion cover is a generalization of periods in the sense that superpositions as well as concatenations are considered to define it whereas only concatenations are considered for periods we consider the all covers problem i e that of computing all the covers of a given string of length n we present an optimal o log log n time crcw pram algorithm for the all covers problem since there is an log log n lower bound on the time complexity of the all covers problem our algorithm is work time optimal

some performances of local bivariate quadratic c 1 quasi interpolating splines on nonuniform type 2 triangulations we investigate spline quasi interpolants defined by c1 bivariate quadratic b splines on nonuniform type 2 triangulations and by discrete linear functionals based on a fixed number of triangular mesh points either in the support or close to the support of such b splines we show they can approximate a real function and its partial derivatives up to an optimal order and we derive local and global upper bounds we also present some numerical and graphical results

structural modeling and psychometrika an historical perspective on growth and achievements the field of linear structural equation modeling with continuous variables is reviewed trends in psychometric theory and data analysis across the five decades of publication ofpsychometrika are discussed especially the clarification of concepts of population and sample explication of the parametric structure of models delineation of concepts of exploratory and confirmatory data analysis expansion of statistical theory in psychometrics estimation via optimization of an explicit objective function and implementation of general function minimization methods developments in the ideas of factor analysis latent variables as well as structural and causal modeling are noted some major conceptual achievements involving general covariance structure representations multiple population models and moment structures are reviewed the major statistical achievements of normal theory generalized least squares estimation elliptical and distribution free estimation and higher moment estimation are discussed computer programs that implement some of the theoretical developments are described

on the approximation power of bivariate quadratic c splines abstract in this paper we investigate the approximation power of local bivariate quadratic c1 quasi interpolating q i spline operators with a four directional mesh in particular we show that they can approximate a real function and its partial derivatives up to an optimal order and we derive local and global upper bounds both for the errors and for the spline partial derivatives in the case the spline is more differentiable than the function then such general results are applied to prove new properties of two interesting q i spline operators proposed and partially studied in chui and wang sci sinica xxvii 1984 1129 1142

the random adversary a lower bound technique for randomized parallel algorithms the random adversary technique is a general method for proving lower bounds on randomized parallel algorithms the bounds apply to the number of communication steps and they apply regardless of the processors instruction sets the lengths of messages etc this paper introduces the random adversary technique and shows how it can be used to obtain lower bounds on randomized parallel algorithms for load balancing compaction padded sorting and finding hamiltonian cycles in random graphs using the random adversary technique we obtain the first lower bounds for randomized parallel algorithms which are provably faster than their deterministic counterparts specifically for load balancing and related problems

minimization of a class of matrix trace functions by means of refined majorization a procedure is described for minimizing a class of matrix trace functions the procedure is a refinement of an earlier procedure for minimizing the class of matrix trace functions using majorization it contains a recently proposed algorithm by koschat and swayne for weighted procrustes rotation as a special case a number of trial analyses demonstrate that the refined majorization procedure is more efficient than the earlier majorization based procedure

weighted least squares fitting using ordinary least squares algorithms a general approach for fitting a model to a data matrix by weighted least squares wls is studied this approach consists of iteratively performing steps of existing algorithms for ordinary least squares ols fitting of the same model the approach is based on minimizing a function that majorizes the wls loss function the generality of the approach implies that for every model for which an ols fitting algorithm is available the present approach yields a wls fitting algorithm in the special case where the wls weight matrix is binary the approach reduces to missing data imputation

fast parallel string prefix matching an o log log m time n log mlog log m processor crcw pram algorithm for the string prefix matching problem over general alphabets is presented the algorithm can also be used to compute the kmp failure function in o log log m time on m log mlog log m processors these results improve on the running time of the best previous algorithm for both problems which was o log m while preserving the same number of operations

fundamental solutions for multivariate difference equations soit b une fonction a support compact definie sur le reseau entier z a on considere l equation aux diferences b a k j zd b k j a j f k k z d

