a mixture model for occupational exposure mean testing with a limit of detection sul lhiary information from detectable exposure measurements randomly sampled from a left truncated log normal distribution may be used to evaluate the distribution of nondetectable values that fall below all analytic limit of detection if the proportion of nondetects is larger than expected under log normality alternative models to account for these unobserved data should be considered we discuss one such model that incorporates a mixture of true zero exposures and a log normal distribution with possible left censoring previously considered ill a different context by manitou and halsey 1995 biometrics 51 1570 1578 a particular relationship is demonstrated between maximum likelihood parameter estimates based on this mixture model and those assuming either left tnlllcated or left censored data these results emphasize the heed for caution when choosing a model to fit data involving nondetectable values a one sided likelihood ratio test for colli paring illeall exposure under the mixture model to an occupational exposure limit is then developed and evaluated via simulations all example demonstrates the potential impact of specifying an incorrect model for the ilondetectable value

linear free resolutions and minimal multiplicity let s k x x be a polynomial ring over a field and let a4 a m be a finitely generated graded module in the most interesting case a4 is an ideal of s for a given natural number p there is a great interest in the question can m be generated by homogeneous elements of degree p no simple answer say in terms of the local cohomology of m is known but somewhat surprisingly the stronger question can the jth syzygy of m be generated by elements of degree qp j for all j 0 l n does admit a simple response the following is neither new nor difficult to prove though it seems not well known

double vogan diagrams and semisimple symmetric spaces a vogan diagram is a set of involution and painting on a dynkin diagram it selects a real form or equivalently an involution from a complex simple lie algebra we introduce the double vogan diagram which is two sets of vogan diagrams superimposed on an affine dynkin diagram they correspond to pairs of commuting involutions on complex simple lie algebras and therefore provide an independent classification of the simple locally symmetric pairs

a rank two vector bundle associated to a three arrangement and its chern polynomial abstract we prove that the poincare polynomial a t of an essential central three arrangement a over a field k of characteristic zero is 1 t ct d 0 a where d 0 a is the sheaf associated to the kernel of the jacobian ideal of a and ct is the chern polynomial this shows that a version of terao s theorem invent math 63 1981 159 179 on free arrangements also holds for all three arrangements we also prove that for such an arrangement d 0 a is a vector bundle on p2 and derive an algorithm which computes ct d 0 a from a free resolution of the jacobian ideal of the defining polynomial of a

estimation of pearson type 3 moments estimates of frequencies of floods and other events are based on statistical distributions estimated from sample data the most common and generally the most robust technique used is the fitting of data by the method of moments it is well known that moments of the data of an order higher than 1 are biased estimates of the moments of the population from which the data represent a sample much work has been done in deriving factors or functions by which the bias can be corrected all of such work has been based on considering the variation of statistics of various samples drawn from a specified population whereas the real interest is in the range of likely parent population parameters corresponding to a statistic obtained from a unique sample it is recognized that there is no solution to this problem without an assumption of the range and distribution of such parameters as they occur in nature the study described herein examines this question with regard to a particular functional form of parent distribution and for the case where the a priori distributions of the parameters are uniform that is where all values of a particular parameter are equally likely on an arithmetic scale the distribution function studied is the pearson type 3 and the parameter of primary attention is the skew coefficient

multigraded castelnuovo mumford regularity we develop a multigraded variant of castelnuovo mumford regularity motivated by toric geometry we work with modules over a polynomial ring graded by a finitely generated abelian group as in the standard graded case our definition of multigraded regularity involves the vanishing of graded components of local cohomology we establish the key properties of regularity its connection with the minimal generators of a module and its behavior in exact sequences for an ideal sheaf on a simplicial toric variety x we prove that its multigraded regularity bounds the equations that cut out the associated subvariety we also provide a criterion for testing if an ample line bundle on x gives a projectively normal embedding

behavior of sensitivities in the one dimensional advection dispersion equation implications for parameter estimation and sampling design the spatial and temporal variability of sensitivities has a significant impact on parameter estimation and sampling design for studies of solute transport in porous media physical insight into the behavior of sensitivities is offered through an analysis of analytically derived sensitivities for the one dimensional form of the advection dispersion equation when parameters are estimated in regression models of one dimensional transport the spatial and temporal variability in sensitivities influences variance and covariance of parameter estimates several principles account for the observed influence of sensitivities on parameter uncertainty 1 information about a physical parameter may be most accurately gained at points in space and time with a high sensitivity to the parameter 2 as the distance of observation points from the upstream boundary increases maximum sensitivity to velocity during passage of the solute front increases and the consequent estimate of velocity tends to have lower variance 3 the frequency of sampling must be in phase with the s shape of the dispersion sensitivity curve to yield the most information on dispersion 4 the sensitivity to the dispersion coefficient is usually at least an order of magnitude less than the sensitivity to velocity 5 the assumed probability distribution of random error in observations of solute concentration determines the form of the sensitivities 6 if variance in random error in observations is large trends in sensitivities of observation points may be obscured by noise and thus have limited value in predicting variance in parameter estimates among designs 7 designs that minimize the variance of one parameter may not necessarily minimize the variance of other parameters 8 the time and space interval over which an observation point is sensitive to a given parameter depends on the actual values of the parameters in the underlying physical system

uncorrelated measurement error in flood frequency inference when measurement error me is present the true value of the annual maximum discharge and of the censoring threshold discharge is unknown the impact of using estimated rather than true discharges on the inference of flood quantiles is considered the likelihood function is formulated for data which consist of annual maximum discharges systematic data and occurrences of floods above some threshold discharge binomial censored data the formulation makes explicit allowance for the corruption of discharges by statistically independent me this formulation can be used to get maximum likelihood estimates or perform a bayesian analysis a limited sampling experiment was conducted to assess the performance of two parameter lognormal maximum likelihood quantile estimators in the presence of simple uncorreiated discontinuous me it was found that me reduces the information content of systematic and binomial censored data with the reduction being greatest for distributions with low coefficients of variation when only using systematic data it was found that the performance of estimators making allowance for me was at best only modestly better than that of estimators ignoring me the principal finding however was that the performance of maximum likelihood estimators using binomial censored data but ignoring me can be substantially worse than that of estimators making explicit allowance for me in fact the loss in performance can be so great that in some cases it may be preferable to ignore the binomial censored data finally it is shown that a bayesian analysis of flood data affected by me provides insights not offered by maximum likelihood estimation when the threshold discharge is in error the posterior distribution of the lognormal parameters can become bimodal as the length of the binomial censored record increases indicating an inconsistency between the information in the systematic and binomial censored data

