locality in gns representations of deformation quantization in the framework of deformation quantization we apply the formal gns construction to find representations of the deformed algebras in pre hilbert spaces over and establish the notion of local operators in these pre hilbert spaces the commutant within the local operators is used to distinguish thermal from pure representations the computation of the local commutant is xemplified in various situations leading to the physically reasonable distinction between thermal representations and pure ones moreover an analogue of von neumann s double commutant theorem is proved in the particular situation of a gns representation with respect to a kms functional and for the schrodinger representation on cotangent bundles finally we prove a formal version of the tomita takesaki theorem

a continuous field of c algebras and the tangent groupoid for manifolds with boundary abstract for a smooth manifold x with boundary we construct a semi groupoid t x and a continuous field c r t x of c algebras which extend connes construction of the tangent groupoid we show the asymptotic multiplicativity of scaled truncated pseudodifferential operators with smoothing symbols and compute the k theory of the associated symbol algebra

the atiyah bott patodi method in deformation quantization we give a new proof of the index theorem for deformation quantization following the atiyah bott patodi scheme the main ingredient consists of tamarkin s theorem on topological invariants of symplectic connections which is a symplectic analog of the well known theorems for riemannian connections

the effect of uncertainty of item parameter estimation on ability estimates the conventional method of measuring ability which is based on items with assumed true parameter values obtained from a pretest is compared to a bayesian method that deals with the uncertainties of such items computational expressions are presented for approximating the posterior mean and variance of ability under the three parameter logistic 3pl model a 1987 american college testing program act math test is used to demonstrate that the standard practice of using maximum likelihood or empirical bayes techniques may seriously underestimate the uncertainty in estimated ability when the pretest sample is only moderately large

a differential complex for poisson manifolds construction du complexe canonique d une variete de poisson homologie canonique des varietes symplectiques application a l homologie de hochschild des algebres non commutatives

batalin vilkovisky quantization and the algebraic index abstract into a geometric setting we import the physical interpretation of index theorems via semi classical analysis in topological quantum field theory we develop a direct relationship between fedosov s deformation quantization of a symplectic manifold x and the batalin vilkovisky bv quantization of a one dimensional sigma model with target x this model is a quantum field theory of aksz type and is quantized rigorously using costello s homotopic theory of effective renormalization we show that fedosov s abelian connections on the weyl bundle produce solutions to the effective quantum master equation moreover bv integration produces a natural trace map on the deformation quantized algebra this formulation allows us to exploit a rigorous localization argument in quantum field theory to deduce the algebraic index theorem via semi classical analysis i e one loop feynman diagram computations

combinatorial quantization of the hamiltonian chern simons theory ii motivated by a recent paper of fock and rosly 6 we describe a mathematically precise quantization of the hamiltonian chern simons theory we introduce the chern simons theory on the lattice which is expected to reproduce the results of the continuous theory exactly the lattice model enjoys the symmetry with respect to a quantum gauge group using this fact we construct the algebra of observables of the hamiltonian chern simons theory equipped with a operation and a positive inner product

analytic and algebraic indices of elliptic operators associated with discrete groups of quantized canonical transformations abstract we consider elliptic operators associated with discrete groups of quantized canonical transformations in order to be able to apply results from algebraic index theory we define the localized algebraic index of the complete symbol of an elliptic operator with the help of a calculus of semiclassical quantized canonical transformations a version of egorov s theorem and a theorem on trace asymptotics for semiclassical fourier integral operators we show that the localized analytic index and the localized algebraic index coincide as a corollary we express the fredholm index in terms of the algebraic index for a wide class of groups in particular for finite extensions of abelian groups

a formal model of berezin toeplitz quantization we give a new construction of symbols of the differential operators on the sections of a quantum line bundle l over a kahler manifold m using the natural contravariant connection on l these symbols are the functions on the tangent bundle tm polynomial on fibres for high tensor powers of l the asymptotics of the composition of these symbols leads to the star product of a deformation quantization with separation of variables on tm corresponding to some pseudo kahler structure on tm surprisingly this star product is intimately related to the formal symplectic groupoid with separation of variables over m we extend the star product on tm to generalized functions supported on the zero section of tm the resulting algebra of generalized functions contains an idempotent element which can be thought of as a natural counterpart of the bergman projection operator using this idempotent we define an algebra of toeplitz elements and show that it is naturally isomorphic to the algebra of berezin toeplitz deformation quantization on m