a lower bound for parallel string matching this paper presents an omega log log m lower bound on the number of rounds necessary for finding occurrences of a pattern string p 1 m in a text string t 1 2m in parallel using m comparisons in each round the bound is within a constant factor of the fastest algorithm for this problem d breslauer and z galil siam j comput 19 1990 pp 1051 1058 and also holds for an m processor crcw pram in the case of a general alphabet consequently the paper derives the parallel complexity of the string matching problem using p processors for general alphabets which is theta frac m p if p leq frac m log log m theta log log m if frac m log log m leq p leq m theta log log 2p m p if m leq p leq m 2 theta 1 if p geq m 2 or in short theta lceil frac m p rceil log log lceil 1 p m rceil 2p

fitting longitudinal reduced rank regression models by alternating least squares an alternating least squares method for iteratively fitting the longitudinal reduced rank regression model is proposed the method uses ordinary least squares and majorization substeps to estimate the unknown parameters in the system and measurement equations of the model in an example with cross sectional data it is shown how the results conform closely to results from eigenanalysis optimal scaling of nominal and ordinal variables is added in a third substep and illustrated with two examples involving cross sectional and longitudinal data

optimal bounds for decision problems on the crcw pram optimal o log n log log n lower bounds on the time for crcw prams with polynomially bounded numbers of processors or memory cells to compute parity and a number of related problems are proven a strict time hierarchy of explicit boolean functions of n bits on such machines that holds up to o log n log log n time is also exhibited that is for every time bound t within this range a function is exhibited that can be easily computed using polynomial resources in time t but requires more than polynomial resources to be computed in time t 1 finally it is shown that almost all boolean functions of n bits require log n log log n o 1 time when the number of processors is at most polynomial in n the bounds do not place restrictions on the uniformity of the algorithms nor on the instruction sets of the machines

parallel detection of all palindromes in a string this paper presents two efficient concurrent read concurrent write parallel algorithms that find all palindromes in a given string 1 1 an o log n time n processor algorithm over general alphabets in the case of constant size alphabets the algorithm requires only nlog n processors and thus achieves an optimalspeedup 2 2 an o log log n time n log nloglog n processor algorithm over general alphabets this is the fastest possible time with the number of processors used these new results improve on the known parallel palindrome detection algorithms by using smaller auxiliary space and either by making fewer operations or by achieving a faster running time

asymptotic properties of estimators for autoregressive models with errors in variables let x t t z be an observable strictly stationary sequence of random variables and let x t u t e t where u t is an ar p and e t is a strictly stationary sequence representing errors of measurement in x t with e e 1 0 under some broad assumptions on e t we establish the consistency properties as well as the rates of convergence for the standard estimators for the autoregressive parameters computed from a set of modified yule walker equations

parallel two dimensional witness computation an optimal parallel crcw pram algorithm to compute witnesses for all non period vectors of an m1 m2 pattern is given the algorithm takes o log log m time and does o m1 m2 work where m max m1 m2 this yields a work optimal algorithm for 2d pattern matching which takes o log log m preprocessing time and o 1 text processing time

an optimal o log n time parallel string matching algorithm an optimal o log log n time parallel algorithm for string matching on crow pram is presented it improves previous results of galil inform and control 67 1985 pp 144 157 and vishkin inform and control 67 1985 pp 91 113

interpolation by multivariate splines a general interpolation scheme by multivariate splines at regular sample points is introduced this scheme guarantees the local optimal order of approximation to sufficiently smooth data functions a discussion on numerical implementation is included 1 introduction in this paper we introduce a very general interpolation scheme by multivariate splines based on the quasi interpolation formulas devel oped in 3 we show that the interpolating multivariate splines so obtained give the optimal order of approximation to sufficiently smooth functions let q be a nonnegative locally supported piecewise polynomial function sym metric with respect to the origin and s the linear span of all the translates q j j e z8 of q hence s is a multivariate spline space on a certain grid partition a with certain smoothness joining conditions and of certain total degree induced by q denote by q the fourier transform of q we assume that q is normalized that is

optimal off line detection of repetitions in a string an algorithm is presented to detect within optimal time o n log n and space o n off line on a ram all of the distinct repetitions in a given textstring on a finite alphabet the proposed strategy is self contained as it depends more heavily on algorithmic design considerations than on the combinatorial properties of the output it is based on a new data structure the leaf tree which is particularly suited to exploit simple properties of the suffix tree associated with the string to be analyzed

