from geometric quantization to moyal quantization it is shown how the moyal product of phase space functions and the weyl correspondence between symbols and operator kernels may be obtained directly using the procedures of geometric quantization applied to the symplectic groupoid constructed by doubling the phase space

linear canonical transformations and quantum phase a unified canonical and algebraic approach the algebra of generalized linear quantum canonical transformations is examined in the perspective of schwinger s unitary canonical operator basis formulation of the quantum phase problem within the theory of quantum canonical transformations and in particular with the generalized quantum action angle phase space formalism is established and it is shown that the conceptual foundation of the quantum phase problem lies within the algebraic properties of the canonical transformations in the quantum phase space the representations of the wigner function in the generalized action angle unitary operator pair for certain hamiltonian systems with dynamical symmetry is examined this generalized canonical formalism is applied to the quantum harmonic oscillator to examine the properties of the unitary quantum phase operator as well as the action angle wigner function

measurement error modelling with an approximate instrumental variable summary consider using regression modelling to relate an exposure predictor variable to a disease outcome response variable if the exposure variable is measured with error but this error is ignored in the analysis then misleading inferences can result this problem is well known and has spawned a large literature on methods which adjust for measurement error in predictor variables one theme is that the requisite assumptions about the nature of the measurement error can be stronger than what is actually known in many practical situations in particular the assumptions that are required to yield a model which is formally identified from the observable data can be quite strong the paper deals with one particular strategy for measurement error modelling namely that of seeking an instrumental variable i e a covariate s which is associated with exposure and conditionally independent of the outcome given exposure if these two conditions hold exactly then we call s an exact instrumental variable and an identified model results however the second is not checkable empirically since the actual exposure is unobserved in practice then investigators typically seek a covariate which is plausibly thought to satisfy it we study inferences which acknowledge the approximate nature of this assumption in particular we consider bayesian inference with a prior distribution that posits that s is probably close to conditionally independent of outcome given exposure we refer to this as an approximate instrumental variable assumption although the approximate instrumental variable assumption is more realistic for most applications concern arises that a non identified model may result thus the paper contrasts inferences arising from the approximate instrumental variable assumption with their exact instrumental variable counterparts with particular emphasis on the benefit of basing inferences on a more realistic model versus the cost of basing inferences on a non identified model

quantum symmetries and the weyl wigner product of group representations in the usual formulation of quantum mechanics groups of automorphisms of quantum states have ray representations by unitary and antiunitary operators on complex hilbert space in accordance with wigner s theorem in the phase space formulation they have real true unitary representations in the space of square integrable functions on phase space each such phase space representation is a weyl wigner product of the corresponding hilbert space representation with its contragredient and these can be recovered by factorizing the weyl wigner product however not every real unitary representation on phase space corresponds to a group of automorphisms so not every such representation is in the form of a weyl wigner product and can be factorized the conditions under which this is possible are examined examples are presented

the moyal lie theory of phase space quantum mechanics a lie algebraic approach to the unitary transformations in weyl quantization is discussed this approach being formally equivalent to the quantization is an extension of the classical poisson lie theory and can be used as an efficient tool in the quantum phase space transformation theory

bayesian sample size determination for prevalence and diagnostic test studies in the absence of a gold standard test planning studies involving diagnostic tests is complicated by the fact that virtually no test provides perfectly accurate results the misclassification induced by imperfect sensitivities and specificities of diagnostic tests must be taken into account whether the primary goal of the study is to estimate the prevalence of a disease in a population or to investigate the properties of a new diagnostic test previous work on sample size requirements for estimating the prevalence of disease in the case of a single imperfect test showed very large discrepancies in size when compared to methods that assume a perfect test in this article we extend these methods to include two conditionally independent imperfect tests and apply several different criteria for bayesian sample size determination to the design of such studies we consider both disease prevalence studies and studies designed to estimate the sensitivity and specificity of diagnostic tests as the problem is typically nonidentifiable we investigate the limits on the accuracy of parameter estimation as the sample size approaches infinity through two examples from infectious diseases we illustrate the changes in sample sizes that arise when two tests are applied to individuals in a study rather than a single test although smaller sample sizes are often found in the two test situation they can still be prohibitively large unless accurate information is available about the sensitivities and specificities of the tests being used

optimal design via curve fitting of monte carlo experiments abstract this article explores numerical methods for stochastic optimization with special attention to bayesian design problems a common and challenging situation occurs when the objective function in bayesian applications the expected utility is very expensive to evaluate perhaps because it requires integration over a space of very large dimensionality our goal is to explore a class of optimization algorithms designed to gain efficiency in such situations by exploiting smoothness of the expected utility surface and borrowing information from neighboring design points the central idea is that of implementing stochastic optimization by curve fitting of monte carlo samples this is done by simulating draws from the joint parameter sample space and evaluating the observed utilities fitting a smooth surface through these simulated points serves as estimate for the expected utility surface the optimal design can then be found deterministically in this article we introduce a general algorithm for cu

