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

the grothendieck teichmuller group action on differential forms and formality morphisms of chains it is known that one can associate a kontsevich type formality morphism to every drinfeld associator we show that this morphism may be extended to a kontsevich shoikhet formality morphism of cochains and chains by describing the action of the grothendieck teichmuller group on such objects up to homotopy

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

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

dynamical systems associated to separated graphs graph algebras and paradoxical decompositions abstract we attach to each finite bipartite separated graph e c a partial dynamical system e c f where e c is a zero dimensional metrizable compact space f is a finitely generated free group and is a continuous partial action of f on e c the full crossed product c algebra o e c c e c f is shown to be a canonical quotient of the graph c algebra c e c of the separated graph e c similarly we prove that for any field k the algebraic crossed product l k ab e c c k e c alg f is a canonical quotient of the leavitt path algebra l k e c of e c the monoid v l k ab e c of isomorphism classes of finitely generated projective modules over l k ab e c is explicitly computed in terms of monoids associated to a canonical sequence of separated graphs using this we are able to construct an action of a finitely generated free group f on a zero dimensional metrizable compact space z such that the type semigroup s z f k is not almost unperforated where k denotes the algebra of clopen subsets of z finally we obtain a characterization of the separated graphs e c such that the canonical partial action of f on e c is topologically free

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

accounting for uncertainty in confounder and effect modifier selection when estimating average causal effects in generalized linear models summary confounder selection and adjustment are essential elements of assessing the causal effect of an exposure or treatment in observational studies building upon work by wang et al 2012 biometrics 68 661 671 and lefebvre et al 2014 statistics in medicine 33 2797 2813 we propose and evaluate a bayesian method to estimate average causal effects in studies with a large number of potential confounders relatively few observations likely interactions between confounders and the exposure of interest and uncertainty on which confounders and interaction terms should be included our method is applicable across all exposures and outcomes that can be handled through generalized linear models in this general setting estimation of the average causal effect is different from estimation of the exposure coefficient in the outcome model due to noncollapsibility we implement a bayesian bootstrap procedure to integrate over the distribution of potential confounders and to estimate the causal effect our method permits estimation of both the overall population causal effect and effects in specified subpopulations providing clear characterization of heterogeneous exposure effects that may vary considerably across different covariate profiles simulation studies demonstrate that the proposed method performs well in small sample size situations with 100 150 observations and 50 covariates the method is applied to data on 15 060 us medicare beneficiaries diagnosed with a malignant brain tumor between 2000 and 2009 to evaluate whether surgery reduces hospital readmissions within 30 days of diagnosis

calcul d un invariant de star produit ferme sur une variete symplectique let m be a symplectic manifold over in cfs the authors construct an invariant in the cyclic cohomology of m for any closed star product they compute this invariant in the de rham complex of m when m t v we generalize this result by computing the image of in the de rham complex for any symplectic manifold and any star product and we show how this invariant is related to the general classification of kontsevich the proof uses the riemann roch theorem for periodic cyclic chains of nest tsygan

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

a new criterion for confounder selection we propose a new criterion for confounder selection when the underlying causal structure is unknown and only limited knowledge is available we assume all covariates being considered are pretreatment variables and that for each covariate it is known i whether the covariate is a cause of treatment and ii whether the covariate is a cause of the outcome the causal relationships the covariates have with one another is assumed unknown we propose that control be made for any covariate that is either a cause of treatment or of the outcome or both we show that irrespective of the actual underlying causal structure if any subset of the observed covariates suffices to control for confounding then the set of covariates chosen by our criterion will also suffice we show that other commonly used criteria for confounding control do not have this property we use formal theory concerning causal diagrams to prove our result but the application of the result does not rely on familiarity with causal diagrams an investigator simply need ask is the covariate a cause of the treatment and is the covariate a cause of the outcome if the answer to either question is yes then the covariate is included for confounder control we discuss some additional covariate selection results that preserve unconfoundedness and that may be of interest when used with our criterion

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

infinite non simple c algebras absorbing the cuntz algebra o abstract the first named author has given a classification of all separable nuclear c algebras a that absorb the cuntz algebra o we say that a absorbs o if a is isomorphic to a o motivated by this classification we investigate here if one can give an intrinsic characterization of c algebras that absorb o this investigation leads us to three different notions of pure infiniteness of a c algebra all given in terms of local algebraic conditions on the c algebra the strongest of the three properties strongly purely infinite is shown to be equivalent to absorbing o for separable nuclear c algebras that either are stable or have an approximate unit consisting of projections in a previous paper 2000 amer j math 122 637 666 we studied an intermediate and perhaps more natural condition purely infinite that extends a well known property for simple c algebras the weakest condition of the three weakly purely infinite is shown to be equivalent to the absence of quasitraces in an ultrapower of the c algebra the three conditions may be equivalent for all c algebras and we prove this to be the case for c algebras that are either simple of real rank zero or approximately divisible

stratification and weighting via the propensity score in estimation of causal treatment effects a comparative study estimation of treatment effects with causal interpretation from observational data is complicated because exposure to treatment may be confounded with subject characteristics the propensity score the probability of treatment exposure conditional on covariates is the basis for two approaches to adjusting for confounding methods based on stratification of observations by quantiles of estimated propensity scores and methods based on weighting observations by the inverse of estimated propensity scores we review popular versions of these approaches and related methods offering improved precision describe theoretical properties and highlight their implications for practice and present extensive comparisons of performance that provide guidance for practical use