expected computation time for hamiltonian path problem one way to cope with an np hard problem is to find an algorithm that is fact on average with respect to a natural probability distribution on inputs we consider from that point of view the hamilto

evaluation of the distribution function of the limited information maximum likelihood estimator the distributions of the limited information maximum likelihood estimator for the coefficient of one endogenous variable are evaluated numerically tables are given for enough values of the parameters to cover all cases of interests comparisons are made with the two stage least squares estimator

the prejudices of least squares principal components and common factors schemes we prove mathematically that the least squares regression scheme is of little use for identification from inexact data even in the low noise case its results depend solely on the prejudice concerning which subsets of variables are chosen as regressands and which as regressors from a given set of data variables in practice least squares regression results are always biased and depend on the relative noise levels while even the signs of the estimates are completely determined by the arbitrary choice of the regressands if the number of underlying relationships is misspecified the principal components or statistical common factor scheme fares a similar fate since the choice of how many principal components or common factors to retain is essentially prejudiced and not determined by the data both schemes produce artificial and unexplained correlations among the residuals for the principal components scheme this occurs because it usually violates wilson s inequality a fortiori we prove exactly why in practice factor indeterminancy occurs the exact ideal multiple common factor scheme of frisch and thurstone has not yet been solved except for small numbers six and less of data variables

gensvm a generalized multiclass support vector machine traditional extensions of the binary support vector machine svm to multiclass problems are either heuristics or require solving a large dual optimization problem here a generalized multiclass svm is proposed called gensvm in this method classification boundaries for a k class problem are constructed in a k 1 dimensional space using a simplex encoding additionally several different weightings of the misclassification errors are incorporated in the loss function such that it generalizes three existing multiclass svms through a single optimization problem an iterative majorization algorithm is derived that solves the optimization problem without the need of a dual formulation this algorithm has the advantage that it can use warm starts during cross validation and during a grid search which significantly speeds up the training phase rigorous numerical experiments compare linear gensvm with seven existing multiclass svms on both small and large data sets these comparisons show that the proposed method is competitive with existing methods in both predictive accuracy and training time and that it significantly outperforms several existing methods on these criteria

the asymptotic covariance matrix of maximum likelihood estimates in factor analysis the case of nearly singular matrix of estimates of unique variances this paper is concerned with the asymptotic covariance matrix acm of maximum likelihood estimates mles of factor loadings and unique variances when one element of mles of unique variances is nearly zero i e the matrix of mles of unique variances is nearly singular in this situation standard formulas break down we give explicit formulas for the acm of mles of factor loadings and unique variances that could be used even when an element of mles of unique variances is very close to zero we also discuss an alternative approach using the augmented information matrix under a nearly singular matrix of mles of unique variances and derive the partial derivatives of the alternative constraint functions with respect to the elements of factor loadings and unique variances 2000 elsevier science inc all rights reserved ams classification 62h25 62f12

shape preserving quasi interpolation and interpolation by box spline surfaces this paper is devoted to the study of shape preserving approximation and interpolation of functions by box spline surfaces on three and four directional meshes the properties of positivity monotonicity and convexity are considered a characterization of the grid spacing is given which guarantees the preservation of these properties for functions in certain lipschitz classes

optimal parallel algorithms for string matching let wram pram be a parallel computer with p processors rams which share a common memory and are allowed simultaneous reads and writes only simultaneous reads the only type of simultaneous writes allowed is a simultaneous and a subset of the processors may write 0 simultaneously into the same memory cell let t be the time bound of the computer we design below families of parallel algorithms that solve the string matching problem with inputs of size n n is the sum of lengths of the pattern and the text and have the following performance in terms of p t and n 1 for wram pt o n for p n log n i e t log n 2 for pram pt o n for p n log 2 n i e t log 2 n 3 for wram t constant for p n 1 e and any e 0 4 for wram t o log n log log n for p n similar families are also obtained for the problem of finding all initial palindromes of a given string

