on the estimation of a probability density function by the maximum penalized likelihood method abstract a class of probability density estimates can be obtained by penalizing the likelihood by a functional which depends on the roughness of the logarithm of the density the limiting case of the estimates as the amount of smoothing increasing has a natural form which makes the method attractive for data analysis and which provides a rationale for a particular choice of roughness penalty the estimates are shown to be the solution of an unconstrained convex optimization problem and mild natural conditions are given for them to exist rates of consistency in various norms and conditions for asymptotic normality and approximation by a gaussian process are given thus breaking new ground in the theory of maximum penalized likelihood density estimation author

on stabilizing effect of elasticity in the rayleigh taylor problem of stratified viscoelastic fluids abstract we investigate the stabilizing effect of elasticity in the rayleigh taylor rt problem of stratified immiscible viscoelastic fluids separated by a free interface and in the presence of a uniform gravitational field in a horizontally periodic domain where the velocities of the fluids are non slip on both upper and lower fixed flat boundaries while the internal surface tension is omitted we establish a discriminant c r for the stability of the stratified viscoelastic rt problem more precisely if c r 1 then the stratified viscoelastic rt equilibrium state is exponentially stable this means that a sufficiently large elasticity coefficient has stabilizing effect so that it can inhibit viscoelastic rt instability on the other hand if c r 1 then we show that the rt equilibrium state is linearly unstable in the hadamard sense moreover for the case of a nonhomogeneous incompressible viscoelastic fluid the condition c r 1 will lead to the nonlinear instability of the rt equilibrium state and this shows that the rt instability still occurs in viscoelastic fluids when the elasticity coefficient is small

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

the essential spectrum of advective equations the geometric optics stability method is extended to a general class of linear advective pde s with pseudodifferential bounded perturbation we give a new short proof of vishik s formula for the essential spectral radius we show that every point in the dynamical spectrum of the corresponding bicharacteristic amplitude system contributes a point into the essential spectrum of the pde generic spectral pictures are obtained in sobolev spaces of sufficiently large smoothness applications to instability are presented

fredholm differential operators with unbounded coefficients abstract we prove that a first order linear differential operator g with unbounded operator coefficients is fredholm on spaces of functions on r with values in a reflexive banach space if and only if the corresponding strongly continuous evolution family has exponential dichotomies on both r and r and a pair of the ranges of the dichotomy projections is fredholm and that the fredholm index of g is equal to the fredholm index of the pair the operator g is the generator of the evolution semigroup associated with the evolution family in the case when the evolution family is the propagator of a well posed differential equation u t a t u t with generally unbounded operators a t t r the operator g is a closure of the operator d dt a t thus this paper provides a complete infinite dimensional generalization of well known finite dimensional results by palmer and by ben artzi and gohberg

quasi hyperbolic semigroups abstract we introduce the notion of quasi hyperbolic operators and c 0 semigroups examples include the push forward operator associated with a quasi anosov diffeomorphism or flow a quasi hyperbolic operator can be characterised by a simple spectral property or as the restriction of a hyperbolic operator to an invariant subspace there is a corresponding spectral property for the generator of a c 0 semigroup and it characterises quasi hyperbolicity on hilbert spaces but not on other banach spaces we exhibit some weaker properties which are implied by the spectral property

standard error of ability estimates and the classification accuracy and consistency of binary decisions while estimation bias is a primary concern in psychological and educational measurement the standard error is of equal importance in linking key aspects of the assessment structure especially when the assessment goal concerns the classification of individuals into categories e g master non mastery in this paper we show analytically how standard error of ability estimates affects expected classification accuracy and consistency when the decision is binary when standard error decreases the conditional classification accuracy and consistency increase given an examinee population and a cut score smaller standard error over the entire latent trait continuum guarantees higher overall expected classification accuracy and consistency we were also able to show the interrelationship between standard error the expected classification consistency and reliability utilizing the relationship between standard error and expected classification accuracy and consistency we derive the upper bounds of the overall expected classification accuracy and consistency of a fixed length computerized adaptive test the lower bound of the expected classification accuracy and consistency is also derived given a number of stopping rules of variable length computerized adaptive testing implications of these analytical results on operational tests are discussed

asymptotic robustness study of the polychoric correlation estimation asymptotic robustness against misspecification of the underlying distribution for the polychoric correlation estimation is studied the asymptotic normality of the pseudo maximum likelihood estimator is derived using the two step estimation procedure the t distribution assumption and the skew normal distribution assumption are used as alternatives to the normal distribution assumption in a numerical study the numerical results show that the underlying normal distribution can be substantially biased even though skewness and kurtosis are not large the skew normal assumption generally produces a lower bias than the normal assumption thus it is worth using a non normal distributional assumption if the normal assumption is dubious

