isotonic ordinal probabilistic models isop the concept of an ordinal instrumental probabilistic comparison is introduced it relies on an ordinal scale given a priori and on the concept of stochastic dominance it is used to define a weakly independently ordered system or isotonic ordinal probabilistic isop model which allows the construction of separate sample free ordinal scales on a set of subjects and a set of items the isop model is a common nonparametric theoretical structure for unidimensional models for quantitative ordinal and dichotomous variables

stochastic ordering using the latent trait and the sum score in polytomous irt models in a restricted class of item response theory irt models for polytomous items the unweighted total score has monotone likelihood ratio mlr in the latent trait mlr implies two stochastic ordering so properties denoted som and sol which are both weaker than mlr but very useful for measurement with irt models therefore these so properties are investigated for a broader class of irt models for which the mlr property does not hold

an analysis of item response theory and rasch models based on the most probable distribution method the most probable distribution method is applied to derive the logistic model as the distribution accounting for the maximum number of possible outcomes in a dichotomous test while introducing latent traits and item characteristics as constraints to the system the item response theory logistic models with a particular focus on the one parameter logistic model or rasch model and their properties and assumptions are discussed for both infinite and finite populations

morphisms of f isocrystals and the finite monodromy theorem for unit root f isocrystals we discuss tate type problems for f isocrystals that is the full faithfulness of the natural restriction functors between categories of overconvergent f isocrystals on schemes of positive characteristic we prove it in the cases of unit root f isocrystals using this result we prove that an overconvergent unit root f isocrystal has a finite monodromy

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

polytomous latent scales for the investigation of the ordering of items we propose three latent scales within the framework of nonparametric item response theory for polytomously scored items latent scales are models that imply an invariant item ordering meaning that the order of the items is the same for each measurement value on the latent scale this ordering property may be important in for example intelligence testing and person fit analysis we derive observable properties of the three latent scales that can each be used to investigate in real data whether the particular model adequately describes the data we also propose a methodology for analyzing test data in an effort to find support for a latent scale and we use two real data examples to illustrate the practical use of this methodology

integral motives and special values of zeta functions for each field k we define a category of rationally decomposed mixed motives with z coefficients when k is finite we show that the category is tannakian and we prove formulas relating the behaviour of zeta functions near integers to certain ext groups

on a simple criterion for the existence of a principal eigenfunction of some nonlocal operators abstract in this paper we are interested in the existence of a principal eigenfunction of a nonlocal operator which appears in the description of various phenomena ranging from population dynamics to micro magnetism more precisely we study the following eigenvalue problem j x y g y y g n y d y a x where r n is an open connected set j a non negative kernel and g a positive function first we establish a criterion for the existence of a principal eigenpair p p we also explore the relation between the sign of the largest element of the spectrum with a strong maximum property satisfied by the operator as an application of these results we construct and characterise the solutions of some nonlinear nonlocal reaction diffusion equations

resident invader dynamics in infinite dimensional systems abstract motivated by evolutionary biology we study general infinite dimensional dynamical systems involving two species the resident and the invader sufficient conditions for competition exclusion phenomena are given when the two species play similar but distinct strategies those conditions are based on invasibility criteria for instance evolutionarily stable strategies in the framework of adaptive dynamics these types of questions were first proposed and studied by s geritz et al 20 and s geritz 19 for a class of ordinary differential equations we extend and generalize previous work in two directions firstly we consider analytic semiflows in infinite dimensional spaces secondly we devise an argument based on hadamard s graph transform method that does not depend on the monotonicity of the two species system our results are applicable to a wide class of reaction diffusion models as well as models with nonlocal diffusion operators

on measurement properties of continuation ratio models three classes of polytomous irt models are distinguished these classes are the adjacent category models the cumulative probability models and the continuation ratio models so far the latter class has received relatively little attention the class of continuation ratio models includes logistic models such as the sequential model tutz 1990 and nonlogistic models such as the acceleration model samejima 1995 and the nonparametric sequential model hemker 1996 four measurement properties are discussed these are monotone likelihood ratio of the total score stochastic ordering of the latent trait by the total score stochastic ordering of the total score by the latent trait and invariant item ordering these properties have been investigated previously for the adjacent category models and the cumulative probability models and for the continuation ratio models this is done here it is shown that stochastic ordering of the total score by the latent trait is implied by all continuation ratio models while monotone likelihood ratio of the total score and stochastic ordering on the latent trait by the total score are not implied by any of the continuation ratio models only the sequential rating scale model implies the property of invariant item ordering also we present a venn diagram showing the relationships between all known polytomous irt models from all three classes