application of the finite difference heterogeneous multiscale method to the richards equation 1 this paper extends the finite difference heterogeneous multiscale method fdhmm to simulate transient unsaturated water flow problems in random porous media the numerical method is based on the use of two different schemes for the original equation at different grid levels which allows numerical results at a lower cost than solving the original equations the main feature of fdhmm is that the necessary data for the macroscopic model are supplied by solving the microscopic model on a sparse spatial domain the generated code is verified by applying the linearization model of the richards equation considering two different constitutive relationships this method is applied to several test examples with different soil textures and boundary conditions both the dirichlet and the periodic boundary conditions are considered for solving the local microscopic model when the water flow in heterogeneous unsaturated soils is simulated by fdhmm the numerical experiments demonstrate that fdhmm can effectively simulate the transient unsaturated water flow in the specific soils the numerical experiments also demonstrate that fdhmm can achieve accurate global mass balance and is a globally convergent algorithm and the spatial correlation length of random coefficients under the specific standard deviation has relatively little influence on the accuracy of the method

estimation in the pearson type 3 distribution although the pearson type 3 p3 is one of the basic models in statistical hydrology its use to model untransformed data has been restrained because of difficulties encountered in fitting this distribution by traditional methods in this paper an adaptive estimation procedure of mixed moments for the p3 family is introduced which is based on several fractional moments of the exponentially transformed data and the mean of the original data the procedure is easy to implement in small samples and is valid over the entire parameter space explicit formulae for the variances and covariances of parameter estimators and of the variance of the t year event are derived in addition two variants of the new procedure are compared with two versions of the method of moments and a version of the method of conditional moments via monte carlo simulation with samples generated from p3 populations it is found that one of the variants of the new procedure is the best overall method in estimating 100 year flood events and the other variant is best in estimating the median and 10 year low flow events the good performance of these two variants is also observed in samples generated from alternatives to p3 distributions a modification of the procedure is also introduced and investigated when a prior assumption of positive skewness is adopted

the structure of the core of ideals the core of an r ideal i is the intersection of all reductions of i this object was introduced by d rees and j sally and later studied by c huneke and i swanson who showed in particular its connection to j lipman s notion of adjoint of an ideal being an a priori infinite intersection of ideals the core is difficult to describe explicitly we prove in a broad setting that core i is a finite intersection of minimal reductions core i is a finite intersection of general minimal reductions core i is the contraction to r of a universal ideal core i behaves well under flat extensions the proofs are based on general multiplicity estimates for certain modules

estimating mean concentrations under transformation for environmental data with detection limits the reporting procedures for potentially toxic pollutants are complicated by the fact that concentrations are measured using small samples that include a number of observations lying below some detection limit furthermore there is often a small number of high concentrations observed in combination with a substantial number of low concentrations this results in small nonnormally distributed censored samples this article presents maximum likelihood estimators for the mean of a population based on censored samples that can be transformed to normality the method estimates the optimal power transformation in the box cox family by searching the censored data likelihood maximum likelihood estimators for the mean in the transformed scale are calculated via the expectation maximization algorithm estimates for the mean in the original scale are functions of the estimated mean and variance in the transformed population confidence intervals are computed using the delta method and the nonparametric percentil

estimation of distributional parameters for censored trace level water quality data 1 estimation techniques a recurring difficulty encountered in investigations of many metals and organic contaminants in ambient waters is that a substantial portion of water sample concentrations are below limits of detection established by analytical laboratories several methods were evaluated for estimating distributional parameters for such censored data sets using only uncensored observations their reliabilities were evaluated by a monte carlo experiment in which small samples were generated from a wide range of parent distributions and censored at varying levels eight methods were used to estimate the mean standard deviation median and interquartile range criteria were developed based on the distribution of uncensored observations for determining the best performing parameter estimation method for any particular data det the most robust method for minimizing error in censored sample estimates of the four distributional parameters over all simulation conditions was the log probability regression method with this method censored observations are assumed to follow the zero to censoring level portion of a lognormal distribution obtained by a least squares regression between logarithms of uncensored concentration observations and their z scores when method performance was separately evaluated for each distributional parameter over all simulation conditions the log probability regression method still had the smallest errors for the mean and standard deviation more but the lognormal maximum likelihood method had the smallest errors for the median and interquartile range when data sets were classified prior to parameter estimation into groups reflecting their probable parent distributions the ranking of estimation methods was similar but the accuracy of error estimates was markedly improved over those without classification less

the information encoded in initial ideals we consider homogeneous ideals i and the initial ideal in i for the revlex order first we give a sequence of invariants computed from i giving better and better approximations to the initial ideal and ending in an equivalent description then we apply this to different settings in algebraic geometry to understand what information is encoded in the generic initial ideal of the ideal of a projective scheme we also consider the higher initial ideals as defined in a paper by fl0ystad in particular we show that giving the generic higher initial ideal of a space curve is equivalent to giving the generic initial ideal of a linked curve

equivalence classes of vogan diagrams abstract a vogan diagram is a dynkin diagram with an involution and the vertices fixed by the involution may be painted they represent real simple lie algebras and two diagrams are said to be equivalent if they represent the same lie algebra in this article we classify the equivalence classes of all vogan diagrams in doing so we find that the underlying dynkin diagrams have certain properties in graph painting we show that this combinatorial property provides an easy classification for most of the simply laced dynkin diagrams

estimation of descriptive statistics for multiply censored water quality data this paper extends the work of gilliom and helsel 1986 on procedures for estimating descriptive statistics of water quality data that contain less than observations previously procedures were evaluated when only one detection limit was present here we investigate the performance of estimators for data that have multiple detection limits probability plotting and maximum likelihood methods perform substantially better than simple substitution procedures now commonly in use therefore simple substitution procedures e g substitution of the detection limit should be avoided probability plotting methods are more robust than maximum likelihood methods to misspecification of the parent distribution and their use should be encouraged in the typical situation where the parent distribution is unknown when utilized correctly less than values frequently contain nearly as much information for estimating population moments and quantiles as would the same observations had the detection limit been below them

