growth rates for the linearized motion of fluid interfaces away from equilibrium we consider the motion of a two dimensional interface separating an inviscid incompressible irrotational fluid influenced by gravity from a region of zero density we show that under certain conditions the equations of motion linearized about a presumed time dependent solution are wellposed that is linear disturbances have a bounded rate of growth if surface tension is neglected the linear equations are well posed provided the underlying exact motion satisfies a condition on the acceleration of the interface relative to gravity similar to the criterion formulated by g i taylor if surface tension is included the linear equations are well posed without qualifications whether the fluid is above or below the interface an interesting qualitative structure is found for the linear equations a lagrangian approach is used like that of numerical work such as 3 except that the interface is assumed horizontal at infinity certain integral equations which occur involving double layer potentials are shown to be solvable in the present case 1993 john wiley sons inc

the foundations of factor analysis summary a new approach to factor analysis and related latent variable methods is proposed which is based on data reduction using the idea of bayesian sufficiency considerations of symmetry invariance and independence are used to determine an appropriate family of models the results are expressed in terms of linear functions of the manifest variables after the manner of principal components analysis the approach justifies some of the practices based on the normal theory factor model and lays a foundation for the treatment of nonnormal including categorical variables 1 background factor analysis is a widely used statistical technique but its theoretical foundations are somewhat obscure and subject to dispute it is one of a family of multivariate methods which also includes latent structure and latent trait analysis the common feature of the models underlying these methods is that the observed random variables are assumed to depend on latent that is unobserved random variables there is sometimes debate about whether these latent variables are real in any sense but they can be viewed simply as constructs designed to simplify and summarize the complex web of interrelated variables with which nature confronts us by expressing these relationships in terms of a small number of latent variables or factors the models effect a reduction in dimensionality which aids comprehension an early theoretical account of the subject is by anderson rubin 1956 and more recent and comprehensive treatments are provided by lawley maxwell 1971 and harman 1968 the present paper is an attempt to provide a coherent framework within which existing methodology can be evaluated and a base from which new methods can be developed our approach is to start from a very general statement of the problem in terms of the distributions of the random variables involved and then to invoke ideas of symmetry invariance and conditional independence to determine the class of models that it is reasonable to consider this not only exhibits the unity of the various models already in existence but resolves many of the ambiguities and obscurities with which the subject has been bedevilled an early approach on these lines is given by anderson 1959 and was recognized by birnbaum in his contribution to lord novick 1968 the same line was followed by bartholomew 1980 in spite of this the practical implications do not seem to have been made fully explicit or generally recognized

characterizing the manifest probabilities of latent trait models the problem of characterizing the manifest probabilities of a latent trait model is considered the item characteristic curve is transformed to the item passing odds curve and a corresponding transformation is made on the distribution of ability this results in a useful expression for the manifest probabilities of any latent trait model the result is then applied to give a characterization of the rasch model as a log linear model for a 2 j contingency table partial results are also obtained for other models the question of the identifiability of guessing parameters is also discussed

nucleation and growth in one dimension we study statistical properties of the kolmogorov avrami johnson mehl nucleation and growth model in one dimension we obtain exact results for the gap density as well as the island distribution when all nucleation events occur simultaneously we show that the island distribution has discontinuous derivatives on the rays mathit x mathit n t nt n 1 2 3 we introduce an accelerated growth mechanism with growth rate increasing linearly with the island size we solve for the interisland gap density and show that the system reaches complete coverage in a finite time and that the near critical behavior of the system is robust i e it is insensitive to details such as the nucleation mechanism textcopyright 1996 the american physical society

convergence of a non stiff boundary integral method for interfacial flows with surface tension boundary integral methods to simulate interfacial flows are very sensitive to numerical instabilities in addition surface tension introduces nonlinear terms with high order spatial derivatives into the interface dynamics this makes the spatial discretization even more difficult and at the same time imposes a severe time step constraint for stable explicit time integration methods a proof of the convergence of a reformulated boundary integral method for two density fluid interfaces with surface tension is presented the method is based on a scheme introduced by hou lowengrub and shelley j comp phys 114 1994 pp 312 338 to remove the high order stability constraint or stiffness some numerical filtering is applied carefully at certain places in the discretization to guarantee stability the key of the proof is to identify the most singular terms of the method and to sho through energy estimates that these terms balance one another the analysis is at a time continuous space discrete level but a fully discrete case for a simple hele shaw interface is also studied the time discrete analysis shows that the high order stiffness is removed and also provides an estimate of how the cfl constraint depends on the curvature and regularity of the solution the robustness of the method is illustrated with several numerical examples a numerical simulation of an unstably stratified two density interfacial flow shows the roll up of the interface the computations proceed up to a time where the interface is about to pinch off and trapped bubbles of fluid are formed the method remains stable even in the full nonlinear regime of motion another application of the method shows the process of drop formation in a falling single fluid