cardinal interpolation by multivariate splines the purpose of this paper is to investigate cardinal interpolation using locally supported piecewise polynomials in particular the notion of a commutator is introduced and its connection with the marsden identity is observed the order of a commutator is shown to be equivalent to the strang and fix conditions that arise in the study of the local approxima tion orders using quasi interpolants we also prove that scaled cardinal interpolants give these local approximation orders introduction cardinal interpolation by bivariate box splines was first studied by de boor hollig and riemenschneider 3 the purpose of our paper is to investigate the cardinal interpolation problem from a different point of view in particular the notion of a commutator is introduced it will be shown that this notion generalizes the marsden identity for univariate splines to the multivariate setting the order of a commutator will be shown to be equivalent to the strang and fix conditions used in the study of the order of controlled approximation by dahmen and micchelli 8 or local approximation by de boor and jia 4 an application to obtain approximation orders through the constructive method of scaled cardinal interpolation will also be studied in this paper 1 preliminaries this section consists of preliminary material for multivariate cardinal interpolation our approach is motivated by the work in 5 and 13 where cardinal interpolation in l2 was connected with certain convolution operators lr let z denote the set of integers and z the nonnegative ones for any given complex sequence by

fast parallel space allocation estimation and integer sorting abstract the following problems are shown to be solvable in o log n time with optimal speedup with high probability on a randomized crcw pram using o n space space allocation given nonnegative integers allocate nonoverlapping blocks of consecutive memory cells of sizes from a base segment of consecutive memory cells estimation given integers in the range 1 compute good estimates of the number of occurrences of each value in the range 1 semisorting given integers in the range 1 store the integers 1 in an array of cells such that for all 1 all elements of 1 and occur together separated only by empty cells integer chain sorting given integers in the range 1 construct a linked list containing the integers 1 such that for all 1 if precedes in the list then moreover given slightly superlinear processor and space bounds these problems or variations of them can be solved in constant time with high probability as a corollary of the integer chain sorting result it follows that n integers in the range 1 n can be sorted in o log n log log n time with optimal speedup with high probability

two stage instrumental variables estimators for the nonlinear errors in variables model abstract estimation for the nonlinear functional errors in variables model is considered under the assumption that instrumental variables are available the approximate bias in the ordinary instrumental variable estimator due to the nonlinearity of the relationship is derived utilizing the nonlinearity of the relationship an estimator of the error covariance matrix is introduced using the error covariance matrix estimator two types of two stage instrumental variable estimators are proposed the two two stage estimators do not have the asymptotic bias due to the nonlinearity a monte carlo experiment also shows the superiority of the two stage estimators over the ordinary estimator

quasiperiodicity and string covering in this paper we study word regularities and in particular extensions of the notion of the word period quasiperiodicity covers and seeds we present overviews of algorithms for computing the quasiperiodicity the covers and the seeds of a given word we also present an overview of an algorithm that finds maximal word factors with the above regularities finally we show how fine and wilf s theorem fails if we try to extend it directly to quasiperiodicity as well as a new property on concatenation of periodic words

transducers and repetitions the factor transducer of a word associates to each of its factors or subwords their first occurrence optimal bounds on the size of minimal factor transducers together with an algorithm for building them are given analogue results and a simple algorithm are given for the case of subsequential suffix transducers algorithms are applied to repetition searching in words le transducteur des facteurs d un mot associe a chacun de ses facteurs leur premiere occurrence on donne des bornes optimales sur la taille du transducteur minimal d un most ainsi qu un algorithme pour sa construction on donne des resultats analogues et un algorithme simple dans le cas du transducteur sous sequentiel des suffixes d un mot on donne une application a la detection de repetitions dans les mots

a multivariate reduced rank growth curve model with unbalanced data a multivariate reduced rank growth curve model is proposed that extends the univariate reducedrank growth curve model to the multivariate case in which several response variables are measured over multiple time points the proposed model allows us to investigate the relationships among a number of response variables in a more parsimonious way than the traditional growth curve model in addition the method is more flexible than the traditional growth curve model for example response variables do not have to be measured at the same time points nor the same number of time points it is also possible to apply various kinds of basis function matrices with different ranks across response variables it is not necessary to specify an entire set of basis functions in advance examples are given for illustration

optimal parallel two dimension text searching on a crew pram4 abstract we present a parallel algorithm for two dimensional text searching over a general alphabet this algorithm is optimal in two ways first the total number of operations on the text is linear second the algorithm takes timeo log m on a crew pram wheremis the length of the longest dimension of the pattern thus matching the lower bound for string matching on a pram without concurrent writes on a crcw the algorithm runs in timeo log log m