log pearson type 3 quantile estimators with regional skew information and low outlier adjustments 1 the recently developed expected moments algorithm ema cohn et al 1997 does as well as maximum likelihood estimations at estimating log pearson type 3 lp3 flood quantiles using systematic and historical flood information needed extensions include use of a regional skewness estimator and its precision to be consistent with bulletin 17b another issue addressed by bulletin 17b is the treatment of low outliers a monte carlo study compares the performance of bulletin 17b using the entire sample with and without regional skew with estimators that use regional skew and censor low outliers including an extended ema estimator the conditional probability adjustment cpa from bulletin 17b and an estimator that uses probability plot regression ppr to compute substitute values for low outliers estimators that neglect regional skew information do much worse than estimators that use an informative regional skewness estimator for lp3 data the low outlier rejection procedure generally results in no loss of overall accuracy and the differences between the mses of the estimators that used an informative regional skew are generally modest in the skewness range of real interest samples contaminated to model actual flood data demonstrate that estimators which give special treatment to low outliers significantly outperform estimators that make no such adjustment

typical ranks for 3 tensors nonsingular bilinear maps and determinantal ideals abstract let m n 3 m 1 n 1 2 p m n and u m n p the set r u n m of all real tensors with size u n m is one to one corresponding to the set of bilinear maps r m r n r u we show that r m n p has plural typical ranks p and p 1 if and only if there exists a nonsingular bilinear map r m r n r u we show that there is a dense open subset o of r u n m such that for any y o the ideal of maximal minors of a matrix defined by y in a certain way is a prime ideal and the real radical of that is the irrelevant maximal ideal if that is not a real prime ideal further we show that there is a dense open subset t of r n p m and continuous surjective open maps o r u p and t r u p where r u p is the set of u p matrices with entries in r such that if y t then rank t p if and only if the ideal of maximal minors of the matrix defined by y is a real prime ideal

confidence intervals for expected moments algorithm flood quantile estimates historical and paleoflood information can substantially improve flood frequency estimates if appropriate statistical procedures are properly applied however the federal guidelines for flood frequency analysis set forth in bulletin 17b rely on an inefficient weighting procedure that fails to take advantage of historical and paleoflood information this has led researchers to propose several more efficient alternatives including the expected moments algorithm ema which is attractive because it retains bulletin 17b s statistical structure method of moments with the log pearson type 3 distribution and thus can be easily integrated into flood analyses employing the rest of the bulletin 17b approach the practical utility of ema however has been limited because no closed form method has been available for quantifying the uncertainty of ema based flood quantile estimates this paper addresses that concern by providing analytical expressions for the asymptotic variance of ema flood quantile estimators and confidence intervals for flood quantile estimates monte carlo simulations demonstrate the properties of such confidence intervals for sites where a 25 to 100 year streamgage record is augmented by 50 to 150 years of historical information the experiments show that the confidence intervals though not exact should be acceptable for most purposes

syzygies and singularities of tensor product surfaces of bidegree 2 1 let u h op1 p1 2 1 be a basepoint free four dimensional vector space the sections corresponding to u determine a regular map u p1 p1 p3 we study the associated bigraded ideal iu k s t u v from the standpoint of commutative algebra proving that there are exactly six numerical types of possible bigraded minimal free resolution these resolutions play a key role in determining the implicit equation for u p1 p1 via work of buse jouanolou 5 buse chardin 6 botbol 2 and botbol dickensteindohm 3 on the approximation complex z in four of the six cases iu has a linear first syzygy remarkably from this we obtain all differentials in the minimal free resolution in particular this allows us to explicitly describe the implicit equation and singular locus of the image

vogan diagrams of real forms of affine kac moody lie algebras abstract a vogan diagram is actually a dynkin diagram with some additional structure this paper develops theory of vogan diagrams for almost compact real forms of indecomposable nontwisted affine kac moody lie algebras here the equivalence classes of vogan diagrams are in one one correspondence with the isomorphism classes of almost compact real forms

the validity of a simple statistical model for estimating fluvial constituent loads an empirical study involving nutrient loads entering chesapeake bay we consider the appropriateness of rating curves and other log linear models to estimate the fluvial transport of nutrients split sample studies using data from tributaries to the chesapeake bay reveal that a minimum variance unbiased estimator mvue based on a simple log linear model provides satisfactory load estimates even in some cases where the model exhibited significant lack of fit for total nitrogen tn the average difference between the mvue estimates and the observed loads ranges from 8 to 2 at the four sites the corresponding range for total phosphorus tp is 6 to 5 none of these differences is statistically significant the observed variability of the mvue load estimates for tn and tp which ranges from 7 to 25 depending on the case is accurately predicted by statistical theory

percentage points for a generalized esd many outlier procedure a generalized extreme studentized deviate esd many outlier procedure is given for detecting from 1 to k outliers in a data set this procedure has an advantage over the original esd many outlier procedure rosner 1975 in that it controls the type i error both under the hypothesis of no outliers and under the alternative hypotheses of 1 2 k l outliers a method is given for approximating percentiles for this procedure based on the t distribution this method is shown to be adequately accurate using monte carlo simulation for detecting up to 10 outliers in samples as small as 25 tables are given for implementing this method for n 25 1 50 10 100 50 500 k 10 05 ol 005

flood frequency analysis with systematic and historical or paleoflood data based on the two parameter general extreme value models historical and paleoflood data have become an important source of information for flood frequency analysis a number of studies have been proposed in the literature regarding the value of historical and paleoflood information for estimating flood quantiles these studies have been generally based on computer simulation experiments in this paper the value of using systematic and historical paleoflood data relative to using systematic records alone is examined analytically by comparing the asymptotic variances of flood quantiles assuming a two parameter general extreme value marginal distribution type 1 and type 2 censored data and maximum likelihood estimation method the results of this study indicate that the value of historical and paleoflood data for estimating flood quantiles can be small or large depending on only three factors the relative magnitudes of the length of the systematic record n and the length of the historical period m the return period t of the flood quantile of interest and the return period h of the threshold level of perception for instance for n 50 m 50 and t 500 the statistical gain for type 2 censoring becomes significantly larger than for type 1 censoring as h becomes greater than 100 years in addition computer experiments have shown that the results regarding the statistical gain based on asymptotic considerations are valid for the usual sample sizes