torsional effects in high order viscoelastic thin filament models the authors present an approximation theory for thin filaments fibers or jets which yields families of transient 1 d models time dependent one dimensional closed systems of pdes the spatial reduction from three dimensions to one is achieved by axisymmetry together with a local expansion in the radial jet coordinate this reduction is in contrast to the predominant viscoelastic models in the literature which average out the radial dimension and thereby require moment equations for the computation of higher order corrections the authors also allow torsional flow effects which are usually ignored in a general johnson segalman constitutive law a formal perturbation theory based on a slenderness parameter and a compatible velocity pressure stress ansatz is then constructed for the full 3 d free surface boundary problem this formalism contains all 1 d transient models that govern slender axisymmetric flows of inviscid viscous or viscoelastic fluids specific models follow by positing the dominant

absence of non trivial asymptotic scaling in the kashchiev model of polynuclear growth in this brief comment we show that contrary to previous claims bartelt and evans the asymptotic behaviour of the kashchiev model of polynuclear growth is trivial in all spatial dimensions and therefore lies outside the kardar parisi zhang universality class

can randomness alone tune the fractal dimension abstract we present a generalized stochastic cantor set by means of a simple cut and delete process and discuss the self similar properties of the arising geometric structure to increase the flexibility of the model two free parameters m and b are introduced which tune the relative strength of the two processes and the degree of randomness respectively in doing so we have identified a new set with a wide spectrum of subsets produced by tuning either m or b measuring the size of the resulting set in terms of fractal dimension we show that the fractal dimension increases with increasing order and reaches its maximum value when the randomness is completely ceased

a rasch model for partial credit scoring a unidimensional latent trait model for responses scored in two or more ordered categories is developed this partial credit model is a member of the family of latent trait models which share the property of parameter separability and so permit specifically objective comparisons of persons and items the model can be viewed as an extension of andrich s rating scale model to situations in which ordered response alternatives are free to vary in number and structure from item to item the difference between the parameters in this model and the category boundaries in samejima s graded response model is demonstrated an unconditional maximum likelihood procedure for estimating the model parameters is developed

long time existence for a slightly perturbed vortex sheet consider a flat two dimensional vortex sheet perturbed initially by a small analytic disturbance by a formal perturbation analysis moore derived an approximate differential equation for the evolution of the vortex sheet we present a simplified derivation of moore s approximate equation and analyze errors in the approximation the result is used to prove existence of smooth solutions for long time if the initial perturbation is of size and is analytic in a strip m existence of a smooth solution of birkhoff s equation is shown for time t k2p if is sufficiently small with 1 as 0 for the particular case of sinusoidal data of wave length and amplitude e moore s analysis and independent numerical results show singularity development at time tc log o log log our results prove existence for t log if is sufficiently small with k 1 as 0 thus our existence results are nearly optimal

independence via uncorrelatedness under certain dependence structures a characterization of independence via uncorrelatedness is shown to hold for the families satisfying positive and negative dependence conditions for the associated random variables the bounds on covariance functions obtained by lebowitz comm math phys 28 1972 313 321 readily yield such a characterization an elementary proof for the same characterization is also given for a condition weaker than association labeled as strong positive negative orthant dependence this condition is compared with the linear positive dependence under which newman and wright ann probab 9 1981 671 675 obtained the characterization

stable methods for vortex sheet motion in the presence of surface tension boundary integral techniques provide a convenient way to study the evolution of an interface between inviscid liquids several studies have revealed that standard numerical approximations tend to lead to unstable methods and various remedies have been introduced and tested in this paper we conduct a stability analysis of the linearized equations with a particular objective in mind the determination of how the discrete system fails to capture the physical dispersion relation precisely for the available discrete modes we discover two reasons for the typical failure in numerical discretizations one is the inability of the mesh to represent the vorticity created by surface tension effects on the finest scale and the other is the inaccuracies in the evaluation of the boundary integral for the velocity with the insight gained from our linear analysis we propose a new method that is spectrally accurate and linearly stable further the exact dispersion relation is obtained for all the available discrete modes numerical tests suggest that the method is also stable in the nonlinear regime however our method runs into difficulties generic to methods based on lagrangian motion the markers accumulate near a stagnation point on the interface forcing us to use an ever decreasing time step in our explicit method we introduce a redistribution of markers to overcome this difficulty when we redistribute according to equal arclength we find excellent agreement with a method based on preserving equal spacing in arclength