performance of modularity maximization in practical contexts although widely used in practice the behavior and accuracy of the popular module identification technique called modularity maximization is not well understood in practical contexts here we present a broad characterization of its performance in such situations first we revisit and clarify the resolution limit phenomenon for modularity maximization second we show that the modularity function q exhibits extreme degeneracies it typically admits an exponential number of distinct high scoring solutions and typically lacks a clear global maximum third we derive the limiting behavior of the maximum modularity q max for one model of infinitely modular networks showing that it depends strongly both on the size of the network and on the number of modules it contains finally using three real world metabolic networks as examples we show that the degenerate solutions can fundamentally disagree on many but not all partition properties such as the composition of the largest modules and the distribution of module sizes these results imply that the output of any modularity maximization procedure should be interpreted cautiously in scientific contexts they also explain why many heuristics are often successful at finding high scoring partitions in practice and why different heuristics can disagree on the modular structure of the same network we conclude by discussing avenues for mitigating some of these behaviors such as combining information from many degenerate solutions or using generative models

identification of the 1pl model with guessing parameter parametric and semi parametric results in this paper we study the identification of a particular case of the 3pl model namely when the discrimination parameters are all constant and equal to 1 we term this model 1pl g model the identification analysis is performed under three different specifications the first specification considers the abilities as unknown parameters it is proved that the item parameters and the abilities are identified if a difficulty parameter and a guessing parameter are fixed at zero the second specification assumes that the abilities are mutually independent and identically distributed according to a distribution known up to the scale parameter it is shown that the item parameters and the scale parameter are identified if a guessing parameter is fixed at zero the third specification corresponds to a semi parametric 1pl g model where the distribution g generating the abilities is a parameter of interest it is not only shown that after fixing a difficulty parameter and a guessing parameter at zero the item parameters are identified but also that under those restrictions the distribution g is not identified it is finally shown that after introducing two identification restrictions either on the distribution g or on the item parameters the distribution g and the item parameters are identified provided an infinite quantity of items is available

line graphs link partitions and overlapping communities in this paper we use a partition of the links of a network in order to uncover its community structure this approach allows for communities to overlap at nodes so that nodes may be in more than one community we do this by making a node partition of the line graph of the original network in this way we show that any algorithm that produces a partition of nodes can be used to produce a partition of links we discuss the role of the degree heterogeneity and propose a weighted version of the line graph in order to account for this

analysis of dispersion of multinomial responses abstract in analogy to analysis of variance for linear models analyses of dispersion for loglinear models for multinomial responses are constructed the analyses which are based on the entropy and concentration measures are used to construct tests of independence and measures of association

on the dynamics of navier stokes and euler equations this is a detailed study on certain dynamics of navier stokes and euler equations via a combination of analysis and numerics we focus upon two main aspects a zero viscosity limit of the spectra of linear navier stokes operator b heteroclinics conjecture for euler equation its numerical verification melnikov integral and simulation and control of chaos due to the difficulty of the problem for the full navier stokes and euler equations we also propose and study two simpler models of them

finding community structure in networks using the eigenvectors of matrices we consider the problem of detecting communities or modules in networks groups of vertices with a higher than average density of edges connecting them previous work indicates that a robust approach to this problem is the maximization of the benefit function known as modularity over possible divisions of a network here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix which plays a role in community detection similar to that played by the graph laplacian in graph partitioning calculations this result leads us to a number of possible algorithms for detecting community structure as well as several other results including a spectral measure of bipartite structure in networks and a centrality measure that identifies vertices that occupy central positions within the communities to which they belong the algorithms and measures proposed are illustrated with applications to a variety of real world complex networks

efficient nonparametric approaches for estimating the operating characteristics of discrete item responses rationale and the actual procedures of two nonparametric approaches called bivariate p d f approach and conditional p d f approach for estimating the operating characteristic of a discrete item response or the conditional probability given latent trait that the examinee s response be that specific response are introduced and discussed these methods are featured by the facts that a estimation is made without assuming any mathematical forms and b it is based upon a relatively small sample of several hundred to a few thousand examinees

spectral theory for linearizations of dynamical systems the description of the asymptotic growth rates for the solution trajectories of a system of differential equations is a central problem in the qualitative theory of dynamical systems these growth rates are described by the eigenvalues of the jacobian matrix for trajectories near a critical point by the floquet exponents for trajectories close to a periodic orbit and generally by the lyapunov characteristic exponents in a neighborhood of an arbitrary trajectory in the examples the asymptotic behavior of the solution trajectories is given by the association of a spectrum and this is a recurrent theme in the method of linearization sacker and sell io recently introduced a spectral theory for differential systems of quite general type the linear skew product flows see section 3 their work is in the spirit of the classical linearization theory and is closely tied to the idea of the lyapunov exponents we prefer to use the word spectrum literally identifying it with the spectrum of an operator on a banach space in general we consider a one parameter group 4 of homeomorphisms of a compact metric space m which for example may be the solution flow of a differential equation on a smooth manifold second we assume that a continuous vector bundle e m is defined i e a locally trivial continuous map n e m with linear fibers which are isomorphic to either real n dimensional space r or complex n dimensional space c in case is the flow of a vector field x on m this vector bundle could be the tangent bundle tm finally we assume that there is group of homeomorphisms on e with n 4 and such that i e t e c is a linear isomorphism for each x e m for instance in case 4 is smooth cp could be the tangent flow on tm given by the derivative of 4 using the compactness of m we define a finsler on e which continuously assigns a norm denoted i to each fiber e with this assignment the space r e of continuous sections of e functions q m e such that 7 o q x x forms a banach space with norm iiqll supxem u x 155 1 i the topology of t e is