multivariate analysis with linearizable regressions we study the class of multivariate distributions in which all bivariate regressions can be linearized by separate transformation of each of the variables this class seems more realistic than the multivariate normal or the elliptical distributions and at the same time its study allows us to combine the results from multivariate analysis with optimal scaling and classical multivariate analysis in particular a two stage procedure which first scales the variables optimally and then fits a simultaneous equations model is studied in detail and is shown to have some desirable properties

approximate periods of strings the study of approximately periodic strings is relevant to diverse applications such as molecular biology data compression and computer assisted music analysis here we study different forms of approximate periodicity under a variety of distance functions we consider three related problems for two of which we derive polynomial time algorithms we then show that the third problem is np complete

em algorithms for ml factor analysis the details of em algorithms for maximum likelihood factor analysis are presented for both the exploratory and confirmatory models the algorithm is essentially the same for both cases and involves only simple least squares regression operations the largest matrix inversion required is for aq q symmetric matrix whereq is the matrix of factors the example that is used demonstrates that the likelihood for the factor analysis model may have multiple modes that are not simply rotations of each other such behavior should concern users of maximum likelihood factor analysis and certainly should cast doubt on the general utility of second derivatives of the log likelihood as measures of precision of estimation

estimating linear statistical relationships this paper on estimating linear statistical relationships includes three lectures on linear functional and structural relationships factor analysis and simultaneous equations models the emphasis is on relating the several models by a general approach and on the similarity of maximum likelihood estimators under normality in the different models in the first two lectures the observable vector is decomposed into a systematic part and a random error the systematic part satisfies the linear relationships estimators are derived for several cases and some of their properties given estimation of the coefficients of a single equation in a simultaneous equations model is shown to be equivalent to estimation of linear functional relationships

computing the λ covers of a string given a string x of length n and an integer constant l the l cover problem is defined to be the identification of all the sets of l substrings each of equal length that cover x this problem can be solved by a general algorithm in o n 2 time for constant alphabet size we also generalize the l cover problem whereby a set of l substrings of different lengths are considered which can be computed using the general algorithm in o n 2 time

fibonacci arrays and their two dimensional repetitions abstract notions related to repetitive substructures in two dimensional arrays are introduced and studied in an attempt to parallel some of the analogous developments already known for strings in particular sequences of fibonacci arrays are defined capable of exhibiting extremal properties in terms of certain repetitive subpatterns called tandems two types of tandems are considered for one type it is shown that the number of occurrences in an m n fibonacci array attains the general upper bound of o m 2 n log n

on the convergence properties of the em algorithm two convergence aspects of the em algorithm are studied i does the em algorithm find a local maximum or a stationary value of the incomplete data likelihood function ii does the sequence of parameter estimates generated by em converge several convergence results are obtained under conditions that are applicable to many practical situations two useful special cases are a if the unobserved complete data specification can be described by a curved exponential family with compact parameter space all the limit points of any em sequence are stationary points of the likelihood function b if the likelihood function is unimodal and a certain differentiability condition is satisfied then any em sequence converges to the unique maximum likelihood estimate a list of key properties of the algorithm is included

multiplicative errors in variables models with applications to recent data released by the u s department of energy abstract in an errors in variables model the predicting variables are observed with errors traditionally the errors are assumed to be additive in this article i consider the case in which the error is multiplicative a situation that arises when analyzing some recent data released by the u s department of energy a consistent estimator is provided for regression coefficients by correcting the asymptotic bias of the least squares estimate it is shown that after being normalized by an estimate of its covariance is asymptotically normally distributed this can therefore be used to construct approximate tests and confidence sets for the results are essentially nonparametric

an alphabet independent approach to two dimensional pattern matching there are many solutions to the string matching problem that are strictly linear in the input size and independent of alphabet size furthermore the model of computation for these algorithms is very weak they allow only simple arithmetic and comparisons of equality between characters of the input in contrast algorithms for two dimensional matching have needed stronger models of computation most notably assuming a totally ordered alphabet the fastest algorithms for two dimensional matching have therefore had a logarithmic dependence on the alphabet size in the worst case this gives an algorithm that runs in o n 2 log m with o m 2 log m preprocessing the authors show an algorithm for two dimensional matching with an o n 2 text scanning phase furthermore the text scan requires no special assumptions about the alphabet i e it runs on the same model as the standard linear time string matching algorithm the pattern preprocessing requires an ordered alphabet and runs with the same alphabet dependency as the previously known algorithms