differential effects and generic biases in observational studies there are two treatments each of which may be applied or withheld yielding a 2 2 factorial arrangement with three degrees of freedom between groups the differential effect of the two treatments is the effect of applying one treatment in lieu of the other in randomised experiments the differential effect is of no more or less interest than other treatment contrasts differential effects play a special role in certain observational studies in which treatments are not assigned to subjects at random where differing outcomes may reflect biased assignments rather than effects caused by the treatments differential effects are immune to certain types of unobserved bias called generic biases which are associated with both treatments in a similar way this is explored using several examples and models differential effects are not immune to differential biases whose possible consequences are examined by sensitivity analysis

the dutch identity a new tool for the study of item response models the dutch identity is a useful way to reexpress the basic equations of item response models that relate the manifest probabilities to the item response functions irfs and the latent trait distribution the identity may be exploited in several ways for example a to suggest how item response models behave for large numbers of items they are approximate submodels of second order loglinear models for 2 j tables b to suggest new ways to assess the dimensionality of the latent trait principle components analysis of matrices composed of second order interactions from loglinear models c to give insight into the structure of latent class models and d to illuminate the problem of identifying the irfs and the latent trait distribution from sample data

singularity formation for complex solutions of the 3d incompressible euler equations abstract moore s approximation method first formulated for vortex sheets is generalized and applied to axi symmetric flow with swirl and with smooth initial data the approximation preserves the forward cascade of energy but neglects any backflow of energy it splits the euler equations into two sets of equations one for u u r z t containing all non negative wavenumbers in z and the second for u u the equations for u are exactly the euler equations but with complex initial data traveling waves solutions u u r z i t with imaginary wave speed are found numerically for this problem the asymptotic properties of the resulting fourier coefficients show a singularity forming in finite time at which the velocity blows up

properties of and algorithms for fitting three way component models with offset terms prior to a three way component analysis of a three way data set it is customary to preprocess the data by centering and or rescaling them harshman and lundy 1984 considered that three way data actually consist of a three way model part which in fact pertains to ratio scale measurements as well as additive offset terms that turn the ratio scale measurements into interval scale measurements they mentioned that such offset terms might be estimated by incorporating additional components in the model but discarded this idea in favor of an approach to remove such terms from the model by means of centering then estimates for the three way component model parameters are obtained by analyzing the centered data in the present paper the possibility of actually estimating the offset terms is taken up again first it is mentioned in which cases such offset terms can be estimated uniquely next procedures are offered for estimating model parameters and offset parameters simultaneously as well as successively i e providing offset term estimates after the three way model parameters have been estimated in the traditional way on the basis of the centered data these procedures are provided for both the candecomp parafac model and the tucker3 model extended with offset terms the successive and the simultaneous approaches for estimating model and offset parameters have been compared on the basis of simulated data it was found that both procedures perform well when the fitted model captures at least all offset terms actually underlying the data the simultaneous procedures performed slightly better than the successive procedures if fewer offset terms are fitted than there are underlying the model the results are considerably poorer but in these cases the successive procedures performed better than the simultaneous ones all in all it can be concluded that the traditional approach for estimating model parameters can hardly be improved upon and that offset terms can sufficiently well be estimated by the proposed successive approach which is a simple extension of the traditional approach

slender jets and thin sheets with surface tension simplified equations governing the potential flow and the shape of slender jets and thin sheets of liquid are derived taking into account surface tension families of similarity solutions of these equations are introduced for jets and for symmetrical sheets they satisfy ordinary differential equations the properties of these similarity solutions are examined analytically and numerically they can be used to describe the motion of a liquid sheet on a solid the thickening and flow following the breaking of jets the merging of two jets the formation or closing of holes or slits in sheets etc some applications to such problems are given

axisymmetric vortex sheet motion accurate evaluation of the principal value integral this paper concerns the accurate evaluation of the principal value integral governing axisymmetric vortex sheet motion previous quadrature rules for this integral lose accuracy near the axis of symmetry an approximation by de bernadinis and moore dbm that converges pointwise at the rate of o h3 has maximal errors near the axis that are o h as a result the discretization error is not smooth it contains high wavenumber frequencies that make it difficult to resolve the vortex sheet motion this paper explains the reason for the degeneracy near the axis and proposes a modified quadrature rule that is uniformly o h3 the results are based on an analytic approximation of the integrand whose integral can be precomputed the modification is implemented at negligible additional cost per timestep as an example it is applied to compute the evolution of an initially spherical vortex sheet