on stability for symmetric hyperbolic systems ii in a very wide spectrum of applications the problem of stability plays a central role there is a vast literature available in the field but still the problem is solved only in special cases the incompleteness of the literature is especially noticeable when the governing equations are partial differential equations the normal procedure in a stability research for such equations is to linearize the equations of perturbation and confine the study to the simpler linear equations without any mathematical justification even though the linearization has been mathematically justified only in a few very special cases it is a fact that usually the linear stability criteria are in excellent agreement with experimental observations in this paper we shall also confine our study to linear partial differential equations the conventional approach to the problem of stability for such equations is the so called normal mode method which under certain restrictions transfers the problem to an eigenvalue problem for a partial differential operator with boundary conditions in general this eigenvalue problem is very complicated it is therefore customary to restrict the study to the special cases where the problem essentially is transferred to an eigenvalue problem for an ordinary differential operator even in these special cases the eigenvalue problem is not completely resolved an alternative approach which has been given some attention in recent years is liapunov s direct method which in principle can be applied to all kinds of stability problems including nonlinear problems the results obtained by this method so far however are rather limited the difficulties in applying the method consist of constructing functionals with specific properties a new approach to the problem of stability for linear hyperbolic equations was given by eckhoff i on a somewhat speculative and conjectural basis the approach is based on the generalized progressing wave expansion method described by friedlander 2 and ludwig 3 and it has been applied to problems of stability in fluid mechanics by eckhoff and storesletten 4 51 the purpose of this paper is to give a rigorous

linear stability in an ideal incompressible fluid we give an explicit construction of approximate eigenfunctions for a linearized euler operator in dimensions two and three with periodic boundary conditions and an estimate from below for its spectral bound in terms of an appropriate lyapunov exponent as a consequence we prove that in dimension 2 the spectral and growth bounds for the corresponding group are equal therefore the linear hydrodynamic stability of a steady state for the euler equations in dimension 2 is equivalent to the fact that the spectrum of the linearized operator is pure imaginary in dimension 3 we prove the estimate from below for the spectral bound that implies the same equality for every example where the relevant lyapunov exponents could be effectively computed for the kinematic dynamo operator describing the evolution of a magnetic field in an ideally conducting incompressible fluid we prove that the growth bound equals the spectral bound in dimensions 2 and 3

instability criteria for the flow of an inviscid incompressible fluid we present a geometric estimate from below on the growth rate of a small perturbation of a three dimensional steady flow of an ideal fluid and thus we obtain effective criteria for local instability for euler s equations we use these criteria to demonstrate the instability of several simple flows and to show that any flow with a hyperbolic stagnation point is unstable

hypergraph topological quantities for tagged social networks recent years have witnessed the emergence of a new class of social networks which require us to move beyond previously employed representations of complex graph structures a notable example is that of the folksonomy an online process where users collaboratively employ tags to resources to impart structure to an otherwise undifferentiated database in a recent paper we proposed a mathematical model that represents these structures as tripartite hypergraphs and defined basic topological quantities of interest in this paper we extend our model by defining additional quantities such as edge distributions vertex similarity and correlations as well as clustering we then empirically measure these quantities on two real life folksonomies the popular online photo sharing site flickr and the bookmarking site citeulike we find that these systems share similar qualitative features with the majority of complex networks that have been previously studied we propose that the quantities and methodology described here can be used as a standard tool in measuring the structure of tagged networks

consistent estimation in the rasch model based on nonparametric margins consider the class of two parameter marginal logistic rasch models for a test ofm true false items where the latent ability is assumed to be bounded using results of karlin and studen we show that this class of nonparametric marginal logistic nml models is equivalent to the class of marginal logistic models where the latent ability assumes at most m 2 2 values this equivalence has two implications first estimation for the nml model is accomplished by estimating the parameters of a discrete marginal logistic model second consistency for the maximum likelihood estimates of the nml model can be shown whenm is odd using the results of kiefer and wolfowitz an example is presented which demonstrates the estimation strategy and contrasts the nml model with a normal marginal logistic model

information matrices and standard errors for mles of item parameters in irt the paper clarifies the relationship among several information matrices for the maximum likelihood estimates mles of item parameters it shows that the process of calculating the observed information matrix also generates a related matrix that is the middle piece of a sandwich type covariance matrix monte carlo results indicate that standard errors ses based on the observed information matrix are robust to many but not all conditions of model distribution misspecifications ses based on the sandwich type covariance matrix perform most consistently across conditions results also suggest that ses based on other matrices are either not consistent or perform not as robust as those based on the sandwich type covariance matrix or the observed information matrix