flatness and fibred powers over smooth varieties abstract we prove the equivalence between flatness of a complex algebraic map to a smooth variety of dimension n and torsion freeness of its n th fibered power under the assumption that the source space is of pure dimension this generalizes the corresponding result for finite maps due to auslander and proves a conjecture of vasconcelos for a large class of objects we develop several constructions in local analytic geometry and commutative algebra useful for our proof

plotting positions for historical floods and their precision plotting positions are needed for situations where in addition to a systematically recorded annual flood series one would have a record of any large floods which occurred during an extended historical period if they occurred many of the published estimators are based on uncensored sampling theory which is not appropriate for such data sets here such historical and systematic flood records are viewed as resulting from a partially censored sampling experiment plotting positions are derived for such experiments using both classical and bayesian viewpoints in general it is impossible to construct highly accurate estimates of the exceedance probabilities of the largest floods using only their rank the number of observed historical floods and the lengths of the historical period and the systematic record for the largest flood the coefficient of variation of exceedance probability estimators is of the order of 1 as it is for complete systematic records examples illustrate the bias and precision of a variety of plotting position formulas the differences among the different plotting positions are generally small in comparison to the sampling variability however plotting positions which are unbiased with uncensored samples are often the most biased when used with a combination of historical and systematic data three appendices consider the effect of misspecification of the length of the historical period the effect of misspecification of the threshold of perception or observation level and plotting positions for situations with several perception thresholds

on a theorem of castelnuovo and the equations defining space curves introduction 491 w notat ion and conventions 493 w a regularity theorem 494 w a rationality theorem 498 w the existence of secant lines 501 w open problems 505 references 506

cyclicity of polynomial nondegenerate centers on center manifolds abstract we consider polynomial families of ordinary differential equations on r 3 parametrized by the admissible coefficients for which the origin is an isolated singularity at which the linear part of the system has one non zero real and two purely imaginary eigenvalues we derive theorems that bound the maximum number of limit cycles within the center manifold that can bifurcate under arbitrarily small perturbation of the coefficients from any center at the origin the bounds are global in that they apply to the system corresponding to any point on any irreducible component of the center variety in the space of parameters we also derive theorems for such bounds when attention is confined to a single irreducible component of the center variety

a connectedness result in positive characteristic let r m be a complete local ring of dimension at least two which contains a separably closed coefficient field of positive characteristic using a vanishing theorem of peskine szpiro lyubeznik proved that the local cohomology module h 1 m r is frobenius torsion if and only if the punctured spectrum of r is connected in the zariski topology we give a simple proof of this theorem and more generally a formula for the number of connected components in terms of the frobenius action on h 1 m r

comparison of probabilistic algorithms for analyzing the components of an affine algebraic variety systems of polynomial equations arise throughout mathematics engineering and the sciences it is therefore a fundamental problem both in mathematics and in application areas to find the solution sets of polynomial systems the focus of this paper is to compare two fundamentally different approaches to computing and representing the solutions of polynomial systems numerical homotopy continuation and symbolic computation several illustrative examples are considered using the software packages bertini and singular

primary decomposition of zero dimensional ideals over finite fields gao shuhong clemson univ dept math sci clemson sc 29634 usa wan daqing univ calif irvine dept math irvine ca 92697 usa wang mingsheng acad sinica inst software informat secur lab beijing 100080 peoples r china

the minimal components of the mayr meyer ideals rifi such that each ri has degree at most deg f kd n mayr and meyer in mm found generators of a family of ideals for which a doubly exponential bound in n is indeed achieved bayer and stillman bs showed that for these mayr meyer ideals any minimal generating set of syzygies has elements of doubly exponential degree in n koh k modified the original ideals to obtain homogeneous quadric ideals with doubly exponential syzygies and ideal membership equations bayer huneke and stillman asked whether the doubly exponential behavior is due to the number of minimal and or associated primes or to the nature of one of them this paper examines the minimal components and minimal primes of the mayr meyer ideals in particular in section 2 it is proved that the intersection of the minimal components of the mayr meyer ideals does not satisfy the doubly exponential property so that the doubly exponential behavior of the mayr meyer ideals must be due to the embedded primes the structure of the embedded primes of the mayr meyer ideals is examined in s2 there exist algorithms for computing primary decompositions of ideals see giannitrager zacharias gtz eisenbud huneke vasconcelos ehv or shimoyama yokoyama sy and they have been partially implemented on the symbolic computer algebra programs singular and macaulay2 however the mayr meyer ideals have variable degree and a variable number of variables over an arbitrary field and there are no algorithms to deal with this generality thus any primary decomposition of the mayr meyer ideals has to be accomplished with traditional proof methods small cases of the primary decomposition analysis were partially verified on macaulay2 and singular and the emphasis here is on partially the computers quickly run out of memory

vanishing theorems a theorem of severi and the equations defining projective varieties in 1903 severi s proved that if x x c p are smooth surfaces whose union is the complete intersection of r 2 hypersurfaces of degrees di dr 2 then hypersurfaces of degree k z di r cut out a complete linear series on x cf sr xiii 9 8 the purpose of this paper is first of all to show that elementary arguments using the kodaira vanishing theorem lead to a simple variant of severi s statement theorem 7 below which extends it in serval directions more importantly we hope to convince the reader that this result has a surprising number of applications to questions involving the equations defining projective varieties consider to begin with a smooth complex projective variety x c pr of dimension n and codimension e r n in this setting our theorem asserts the vanishing of the higher cohomology of suitable twists of the ath power of the ideal sheaf yx of x in apr proposition 1 assume that x is cut out scheme theoretically in p by hypersurfaces of degrees d1 d2 d then h p r k 0 for i 1 provided k ad d2 de r note that only the degrees of the first e codim x pr defining equations come into play here when n 2 and a 1 this is a consequence of severi s

lh moments for statistical analysis of extreme events statistical analysis of extremes is often conducted for predicting large return period events in this paper lh moments a generalization of l moments that are based on linear combinations of higher order statistics are introduced for characterizing the upper part of distributions and larger events in data using lh moments reduces undesirable influences that small sample events may have on the estimation of large return period events the method of lh moments is formulated for the generalized extreme value gev distribution along with two detailed examples monte carlo simulations are conducted to illustrate the performance of using the method of lh moments to fit the gev distribution to both gev and non gev samples lh moment diagrams are constructed using annual maximum flow data for 107 streams worldwide to examine the ability of the gev distribution to model those series