a characterization of multivariate quasi interpolation formulas and its applications let be a compactly supported function on s ands the linear space withgenerator that is s is the linear span of the multiinteger translates of it is well known that corresponding to a generator there are infinitely many quasi interpolation formulas a characterization of these formulas is presented which allows for their direct calculation in a variety of forms suitable to particular applications and in addition provides a clear formulation of the difficult problem of minimally supported quasi interpolants we introduce a generalization of interpolation called interpolation and a notion of higher order quasi interpolation called approximation a characterization of approximants similar to that of quasi interpolants is obtained with similar applications among these applications are estimating least squares approximants without matrix inversion surface fitting to incomplete or semi scattered discrete data and constructing generators with one point quasi interpolation formulas it will be seen that the exact values of the generator at the multi integers s facilitates the above study an algorithm to yield this information for box splines is discussed

approximation order from certain spaces of smooth bivariate splines on a three direction mesh determination de l ordre exact d approximation de certains espaces de fonctions splines regulieres a deux variables

panel models with interactive effects abstract the multiplication of individual specific effects and time specific effects provides a more general formulation than the traditionally used additive form to capture the unobserved heterogeneity in panel data modeling it is also a useful approach for dimension reduction for modeling cross section dependence however and are unobservable we explore the implications for econometric modeling under various formulations of the interactive effects models and suggest a quasi likelihood approach as a common framework to study issues of estimation and statistical inference when regressors are either strictly exogenous or predetermined and under different combinations of the data size of cross sectional dimension n and time series dimensions t we also suggest some computationally simpler estimation methods in light of the quasi likelihood approach monte carlo studies are conducted to highlight the issues involved

two dimensional periodicity in rectangular arrays string matching is rich with a variety of algorithmic tools in contrast multidimensional matching has had a rather sparse set of techniques this paper presents a new algorithmic technique for two dimensional matching periodicity analysis its strength appears to lie in the fact that it is inherently two dimensional periodicity in strings has been used to solve string matching problems multidimensional periodicity however is not as simple as it is in strings and was not formally studied or used in pattern matching in this paper we define and analyze two dimensional periodicity in rectangular arrays one definition of string periodicity is that a periodic string can self overlap in a particular way an analogous concept is true in two dimensions the self overlap vectors of a rectangle generate a regular pattern of locations where the rectangle may originate based on this regularity we define four categories of periodic arrays nonperiodic lattice periodic line periodic and radiant periodic and prove theorems about the properties of the classes we give serial and parallel algorithms that find all locations where an overlap originates in addition our algorithms find a witness proving that the array does not self overlap in any other location the serial algorithm runs in time o m2 linear time when the alphabet size is finite and in o m2log m otherwise the parallel algorithm runs in time o log m using o m2 crcw processors

an optimal o log log n time parallel algorithm for detecting all squares in a string an optimal o log log n time concurrent read concurrent write parallel algorithm for detecting all squares in a string is presented a tight lower bound shows that over general alphabets this is the fastest possible optimal algorithm when p processors are available the bounds become theta lceil n log n p rceil log log lceil 1 p n rceil 2p the algorithm uses an optimal parallel string matching algorithm together with periodicity properties to locate the squares within the input string

efficient detection of quasiperiodicities in strings a string z is quasiperiodic if there is a second string w z such that the occurrences of w in z cover z entirely i e every position of z falls within some occurrence of w in z it is shown here that all maximal quasiperiodic substrings of a string x of n symbols can be detected in time o n log2 n