quantum harmonic analysis and geometric invariants we develop two topics in parallel and show their inter relation the first centers on the notion of a fractional differentiable structure on a commutative or a non commutative space we call this studyquantum harmonic analysis the second concerns homotopy invariants for these spaces and is an aspect of non commutative geometry we study an algebra a which will be a banach algebra with unit represented as an algebra of operators on a hilbert space h in order to obtain a geometric interpretation of a we define a derivative on elements of a we do this in a hilbert space context takingdaas a commutatorda q a hereqis a basic self adjoint operator with discrete spectrum increasing sufficiently rapidly that exp q 2has a trace whenever 0 we can define fractional differentiability of order with 0 0 we concentrate on subalgebras a of j which have certain additional covariance properties under a group z2 g acting on h by a unitary representation u g in addition the derivativeqis assumed to be g invariant the geometric interpretation flows from the assumption that elements of a possess an arbitrarily small fractional derivative we study homotopy invariants of a in terms of equivariant entire cyclic cohomology in fact the existence of a fractional derivative on a allows the construction of the cochain jlo which plays the role of the integral of differential forms we give a simple expression for a homotopy invariant zq a g determined by pairing jlo with a g invariant elementa a such thatais a square root of the identity this invariant is zq a g 1 e t2tr u g ae q2 it da dt this representation of the pairing is reminiscent of the heat kernel representation for an index in fact this quantity is an invariant in the following sense we isolate a simple condition on a familyq of differentiations that yields a continuously differentiable family jlo of cochains since zq a g need not be an integer continuity of jlo in is insufficient to prove the constancy of the pairing however the existence of the derivative leads to the existence of the homotopy as a vanishes for a coboundary and asd jlo d is a coboundary our condition onq ensures that zq a g is independent of hence it is a homotopy invariant the theory of zq a g reduces to the study of the radon transform of sequences of certain functions the fractional differentiability properties of elements of a translate into properties of the asymptotics of the sequences of radon transforms the condition that jlofit into the framework of entire cyclic cohomology translates to the existence of some fractional derivative for functions in the algebra under study and in particular the assumption 1 thus the study of fractionally differentiable structures dove tails naturally with the theory of homotopy invariants in our study of quantum harmonic analysis we introduce spaces t of operator valued distributions these spaces are bounded linear operators between sobolev spaces the elements of the interpolation spaces the banach algebras j have derivativesdawhich belong to the spaces t for a certain range of and we extend the theory of the radon transform from products of regularized bounded operators to products of regularized operator valued distributions we sometimes wish to evaluate such an invariant at the endpoint of an interval such as 0 1 where zq a g becomes singular as 0 we discuss in brief a procedure to regularize the endpoint and a method to recover zq a g fully from certain partial information at the endpoint finally we generalize this approach to cover the case whenqcan be split into the sum of independent partsq1 q2 such that q1 q2 2 q1 2 q2 2 here we assume thatq1and q2 2are g invariant but not necessarilyq2 with further assumptions ona the most important being that q1 2 q2 2commutes witha we obtain a modified formula for an invariant namely z qj a g 1 e t2tr u g ae q21 q22 2 itd1a dt

fedosov differentials and catalan numbers the aim of the paper is to establish a non recursive formula for the general solution of fedosov s quadratic fixed point equation fedosov 1994 j diff geom 40 213 38 fedosov s geometrical fixed point equation for a differential is rewritten in a form similar to the functional equation for the generating function of catalan numbers this allows us to guess the solution an adapted example for kaehler manifolds of constant sectional curvature is considered in detail also for every connection on a manifold a familiar classical differential will be introduced