comprehensive at site flood frequency analysis using monte carlo bayesian inference in flood frequency applications where the design flood is required to have a specified exceedance probability expected probability should be used its computation however presents formidable difficulties this study presents a monte carlo bayesian method for computing the expected probability distribution as well as quantile confidence limits for any flood frequency distribution using data on gauged flows possibly corrupted by rating curve error and on censored flows this is achieved by a three step process 1 formulate the likelihood function for the given data 2 approximate the likelihood function using a multinomial distribution and 3 integrate the expected probability integral using importance sampling the flike software for performing this is described and an example is given

admissible square quadruplets and semisimple symmetric spaces abstract we show that there is a one to one correspondence between the set of semisimple locally symmetric spaces and the set of admissible square quadruplets this correspondence leads to a new approach in the classification and a simple parametrization of irreducible locally symmetric spaces

algebraic geometric comparison of probability distributions we propose a novel algebraic algorithmic framework for dealing with probability distributions represented by their cumulants such as the mean and covariance matrix as an example we consider the unsupervised learning problem of finding the subspace on which several probability distributions agree instead of minimizing an objective function involving the estimated cumulants we show that by treating the cumulants as elements of the polynomial ring we can directly solve the problem at a lower computational cost and with higher accuracy moreover the algebraic viewpoint on probability distributions allows us to invoke the theory of algebraic geometry which we demonstrate in a compact proof for an identifiability criterion

a monte carlo study of some two sample rank tests with censored data abstract the powers of several nonparametric tests for the two sample problem with censored data are compared by simulation the tests studied include gehan s efron s and peto s and prentice s generalized wilcoxon tests along with the logrank test the test with the greatest power changes with the sample sizes censoring mechanism and distribution of the random variables the test that performed the best overall was the peto prentice generalized wilcoxon statistic with an asymptotic variance estimate

low flow analysis with a conditional weibull tail model estimates of low flow quantiles such as the 7 day 10 year low flow which are usually obtained by statistical modeling of observed data series are widely used in water quality management this paper presents a conditional modeling approach to low flow analysis that employs only those data values which are less than or equal to a ceiling value modeling in this fashion has been motivated by the observation that annual low flows may derive from mixed processes and by the subjective nature of graphical methods such as those employed by the u s geological survey which are often employed in such cases results of monte carlo experiments demonstrate that the conditional modeling approach yields a low flow quantile estimator whose bias and rmse are comparable to more conventional modeling approaches of fitting a classical textbook probability distribution on the basis of all observed data values even when the underlying population is of a well behaved form since the complex forms of mixed low flow data distributions are not capable of being represented by classical textbook distributions and since the conditional modeling approach performs comparably to those models even when the data derive from well behaved probability distributions these results imply that the conditional modeling approach is worthy of consideration for use by hydrologists the conditional modeling approach also leads rather naturally to a scheme much like that used in index flood methods whereby a regional low flow estimator might be devised an application of the conditional modeling approach to 48 low flow data series in alabama is presented

estimating constituent loads several recent articles have called attention to the problem of retransformation bias which can arise when log linear regression models are used to estimate sediment or other constituent loads in some cases the bias can lead to underestimation of constituent loads by as much as 50 and several procedures have been suggested for reducing or eliminating it however some of the procedures recommended for reducing the bias can actually increase it this paper compares the bias and variance of three procedures that can be used with log linear regression models the traditional rating curve estimator a modified rating curve method and a minimum variance unbiased estimator mvue analytical derivations of the bias and efficiency of all three estimators are presented it is shown that for many conditions the traditional and the modified estimator can provide satisfactory estimates however other conditions exist where they have substantial bias and a large mean square error these conditions commonly occur when sample sizes are small or when loads are estimated during high flow conditions the mvue however is unbiased and always performs nearly as well or better than the rating curve estimator or the modified estimator provided that the hypothesis of the log linear model is correct since an efficient unbiased estimator is available there seems to be no reason to employ biased estimators

finite generation of hochschild homology algebras we prove converses of the hochschild kostant rosenberg theorem in particular if a commutative algebra s is flat and essentially of finite type over a noetherian ring mathbb k and the hochschild homology hh s mathbb k is a finitely generated s algebra for shuffle products then s is smooth over mathbb k

a behavioral approach to the pole structure of one dimensional and multidimensional linear systems we use the tools of behavioral theory and commutative algebra to produce a new definition of a finite pole of a linear system this definition agrees with the classical one and allows a direct dynamical interpretation it also generalizes immediately to the case of a multidimensional nd system we make a natural division of the poles into controllable and uncontrollable poles when the behavior in question has latent variables we make a further division into observable and unobservable poles in the case of a one dimensional 1d state space model the uncontrollable and unobservable poles correspond respectively to the input and output decoupling zeros whereas the observable controllable poles are the transmission poles most of these definitions can be interpreted dynamically in both the 1d and nd cases and some can be connected to properties of kernel representations we also examine the connections between poles transfer matrices and their left and right matrix fraction descriptions mfds we find behavioral results which correspond to the concepts that a controllable system is precisely one with no input decoupling zeros and an observable system is precisely one with no output decoupling zeros we produce a decomposition of a behavior as the sum of subbehaviors associated with various poles this is related to the integral representation theorem which describes every system trajectory as a sum of integrals of polynomial exponential trajectories

flood frequency analysis with historical and paleoflood information an investigation is made of flood quantile estimators which can employ historical and paleoflood information in flood frequency analyses two categories of historical information are considered censored data where the magnitudes of historical flood peaks are known and binomial data where only threshold exceedance information is available a monte carlo study employing the two parameter lognormal distribution shows that maximum likelihood estimators mles can extract the equivalent of an additional 10 30 years of gage record from a 50 year period of historical observation the mle routines are shown to be substantially better than an adjusted moment estimator similar to the one recommended in bulletin 17b of the united states water resources council hydrology committee 1982 the mle methods performed well even when floods were drawn from other than the assumed lognormal distribution