enhanced string covering a factor u of a string y is a cover of y if every letter of y lies within some occurrence of u in y thus every cover u is also a border both prefix and suffix of y if u is a cover of a superstring of y then u is a seed of y covers and seeds are two formalisations of quasiperiodicity and there exist linear time algorithms for computing all the covers and seeds of y a string y covered by u thus generalises the idea of a repetition that is a string composed of exact concatenations of u even though a string is coverable somewhat more frequently than it is a repetition still a string that can be covered by a single u is rare as a result seeking to find a more generally applicable and descriptive notion of cover many articles were written on the computation of a minimum k cover of y that is the minimum cardinality set of strings of length k that collectively cover y unfortunately this computation turns out to be np hard therefore in this article we propose new simple easily computed and widely applicable notions of string covering that provide an intuitive and useful characterisation of a string the enhanced cover the enhanced left cover and the enhanced left seed

deterministic sampling a new technique for fast pattern matching consider the following three stage strategy for recognizing patterns in larger scenes mimic randomization deterministically sample several positions of the pattern search for sample find all occurrences of the sample in the scene verify for each occurrence of the sample verify occurrence of the full pattern this strategy has led to the core of the new idea given in this paper consider the string matching problem given the pattern a sample of its positions is carefully selected whose size is at most logarithmic the deterministic sample then the sample is searched for for nonperiodic patterns the sample has the following perhaps surprising property it is possible to disqualify all occurrences of the sample positions but one within each neighborhood of locations in the text without any further comparisons of characters this provides sparse verification this approach enables the text analysis stages search for sample and verify to be performed in o log n time and optimal spe

frequency domain system identification using non parametric noise models estimated from a small number of data sets abstract this paper discusses the problem of identifying a linear system from the frequency data when the measurements of the input and the output signals are both disturbed with noise a typical example of such a problem is the identification of a system in a feedback loop it is known that this problem can be solved using errors in varaibles methods if the covariance matrices of the disturbing noise on input and output measurements are a priori known it is shown that the exact covariance matrices can be replaced by the sample covariance matrices the system can be identified from the sample means and sample covariance matrices calculated from a small number m of independently repeated experiments it is shown that under these conditions the estimates are still strongly consistent for an increasing number of data points n in each experiment n if m 4 the loss in efficiency is quantified m 6 and the expected value of the cost function m 4 and its variance m 6 are calculated

quasiperiodic and lyndon episturmian words recently the second two authors characterized quasiperiodic sturmian words proving that a sturmian word is non quasiperiodic if and only if it is an infinite lyndon word here we extend this study to episturmian words a natural generalization of sturmian words by describing all the quasiperiods of an episturmian word which yields a characterization of quasiperiodic episturmian words in terms of their directive words even further we establish a complete characterization of all episturmian words that are lyndon words our main results show that unlike the sturmian case there is a much wider class of episturmian words that are non quasiperiodic besides those that are infinite lyndon words our key tools are morphisms and directive words in particular normalized directive words which we introduced in an earlier paper also of importance is the use of return words to characterize quasiperiodic episturmian words since such a method could be useful in other contexts

a faber series approach to cardinal interpolation for a compactly supported function 9 in rd we study quasiinterpolants based on point evaluations at the integer lattice we restrict ourselves to the case where the coefficient sequence af for given data f is computed by applying a univariate polynomial q to the sequence i zd and then convolving with the data flzd such operators appear in the well known neumann series formulation of quasi interpolation a criterion for the polynomial q is given such that the corresponding operator defines a quasi interpolant since our main application is cardinal interpolation which is well defined if the symbol of p does not vanish we choose q as the partial sum of a certain faber series this series can be computed recursively by this approach we avoid the restriction that the range of the symbol of p must be contained in a disk of the complex plane excluding the origin which is necessary for convergence of the neumann series furthermore for symmetric a we prove that the rate of convergence to the cardinal interpolant is superior to the one obtainable from the neumann series

dynamic structural systems under indirect observation identifiability and estimation aspects from a system theoretic perspective in this partly expository paper the parameter identifiability and estimation of a general dynamic structural model under indirect observation will be considered from a system theoretic perspective the general dynamic model covers dynamic factor analytic models dynamic mimic models and joreskog s linear structural model as special cases its reduced form is under a slightly different specification known in system theory and econometrics as the stochastic stationary version of the state space model by using concepts and methods from system theory such as the observability and controllability concept the steady state kalman filter and a general nonlinear ml estimation procedure known as prediction error estimation the general dynamic model will be identified it will be shown that joreskog s lisrel procedure is a special case of the prediction error estimation procedure

