long correlations and levy models applied to the study of memory effects in high frequency tick data abstract this work is devoted to the study of long correlations memory effects and other statistical properties of high frequency tick data we use a sample of 25 stocks for this purpose we verify that the behavior of the return is compatible with that of continuous time levy processes we also study the presence of memory effects and long range correlations in the values of the return

the analysis of rates using poisson regression models models are considered in which the underlying rate at which events occur can be represented by a regression function that describes the relation between the predictor variables and the unknown parameters estimates of the parameters can be obtained by means of iteratively reweighted least squares irls when the events of interest follow the poisson distribution the irls algorithm is equivalent to using the method of scoring to obtain maximum likelihood ml estimates the general poisson regression models include log linear quasilinear and intrinsically nonlinear models the approach considered enables one to concentrate on describing the relation between the dependent variable and the predictor variables through the regression model standard statistical packages that support irls can then be used to obtain ml estimates their asymptotic covariance matrix and diagnostic measures that can be used to aid the analyst in detecting outlying responses and extreme points in the model space applications of these methods to epidemiologic follow up studies with the data organized into a life table type of format are discussed the method is illustrated by using a nonlinear model derived from the multistage theory of carcinogenesis to analyze lung cancer death rates among british physicians who were regular cigarette smokers

quantum probabilities for time extended alternatives we study the probability assignment for the outcomes of time extended measurements we construct the class operator that incorporates the information about a generic time smeared quantity these class operators are employed for the construction of positive operator valued measures for the time averaged quantities the scheme highlights the distinction between velocity and momentum in quantum theory propositions about velocity and momentum are represented by different class operators hence they define different probability measures we provide some examples we study the classical limit and we construct probabilities for generalized time extended phase space variables

on mutual information in multipartite quantum states and equality in strong subadditivity of entropy the challenge of equality in the strong subadditivity inequality of entropy is approached via a general additivity of correlation information in terms of nonoverlapping clusters of subsystems in multipartite states density operators a family of tripartite states satisfying equality is derived

on state dependent implication in quantum mechanics this paper studies a generalization of the a priori implication e or f meaning of course ef e in the quantum logic p h of all projectors the new definition can be applied also to new pairs of events being based on the indistinguishability of some events when considered from the standpoint of a fixed state rho the mathematical theory of factor boolean algebras on which this extension is based is clarified

the uncertainty principle on considere l existence et la regularite des solutions d equations aux derivees partielles la construction de solutions fondamentales explicites et les valeurs propres d operateurs de schrodinger

continuous time and consistent histories we discuss the use of histories labelled by a continuous time in the approach to consistent histories quantum theory in which propositions about the history of the system are represented by projection operators on a hilbert space this extends earlier work by two of us c j isham and n linden j math phys 36 5392 5408 1995 where we showed how a continuous time parameter leads to a history algebra that is isomorphic to the canonical algebra of a quantum field theory we describe how the appropriate representation of the history algebra may be chosen by requiring the existence of projection operators that represent propositions about the time average of the energy we also show that the history description of quantum mechanics contains an operator corresponding to velocity that is quite distinct from the momentum operator finally the discussion is extended to give a preliminary account of quantum field theory in this approach to the consistent histories formalism

moment reconstruction and moment adjusted imputation when exposure is generated by a complex nonlinear random effects modeling process for the classical homoscedastic measurement error model moment reconstruction freedman et al 2004 2008 and moment adjusted imputation thomas et al 2011 are appealing computationally simple imputation like methods for general model fitting like classical regression calibration the idea is to replace the unobserved variable subject to measurement error with a proxy that can be used in a variety of analyses moment reconstruction and moment adjusted imputation differ from regression calibration in that they attempt to match multiple features of the latent variable and also to match some of the latent variable s relationships with the response and additional covariates in this note we consider a problem where true exposure is generated by a complex nonlinear random effects modeling process and develop analogues of moment reconstruction and moment adjusted imputation for this case this general model includes classical measurement errors berkson measurement errors mixtures of berkson and classical errors and problems that are not measurement error problems but also cases where the data generating process for true exposure is a complex nonlinear random effects modeling process the methods are illustrated using the national institutes of health aarp diet and health study where the latent variable is a dietary pattern score called the healthy eating index 2005 we also show how our general model includes methods used in radiation epidemiology as a special case simulations are used to illustrate the methods

are there realistically interpretable local theories although it rests on strongly established proofs the statement that no realistically interpretable local theory is compatible with some experimentally testable predictions of quantum mechanics seems at first sight to be incompatible with a few general ideas and clear cut statements occurring in recent theoretical work by griffiths omnes and ballentine and jarrett it is shown here that in fact none of the developments due to these authors can be considered as a realistically interpretable local theory so that there is no valid reason for suspecting that the existing proofs of the statement in question are all flawed