extended vogan diagrams an extended vogan diagram is an extended dynkin diagram with a diagram involution such that the vertices fixed by the involution can be painted or unpainted every extended vogan diagram represents an almost compact real form of some affine kac moody lie algebra two diagrams may represent isomorphic algebras and in this case we say that the diagrams are equivalent in this paper we classify the equivalence classes of extended vogan diagrams and provide a complete list of all diagrams within each class it gives a combinatorial classification of the isomorphic classes of almost compact real forms of the affine kac moody lie algebras

regularity of prime ideals we answer several natural questions which arise from a recent paper of mccullough and peeva providing counterexamples to the eisenbud goto regularity conjecture we give counterexamples using rees algebras and also construct counterexamples that do not rely on the mayr meyer construction furthermore examples of prime ideals for which the difference between the maximal degree of a minimal generator and the maximal degree of a minimal first syzygy can be made arbitrarily large are given using a result of ananyan hochster we show that there exists an upper bound on regularity of prime ideals in terms of the multiplicity alone

development of regional regression relationships with censored data when no discharge record is available for a site a regional regression relationship can be used to estimate low flow quantiles problems arise in the derivation of such models when some at site quantile estimates are reported as zero one concern is that quantile estimates reported as zero may be in the range from zero to the measurement threshold a second concern is that a logarithmic transformation cannot be used with zero quantile estimates so traditional log linear least squares estimators cannot be computed this paper uses visual examples and monte carlo simulation to compare the performance of techniques for estimating the parameters of a regional regression model when some at site quantile estimates are zero ordinary least squares ols techniques employed in practice include adding a small constant to all at site quantile estimates denoted olsc or neglecting all observation reported as zero denoted olsd olsc and olsd performed poorly compared to the use of a tobit model which is a maximum likelihood estimator mle procedure that represents the below threshold estimates as a range from zero to the threshold level for a small amount of censoring the olsd method can be acceptable a weighted tobit model that accounts for the heteroscedasticity of the residuals in the regression model provided relatively little gain over the ordinary tobit model

key problems in the extension of module behaviour duality the duality for linear constant coefficient partial differential equations between behaviours and finitely generated modules over the operator ring is a very powerful tool linking equation structure to dynamic behaviour this duality is critically dependent on the choice of signal space in this paper we discuss two key algebraic problems which form an obstacle to the extension of this theory to general signal spaces the first of these is the so called willems closure problem which limits the ability of system equations to directly describe the system the second is the elimination problem the general solution of which depends upon an algebraic property injectivity of the signal space we demonstrate the importance of these problems in the module behaviour framework and some of the useful consequences of a full or partial solution the issues here are of particular relevance to the extension of the current duality theory for behaviours defined by linear partial differential equations from the case of constant to non constant coefficients

contragredient supersymmetric pairs the symmetric pairs of complex semisimple lie algebras can be characterized by commuting involutions we present its analogue on the contragredient lie superalgebras so that their symmetric pairs correspond to some commuting automorphisms as an application we classify the symmetric pairs of the exceptional lie superalgebras f 4 and g 3

robust flood frequency models the concept of a robust model is briefly explored in the context of flood frequency analysis two necessary properties of a robust model are advanced namely resistance and efficiency strategies for seeking more robust models are discussed because of its versatility the five parameter wakeby distribution can credibly be considered a parent flood distribution four regionalized wakeby parents are employed in simulation studies to search for robust models these parents were shown by houghton to be representative of u s flood experience in the sense that certain raw flood data characteristics could be reproduced a limited range of sampling experiments were undertaken the results suggest that of the site specific estimators considered the two parameter log normal maximum likelihood estimator is most resistant with gumbel estimators employing either maximum likelihood or probability weighted moments displaying comparable resistance several estimators which utilize regional flood information were compared included were empirical bayes estimators which are structurally similar to james stein rules and regionalized estimators based on the flood index method these estimators exhibited substantial improvements in aggregate risk performance over their site specific counterparts particularly for short record lengths regionalized estimators appear to be preferable for short record lengths while estimators which combine both site and regional flood information are preferable for longer record lengths when such estimation procedures are considered other distributional models such as log pearson type iii and wakeby become practical alternatives to the two parameter log normal model

generalized extreme value distribution fitted by lh moments for low flow frequency analysis 1 this study introduces a method based on lh moments to use the generalized extreme value gev distribution for low flow frequency analysis and investigates the capability of the gev distribution fitted by lh moments to effectively model the lower tail of the low flow frequency curve without explicitly censoring the data sample the performance of the gev l moment the gev distribution fitted by l moments and gev lh moment the gev distribution fitted by lh moments methods are assessed by evaluating the bias mean square error and relative accuracy of quantile estimates through monte carlo simulations it is shown that when both frequent low flows and extreme low flows can be adequately described by an assumed parent distribution both gev l2 moment and gev l moment methods make equally accurate quantile estimates however when frequent low flows and extreme low flows do not follow a single trend the bias of the gev l2 moment estimator is negligible while the bias of the gev l moment estimator is significant at large annual recurrence intervals on average the gev l2 moment quantile estimator displays less bias than the gev l moment quantile estimator furthermore as the annual recurrence interval increases the relative accuracy of the gev l2 moment method consistently improves over the gev l moment method the gev lh moment method is thus considered to be the more suitable method to model low flows

nonparametric statistical methods for comparing two sites based on data with multiple nondetect limits as concern over the effects of trace amounts of pollutants has increased so has the need for statistical methods that deal appropriately with data that include values reported as less than the detection limit it has become increasingly common for water quality data to include censored values that reflect more than one detection limit for a single analyte for such multiply censored data sets standard statistical methods for example to compare analyte concentration in two areas are not valid in such cases methods from the biostatistical field of survival analysis are applicable several common two sample censored data rank tests are explained and their behaviors are studied via a monte carlo simulation in which sample sizes and censoring mechanisms are varied under an assumed lognormal distribution these tests are applied to shallow groundwater chemistry data from two sites in the san joaquin valley california the best overall test in terms of maintained level is the normal scores test based on a permutation variance in cases where the level is maintained however the peto prentice statistic based on an asymptotic variance performs as well or better