the construction of a quantum markov partition we present a method for constructing a quantum markov partition its elements are obtained by quantizing the characteristic function of the classical rectangles the result is a set of quantum operators which behave asymptotically as projectors over the classical rectangles apart from edge and corner effects we investigate their spectral properties and different methods of construction the quantum partition is shown to induce a symbolic decomposition of the quantum evolution operator in particular an exact expression for the traces of the propagator is obtained having the same structure as the gutzwiller periodic orbit sum

bounds on integrals of the wigner function the integral of the wigner function over a subregion of the phase space of a quantum system may be less than zero or greater than one it is shown that for systems with 1 degree of freedom the problem of determining the best possible upper and lower bounds on such an integral over an possible states reduces to the problem of finding the greatest and least eigenvalues of a hermitian operator corresponding to the subregion the problem is solved exactly in the case of an arbitrary elliptical region these bounds provide checks on experimentally measured quasiprobability distributions

numerical experimentsregarding the distributed control of semilinear parabolic problems this work deals with some numerical experiments regarding the distributed control ofsemilinear parabolic equations of the type yt y g g f y u g w in 0 1 x 0 t with neumann and initial auxiliary conditions where w is an open subset of 0 1 f is a c1 nondecreasing real function u is the output control and t 0 is arbitrarily fixed given a target state yt we study the associated approximate controllability problem given e 0 find u e l2 0 t such that y t u yt l 2 0 1 by passing to the limit when k in the penalized optimal control problem find uk as the minimum of jk u 1 2 u l 0 t 2 k 2 y t u yt l 22l2 o t l2 0 1 in the superlinear case e g f y y n 1 y n 1 the existence of two obstruction functions y shows that the approximate controllability is only possible if y x t yt x y x t for a e x e 0 1 we carry out some numerical experiments showing that for a fixed k the minimal cost jk u and the norm of the optimal control uk for a superlinear function f becomes much larger when this condition is not satisfied we also compare the values of jk u and the norm of the optimal control u k for a fixed yt associated with two nonlinearities one sublinear and the other one superlinear

bayesian approaches to modeling the conditional dependence between multiple diagnostic tests many analyses of results from multiple diagnostic tests assume the tests are statistically independent conditional on the true disease status of the subject this assumption may be violated in practice especially in situations where none of the tests is a perfectly accurate gold standard classical inference for models accounting for the conditional dependence between tests requires that results from at least four different tests be used in order to obtain an identifiable solution but it is not always feasible to have results from this many tests we use a bayesian approach to draw inferences about the disease prevalence and test properties while adjusting for the possibility of conditional dependence between tests particularly when we have only two tests we propose both fixed and random effects models since with fewer than four tests the problem is nonidentifiable the posterior distributions are strongly dependent on the prior information about the test properties and the disease prevalence even with large sample sizes if the degree of correlation between the tests is known a priori with high precision then our methods adjust for the dependence between the tests otherwise our methods provide adjusted inferences that incorporate all of the uncertainty inherent in the problem typically resulting in wider interval estimates we illustrate our methods using data from a study on the prevalence of strongyloides infection among cambodian refugees to canada

weyl wigner formulation of noncommutative quantum mechanics we address the phase space formulation of a noncommutative extension of quantum mechanics in arbitrary dimension displaying both spatial and momentum noncommutativities by resorting to a covariant generalization of the weyl wigner transform and to the darboux map we construct an isomorphism between the operator and the phase space representations of the extended heisenberg algebra this map provides a systematic approach to derive the entire structure of noncommutative quantum mechanics in phase space we construct the extended star product and moyal bracket and propose a general definition of noncommutative states we study the dynamical and eigenvalue equations of the theory and prove that the entire formalism is independent of the particular choice of the darboux map our approach unifies and generalizes all the previous proposals for the phase space formulation of noncommutative quantum mechanics for concreteness we rederive these proposals by restricting our formalism to some two dimensional spaces