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

căldăraru s conjecture and tsygan s formality in this paper we complete the proof of caldararu s conjecture on the compatibility between the module structures on differential forms over poly vector fields and on hochschild homology over hochschild cohomology in fact we show that twisting with the square root of the todd class gives an isomorphism of precalculi between these pairs of objects our methods use formal geometry to globalize the local formality quasi isomorphisms introduced by kontsevich and shoikhet the existence of the latter was conjectured by tsygan we also rely on the fact recently proved by the first two authors that shoikhet s quasi isomorphism is compatible with cap products after twisting with a maurer cartan element

bayesian model averaging for linear regression models abstract we consider the problem of accounting for model uncertainty in linear regression models conditioning on a single selected model ignores model uncertainty and thus leads to the underestimation of uncertainty when making inferences about quantities of interest a bayesian solution to this problem involves averaging over all possible models i e combinations of predictors when making inferences about quantities of interest this approach is often not practical in this article we offer two alternative approaches first we describe an ad hoc procedure occam s window which indicates a small set of models over which a model average can be computed second we describe a markov chain monte carlo approach that directly approximates the exact solution in the presence of model uncertainty both of these model averaging procedures provide better predictive performance than any single model that might reasonably have been selected in the extreme case where there are many candidate predictors but

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

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

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

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

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

simple purely infinite c algebras and n filling actions let n be a positive integer we introduce a concept which we call the n filling property for an action of a group on a separable unital c algebra a if a c is a commutative unital c algebra and the action is induced by a group of homeomorphisms of then the n filling property reduces to a weak version of hyperbolicity the n filling property is used to prove that certain crossed product c algebras are purely infinite and simple a variety of group actions on boundaries of symmetric spaces and buildings have the n filling property an explicit example is the action of sln z on the projective n space

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

kontsevich s graph complex grt and the deformation complex of the sheaf of polyvector fields we generalize kontsevich s construction of l1 derivations of polyvector elds from the ane space to an arbitrary smooth algebraic variety more precisely we construct a map in the homotopy category from kontsevich s graph complex to the deformation complex of the sheaf of polyvector elds on a smooth algebraic variety we show that the action of deligne drinfeld

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

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

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

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

m kontsevich s graph complex and the grothendieck teichmuller lie algebra we show that the zeroth cohomology of m kontsevich s graph complex is isomorphic to the grothendieck teichmuller lie algebra mathfrak grt 1 the map is explicitly described this result has applications to deformation quantization and duflo theory we also compute the homotopy derivations of the gerstenhaber operad they are parameterized by mathfrak grt 1 up to one class or two depending on the definitions more generally the homotopy derivations of the non unital e n operads may be expressed through the cohomology of a suitable graph complex our methods also give a second proof of a result of h furusho stating that the pentagon equation for mathfrak grt 1 elements implies the hexagon equation

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

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

extending the bayesian adjustment for confounding algorithm to binary treatment covariates to estimate the effect of smoking on carotid intima media thickness the multi ethnic study of atherosclerosis abstract we illustrate the application of the bayesian adjustment for confounding bac algorithm when the treatment covariate is binary using data from the multi ethnic study of atherosclerosis we estimate the effect of ever smoking on common carotid artery intimal medial thickness among adult caucasian participants n 1378 our novel implementation of the bac algorithm is performed first from an outcome model perspective and second from a treatment model perspective with both inverse probability weighting and doubly robust estimation techniques the bac results are compared with the results obtained using standard model averaging and full model strategies giving a range of adjusted estimates between 45 50 and 65 30 m for increased common carotid artery intimal medial thickness among ever smokers for both perspectives we observe that bac offers similar performance to using the fully specified outcome and or treatment model the full outcome model ever smoking effect is 48 61 m 95 ci 0 62 96 60 we then redo the analyses for the african american hispanic and chinese adult participants to study the robustness of these findings with reduced sample size for the chinese subcohort which corresponds to the smallest sample size n 436 we find that from a treatment model perspective bac reduces the variability of the estimates in comparison with using a full model approach this suggests that the use of bac in conjunction with inverse probability weighting and doubly robust estimation can be advantageous when applied to relatively small sample sizes this conjecture is subsequently verified on the basis of three simulated experiments

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

adjustment uncertainty in effect estimation summary often there is substantial uncertainty in the selection of confounders when estimating the association between an exposure and health we define this type of uncertainty as adjustment uncertainty we propose a general statistical framework for handling adjustment uncertainty in exposure effect estimation for a large number of confounders we describe a specific implemen tation and we develop associated visualization tools theoretical results and simulation studies show that the proposed method provides consistent estimators of the exposure effect and its variance we also show that when the goal is to estimate an exposure effect accounting for ad justment uncertainty bayesian model averaging with posterior model probabilities approximated using information criteria can fail to estimate the exposure effect and can over or underestimate its variance we compare our approach to bayesian model averaging using time series data on levels of fine particulate matter and mortality