linear mixed models with flexible distributions of random effects for longitudinal data normality of random effects is a routine assumption for the linear mixed model but it may be unrealistic obscuring important features of among individual variation we relax this assumption by approximating the random effects density by the seminonparameteric snp representation of gallant and nychka 1987 econometrics 55 363 390 which includes normality as a special case and provides flexibility in capturing a broad range of nonnormal behavior controlled by a user chosen tuning parameter an advantage is that the marginal likelihood may be expressed in closed form so inference may be carried out using standard optimization techniques we demonstrate that standard information criteria may be used to choose the tuning parameter and detect departures from normality and we illustrate the approach via simulation and using longitudinal data from the framingham study

marginal maximum likelihood estimation of item parameters application of an em algorithm maximum likelihood estimation of item parameters in the marginal distribution integrating over the distribution of ability becomes practical when computing procedures based on an em algorithm are used by characterizing the ability distribution empirically arbitrary assumptions about its form are avoided the em procedure is shown to apply to general item response models lacking simple sufficient statistics for ability this includes models with more than one latent dimension

perron frobenius theorem for nonnegative multilinear forms and extensions we prove an analog of perron frobenius theorem for multilinear forms with nonnegative coefficients and more generally for polynomial maps with nonnegative coefficients we determine the geometric convergence rate of the power algorithm to the unique normalized eigenvector

loglinear rasch model tests existing statistical tests for the fit of the rasch model have been criticized because they are only sensitive to specific violations of its assumptions contingency table methods using loglinear models have been used to test various psychometric models in this paper the assumptions of the rasch model are discussed and the rasch model is reformulated as a quasi independence model the model is a quasi loglinear model for the incomplete subgroup score item 1 item 2 itemk contingency table using ordinary contingency table methods the rasch model can be tested generally or against less restrictive quasi loglinear models to investigate specific violations of its assumptions

on instability and stability of three dimensional gravity driven viscous flows in a bounded domain abstract we investigate the instability and stability of some steady states of a three dimensional nonhomogeneous incompressible viscous flow driven by gravity in a bounded domain of class c 2 when the steady density is heavier with increasing height i e the rayleigh taylor steady state we show that the steady state is linear unstable i e the linear solution grows in time in h 2 by constructing a standard energy functional and exploiting the modified variational method then by introducing a new energy functional and using a careful bootstrap argument we further show that the steady state is nonlinear unstable in the sense of hadamard when the steady density is lighter with increasing height we show with the help of a restricted condition imposed on steady density that the steady state is linearly globally stable and nonlinearly asymptotically stable in the sense of hadamard

prediction functions for categorical panel data prediction of categorical responses in panel studies is considered prediction functions based on general conditional log linear models are investigated for statistical properties both from a population perspective and a sampling perspective problems such as existence and uniqueness of optimal prediction functions are addressed and basic properties of measures of prediction quality are examined estimation consistency and asymptotic normality are studied for the proposed parameter estimates and measures of prediction quality

flexible parsimonious smoothing and additive modeling a simple method is presented for fitting regression models that are nonlinear in the explanatory variables despite its simplicity or perhaps because of it the method has some powerful characteristics that cause it to be competitive with and often superior to more sophisticated techniques especially for small data sets in the presence of high noise

a comparison of the efficiency and accuracy of bilog and logist comparisons are made between bilog version 2 2 and logist 5 0 version 2 5 in estimating the item parameters traits item characteristic functions icfs and test characteristic functions tcfs for the three parameter logistic model data analyzed are simulated item responses for 1000 simulees and one 10 item test four 20 item tests and four 40 item tests logist usually was faster than bilog in producing maximum likelihood estimates bilog almost always produced more accurate estimates of individual item parameters in estimating icfs and tcfs bilog was more accurate for the 10 item test and the two programs were about equally accurate for the 20 and 40 item tests

binomial regression with monotone splines a psychometric application abstract a binomial regression function p x models the probability of rj successes in nj trials as a function of the values of an observed covariate xj and or a latent variable j j 1 j this article explores the use of monotone regression splines to define p and applies them to the representation of test items as functions of examinee ability some illustrative data suggest that the flexibility of monotone splines permits the detection of item characteristics not observable using logistic based or log linear approaches a simulation study indicates that estimates of both item characteristic curves and ability are reasonably precise for numbers of items and examinees typical of large university lectures given a set of such binomial regression functions it can be useful to study the principal components of functional variation the extension of multivariate principal components analysis to permit the analysis of many item characteristic curves is described

evolution of wavelike disturbances in shear flows a class of exact solutions of the navier stokes equations new classes of exact solutions of the incompressible navier stokes equations are presented the method of solution has its origins in that first used by kelvin phil mag 24 5 188 196 1887 to solve the linearized equations governing small disturbances in unbounded plane couette flow the new solutions found describe arbitrarily large spatially periodic disturbances within certain two and three dimensional basic shear flows of unbounded extent the admissible classes of basic flow possess spatially uniform strain rates they include two and three dimensional stagnation point flows and two dimensional flows with uniform vorticity the disturbances though spatially periodic have time dependent wavenumber and velocity components it is found that solutions for the disturbance do not always decay to zero but in some instances grow continuously in spite of viscous dissipation this behaviour is explained in terms of vorticity dynamics