formality and kontsevich duflo type theorems for lie pairs newcommand poly operatorname poly bullet newcommand td operatorname td l a nabla frac 1 2 newcommand cx 1 operatorname tot big gamma lambda bullet a vee otimes r mathcal 1 poly big newcommand cy 1 mathbb h bullet operatorname ce a mathcal 1 poly kontsevich s formality theorem states that there exists an l infty quasi isomorphism from the dgla t poly m of polyvector fields on a smooth manifold m to the dgla d poly m of polydifferential operators on m which extends the classical hochschild kostant rosenberg map in this paper we extend kontsevich s formality theorem to lie pairs a framework which includes a range of diverse geometric contexts such as complex manifolds foliations and mathfrak g manifolds the spaces cx t and cx d associated with a lie pair l a each carry an l infty algebra structure canonical up to l infty isomorphism these two spaces serve as replacements for the spaces of polyvector fields and polydifferential operators respectively their corresponding cohomology groups cy t and cy d admit canonical gerstenhaber algebra structures we establish the following formality theorem for lie pairs there exists an l infty quasi isomorphism from cx t to cx d whose first taylor coefficient is equal to operatorname hkr circ td here td acts on cx t by contraction furthermore we prove a kontsevich duflo type theorem for lie pairs the hochschild kostant rosenberg map twisted by the square root of the todd class of the lie pair l a is an isomorphism of gerstenhaber algebras from cy t to cy d as applications we establish formality theorems and kontsevich duflo type theorems for complex manifolds foliations and mathfrak g manifolds in the case of complex manifolds we recover the kontsevich duflo theorem of complex geometry

additional criteria in fuzzy two level pattern recognition abstract pattern recognition with fuzzy sets is considered with regard to medical diagnostic problems an alternative interpretation of membership grade is suggested which expresses the degree of illness of a patient with respect to a certain disease a formal statement of a two level fuzzy classifier is presented the main emphasis is put on additional criteria designed to evaluate a fuzzy diagnostic decision for an unknown object two groups of criteria are formed decision making connected and domain dependent the decision making group of criteria can be viewed as related to the soft consensus measure in group decisions theory interconnections between criteria are discussed the notions proposed are illustrated with real medical data from the fields of aviation medicine and neonatology

pseudodifferential extension and todd class let m be a closed manifold wodzicki shows that in the stable range the cyclic cohomology of the associative algebra of pseudodierential symbols of order 0 is isomorphic to the homology of the cosphere bundle of m in this article we develop a formalism which allows to calculate that under this isomorphism the radul cocycle corresponds to the poincar e dual of the todd class as an immediate corollary we obtain a purely algebraic proof of the atiyah singer index theorem for elliptic pseudodifferential operators on closed manifolds

investigating the impact of uncertainty about item parameters on ability estimation asymptotic expansions of the maximum likelihood estimator mle and weighted likelihood estimator wle of an examinee s ability are derived while item parameter estimators are treated as covariates measured with error the asymptotic formulae present the amount of bias of the ability estimators due to the uncertainty of item parameter estimators a numerical example is presented to illustrate how to apply the formulae to evaluate the impact of uncertainty about item parameters on ability estimation and the appropriateness of estimating ability using the regular mle or wle method

an investigation of hierarchical bayes procedures in item response theory hierarchical bayes procedures for the two parameter logistic item response model were compared for estimating item and ability parameters simulated data sets were analyzed via two joint and two marginal bayesian estimation procedures the marginal bayesian estimation procedures yielded consistently smaller root mean square differences than the joint bayesian estimation procedures for item and ability estimates as the sample size and test length increased the four bayes procedures yielded essentially the same result

a valuation of state of object based on weighted mahalanobis distance abstract a method of valuation of the state of a multidimensional object is presented the considered object may be described by continuous and discrete variables as well the method consists in evaluating the weighted mahalanobis distance between the object and a multidimensional norm estimate this distance can be standardized to take the values from the interval 0 1

bivariant chern character and longitudinal index in this paper we consider a family of dirac type operators on fibration p b equivariant with respect to an action of an etale groupoid such a family defines an element in the bivariant k theory we compute the action of the bivariant chern character of this element on the image of connes map in the cyclic cohomology a particular case of this result is connes index theorem for etale groupoids a connes noncommutative geometry academic press 1994 in the case of fibrations

a proof of the tsygan formality conjecture for chains abstract we extend the kontsevich formality l morphism u t poly r d d poly r d to an l morphism of l modules over t poly r d u c a a r d a c r d the construction of the map u is given in kontsevich type integrals the conjecture that such an l morphism exists is due to boris tsygan formality conjecture for chains math qa 9904132 as an application we obtain an explicit formula for isomorphism a a a a a a a is the kontsevich deformation quantization of the algebra a by a poisson bivector field and is the poisson bracket we also formulate a conjecture extending the kontsevich theorem on cup products to this context the conjecture implies a generalization of the duflo formula and many other things