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

covariant and equivariant formality theorems abstract we give a proof of kontsevich s formality theorem for a general manifold using fedosov resolutions of algebras of polydifferential operators and polyvector fields the main advantage of our construction of the formality quasi isomorphism is that it is based on the use of covariant tensors unlike kontsevich s original proof which is based on jets of polydifferential operators and polyvector fields using our construction we prove that if a group g acts smoothly on a manifold m and m admits a g invariant affine connection then there exists a g equivariant quasi isomorphism of formality this result implies that if a manifold m is equipped with a smooth action of a finite or compact group g or equipped with a free action of a lie group g then m admits a g equivariant formality quasi isomorphism in particular this gives a solution of the deformation quantization problem for an arbitrary poisson orbifold

the character map in deformation quantization the third author recently proved that the shoikhet dolgushev l morphism from hochschild chains of the algebra of smooth functions on a manifold to differential forms extends to cyclic chains localization at a solution of the maurer cartan equation gives an isomorphism which we call character map from the periodic cyclic homology of a formal associative deformation of the algebra of functions to de rham cohomology we prove that the character map is compatible with the gauss manin connection extending a result of calaque and rossi on the compatibility with the cap product as a consequence the image of the periodic cyclic cycle 1 is independent of the deformation parameter and we compute it to be the a roof genus of the manifold our results also imply the tamarkin tsygan index theorem

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

from local to global deformation quantization of poisson manifolds we give an explicit construction of a deformation quantization of the algebra of functions on a poisson manifold based on m kontsevich s local formula the deformed algebra of functions is realized as the algebra of horizontal sections of a vector bundle with flat connection

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

a path integral approach to the kontsevich quantization formula we give a quantum field theory interpretation of kontsevich s deformation quantization formula for poisson manifolds we show that it is given by the perturbative expansion of the path integral of a simple topological bosonic open string theory its batalin vilkovisky quantization yields a superconformal field theory the associativity of the star product and more generally the formality conjecture can then be understood by field theory methods as an application we compute the center of the deformed algebra in terms of the center of the poisson algebra

formality theorems for hochschild chains in the lie algebroid setting in this paper we prove lie algebroid versions of tsygan s formality conjecture for hochschild chains both in the smooth and holomorphic settings in the holomorphic setting our result implies a version of tsygan s formality conjecture for hochschild chains of the structure sheaf of any complex manifold and in the smooth setting this result allows us to describe quantum traces for an arbitrary poisson lie algebroid the proofs are based on the use of kontsevich s quasi isomorphism for hochschild cochains of r y 1 y d shoikhet s quasi isomorphism for hochschild chains of r y 1 y d and fedosov s resolutions of the natural analogues of hochschild co chain complexes associated with a lie algebroid

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

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

non simple purely infinite c algebras a c algebra a is defined to be purely infiniteif there are no characters on a a nd if for every pair of positive elements a b in a such that b lies in the closed two sided ideal generated by a there exists a sequence rn in a such that rn arn b this definition agrees with the usual definition by j cuntz when a is simple it is shown that the property of being purely infinite is preserved under extensions morita equivalence inductive limits and it passes to quotients and to hereditary sub c algebras it is shown that a is purely infinite for every c algebra a purely infinite c algebras admit no traces and conversely an approximately divisible exact c algebra is purely infinite if it admits no nonzero trace

bayesian effect estimation accounting for adjustment uncertainty model based estimation of the effect of an exposure on an outcome is generally sensitive to the choice of which confounding factors are included in the model we propose a new approach which we call bayesian adjustment for confounding bac to estimate the effect of an exposure of interest on the outcome while accounting for the uncertainty in the choice of confounders our approach is based on specifying two models 1 the outcome as a function of the exposure and the potential confounders the outcome model and 2 the exposure as a function of the potential confounders the exposure model we consider bayesian variable selection on both models and link the two by introducing a dependence parameter denoting the prior odds of including a predictor in the outcome model given that the same predictor is in the exposure model in the absence of dependence 1 bac reduces to traditional bayesian model averaging bma in simulation studies we show that bac with 1 estimates the exposure effect with smaller bias than traditional bma and improved coverage we then compare bac a recent approach of crainiceanu dominici and parmigiani 2008 biometrika 95 635 651 and traditional bma in a time series data set of hospital admissions air pollution levels and weather variables in nassau ny for the period 1999 2005 using each approach we estimate the short term effects of on emergency admissions for cardiovascular diseases accounting for confounding this application illustrates the potentially significant pitfalls of misusing variable selection methods in the context of adjustment uncertainty

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

formality of cyclic cochains abstract we prove m kontsevich s cyclic formality conjecture this conjecture is the cyclic analog of the formality theorem for hochschild chains concretely it states that the differential graded lie algebra of polydifferential cyclic cochains of the algebra of smooth functions on a manifold m is l quasi isomorphic to the second term in the spectral sequence computing its cohomology as an application we can classify all closed star products on m

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

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