estimating latent distributions consider vectors of item responses obtained from a sample of subjects from a population in which ability is distributed with densityg where the are unknown parameters assuming the responses depend on through a fully specified item response model this paper presents maximum likelihood equations for the estimation of the population parameters directly from the observed responses i e without estimating an ability parameter for each subject also provided are asymptotic standard errors and tests of fit computing approximations and details of four special cases a non parametric approximation a normal solution a resolution of normal components and a beta binomial solution

nonlinear instability in two dimensional ideal fluids the case of a dominant eigenvalue it is proved that any steady 2 dimensional ideal fluid flow is nonlinearly unstable with respect to l2 growth in the velocity provided there exists an eigenvalue for the linearised euler equation with re here is the maximal lyapunov exponent of the steady flow

the nonlinear mixed effects model with a smooth random effects density summary the fixed parameters of the nonlinear mixed effects model and the density of the random effects are estimated jointly by maximum likelihood the density of the random effects is assumed to be smooth but is otherwise unrestricted the method uses a series expansion that follows from the smoothness assumption to represent the density and quadrature to compute the likelihood standard algorithms are used for optimization empirical bayes estimates of random coefficients are obtained by computing posterior modes the method is applied to data from pharmacokinetics and properties of the method are investigated by application to simulated data

evolution semigroups translation algebras and exponential dichotomy of cocycles abstract we study the exponential dichotomy of an exponentially bounded strongly continuous cocycle over a continuous flow on a locally compact metric space acting on a banach space x our main tool is the associated evolution semigroup on c 0 x we prove that the cocycle has exponential dichotomy if and only if the evolution semigroup is hyperbolic if and only if the imaginary axis is contained in the resolvent set of the generator of the evolution semigroup to show the latter equivalence we establish the spectral mapping annular hull theorem for the evolution semigroup in addition dichotomy is characterized in terms of the hyperbolicity of a family of weighted shift operators defined on c 0 z x here we develop banach algebra techniques and study weighted translation algebras that contain the evolution operators these results imply that dichotomy persists under small perturbations of the cocycle and of the underlying compact metric space also exponential dichotomy follows from pointwise discrete dichotomies with uniform constants finally we extend to our situation the classical perron theorem which says that dichotomy is equivalent to the existence and uniqueness of bounded continuous mild solutions to the inhomogeneous equation

a similarity based smoothing approach to nondimensional item analysis the probability that an examinee chooses a particular option within an item is estimated by averaging over the responses to that item of examinees with similar response patterns for the whole test the approach does not presume any latent variable structure or any dimensionality but simulated and actual data analyses are presented to show that when the responses are determined by a latent ability variable this similarity based smoothing procedure can reveal the dimensionality of ability very satisfactorily

kernel smoothing approaches to nonparametric item characteristic curve estimation the option characteristic curve the relation between ability and probability of choosing a particular option for a test item can be estimated by nonparametric smoothing techniques what is smoothed is the relation between some function of estimated examinee ability rankings and the binary variable indicating whether or not the option was chosen this paper explores the use of kernel smoothing which is particularly well suited to this application examples show that with some help from the fast fourier transform estimates can be computed about 500 times as rapidly as when using commonly used parametric approaches such as maximum marginal likelihood estimation using the three parameter logistic distribution simulations suggest that there is no loss of efficiency even when the population curves are three parameter logistic the approach lends itself to several interesting extensions

the spectrum of a hyperbolic evolution operator abstract we study the time t map u which maps initial data u 0 u 1 to the solution and its derivative u t u t t of the homogeneous wave equation in a domain with time t periodic boundary the spectrum of u and the type of the spectrum are completely analyzed the spectrum is the unit circle if a certain rotation number is irrational it is a full annulus if this rotation number is rational and a weak additional assumption is satisfied

evolutionary semigroups and lyapunov theorems in banach spaces we present a spectral mapping theorem for continuous semigroups of operators on any banach space e the condition for the hyperbolicity of a semigroup on e is given in terms of the generator of an evolutionary semigroup acting in the space of e valued functions the evolutionary semigroup generated by the propagator of a nonautonomous differential equation in e is also studied a discrete technique for investigating the evolutionary semigroup is developed and applied in describing the hyperbolicity exponential dichotomy of the nonautonomous equation