universal large deviation function of the kardar parisi zhang equation in one dimension using the bethe ansatz we calculate the whole large deviation function of the displacement of particles in the asymmetric simple exclusion process asep on a ring when the size of the ring is large the central part of this large deviation function takes a scaling form independent of the density of particles we suggest that this scaling function found for the asep is universal and should be characteristic of all the systems described by the kardar parisi zhang equation in 1 1 dimension simulations done on two simple growth models are in reasonable agreement with this conjecture

conditional association and unidimensionality in monotone latent variable models latent variable models represent the joint distribution of observable variables in terms of a simple structure involving unobserved or latent variables usually assuming the conditional independence of the observable variables given the latent variables these models play an important role in educational measurement and psychometrics in sociology and in population genetics and are implicit in some work on systems reliability we study a broad class of latent variable models namely the monotone unidimensional models in which the latent variable is a scalar the observable variables are conditionally independent given the latent variable and the conditional distribution of the observables given the latent variable is stochastically increasing in the latent variable all models in this class imply a new strong form of positive dependence among the observable variables namely conditional positive association this positive dependence condition may be used to test whether any model in this class can provide an adequate fit to observed data various applications generalizations and a numerical example are discussed

the central role of the propensity score in observational studies for causal effects abstract the results of observational studies are often disputed because of nonrandom treatment assignment for example patients at greater risk may be overrepresented in some treatment group this paper discusses the central role of propensity scores and balancing scores in the analysis of observational studies the propensity score is the estimated conditional probability of assignment to a particular treatment given a vector of observed covariates both large and small sample theory show that adjustment for the scalar propensity score is sufficient to remove bias due to all observed covariates applications include matched sampling on the univariate propensity score which is equal percent bias reducing under more general conditions than required for discriminant matching multivariate adjustment by subclassification on balancing scores where the same subclasses are used to estimate treatment effects for all outcome variables and in all subpopulations and visual representation of multivariate adjustment by a two dimensional plot author

a boundary integral approach to unstable solidification we consider the supercooled stefan problem with a general anisotropic curvature and velocity dependent boundary condition on the moving interface we present numerical methods based on an integral equation formulation and including a new algorithm for moving curves with curvature dependent velocity these methods compute a periodic interface with o t accuracy where t is the time step previous work has been limited to short time spans and achieved slightly less than o t12 accuracy accurate numerical results are seen to agree with the predictions of linear stability theory this agreement has eluded previous authors because their numerical methods suffered from grid effects and their linear stability theory was incorrect we study the long time evolution of an unstable interface our computations exhibit the beginnings of a sidebranching instability when the boundary condition includes anisotropy and tip splitting in the isotropic case

reconstructing dna replication kinetics from small dna fragments in higher organisms dna replicates simultaneously from many origins recent in vitro experiments have yielded large amounts of data on the state of replication of dna fragments from measurements of the time dependence of the average size of replicated and nonreplicated domains one can estimate the rate of initiation of dna replication origins as well as the average rate at which dna bases are copied one problem in making such estimates is that in the experiments the dna is broken up into small fragments whose finite size can bias downward the measured averages here we present a systematic way of accounting for this bias by deriving theoretical relationships between the original domain length distributions and fragment domain length distributions we also derive unbiased average domain length estimators that yield accurate results even in cases where the replicated or nonreplicated domains are larger than the average dna fragment then we apply these estimators to previously obtained experimental data to extract improved estimates of replication kinetics parameters

nucleation and growth in one dimension i the generalized kolmogorov johnson mehl avrami model motivated by a recent application of the kolmogorov johnson mehl avrami skjmad model to the study of dna replication we consider the one dimensional s1dd version of this model we generalize previous work to the case where the nucleation rate is an arbitrary function istd and obtain analytical results for the timedependent distributions of various quantities ssuch as the island distributiond we also present improved computer simulation algorithms to study the 1d kjma model the analytical results and simulations are in excellent agreement