the turnpike property in finite dimensional nonlinear optimal control turnpike properties have been established long time ago in finite dimensional optimal control problems arising in econometry they refer to the fact that under quite general assumptions the optimal solutions of a given optimal control problem settled in large time consist approximately of three pieces the first and the last of which being transient short time arcs and the middle piece being a long time arc staying exponentially close to the optimal steady state solution of an associated static optimal control problem we provide in this paper a general version of a turnpike theorem valuable for nonlinear dynamics without any specific assumption and for very general terminal conditions not only the optimal trajectory is shown to remain exponentially close to a steady state but also the corresponding adjoint vector of the pontryagin maximum principle the exponential closedness is quantified with the use of appropriate normal forms of riccati equations we show then how the property on the adjoint vector can be adequately used in order to initialize successfully a numerical direct method or a shooting method in particular we provide an appropriate variant of the usual shooting method in which we initialize the adjoint vector not at the initial time but at the middle of the trajectory

control of 1 d parabolic pdes with volterra nonlinearities part i design boundary control of nonlinear parabolic pdes is an open problem with applications that include fluids thermal chemically reacting and plasma systems in this paper we present stabilizing control designs for a broad class of nonlinear parabolic pdes in 1 d our approach is a direct infinite dimensional extension of the finite dimensional feedback linearization backstepping approaches and employs spatial volterra series nonlinear operators both in the transformation to a stable linear pde and in the feedback law the control law design consists of solving a recursive sequence of linear hyperbolic pdes for the gain kernels of the spatial volterra nonlinear control operator these pdes evolve on domains t n of increasing dimensions n 1 and with a domain shape in the form of a hyper pyramid 0 x n x n 1 x 1 x 1 we illustrate our design method with several examples one of the examples is analytical while in the remaining two examples the controller is numerically approximated for all the examples we include simulations showing blow up in open loop and stabilization for large initial conditions in closed loop in a companion paper we give a theoretical study of the properties of the transformation showing global convergence of the transformation and of the control law nonlinear volterra operators and explicitly constructing the inverse of the feedback linearizing volterra transformation this in turn allows us to prove l 2 and h 1 local exponential stability with an estimate of the region of attraction where possible and explicitly construct the exponentially decaying closed loop solutions

sample size determination for diagnostic accuracy studies involving binormal roc curve indices receiver operating characteristic roc curves and their associated indices are valuable tools for the assessment of the accuracy of diagnostic tests the area under the roc curve is a popular summary measure of the accuracy of a test the full area under the roc curve however has been criticized because it gives equal weight to all false positive error rates alternative indices include the area under the roc curve in a particular range of false positive rates partial area and the sensitivity of the test for a single fixed false positive rate fpr we present a unified approach for computing sample size for binormal roc curves and their indices our method uses taylor series expansions to derive approximate large sample estimates of the variance and covariance of binormal roc curve parameters several examples from diagnostic radiology illustrate the proposed method

modeling continuous diagnostic test data using approximate dirichlet process distributions there is now a large literature on the analysis of diagnostic test data in the absence of a gold standard test latent class analysis is most often used to estimate the prevalence of the condition of interest and the properties of the diagnostic tests when test results are measured on a continuous scale both parametric and nonparametric models have been proposed parametric methods such as the commonly used bi normal model may not fit the data well nonparametric methods developed to date have been relatively complex to apply in practice and their properties have not been carefully evaluated in the diagnostic testing context in this paper we propose a simple yet flexible bayesian nonparametric model which approximates a dirichlet process for continuous data we compare results from the nonparametric model with those from the bi normal model via simulations investigating both how much is lost in using a nonparametric model when the bi normal model is correct and how much can be gained in using a nonparametric model when normality does not hold we also carefully investigate the trade offs that occur between flexibility and identifiability of the model as different dirichlet process prior distributions are used motivated by an application to tuberculosis clustering we extend our nonparametric model to accommodate two additional dichotomous tests and proceed to analyze these data using both the continuous test alone as well as all three tests together copyright 2011 john wiley sons ltd

wigner functions on non standard symplectic vector spaces we consider the weyl quantization on a flat non standard symplectic vector space we focus mainly on the properties of the wigner functions defined therein in particular we show that the sets of wigner functions on distinct symplectic spaces are different but have non empty intersections this extends previous results to arbitrary dimension and arbitrary constant symplectic structure as a by product we introduce and prove several concepts and results on non standard symplectic spaces which generalize those on the standard symplectic space namely the symplectic spectrum williamson s theorem and narcowich wigner spectra we also show how wigner functions on non standard symplectic spaces behave under the action of an arbitrary linear coordinate transformation

the quantum state vector in phase space and gabor s windowed fourier transform representations of quantum state vectors by complex phase space amplitudes complementing the description of the density operator by the wigner function have been defined by applying the weyl wigner transform to dyadic operators linear in the state vector and anti linear in a fixed window state vector here aspects of this construction are explored and a connection is established with gabor s windowed fourier transform the amplitudes that arise for simple quantum states from various choices of windows are presented as illustrations generalized bargmann representations of the state vector appear as special cases associated with gaussian windows for every choice of window amplitudes lie in a corresponding linear subspace of square integrable functions on phase space a generalized born interpretation of amplitudes is described with both the wigner function and a generalized husimi function appearing as quantities linear in an amplitude and anti linear in its complex conjugate schrodinger s time dependent and time independent equations are represented on phase space amplitudes and their solutions described in simple cases