l moment diagrams for censored observations observed data sets containing values above or below the analytical threshold of measuring equipment are referred to as censored such data are frequently encountered in quality and quantity monitoring applications of water soil and air samples most of the previous literature on the statistical analysis of censored data relates to the problems of moment parameter and quantile estimation methods such estimation methods usually assume an underlying probability distribution few goodness of fit methods exist for censored data we introduce l moment diagrams for the evaluation of the goodness of fit of alternative distributional hypotheses for left censored data experiments with artificial censored data sets document the conditions under which l moment diagrams should be useful our approach like hosking s 1995 approach for right censoring derived l moment diagrams for left censored observations from partial probability weighted moments

local cohomology of stanley reisner rings with supports in general monomial ideals we study the local cohomology modules hii k of the stanley reisner ring k of a simplicial complex with support in the ideal i k corresponding to a subcomplex we give a combinatorial topological formula for the multigraded hilbert series and in the case where the ambient complex is gorenstein compare this with a second combinatorial formula that generalizes results of mustata and terai the agreement between these two formulae is seen to be a disguised form of alexander duality other results include a comparison of the local cohomology with certain ext modules results about when it is concentrated in a single homological degree and combinatorial topological interpretations of some vanishing theorems

direct methods for primary decomposition leti be an ideal in a polynomial ring over a perfect field we given new methods for computing the equidimensional parts and radical ofi for localizingi with respect to another ideal and thus for finding the primary decomposition ofi our methods rest on modern ideas from commutative algebra and are direct in the sense that they avoid the generic projections used by hermann 1926 and all others until now

approximate confidence intervals for design floods for a single site using a neural network a basic problem in hydrology is the computation of confidence levels for the value of the t year flood when it is obtained from a log pearson iii distribution using the estimated mean estimated standard deviation and estimated skew here we give a practical method for finding approximate one sided or two sided confidence intervals for the 100 year flood based on data from a single site these confidence intervals are generally accurate to within a percent or two as tested by simulations and are obtained by use of a neural network

estimation of moments and quantiles using censored data censored data sets are often encountered in water quality investigations and streamflow analyses a monte carlo analysis examined the performance of three techniques for estimating the moments and quantiles of a distribution using censored data sets these techniques include a lognormal maximum likelihood estimator mle a log probability plot regression estimator and a new log partial probability weighted moment estimator data sets were generated from a number of distributions commonly used to describe water quality and water quantity variables a robust fill in method which circumvents transformation bias in the real space moments was implemented with all three estimation techniques to obtain a complete sample for computation of the sample mean and standard deviation regardless of the underlying distribution the mle generally performed as well as or better than the other estimators though the moment and quantile estimators using all three techniques had comparable log space root mean square errors rmse for censoring at or below the 20th percentile for samples sizes of n 10 the 40th percentile for n 25 and the 60th percentile for n 50 comparison of the log space rmse and real space rmse indicated that a log space rmse was a better overall metric of estimator precision

invariants of real forms of affine kac moody lie algebras abstract the theory of vogan diagrams which are dynkin diagrams with an overlay of certain additional information allows one to give a rapid classification of finite dimensional real semisimple lie algebras and to make use of this classification in practice this paper develops a corresponding theory of vogan diagrams for almost compact real forms of indecomposable nontwisted affine kac moody lie algebras in this case also the equivalence classes of vogan diagrams correspond to the isomorphism classes of almost compact real forms although the real forms of such algebras had already been classified the theory of vogan diagrams introduces invariants for such algebras and makes it possible to locate a given real form within the classification

robust flood frequency analysis performance of ema with multiple grubbs beck outlier tests flood frequency analysis generally involves the use of simple parametric probability distributions to smooth and extrapolate the information provided by short flood records to estimate extreme flood flow quantiles parametric probability distributions can have difficulty simultaneously fitting both the largest and smallest floods a danger is that the smallest observations in a record can distort the exceedance probabilities assigned to the large floods of interest the identification and treatment of such potentially influential low floods pilfs frees a fitting algorithm to describe the distribution of the larger observations this can allow parametric flood frequency analysis to be both efficient and also robust to deviations from the proposed probability model s lower tail historically pilf identification involved subjective judgement we propose a new multiple grubbs beck outlier test mgbt for objective pilf identification mgbt pilf identification rates akin to type i errors are reported for the lognormal ln distribution and the log pearson type iii lp3 distribution with a variety of skew coefficients mgbt pilf identification generally matched subjective identification from a recent california flood frequency study monte carlo results show that censoring of pilfs identified by the mgbt algorithm improves the extreme quantile estimator efficiency of the expected moments algorithm ema for negatively skewed lp3 distributions and has little effect for zero or positive skews simultaneously it protects against deviations from the lp3 in the lower tail as illustrated by distorted ln examples thus mgbt generally makes flood frequency analysis based on the lp3 distribution with ema both more accurate and more robust

maximum likelihood inference for left censored hiv rna data left censored data are characteristic of many bioassays due to inherent limit of detection and limit of quantitation loq in the assays this paper examines how the left censoring of plasma hiv rna measurements collected for the hemophilia growth and development study affects the quantification of viral load and the assessment of its association with a continuous or dichotomous outcome data analyses using maximum likelihood estimation are compared to analyses where the loq or loq 2 value is substituted for the left censored observations and also to other methods like multiple imputation a gaussian distribution is assumed for the log transformed plasma hiv rna data and simulations are used to explore the sensitivity of the results to changes in the model parameters the robustness of the estimators is also investigated when the data are generated from a mixture of two gaussian distributions maximum likelihood is in general the least biased method however multiple imputation assuming a censored gaussian imputation model and substituting the censored values with the expectation of its conditional predictive distribution are also competitive to maximum likelihood and may be appealing because of their simpler computational algorithms

plotting positions of annual flood extremes considering extraordinary values a generalized plotting position formula for estimation of the recurrence interval or its reciprocal the exceedance probability of hydrologic events in an incomplete data sample containing both extraordinarily large and small historical values is derived the derivation is based on order statistics analysis and is independent of the probability distribution of the hydrologic variable it is shown that the weibull formula is a special case of the generalized formula