existence uniqueness and stability of the stationary solution to a nonlocal evolution equation arising in population dispersal this paper is concerned with a nonlocal evolution equation which is used to model the spatial dispersal of organisms we study the existence uniqueness and stability of the positive steady solution for this nonlocal evolution equation under general conditions the global dynamics are also investigated and a trichotomy of the global asymptotics is established

center manifolds for smooth invariant manifolds this is the published version also available here http dx doi org 10 1090 s0002 9947 00 02443 0 first published in trans amer math soc in 2000 published by the american mathematical society

persistence of overflowing manifolds for semiflow this paper which is a sequel to a previous one 4 by the same authors is devoted to the persistence of overflowing manifolds and inflowing manifolds for a semiflow in a banach space we consider a c1 semiflow defined on a banach space x that is it is continuous on 0 x and for each t 0 t t x x is c1 and t t t x t t s x for all t s 0 and x x a typical example is the solution operator for a differential equation in 4 we proved that a compact normally hyperbolic invariant manifold m persists under small c1 perturbations in the semiflow we also showed that in a neighborhood of m there exist a center stable manifold and a center unstable manifold that intersect in the manifold m in 4 the compactness and invariance of the manifold m were important assumptions in the present paper we study the more general case where the manifold m is overflowing negatively invariant and the semiflow crosses the boundary transversally or inflowing positively invariant and the semiflow crosses the boundary transversally we do not assume that m is compact or finite dimensional also m is not necessarily an imbedded manifold but an immersed manifold as an example a local unstable manifold of an equilibrium point is an overflowing manifold in brief our main results on the overflowing manifolds may be summarized as follows the precise statements are given in section 2 we assume that the immersed manifoldm does not twist very much locally m is covered by the image under t t of a subset a positive distance away from boundary dt t contracts along the normal direction and does so more strongly than it does along the tangential direction and dt t has a certain uniform continuity in a neighborhood of m if the c1 perturbation t t of t t is sufficiently close to t t then t t has a unique c1 immersed overflowing manifold m nearm furthermore if t t isck and a spectral gap condition holds then m isck similar results for inflowing manifolds are also obtained and given in section 7

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

nonparametric polytomous irt models for invariant item ordering with results for parametric models it is often considered desirable to have the same ordering of the items by difficulty across different levels of the trait or ability such an ordering is an invariant item ordering iio an iio facilitates the interpretation of test results for dichotomously scored items earlier research surveyed the theory and methods of an invariant ordering in a nonparametric irt context here the focus is on polytomously scored items and both nonparametric and parametric irt models are considered

an isotonic partial credit model for ordering subjects on the basis of their sum scores in practice the sum of the item scores is often used as a basis for comparing subjects for items that have more than two ordered score categories only the partial credit model pcm and special cases of this model imply that the subjects are stochastically ordered on the common latent variable however the pcm is very restrictive with respect to the constraints that it imposes on the data in this paper sufficient conditions for the stochastic ordering of subjects by their sum score are obtained these conditions define the isotonic nonparametric pcm model the isotonic pcm is more flexible than the pcm which makes it useful for a wider variety of tests also observable properties of the isotonic pcm are derived in the form of inequality constraints it is shown how to obtain estimates of the score distribution under these constraints by using the gibbs sampling algorithm a small simulation study shows that the bayesian p values based on the log likelihood ratio statistic can be used to assess the fit of the isotonic pcm to the data where model data fit can be taken as a justification of the use of the sum score to order subjects

the unique correspondence of the item response function and item category response functions in polytomously scored item response models the item response function irf for a polytomously scored item is defined as a weighted sum of the item category response functions icrf the probability of getting a particular score for a randomly sampled examinee of ability this paper establishes the correspondence between an irf and a unique set of icrfs for two of the most commonly used polytomous irt models the partial credit models and the graded response model specifically a proof of the following assertion is provided for these models if two items have the same irf then they must have the same number of categories moreover they must consist of the same icrfs as a corollary for the rasch dichotomous model if two tests have the same test characteristic function tcf then they must have the same number of items moreover for each item in one of the tests an item in the other test with an identical irf must exist theoretical as well as practical implications of these results are discussed