application of adaptive quadrature to axi symmetric vortex sheet motion studies of the formation of fine structures on free surfaces in liquids such as curvature singularities or interface pinching demand that the motion of the interface must be computed very accurately boundary integral techniques are a popular choice in such studies because they reduce the dimension of the problem by one on the other hand the boundary integrals are singular and their accurate evaluation can prove quite challenging in two dimensional motion the interface is just a curve when this curve is closed or periodic the singularity in the integrand may be removed and the trapezoidal rule may be applied with spectral accuracy unfortunately the nature of the singularity in the integrand for three dimensional motion is much more difficult to treat in this paper we present an accurate adaptive quadrature to compute the motion of a vortex sheet in axi symmetric flow the technique is based on a vector potential formulation which offers some computational advantages over other methods based on the biot savart integral direct numerical computations show that our technique is much more accurate and efficient than existing techniques we apply our technique to study the evolution of an initially spherical vortex sheet we present evidence of the formation of a 3 2 power singularity in the curvature of the vortex sheet

droplet and bubble pinch off computations using level sets a two fluid potential flow model is employed to analyze the pinching characteristics of an inviscid fluid immersed in a second inviscid fluid of different density the system behavior is controlled by the relative density of the two fluids d r e r i where d 0 corresponds to droplets in air and d 100 to bubbles in water the numerical method employed combines the level set method for advancing the free surface position and boundary condition together with a 3d axisymmetric boundary integral formulation to obtain fluid velocities this approach provides a numerical methodology to analyze the pinch off behavior up to and beyond the initial break up of the inner fluid the combined algorithm is validated using the analytical solution for an oscillating sphere a series of numerical experiments up to and beyond the initial break up of the inner fluid have been carried out for the two extremes d 0 and d 100 the calculated scaling exponents match the theoretical values and the computed front profiles are in good agreement with recent experimental findings

study of cylindrical jet breakup using one dimensional approximations of the euler equations we study the phenomenon of pinching of inviscid incompressible jets when surface tension is important this is done by analyzing one dimensional models derived by use of slender jet theory equations are derived for both single and two fluid arrangements higher order terms are retained for regularization purposes in the absence of a surrounding fluid these equations are the inviscid cosserat system it is shown that the leading order system terminates in infinite slope singularities before pinching happens this is achieved by studying a 2 x 2 system of conservation laws in the complex plane and by numerical solution of the evolution equations inclusion of higher order terms changes the order of the evolution equations and enables the one dimensional models to produce the phenomenon of pinching and drop formation in many cases the evolution equations are solved numerically and the numerical experiments suggest that the interface develops a cusp locally as the jet pinches local similarity solutions

multi valued solutions and branch point singularities for nonlinear hyperbolic or elliptic systems multi valued solutions are constructed for 2 2 first order systems using a generalization of the hodograph transformation the solution is found as a complex analytic function on a complex riemann surface for which the branch points move as part of the solution the branch point singularities are envelopes for the characteristics and thus move at the characteristic speeds we perform an analysis of stability of these singularities with respect to perturbations of the initial data the generic singularity types are folds cusps and nondegenerate umbilic points with non zero 3 jet an isolated singularity is generically a square root branch point corresponding to a fold two types of collisions between singularities are generic at a tangential collision between two singularities moving at the same characteristic speed a cube root branch point is formed corresponding to a cusp a non tangential collision between two square root branch points moving at different characteristic speeds remains a square root branch point at the collision and corresponds to a nondegenerate umbilic point these results are also valid for a diagonalizable n th order system for which there are exactly two speeds 1993 john wiley sons inc

design sensitivity in observational studies summary outside the field of statistics the literature on observational studies offers advice about research designs or strategies for judging whether or not an association is causal such as multiple operationalism or a dose response relationship these useful suggestions are typically informal and qualitative a quantitative measure design sensitivity is proposed for measuring the contribution such strategies make in distinguishing causal effects from hidden biases several common strategies are then evaluated in terms of their contribution to design sensitivity a related method for computing the power of a sensitivity analysis is also developed

testing the conditional independence and monotonicity assumptions of item response theory when item characteristic curves are nondecreasing functions of a latent variable the conditional or local independence of item responses given the latent variable implies nonnegative conditional covariances between all monotone increasing functions of a set of item responses given any function of the remaining item responses this general result provides a basis for testing the conditional independence assumption without first specifying a parametric form for the nondecreasing item characteristic curves the proposed tests are simple have known asymptotic null distributions and possess certain optimal properties in an example the conditional independence hypothesis is rejected for all possible forms of monotone item characteristic curves