comparisons of two moments based estimators that utilize historical and paleoflood data for the log pearson type iii distribution 1 the expected moments algorithm ema cohn et al 1997 and the bulletin 17b interagency committee on water data 1982 historical weighting procedure b17h for the log pearson type iii distribution are compared by monte carlo computer simulation for cases in which historical and or paleoflood data are available the relative performance of the estimators was explored for three cases fixed threshold exceedances a fixed number of large floods and floods generated from a different parent distribution ema can effectively incorporate four types of historical and paleoflood data floods where the discharge is explicitly known unknown discharges below a single threshold floods with unknown discharge that exceed some level and floods with discharges described in a range the b17h estimator can utilize only the first two types of historical information including historical paleoflood data in the simulation experiments significantly improved the quantile estimates in terms of mean square error and bias relative to using gage data alone ema performed significantly better than b17h in nearly all cases considered b17h performed as well as ema for estimating x100 in some limited fixed threshold exceedance cases ema performed comparatively much better in other fixed threshold situations for the single large flood case and in cases when estimating extreme floods equal to or greater than x500 b17h did not fully utilize historical information when the historical period exceeded 200 years robustness studies using gev simulated data confirmed that ema performed better than b17h overall ema is preferred to b17h when historical and paleoflood data are available for flood frequency analysis

algebraic groups with a commuting pair of involutions and semisimple symmetric spaces let g be a connected reductive algebraic group defined over an algebraically closed field f of characteristic not 2 denote the lie algebra of g by 9 in this paper we shall classify the isomorphism classes of ordered pairs of commuting involutorial automorphisms of g this is shown to be independent of the characteristic of f and can be applied to describe all semisimple locally symmetric spaces together with their line structure involutorial automorphisms of g occur in several places in the literature cartan has already shown that for f c the isomorphism classes of involutorial automorphisms of g correspond bijectively to the isomorphism classes of real semisimple lie algebras which correspond in their turn to the isomorphism classes of riemannian symmetric spaces see helgason 111 if one lifts this involution to the group g then the present work gives a characteristic free description of these isomorphism classes in a similar manner we can show that semisimple locally symmetric spaces correspond to pairs of commuting involutorial automorphisms of g namely let go a be a semisimple locally symmetric pair i e go is a real semisimple lie algebra and rr e aut g an involution then by a result of berger 2 there exists a cartan involution 8 of go such that 00 ea if we denote the complexilication of go by g then o and 8 induce a pair of commuting involutions of g conversely if c 8 e aut g are commuting involutions then c and 8 determine two locally semisimple symmetric pairs for if u is a o and o stable compact real form with conjugation r then ger 1 ge and g f3 i ger are semisimple locally symmetric pairs where

the common invariant subspace problem an approach via grobner bases let a be an n n matrix it is a relatively simple process to construct a homogeneous ideal generated by quadrics whose associated projective variety parametrizes the one dimensional invariant subspaces of a given a finite collection of n n matrices one can similarly construct a homogeneous ideal again generated by quadrics whose associated projective variety parametrizes the one dimensional subspaces which are invariant subspaces for every member of the collection grobner basis techniques then provide a finite rational algorithm to determine how many points are on this variety in other words a finite rational algorithm is given to determine both the existence and quantity of common one dimensional invariant subspaces to a set of matrices this is then extended for each d to an algorithm to determine both the existence and quantity of common d dimensional invariant subspaces to a set of matrices 2004 published by elsevier inc

alexander duality for stanley reisner rings and squarefree nn graded modules abstract let s k x1 xn be a polynomial ring and let s be its canonical module first we will define squarefreeness for n n graded s modules a stanley reisner ring k s i its syzygy module syzi k and extis k s are always squarefree this notion will simplify some standard arguments in the stanley reisner ring theory next we will prove that the i linear strand of the minimal free resolution of a stanley reisner ideal i s has the same information as the module structure of extis k s where is the alexander dual of in particular if k has a linear resolution we can describe its minimal free resolution using the module structure of the canonical module of k which is cohen macaulay in this case we can also give a new interpretation of a result of herzog and co workers which states that k is sequentially cohen macaulay if and only if i is componentwise linear

stochastic models applied to cluster analysis of censored water quality data a clustering method is presented which is appropriate when a mixture of multivariate distributions is used to model the data the procedure assumes that the measurements made on several independent characteristics follow probability distributions of different nature e g normal poisson multinomial likelihood methods are used to both estimate the parameters of the models and perform the cluster analysis the procedure is applicable when the data are subject to censoring a data set on the concentrations of volatile halocarbon contaminant in lake ontario is used to illustrate the methods of this paper

an algorithm for computing moments based flood quantile estimates when historical flood information is available this paper presents the expected moments algorithm ema a simple and efficient method for incorporating historical and paleoflood information into flood frequency studies ema can utilize three types of at site flood information systematic stream gage record information about the magnitude of historical floods and knowledge of the number of years in the historical period when no large flood occurred ema employs an iterative procedure to compute method of moments parameter estimates initial parameter estimates are calculated from systematic stream gage data these moments are then updated by including the measured historical peaks and the expected moments given the previously estimated parameters of the below threshold floods from the historical period the updated moments result in new parameter estimates and the last two steps are repeated until the algorithm converges monte carlo simulations compare ema bulletin 17b s united states water resources council 1982 historically weighted moments adjustment and maximum likelihood estimators when fitting the three parameters of the log pearson type iii distribution these simulations demonstrate that ema is more efficient than the bulletin 17b method and that it is nearly as efficient as maximum likelihood estimation mle the experiments also suggest that ema has two advantages over mle when dealing with the log pearson type iii distribution it appears that ema estimates always exist and that they are unique although neither result has been proven ema can be used with binomial or interval censored data and with any distributional family amenable to method of moments estimation

inferences about the mean from censored water quality data several methods which are commonly used for making inferences about the levels of many metals and organic contaminants in ambient waters from type i censored data are critically evaluated and their applications are illustrated using the concentrations of polychlorinated biphenyls in water samples from the niagara river difficulties encountered in the application of all the methods except the method of maximum likelihood include ignoring the information available about the analytical detection limit and the unavailability of the standard errors for these estimates under the assumption that the distribution of the data is lognormal the log regression method is modified to produce estimates of the censored values which use the detection limit information and the properties of the maximum likelihood estimates for the lognormal mean are derived furthermore an approximate confidence interval for the lognormal mean is given and its use for estimating the load to and from the niagara river is illustrated the above methods along with a modification to the method of maximum likelihood are evaluated using monte carlo simulation