central limit theorem for exponentially quasi local statistics of spin models on cayley graphs central limit theorems for linear statistics of lattice random fields including spin models are usually proven under suitable mixing conditions or quasi associativity many interesting examples of spin models do not satisfy mixing conditions and on the other hand it does not seem easy to show central limit theorem for local statistics via quasi associativity in this work we prove general central limit theorems for local statistics and exponentially quasi local statistics of spin models on discrete cayley graphs with polynomial growth further we supplement these results by proving similar central limit theorems for random fields on discrete cayley graphs taking values in a countable space but under the stronger assumptions of alpha mixing for local statistics and exponential alpha mixing for exponentially quasi local statistics all our central limit theorems assume a suitable variance lower bound like many others in the literature we illustrate our general central limit theorem with specific examples of lattice spin models and statistics arising in computational topology statistical physics and random networks examples of clustering spin models include quasi associated spin models with fast decaying covariances like the off critical ising model level sets of gaussian random fields with fast decaying covariances like the massive gaussian free field and determinantal point processes with fast decaying kernels examples of local statistics include intrinsic volumes face counts component counts of random cubical complexes while exponentially quasi local statistics include nearest neighbour distances in spin models and betti numbers of sub critical random cubical complexes

optimal scores an alternative to parametric item response theory and sum scores the aim of this paper is to discuss nonparametric item response theory scores in terms of optimal scores as an alternative to parametric item response theory scores and sum scores optimal scores take advantage of the interaction between performance and item impact that is evident in most testing data the theoretical arguments in favor of optimal scoring are supplemented with the results from simulation experiments and the analysis of test data suggests that sum scored tests would need to be longer than an optimally scored test in order to attain the same level of accuracy because optimal scoring is built on a nonparametric procedure it also offers a flexible alternative for estimating item characteristic curves that can fit items that do not show good fit to item response theory models

bootstrap calibrated interval estimates for latent variable scores in item response theory in most item response theory applications model parameters need to be first calibrated from sample data latent variable lv scores calculated using estimated parameters are thus subject to sampling error inherited from the calibration stage in this article we propose a resampling based method namely bootstrap calibration bc to reduce the impact of the carryover sampling error on the interval estimates of lv scores bc modifies the quantile of the plug in posterior i e the posterior distribution of the lv evaluated at the estimated model parameters to better match the corresponding quantile of the true posterior i e the posterior distribution evaluated at the true model parameters over repeated sampling of calibration data furthermore to achieve better coverage of the fixed true lv score we explore the use of bc in conjunction with jeffreys prior we investigate the finite sample performance of bc via monte carlo simulations and apply it to two empirical data examples

an integrability condition on the resolvent for hyperbolicity of the semigroup abstract in this paper we present necessary and sufficient conditions on the resolvent of the generator of a strongly continuous semigroup in order that the corresponding semigroup is hyperbolic the proof is based on a new characterization of the growth bound in terms of the resolvent as an application we discuss three examples

item response theory with estimation of the latent population distribution using spline based densities the purpose of this paper is to introduce a new method for fitting item response theory models with the latent population distribution estimated from the data using splines a spline based density estimation system provides a flexible alternative to existing procedures that use a normal distribution or a different functional form for the population distribution a simulation study shows that the new procedure is feasible in practice and that when the latent distribution is not well approximated as normal two parameter logistic 2pl item parameter estimates and expected a posteriori scores eaps can be improved over what they would be with the normal model an example with real data compares the new method and the extant empirical histogram approach

on the nonlinear instability of euler and prandtl equations in this paper we give examples of nonlinearly unstable solutions of euler equations in the whole space 2 the half space the periodic strip the strip 1 1 and the periodic torus 2 with an application to vortex sheets using the same methods we prove an instability result for prandtl type boundary layers that appear in and 2000 john wiley sons inc

dispersion of categorical variables and penalty functions derivation estimation and comparability abstract measures of dispersion for categorical random variables based on penalty functions play a central role in establishing relevant measures of association between such variables the literature concerning these measures provides little systematic treatment of such aspects of these measures as comparability efficient estimation and large sample properties this article provides a systematic and rigorous construction of dispersion measures based on penalty functions efficient estimation procedures and asymptotic properties of estimates are examined conditions from majorization theory that ensure a meaningful comparability of dispersion measures based on penalty functions are discussed a large class of familiar dispersion measures is then given a new interpretation using these conditions

the spectrum of the kinematic dynamo operator for an ideally conducting fluid the spectrum of the kinematic dynamo operator for an ideally conducting fluid and the spectrum of the corresponding group acting in the space of continuous divergence free vector fields on a compact riemannian manifold are described we prove that the spectrum of the kinematic dynamo operator is exactly one vertical strip whose boundaries can be determined in terms of the lyapunov oseledets exponents with respect to all ergodic measures for the eulerian flow also we prove that the spectrum of the corresponding group is obtained from the spectrum of its generator by exponentiation in particular the growth bound for the group coincides with the spectral bound for the generator

evolutionary semigroups and dichotomy of linear skew product flows on locally compact spaces with banach fibers abstract we study evolutionary semigroups generated by a strongly continuous semi cocycle over a locally compact metric space acting on banach fibers this setting simultaneously covers evolutionary semigroups arising from non autonomous abstract cauchy problems and c 0 semigroups and linear skew product flows the spectral mapping theorem for these semigroups is proved the hyperbolicity of the semigroup is related to the exponential dichotomy of the corresponding linear skew product flow to this end a banach algebra of weighted composition operators is studied the results are applied in the study of roughness of the dichotomy dichotomy and solutions of nonhomogeneous equations green s function for a linear skew product flow pointwise dichotomy versus global dichotomy and evolutionary semigroups along trajectories of the flow