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

formal series of generalized functions and their application to deformation quantization foundations of the formal series calculus in deformation quantization are discussed several classes of continuous linear functionals over algebras applied in classical and quantum physics are introduced the notion of non negativity in formal series calculus is proposed problems with defining quantum states over the set of formal series are analyzed foundations of the formal series calculus in deformation quantization are discussed several classes of continuous linear functionals over algebras applied in classical and quantum physics are introduced the notion of non negativity in formal series calculus is proposed problems with defining quantum states over the set of formal series are analyzed

brst cohomology and phase space reduction in deformation quantization in this article we consider quantum phase space reduction when zero is a regular value of the momentum map by analogy with the classical case we define the brst cohomology in the framework of deformation quantization we compute the quantum brst cohomology in terms of a quantum chevalley eilenberg cohomology of the lie algebra on the constraint surface to prove this result we construct an explicit chain homotopy both in the classical and quantum case which is constructed out of a prolongation of functions on the constraint surface we have observed the phenomenon that the quantum brst cohomology cannot always be used for quantum reduction because generally its zero part is no longer a deformation of the space of all smooth functions on the reduced phase space but in case the group action is sufficiently nice e g proper which is the case for all compact lie group actions it is shown for a strongly invariant star product that the brst procedure always induces a star product on the reduced phase space in a rather explicit and natural way simple examples and counterexamples are discussed

posterior convergence given the mean for various applications one wants to know the asymptotic behavior of x the posterior density of a parameter given the mean x of the data rather than the full data set here we show that x is asymptotically normal in an l 1 sense and we identify the mean of the limiting normal and its asymptotic variance the main results are first proved assuming that x 1 x n are independent and identical suitable modifications to obtain results for the nonidentical case are given separately our results may be used to construct approximate hpd highest posterior density sets for the parameter which is of use in the statistical theory of standardized educational tests they may also be used to show the covariance between two test items conditioned on the mean is asymptotically nonpositive this has implications for constructing tests of item independence

on the chern character of a theta summable fredholm module on montre qu il est possible de simplifier la theorie de connes du caractere de chern a partir d une k homologie d une algebre de banach vers une cohomologie cyclique entiere

fuzzy characterization of coronary disease abstract the paper presents a methodology based on fuzzy set theory to study the influence of social and psychological factors on the coronary disease a life history questionnaire has been used to collect data from control subjects and coronary patients the two groups made homogeneous in respect to objective features like sex age job etc have been used as training sets to learn the most relevant combinations of social and psychological features in the characterization of the coronary disease each of these features like stress social mobility hysteria etc is represented by means of a fuzzy linguistic variable whose membership value is evaluated on the basis of the answers to the questions relative to the particular feature

moduli spaces of curves and representation theory we establish a canonical isomorphism between the second cohomology of the lie algebra of regular differential operators on x of degree 1 and the second singular cohomology of the moduli space hat f g 1 of quintuples c p z l wherec is a smooth genusg riemann surface p a point onc z a local parameter atp l a degreeg 1 line bundle onc and a class of local trivializations ofl atp which differ by a non zero factor the construction uses an interplay between various infinite dimensional manifolds based on the topological spaceh of germs of holomorphic functions in a neighborhood of 0 in x and related topological spaces the basic tool is a canonical map from hat f g 1 to the infinite dimensional grassmannian of subspaces ofh which is the orbit of the subspaceh of holomorphic functions on x vanishing at under the group auth as an application we give a lie algebraic proof of the mumford formula n 6n2 6n 1 1 where n is the determinant line bundle of the vector bundle on the moduli space of curves of genusg whose fiber overc is the space of differentials of degreen onc

an algebraic index theorem for orbifolds abstract using the concept of a twisted trace density on a cyclic groupoid a trace is constructed on a formal deformation quantization of a symplectic orbifold an algebraic index theorem for orbifolds follows as a consequence of a local riemann roch theorem for such densities in the case of a reduced orbifold this proves a conjecture by fedosov schulze and tarkhanov finally it is shown how the kawasaki index theorem for elliptic operators on orbifolds follows from this algebraic index theorem

the deformation quantizations of the hyperbolic plane we describe the space of all invariant both formal and non formal deformation quantizations on the hyperbolic plane mathbb d as solutions of the evolution of a second order hyperbolic differential operator the construction is entirely explicit and relies on non commutative harmonic analytical techniques on symplectic symmetric spaces the present work presents a unified method producing every quantization of mathbb d and provides in the 2 dimensional context an exact solution to weinstein s wkb quantization program within geometric terms the construction reveals the existence of a metric of lorentz signature canonically attached or dual to the geometry of the hyperbolic plane through the quantization process