bayesian and mixed bayesian likelihood criteria for sample size determination sample size estimation is a major component of the design of virtually every experiment in medicine prudent use of the available prior information is a crucial element of experimental planning most sample size formulae in current use employ this information only in the form of point estimates even though it is usually more accurately expressed as a distribution over a range of values in this paper we review several bayesian and mixed bayesian likelihood approaches to sample size calculations based on lengths and coverages of posterior credible intervals we apply these approaches to the design of an experiment to estimate the difference between two binomial proportions and we compare results to those derived from standard formulae consideration of several criteria can contribute to selection of a final sample size

symbolic calculus on the time frequency half plane this study concerns a special symbolic calculus of interest for signal analysis this calculus associates functions on the time frequency half plane f 0 with linear operators defined on the positive frequency signals full attention is given to its construction which is entirely based on the study of the affine group in a simple and direct way the correspondence rule is detailed and the associated wigner function is given formulas expressing the basic operation star bracket of the lie algebra of symbols which is isomorphic to that of the operators are obtained in addition it is shown that the resulting calculus is covariant under a three parameter group which contains the affine group as subgroup this observation is the starting point of an investigation leading to a whole class of symbolic calculi which can be considered as modifications of the original one

moyal quantization with compact symmetry groups and noncommutative harmonic analysis the phase space approach to quantization of systems whose symmetry group is compact and semisimple is developed from two basic principles covariance and traciality this generalizes results and methods already implemented for spin systems j c varilly and j m gracia bondia ann phys 190 107 1989 the twisted product of phase space functions is shown to be the image of group convolution in the context of a novel fourier theory on the coadjoint orbits

bounds on integrals of the wigner function the hyperbolic case wigner functions play a central role in the phase space formulation of quantum mechanics although closely related to classical liouville densities wigner functions are not positive definite and may take negative values on subregions of phase space we investigate the accumulation of these negative values by studying bounds on the integral of an arbitrary wigner function over noncompact subregions of the phase plane with hyperbolic boundaries we show using symmetry techniques that this problem reduces to computing the bounds on the spectrum associated with an exactly solvable eigenvalue problem and that the bounds differ from those on classical liouville distributions in particular we show that the total quasiprobability on such a region can be greater than 1 or less than zero c 2005 american institute of physics

global steady state controllability of 1 d semilinear heat equations we investigate the problem of exact boundary controllability of semilinear one dimensional heat equations we prove that it is possible to move from any steady state to any other one by means of a boundary control provided that they are in the same connected component of the set of steady states the proof is based on an effective feedback stabilization procedure which is implemented

phase space observables and isotypic spaces we give necessary and sufficient conditions for the set of neumark projections of a countable set of phase space observables to constitute a resolution of the identity and we give a criteria for a phase space observable to be informationally complete the results will be applied to the phase space observables arising from an irreducible representation of the heisenberg group

wigner measures in noncommutative quantum mechanics we study the properties of quasi distributions or wigner measures in the context of noncommutative quantum mechanics in particular we obtain necessary and sufficient conditions for a phase space function to be a noncommutative wigner measure for a gaussian to be a noncommutative wigner measure and derive certain properties of the marginal distributions which are not shared by ordinary wigner measures moreover we derive the robertson schrodinger uncertainty principle finally we show explicitly how the set of noncommutative wigner measures relates to the sets of liouville and commutative wigner measures

wigner distribution functions and the representation of a non bijective canonical transformation in quantum mechanics in a previous paper with a similar title the authors showed that for bijective i e one to one onto canonical transformations they can obtain their quantum mechanical representations in the form of a kernel in the phase space of wigner distribution functions and recover the classical expectation for this kernel in the limit to 0 for non bijective canonical transformations the situation is more complex as the phase space acquires either a riemann surface structure or requires the introduction of the concept of an ambiguity group by discussing the non bijective canonical transformation taking them from an oscillator of frequency kappa 1 where kappa is an integer to one of unit frequency they see how the kernel is generalised to include the indices associated with the irreducible representations of the ambiguity group i e the ambiguity spins they obtain the kernel explicitly and show that in the limit to 0 they recover the form that they expect in the riemann surface picture of their phase space while they illustrate their analysis through the representation in wigner distribution phase space of a specific non bijective canonical transformation the procedure is clearly extendable to the representations of general canonical transformations of this type