on the approximation of the quadratic exponential distribution in a latent variable context summary following cox wermuth 1994 2002 we show that the distribution of a set of binary observable variables induced by a certain discrete latent variable model may be approximated by a quadratic exponential distribution this discrete latent variable model is equivalent to the latent class version of the two parameter logistic model of birnbaum 1968 which may be seen as a generalized version of the rasch model rasch 1960 1961 on the basis of this result we develop an approximate maximum likelihood estimator of the item parameters of the two parameter logistic model which is very simply implemented the proposed approach is illustrated through an example based on a dataset on educational assessment

on the sampling theory roundations of item response theory models item response theory it models are now in common use for the analysis of dichotomous item responses this paper examines the sampling theory foundations for statistical inference in these models the discussion includes some history on the stochastic subject versus the random sampling interpretations of the probability in irt models the relationship between three versions of maximum likelihood estimation for irt models estimating versus estimating predictors irt models and loglinear models the identifiability of irt models and the role of robustness and bayesian statistics from the sampling theory perspective

linear inviscid damping for a class of monotone shear flow in sobolev spaces in this paper we prove the decay estimates of the velocity and h1 scattering for the two dimensional linearized euler equations around a class of monotone shear flow in a finite channel our result is consistent with the decay rate predicted by case in 1960 2016 wiley periodicals inc

multicategorical spline model for item response theory additional information contained in incorrect responses calls for a multicategorical rather than a binary analysis of multiple choice data a nonparametric divided by total model for joint maximum likelihood estimation of probability of choice functions for particular responses and of latent ability is proposed the model approximates probability functions by rational splines some illustrative examples of real test data analysis and the results of a monte carlo study are presented

operator algebras and the fredholm spectrum of advective equations of linear hydrodynamics abstract in this paper we give a complete description of the fredholm spectrum of the linearized 3d euler equation in terms of the dynamical spectrum of the cocycle governing the evolution of shortwave perturbations the argument is based on the pseudo differential representation of the euler group and an application of an abstract isomorphism theorem for operator c algebras we further show that for all but countably many times the fredholm spectrum of the group is rotationally invariant and thus may consist of one or two concentric annuli the results are obtained for a variety of other equations of ideal hydrodynamics

semi nonparametric maximum likelihood estimation on developpe une approche basee sur une innovation due a phillips 1983 sur les approximations des fonctions de densite

a riemannian optimization algorithm for joint maximum likelihood estimation of high dimensional exploratory item factor analysis there has been regained interest in joint maximum likelihood jml estimation of item factor analysis ifa recently primarily due to its efficiency in handling high dimensional data and numerous latent factors it has been established under mild assumptions that the jml estimator is consistent as both the numbers of respondents and items tend to infinity the current work presents an efficient riemannian optimization algorithm for jml estimation of exploratory ifa with dichotomous response data which takes advantage of the differential geometry of the fixed rank matrix manifold the proposed algorithm takes substantially less time to converge than a benchmark method that alternates between gradient ascent steps for person and item parameters the performance of the proposed algorithm in the recovery of latent dimensionality response probabilities item parameters and factor scores is evaluated via simulations

alignment and integration of complex networks by hypergraph based spectral clustering complex networks possess a rich multiscale structure reflecting the dynamical and functional organization of the systems they model often there is a need to analyze multiple networks simultaneously to model a system by more than one type of interaction or to go beyond simple pairwise interactions but currently there is a lack of theoretical and computational methods to address these problems here we introduce a framework for clustering and community detection in such systems using hypergraph representations our main result is a generalization of the perron frobenius theorem from which we derive spectral clustering algorithms for directed and undirected hypergraphs we illustrate our approach with applications for local and global alignment of protein protein interaction networks between multiple species for tripartite community detection in folksonomies and for detecting clusters of overlapping regulatory pathways in directed networks

population stratification using a statistical model on hypergraphs population stratification is a problem encountered in several areas of natural science engineering and public health we tackle this problem by mapping a population and its element attributes onto a hypergraph a natural extension of the concept of graph or network to encode associations among any number of elements on this hypergraph we construct a statistical model reflecting our intuition about how the element attributes can emerge from a postulated population structure finally we introduce the concept of stratification representativeness as a mean to identify the simplest stratification already containing most of the information about the population structure we demonstrate the power of this framework stratifying an animal and a human population based on phenotypic and genotypic properties respectively

some stability and instability criteria for ideal plane flows we investigate stability and instability of steady ideal plane flows for an arbitrary bounded domain first we obtain some general criteria for linear and nonlinear stability second we find a sufficient condition for the existence of a growing mode to the linearized equation third we construct a steady flow which is nonlinearly and linearly stable in the l2 norm of vorticity but linearly unstable in the l2 norm of velocity