convergence of the wick star product we construct a frechet space as a subspace of c omega mathbb c n where the wick star product converges and is continuous the resulting frechet algebra mathcal a is studied in detail including a representation of mathcal a in the bargmann fock space and a discussion of star exponentials and coherent states

homogeneous fedosov star products on cotangent bundles i weyl and standard ordering with differential operator representation in this paper we construct homogeneous star products of weyl type on every cotangent bundle t q by means of the fedosov procedure using a symplectic torsion free connection on t q homogeneous of degree zero with respect to the liouville vector field by a fibrewise equivalence transformation we construct a homogeneous fedosov star product of standard ordered type equivalent to the homogeneous fedosov star product of weyl type representations for both star product algebras by differential operators on functions on q are constructed leading in the case of the standard ordered product to the usual standard ordering prescription for smooth complex valued functions on t q polynomial in the momenta where an arbitrary fixed torsion free connection 0 on q is used motivated by the flat case t n another homogeneous star product of weyl type corresponding to the weyl ordering prescription is constructed the example of the cotangent bundle of an arbitrary lie group is explicitly computed and the star product given by gutt is rederived in our approach

on representations of star product algebras over cotangent spaces on hermitian line bundles abstract for every formal power series b of closed two forms on a manifold q and every value of an ordering parameter 0 1 we construct a concrete star product b on the cotangent bundle t q the star product b is associated to the symplectic form on t q given by the sum of the canonical symplectic form and the pull back of b to t q deligne s characteristic class of b is calculated and shown to coincide with the formal de rham cohomology class of b divided by i therefore every star product on t q corresponding to the canonical poisson bracket is equivalent to some b it turns out that every b is strongly closed in this paper we also construct and classify explicitly formal representations of the deformed algebra as well as operator representations given by a certain global symbol calculus for pseudodifferential operators on q moreover we show that the latter operator representations induce the formal representations by a certain taylor expansion we thereby obtain a compact formula for the wkb expansion

on the homology of algebras of whitney functions over subanalytic sets in this article we study several homology theories of the algebra e x of whitney functions over a subanalytic set x r n with a view towards noncommutative geometry using a localization method going back to teleman we prove a hochschild kostant rosenberg type theorem for e x when x is a regular subset of r n having regularly situated diagonals this includes the case of subanalytic x we also compute the hochschild cohomology of e x for a regular set with regularly situated diagonals and derive the cyclic and periodic cyclic theories it is shown that the periodic cyclic homology coincides with the de rham cohomology thus generalizing a result of feigin tsygan motivated by the algebraic de rham theory of grothendieck we finally prove that for subanalytic sets the de rham cohomology of e x coincides with the singular cohomology for the proof of this result we introduce the notion of a bimeromorphic subanalytic triangulation and show that every bounded subanalytic set admits such a triangulation contents

formal symplectic groupoid of a deformation quantization we give a self contained algebraic description of a formal symplectic groupoid over a poisson manifold m to each natural star product on m we then associate a canonical formal symplectic groupoid over m finally we construct a unique formal symplectic groupoid with separation of variables over an arbitrary kahler poisson manifold

a formality theorem for hochschild chains abstract we prove tsygan s formality conjecture for hochschild chains of the algebra of functions on an arbitrary smooth manifold m using the fedosov resolutions proposed in math qa 0307212 and the formality quasi isomorphism for hochschild chains of r y 1 y d proposed in paper math qa 0010321 by shoikhet this result allows us to describe traces on the quantum algebra of functions on an arbitrary poisson manifold

deformation quantization and the baum connes conjecture alternative titles of this paper would have been index theory without index or the baum connes conjecture without baum

a person fit test for irt models for polytomous items a person fit test based on the lagrange multiplier test is presented for three item response theory models for polytomous items the generalized partial credit model the sequential model and the graded response model the test can also be used in the framework of multidimensional ability parameters it is shown that the lagrange multiplier statistic can take both the effects of estimation of the item parameters and the estimation of the person parameters into account the lagrange multiplier statistic has an asymptotic 2 distribution the type i error rate and power are investigated using simulation studies results show that test statistics that ignore the effects of estimation of the persons ability parameters have decreased type i error rates and power incorporating a correction to account for the effects of the estimation of the persons ability parameters results in acceptable type i error rates and power characteristics incorporating a correction for the estimation of the item parameters has very little additional effect it is investigated to what extent the three models give comparable results both in the simulation studies and in an example using data from the neo personality inventory revised