m matrices as covariance matrices of multinormal distributions abstract the class of multivariate normal densities n 0 whose inverse covariance matrix 1 is an m matrix is equivalent to this normal density being multivariate totally positive of order 2 mtp 2 equivalent characterizations are given in terms of certain partial correlation coefficients being positive it is further shown that related partial and multiple regression coefficients and canonical correlation are positive when is an m matrix the corresponding normal random vector components are negatively associated this concept and some extensions are discussed

mean field theory of polynuclear surface growth we study statistical properties of a continuum model of polynuclear surface growth on an infinite substrate we develop a self consistent mean field theory which is solved to deduce the growth velocity and the extremal behaviour of the coverage numerical simulations show that this theory gives an improved approximation for the coverage compared to the previous linear recursion relations approach furthermore these two approximations provide useful upper and lower bounds for a number of characteristics including the coverage growth velocity and the width exponent

computation of axisymmetric suction flow through porous media in the presence of surface tension abstract the effect of small surface tension on a class of axisymmetric flows with suction is studied numerically the dynamic evolution of a blob of incompressible viscous fluid surrounded by air and drawn into an interior sink is considered the velocity field of the viscous fluid is assumed to satisfy darcy s law and thus the motion is that of a flow through porous media the fluid interface motion is computed using a highly accurate boundary integral method this method combines recent numerical techniques to achieve efficient and high order space and time discretizations for this type of flow through accurate computations it is shown that in the presence of small surface tension the dynamic behavior of the axisymmetric flows is very similar to that of the two dimensional hele shaw counterparts a long finger develops in the fluid interface and forms a cone singularity when it reaches the sink before all the fluid is sucked out the finger bulges and develops a neck for sufficiently small surface tension the bulge neck formation is enhanced by the additional component of the mean curvature in the three dimensional flow however its effect is not strong enough to cause the interface to pinch off at the neck for the data considered here

mean field theory for skewed height profiles in kpz growth processes we propose a mean field theory for interfaces growing according to the kardar parisi zhang kpz equation in 1 1 dimensions the mean field equations are formulated in terms of densities at different heights taking surface tension and the influence of the nonlinear term in the kpz equation into account although spatial correlations are neglected the mean field equations still reflect the spatial dimensionality of the system in the special case of edwards wilkinson growth our mean field theory correctly reproduces all features in the presence of a nonlinear term one observes a crossover to a kpz like behaviour with the correct dynamical exponent z 3 2 in particular we compute the skewed interface profile during roughening and we study the influence of a co moving reflecting wall which has been discussed recently in the context of nonequilibrium wetting and synchronization transitions also here the mean field approximation reproduces all qualitative features of the full kpz equation although with different values of the surface exponents

comparing item characteristic curves test items are often evaluated and compared by contrasting the shapes of their item characteristics curves icc s or surfaces the current paper develops and applies three general i e nonparametric comparisons of the shapes of two item characteristic surfaces i proportional latent odds ii uniform relative difficulty and iii item sensitivity two items may be compared in these ways while making no assumption about the shapes of item characteristic surfaces for other items and no assumption about the dimensionality of the latent variable also studied is a method for comparing the relative shapes of two item characteristic curves in two examinee populations

asymptotic separability in sensitivity analysis summary in an observational study in which each treated subject is matched to several untreated controls by using observed pretreatment covariates a sensitivity analysis asks how hidden biases due to unobserved covariates might alter the conclusions the bounds required for a sensitivity analysis are the solution to an optimization problem in general this optimization problem is not separable in the sense that one cannot find the needed optimum by performing a separate optimization in each matched set and combining the results we show however that this optimization problem is asymptotically separable so that when there are many matched sets a separate optimization may be performed in each matched set and the results combined to yield the correct optimum with negligible error this is true when the wilcoxon rank sum test or the hodgeslehmann aligned rank test is applied in matching with multiple controls numerical calculations show that the asymptotic approximation performs well with as few as 10 matched sets in the case of the rank sum test a table is given containing the separable solution with this table only simple arithmetic is required to conduct the sensitivity analysis the method also supplies estimates such as the hodges lehmann estimate and confidence intervals associated with rank tests the method is illustrated in a study of dropping out of us high schools and the effects on cognitive test scores