spectrum reducing extension for one operator on a banach space on montre que etant donne un operateur t sur un espace de banach x il y a une extension y de x telle que t s etend de facon naturelle a un operateur t sur y et le spectre de t est le spectre ponctuel approche de t

modeling and testing differential item functioning in unidimensional binary item response models with a single continuous covariate a functional data analysis approach differential item functioning dif referring to between group variation in item characteristics above and beyond the group level disparity in the latent variable of interest has long been regarded as an important item level diagnostic the presence of dif impairs the fit of the single group item response model being used and calls for either model modification or item deletion in practice depending on the mode of analysis methods for testing dif with continuous covariates rather than categorical grouping variables have been developed however they are restrictive in parametric forms and thus are not sufficiently flexible to describe complex interaction among latent variables and covariates in the current study we formulate the probability of endorsing each test item as a general bivariate function of a unidimensional latent trait and a single covariate which is then approximated by a two dimensional smoothing spline the accuracy and precision of the proposed procedure is evaluated via monte carlo simulations if anchor items are available we proposed an extended model that simultaneously estimates item characteristic functions icfs for anchor items icfs conditional on the covariate for non anchor items and the latent variable density conditional on the covariate all using regression splines a permutation dif test is developed and its performance is compared to the conventional parametric approach in a simulation study we also illustrate the proposed semiparametric dif testing procedure with an empirical example

the non analytic growth bound of a c0 semigroup and inhomogeneous cauchy problems abstract the non analytic growth bound t of a c0 semigroup t measures the extent to which t can be approximated by a holomorphic function and it is related to spectral properties of the generator a in regions of c far from the real axis we show that t can be characterised by means of fourier multiplier properties of the resolvent of a far from the real axis and also by existence and uniqueness of mild solutions of inhomogeneous cauchy problems of the form u t au t f t on r where the carleman spectra of f and u are far from the origin the corresponding results for the exponential growth bound 0 t have been established earlier by other authors

on the bayesian nonparametric generalization of irt type models we study the identification and consistency of bayesian semiparametric irt type models where the uncertainty on the abilities distribution is modeled using a prior distribution on the space of probability measures we show that for the semiparametric rasch poisson counts model simple restrictions ensure the identification of a general distribution generating the abilities even for a finite number of probes for the semiparametric rasch model only a finite number of properties of the general abilities distribution can be identified by a finite number of items which are completely characterized the full identification of the semiparametric rasch model can be only achieved when an infinite number of items is available the results are illustrated using simulated data

on dispersion for linear waves in nonuniform media motivated by several well known examples of linear waves in uniform media a general definition of a dispersionfree wave valid for both uniform and nonuniform media is set up examples of dispersionfree generalizations of the classical wave equation to nonuniform media are given although dispersionfree waves are exceptional both in the uniform and in the nonuniform case it is proved that hyperbolic systems have the property that in the limit of short wavelengths the solutions behave like a linear combination of dispersionfree waves on that basis it is possible to study the dispersion properties of hyperbolic waves by an asymptotic expansion explicit calculations are given for such expansions for a family of generalizations of the classical wave equation to nonuniform media

maximum marginal likelihood estimation of a monotonic polynomial generalized partial credit model with applications to multiple group analysis we present a semi parametric approach to estimating item response functions irf useful when the true irf does not strictly follow commonly used functions our approach replaces the linear predictor of the generalized partial credit model with a monotonic polynomial the model includes the regular generalized partial credit model at the lowest order polynomial our approach extends liang s a semi parametric approach to estimate irfs unpublished doctoral dissertation 2007 method for dichotomous item responses to the case of polytomous data furthermore item parameter estimation is implemented with maximum marginal likelihood using the bock aitkin em algorithm thereby facilitating multiple group analyses useful in operational settings our approach is demonstrated on both educational and psychological data we present simulation results comparing our approach to more standard irf estimation approaches and other non parametric and semi parametric alternatives

dynamics near unstable interfacial fluids we study three examples of unstable interfacial fluid motions vortex sheets with surface tension hele shaw flows with surface tension and vortex patches in all three cases the nonlinear dynamics of a large class of smooth perturbations is proven to be characterized by the corresponding fastest linear growing mode s up to the time scale of log frac 1 delta where delta is the magnitude of the initial perturbation in all three cases the analysis is based on an unified analytical framework that includes precise bounds on the growth of the linearized operator given by an explicit solution formula as well as a special sharp nonlinear energy growth estimate our main contribution is establishing this nonlinear energy growth estimate for each interface problem in certain high energy norms

cocycles and mane sequences with an application to ideal fluids abstract exponential dichotomy of a strongly continuous cocycle is proved to be equivalent to existence of a mane sequence either for or for its adjoint as a consequence we extend some of the classical results to general banach bundles the dynamical spectrum of a product of two cocycles one of which is scalar is investigated and applied to describe the essential spectrum of the euler equation in an arbitrary spacial dimension