formal gns construction and states in deformation quantization in this paper we develop a method of constructing hilbert spaces and the representation of the formal algebra of quantum observables in deformation quantization which is an analog of the well known gns construction for complex c algebras in this approach the corresponding positive linear functionals states take their values not in the field of complex numbers but in a suitable extension field of the field of formal complex laurent series in the formal parameter by using the algebraic and topological properties of these fields we prove that this construction makes sense and show in physical examples that standard representations such as the bargmann and schrodinger representation come out correctly both formally and in a suitable convergence scheme for certain hamiltonian functions contained in the gel fand ideal of the positive functional a formal solution to the time dependent schrodinger equation is shown to exist moreover we show that for every kahler manifold equipped with the fedosov star product of wick type all the classical delta functionals are positive and give rise to some formal bargmann representation of the deformed algebra

riemann roch theorems via deformation quantization i abstract we deduce the riemann roch type formula expressing the microlocal euler class of a perfect complex of d modules in terms of the chern character of the associated symbol complex and the todd class of the manifold from the riemann roch type theorem for periodic cyclic cocycles of a symplectic deformation quantization the proof of the latter is contained in the sequel to this paper

trace functionals on noncommutative deformations of moduli spaces of flat connections abstract we describe an efficient construction of a canonical noncommutative deformation of the algebraic functions on the moduli spaces of flat connections on a riemann surface the resulting algebra is a variant of the quantum moduli algebra introduced by alekseev grosse and schomerus and buffenoir and roche we construct a natural trace functional on this algebra and show that it is related to the canonical trace in the formal index theory of fedosov and nest and tsygan via verlinde s formula

cyclic cocycles on deformation quantizations and higher index theorems abstract we construct a nontrivial cyclic cocycle on the weyl algebra of a symplectic vector space using this cyclic cocycle we construct an explicit local quasi isomorphism from the complex of differential forms on a symplectic manifold to the complex of cyclic cochains of any formal deformation quantization thereof we give a new proof of nest tsygan s algebraic higher index theorem by computing the pairing between such cyclic cocycles and the k theory of the formal deformation quantization furthermore we extend this approach to derive an algebraic higher index theorem on a symplectic orbifold as an application we obtain the analytic higher index theorem of connes moscovici and its extension to orbifolds

the characteristic classes of morita equivalent star products on symplectic manifolds in this paper we give a complete characterization of morita equivalent star products on symplectic manifolds in terms of their characteristic classes two star products and on m are morita equivalent if and only if there exists a symplectomorphism colon m m such that the relative class t is 2 i integral for star products on cotangent bundles we show that this integrality condition is related to dirac s quantization condition for magnetic charges

cyclic cohomology of the weyl algebra abstract we give an explicit formula for sp 2 n basic representatives of the cyclic cohomology of the weyl algebra h c a 2 n as an application we prove a generalization of a theorem of nest and tsygan concerning the relation of the todd class and the cyclic cohomology of the differential operators on a complex manifold

algebraic index theorem we prove the atiyah singer index theorem where the algebra of pseudodifferential operators is replaced by an arbitrary deformation quantization of the algebra of functions on a symplectic manifold

characters of cycles equivariant characteristic classes and fredholm modules we derive simple explicit formula for the character of a cycle in the connes b b bicomplex of cyclic cohomology and apply it to write formulas for the equivariant chern character and characters of finitely summable bounded fredholm modules

a note on the usefulness of linguistic variables for differentiating between some respiratory diseases abstract an uncommon application of linguistic variables as predictor variables for obtaining classical discriminant functions is presented commonly only quantitative features are used as predictor variables for evaluating linear quadratic or canonical discriminant functions because of the assumption of normality this paper deals with results of discrimination between various respiratory diseases using quantitative and linguistic variables together linguistic variables in medical applications were obtained by saitta and torasso fuzzy sets and systems 5 1981 245 258 as a conversion of the groups of original discrete features the classical linear quadratic and canonical discriminant functions were calculated for our data to make a trial of automatical diagnosis we obtain a considerable amelioration of the results of discrimination using the complete set of variables quantitative and linguistic instead of only quantitative ones the percentage of correctly classified patients increased from 86 to 97 percent in the case of linear discriminant function the variables with the greatest discriminative power were also chosen these were the linguistic variables character of dyspnoea physical examination of the chest and x ray examination of the chest the presented method enables the simultaneous use of quantitative and qualitative features to the description of the patient s state for this reason linguistic variables seem to be an efficient tool in medical applications