tail measurability in monotone latent variable models we consider latent variable models for an infinite sequence or universe of manifest observable variables that may be discrete continuous or some combination of these the main theorem is a general characterization by empirical conditions of when it is possible to construct latent variable models that satisfy unidimensionality monotonicity conditional independence andtail measurability tail measurability means that the latent variable can be estimated consistently from the sequence of manifest variables even though an arbitrary finite subsequence has been removed the characterizing necessary and sufficient conditions that the manifest variables must satisfy for these models are conditional association and vanishing conditional dependence as one conditions upon successively more other manifest variables our main theorem considerably generalizes and sharpens earlier results of ellis and van den wollenberg 1993 holland and rosenbaum 1986 and junker 1993 it is also related to the work of stout 1990 the main theorem is preceded by many results for latent variable modelsin general not necessarily unidimensional and monotone they pertain to the uniqueness of latent variables and are connected with the conditional independence theorem of suppes and zanotti 1981 we discuss new definitions of the concepts of true score and subpopulation which generalize these notions from the stochastic subject random sampling and domain sampling formulations of latent variable models e g holland 1990 lord novick 1968 these definitions do not require the a priori specification of a latent variable model

kinetics of magnetization switching in a 1 d system size distribution of unswitched domains abstract we construct the evolution equation of the size distribution function of the unswitched domains of a model of a 1 d system in a switching field and solve it as an initial value problem as the time goes on the distribution approaches to the fixed point which is the exponential distribution this feature is unaffected by the finiteness of the critical radius of nucleation

quantiles in nonrandom samples and observational studies abstract in a nonrandom sample or a nonrandomized comparison of treated and control groups methods are developed for displaying the sensitivity of confidence intervals for population quantiles to the magnitude of the departure from random selection quantiles of a single distribution and for a shift in two distributions are both discussed these confidence intervals are based on a new inequality for the distribution of the number of successes in a nonrandom sample or nonrandomized comparison the inequality has additional applications in particular it greatly accelerates the computations in a sensitivity analysis for the mantel haenszel statistic in a 2 2 s contingency table examples include a nonrandom collection of blood samples from a town with comparatively high levels of radon gas an observational study of chromosome damage from mercury and a study of the drug allopurinol as a cause of skin rash the proof of the inequality makes use of savage s lattice for ranks and holley s inequality wh

comparing latent structures of the grade of membership rasch and latent class models this paper focuses on model interpretation issues and employs a geometric approach to compare the potential value of using the grade of membership gom model in representing population heterogeneity we consider population heterogeneity manifolds generated by letting subject specific parameters vary over their natural range while keeping other population parameters fixed in the marginal space based on marginal probabilities and in the full parameter space based on cell probabilities the case of a 2 2 contingency table is discussed in detail and a generalization to 2j tables with j 3 is sketched our approach highlights the main distinction between the gom model and the probabilistic mixture of classes by demonstrating geometrically the difference between the concepts of partial and probabilistic memberships by using the geometric approach we show that in special cases the gom model can be thought of as being similar to an item response theory irt model in representing population heterogeneity finally we show that the gom item parameters can provide quantities analogous to more general logistic irt item parameters as a latent structure model the gom model might be considered a useful alternative for a data analysis when both classes of extreme responses and additional heterogeneity that cannot be captured by those latent classes are expected in the population

statistical self similarity of one dimensional growth processes abstract for one dimensional growth processes we consider the distribution of the height above a given point of the substrate and study its scale invariance in the limit of large times we argue that for self similar growth from a single seed the universal distribution is the tracy widom distribution from the theory of random matrices and that for the growth from a flat substrate it is some other only numerically determined distribution in particular for the polynuclear growth model in the droplet geometry the height maps onto the longest increasing subsequence of a random permutation from which the height distribution is identified as the tracy widom distribution

removing the stiffness from interfacial flows with surface tension a new formulation and new methods are presented for computing the motion of fluid interfaces with surface tension in two dimensional irrotational and incompressible fluids through the laplace young condition at the interface surface tension introduces high order terms both nonlinear and nonlocal into the dynamics this leads to severe stability constraints for explicit time integration methods and makes the application of implicit methods difficult this new formulation has all the nice properties for time integration methods that are associated with having a linear constant coefficient highest order term that is using this formulation we give implicit time integration methods that have no high order time step stability constraint associated with surface tension and are explicit in fourier space the approach is based on a boundary integral formulation and applies more generally even to problems beyond the fluid mechanical context here they are applied to computing with high resolution the motion of interfaces in hele shaw flows and the motion of free surfaces in inviscid flows governed by the euler equations one hele shaw computation shows the behavior of an expanding gas bubble over long time as the interface undergoes successive tip splittings and finger competition a second computation shows the formation of a very ramified interface through the interaction of surface tension with an unstable density stratification in euler flows the computation of a vortex sheet shows its roll up through the kelvin helmholtz instability this motion culminates in the late time self intersection of the interface creating trapped bubbles of fluid this is we believe a type of singularity formation previously unobserved for such flows in 2d finally computations of falling plumes in an unstably stratified boussinesq fluid show a very similar behavior