usefulness of the karp miller rosenberg algorithm in parallel computations on strings and arrays abstract the karp miller rosenberg 1972 algorithm was one of the first efficient almost linear sequential algorithms for finding repeated patterns and for string matching in the area of efficient sequential computations on strings it was soon superseded by more efficient and more sophisticated algorithms we show that the karp miller rosenberg algorithm kmr must be considered as a basic technique in parallel computations for many problems variations of kmr give the known most efficient parallel algorithms the representation of the set of basic factors subarrays of a string array produced by the algorithm is an extremely useful data structure in parallel algorithms on strings and arrays this gives also a general unifying framework for a large variety of problems we show that the following problems for strings and arrays can be solved by almost optimal parallel algorithms pattern matching longest repeated factor subarray longest common factor subarray maximal symmetric factor subarray also the following problems for strings can be solved within the same complexity bounds finding squares testing even palstars and compositions of k palindromes for k 2 3 4 computing lyndon factorization and building minimal pattern matching automata in the model without concurrent writes the parallel time is o log n 2 with n processors and in the model with concurrent writes the time for most of the problems is o log n with n processors for two problems related to the one dimensional case longest repeated factor and longest common factor there were designed parallel algorithms using suffix trees apostolico et al 1988 however our data structure is simpler and furthermore for the two dimensional case suffix trees do not work the complexity of our algorithms does not depend on the size of the alphabet except for the computation of pattern matching automata

alphabet independent two dimensional witness computation we study two dimensional periodicity introduced by amir and benson we characterize periods of a two dimensional array namely the vectors such that two copies of the array one shifted by the vector over the other overlap without a mismatch using this characterization we design an alphabet independent linear time algorithm for two dimensional witness computation i e an o m 2 time algorithm that finds periods of an m times m array as well as witnesses against nonperiods of the array among the vectors whose length is less than m 4 the constant in the o notation does not depend on the alphabet size combined with the alphabet independent text processing algorithm of amir benson and farach siam j comput 23 1994 pp 313 323 this leads to the first alphabet independent linear time algorithm for two dimensional pattern matching

consistent estimation for some nonlinear errors in variables models abstract the issues of identification and estimation of nonlinear errors in variables models are explored the deficiencies of the conventional definition of identification are discussed and an alternative definition in terms of observed samples is suggested the consistency and asymptotic normality of minimum distance estimators are studied to simplify the computation a two step estimation procedure is also suggested in which a consistent estimate of a subset of parameters is first obtained and treated as if they were known in the second step estimation of the rest of the parameters conditions for the consistency of this two step estimator and its asymptotic variance covariance matrix are also derived

detecting regularities on grammar compressed strings we address the problems of detecting and counting various forms of regularities in a string represented as a straight line program slp which is essentially a context free grammar in the chomsky normal form given an slp of size n that represents a string s of length n our algorithm computes all runs and squares in s in o n 3 h time and o n 2 space where h is the height of the derivation tree of the slp we also show an algorithm to compute all gapped palindromes in o n 3 h g n h log n time and o n 2 space where g is the length of the gap as one of the main components of the above solution we propose a new technique called approximate doubling which seems to be a useful tool for a wide range of algorithms on slps indeed we show that the technique can be used to compute the periods and covers of the string in o n 2 h time and o n h n log 2 n time respectively

estimating and testing interactions in linear regression models when explanatory variables are subject to classical measurement error estimating and testing interactions in a linear regression model when normally distributed explanatory variables are subject to classical measurement error is complex since the interaction term is a product of two variables and involves errors of more complex structure our aim is to develop simple methods based on the method of moments mm and regression calibration rc that yield consistent estimators of the regression coefficients and their standard errors when the model includes one or more interactions in contrast to previous work using structural equations models framework our methods allow errors that are correlated with each other and can deal with measurements of relatively low reliability using simulations we show that under the normality assumptions the rc method yields estimators with negligible bias and is superior to mm in both bias and variance we also show that the rc method also yields the correct type i error rate of the test of the interaction however when the true covariates are not normally distributed we recommend using mm we provide an example relating homocysteine to serum folate and b12 levels