the impact of fallible item parameter estimates on latent trait recovery in this paper we propose an upward correction to the standard error se estimation of ml the maximum likelihood ml estimate of the latent trait in item response theory irt more specifically the upward correction is provided for the se of ml when item parameter estimates obtained from an independent pretest sample are used in irt scoring when item parameter estimates are employed the resulting latent trait estimate is called pseudo maximum likelihood pml estimate traditionally the se of ml is obtained on the basis of test information only as if the item parameters are known the upward correction takes into account the error that is carried over from the estimation of item parameters in addition to the error in latent trait recovery itself our simulation study shows that both types of se estimates are very good when is in the middle range of the latent trait distribution but the upward corrected ses are more accurate than the traditional ones when takes more extreme values

identification of berezin toeplitz deformation quantization we give a complete identification of the deformation quantization which was obtained from the berezin toeplitz quantization on an arbitrary compact kahler manifold the deformation quantization with the opposite star product proves to be a differential deformation quantization with separation of variables whose dassifying form is explicitly calculated its characteristic dass which dassifies star products up to equivalence is obtained the proof is based on the microlocal description of the szego kernel of a strictly pseudoconvex domain given by boutet de monvel and sjostrand

free products cyclic homology and the gauss manin connection abstract we use the techniques of cuntz and quillen to present a new approach to periodic cyclic homology our construction is based on a t d t i a noncommutative equivariant de rham complex of an associative algebra a here d is the karoubi de rham differential and i is an operation analogous to contraction with a vector field as a byproduct we give a simple explicit construction of the gauss manin connection introduced earlier by e getzler on the relative periodic cyclic homology of a flat family of associative algebras over a central base ring we introduce and study free product deformations of an associative algebra a new type of deformation over a not necessarily commutative base ring natural examples of free product deformations arise from preprojective algebras and group algebras for compact surface groups

involutions and representations for reduced quantum algebras abstract in the context of deformation quantization there exist various procedures to deal with the quantization of a reduced space m red we shall be concerned here mainly with the classical marsden weinstein reduction assuming that we have a proper action of a lie group g on a poisson manifold m with a moment map j for which zero is a regular value for the quantization we follow bordemann et al 2000 6 with a simplified approach and build a star product red on m red from a strongly invariant star product on m the new questions which are addressed in this paper concern the existence of natural involutions on the reduced quantum algebra and the representation theory for such a reduced algebra we assume that is hermitian and we show that the choice of a formal series of smooth densities on the embedded coisotropic submanifold c j 1 0 with some equivariance property defines a involution for red on the reduced space looking into the question whether the corresponding involution is the complex conjugation which is a involution in the marsden weinstein context yields a new notion of quantized modular class we introduce a left c m submodule and a right c m red red submodule c cf c of c c we define on it a c m red valued inner product and we establish that this gives a strong morita equivalence bimodule between c m red and the finite rank operators on c cf c the crucial point is here to show the complete positivity of the inner product we obtain a rieffel induction functor from the strongly non degenerate representations of c m red red on pre hilbert right d modules to those of c m for any auxiliary coefficient algebra d over c

stochastic order in dichotomous item response models for fixed adaptive and multidimensional tests dichotomous irt models can be viewed as families of stochastically ordered distributions of responses to test items this paper explores several properties of such distributions in particular it is examined under what conditions stochastic order in families of conditional distributions is transferred to their inverse distributions from two families of related distributions to a third family or from multivariate conditional distributions to a marginal distribution the main results are formulated as a series of theorems and corollaries which apply to dichotomous irt models one part of the results holds for unidimensional models with fixed item parameters the other part holds for models with random item parameters as used for example in adaptive testing or for tests with multidimensional abilities

geometric quantization of vector bundles and the correspondence with deformation quantization i repeat my definition for quantization of a vector bundle for the cases of the toeplitz and geometric quantizations of a compact kahler manifold i give a construction for quantizing any smooth vector bundle which depends functorially on a choice of connection on the bundle