dynamics of slender viscoelastic free jets previous studies of slender viscoelastic and newtonian free surface jets have focused mainly on steady state predictions guided primarily by industrial textile applications dynamical analyses and simulations of fiber flows even the linearized stability analysis of nontrivial steady states have lagged behind considerable experimental and textile processing observations and advances the foundational work of chang and lodge rheol acta 10 1971 pp 448 449 and petrie rheol acta 14 1975 pp 955 957 elongational flows pitman london 1979 has been extended by the axisymmetric modeling and simulation of beris and liu j non newtonian fluid mech 26 1988 pp 363 394 comput methods appl mech engrg 76 1989 pp 179 204 for maxwell fluids and markovich and renardy j non newtonian fluid mech 17 1985 pp 13 22 for johnson segalman fluids the model in markovich and renardy is a single nonlinear parabolic equation in which elastic retardation provides dominant smooth

numerical simulations of inviscid capillary pinchoff inviscid capillary pinchoff is studied numerically for an axisymmetric model problem in which a bubble pinches at two points on the symmetry plane breaking into two symmetric end bubbles and a satellite bubble in between results are presented for a range of density jumps across the bubble the numerical method uses a formulation in terms of arclength and tangent angle and incorporates a new procedure to redistribute the computational points dynamically in order to maintain resolution in regions of high curvature the results are compared with alternative computations by lepinnen and lister phys fluids 15 2003 568 where available new results include details about the cone crater structure near pinchoff and the dependence of satellite bubble volume and pinchoff time on the density ratio

high order quadratures for the evaluation of interfacial velocities in axi symmetric stokes flows we propose new high order accurate methods to compute the evolution of axi symmetric interfacial stokes flow the velocity at a point on the interface is given by an integral over the surface quadrature rules to evaluate these integrals are developed using asymptotic expansions of the integrands both locally about the point of evaluation and about the poles where the interface crosses the axis of symmetry the local expansions yield methods that converge to the chosen order pointwise for fixed evaluation point the pole expansions yield corrections that remove maximal errors of low order introduced by singular behaviour of the integrands as the evaluation point approaches the poles an interesting example of roundoff error amplification due to cancellation is also addressed the result is a uniformly accurate fifth order method second order pointwise fifth order and uniform fifth order methods are applied to compute three sample flows each of which presents a different computational difficulty an initially bar belled drop that pinches in finite time a drop in a strain flow that approaches a steady state and a continuously extending drop in each case the fifth order methods significantly improve the ability to resolve the flow the examples furthermore give insight into the effect of the corrections needed for uniformity we determine conditions under which the pointwise method is sufficient to obtain resolved results and others under which the corrections significantly improve the results

initial evolution of kashchiev models of thin film growth the authors consider a continuum model of thin film growth on an infinite perfect substrate multilayers grow by random nucleation of islands at fixed rate followed by lateral expansion at constant speed the focus is on the evolution of the film profile in the regime of small thicknesses they present results for the layer coverages the interface width and the bragg intensity oscillations obtained by numerical integration of the original kashchiev recursion relations asymptotically the model shows kardar parisi zhang universality scaling expressions for spatial correlation functions are also developed

when are item response models consistent with observed data the problem of deciding whether a set of mental test data is consistent with any one of a large class of item response models is considered the classical assumption of locla independence is weakened to a new condition local nonnegative dependence lnd necessary and sufficient conditions are derived for a lnd item response model to fit a set of data this leads to a condition that a set of data must satisfy if it is to be representable by any item response model that assumes both local independence and monotone item characteristic curves an example is given to show that lnd is strictly weaker than local independence thus rejection of lnd models implies rejection of all item response models that assume local independence for a given set of data

the korteweg de vries hierarchy as dynamics of closed curves in the plane the korteweg de vries modified korteweg de vries and harry dym hierarchies of integrable systems are shown to be equivalent to a hierarchy of chiral shape dynamics of closed curves in the plane these purely local dynamics conserve an infinite number of global geometric properties of the curves such as perimeter and enclosed area several techniques used to study these integrable systems are shown to have simple differential geometric interpretations connections with incompressible inviscid fluid flow in two dimensions are suggested