symmetry and history quantum theory an analog of wigner s theorem the basic ingredients of the consistent histories approach to quantum theory are a space up of history propositions and a space d of decoherence functionals in this article we consider such history quantum theories in the case where up is given by the set of projectors p v on some hilbert space v we define the notion of a physical symmetry of a history quantum theory pshqt and specify such objects exhaustively with the aid of an analog of wigner s theorem in order to prove this theorem we investigate the structure of d define the notion of an elementary decoherence functional and show that each decoherence functional can be expanded as a certain combination of these functionals we call two history quantum theories that are related by a pshqt physically equivalent and show explicitly in the case of history quantum mechanics how this notion is compatible with one that has appeared previously

painless nonorthogonal expansions in a hilbert space h discrete families of vectors hj with the property that f j hj f hj for every f in h are considered this expansion formula is obviously true if the family is an orthonormal basis of h but also can hold in situations where the hj are not mutually orthogonal and are overcomplete the two classes of examples studied here are i appropriate sets of weyl heisenberg coherent states based on certain non gaussian fiducial vectors and ii analogous families of affine coherent states it is believed that such quasiorthogonal expansions will be a useful tool in many areas of theoretical physics and applied mathematics

approximate quasi likelihood estimation in models with surrogate predictors abstract we consider quasi likelihood estimation with estimated parameters in the variance function when some of the predictors are measured with error we review and extend four approaches to estimation in this problem all of them based on small measurement error approximations a taxonomy of the data sets likely to be available in measurement error studies is developed an asymptotic theory based on this taxonomy is obtained and includes measurement error and berkson error models as special cases

consistent quantum realism a reply to bassi and ghirardi a recent claim by bassi and ghirardi that the consistent decoherent histories approach cannot provide a realistic interpretation of quantum theory is shown to be based upon a misunderstanding of the single framework rule they have replaced the correct rule with a principle which directly contradicts it it is their assumptions not those of the consistent histories approach which lead to a logical contradiction

a general approach to analyzing epidemiologic data that contain misclassification errors misclassification is a common source of bias and reduced efficiency in the analysis of discrete data several methods have been proposed to adjust for misclassification using information on error rates i gathered by resampling the study population ii gathered by sampling a separate population or iii assumed a priori we present unified methods for incorporating these types of information into analyses based on log linear models and maximum likelihood estimation general variance expressions are developed examples from epidemiologic studies are used to demonstrate the proposed methodology

completeness of decoherence functionals the basic ingredients of the consistent histories approach to a generalized quantum theory are histories and decoherence functionals the main aim of this program is to find and to study the behavior of consistent sets associated with a particular decoherence functional d in its recent formulation by isham quantum logic and the histories approach to quantum theory j math phys 35 2157 2185 1994 it is natural to identify the space up of propositions about histories with an orthoalgebra or lattice when up is given by the lattice of projectors p v in some hilbert space v consistent sets correspond to certain partitions of the unit operator in v into mutually orthogonal projectors 1 2 such that the function d is a probability distribution on the boolean algebra generated by 1 2 using the classification theorem for decoherence functionals proven in isham et al the classification of decoherence functionals an analog of gleason s theorem j math phys 35 6

the role of coherence entropy of physical twin observables in entanglement the concept of physical twin observables pto for bipartite quantum states introduced and proved relevant for quantum information theory in recent work is substantially simplified the relation of observable and state is studied in detail from the point of view of coherence entropy properties of this quantity are further explored it is shown that besides for pure states also for a class of mixed states quantum discord measure of entanglement can be expressed through the coherence entropy of a pto complete in relation to the state

on the effect of misclassification on bias of perfectly measured covariates in regression this note clarifies under what conditions a naive analysis using a misclassified predictor will induce bias for the regression coefficients of other perfectly measured predictors in the model an apparent discrepancy between some previous results and a result for measurement error of a continuous variable in linear regression is resolved we show that similar to the linear setting misclassification even when not related to the other predictors induces bias in the coefficients of the perfectly measured predictors unless the misclassified variable and the perfectly measured predictors are independent conditional and asymptotic biases are discussed in the case of linear regression and explored numerically for an example relating birth weight to the weight and smoking status of the mother

a modified partial likelihood score method for cox regression with covariate error under the internal validation design we develop a new method for covariate error correction in the cox survival regression model given a modest sample of internal validation data unlike most previous methods for this setting our method can handle covariate error of arbitrary form asymptotic properties of the estimator are derived in a simulation study the method was found to perform very well in terms of bias reduction and confidence interval coverage the method is applied to data from the health professionals follow up study hpfs on the effect of diet on incidence of type ii diabetes

stochastic description for open quantum systems abstract a linear quantum brownian motion model with a general spectral density function is considered in the framework of the influence functional formalism a langevin equation can be introduced to describe the system s fully quantum properties even beyond the semiclassical regime in particular we show that the reduced wigner function for the system can be formally written as a double average over both the initial conditions and the stochastic source of the langevin equation this is exploited to provide a derivation of the master equation for the reduced density matrix alternative to those existing in the literature furthermore we prove that all the correlation functions obtained in the context of the stochastic description associated to the langevin equation actually correspond to quantum correlation functions for system observables in doing so we also compute the closed time path generating functional of the open system

quantum classical correspondence using projection operators classical properties associated with a large phase space domain with a smooth boundary as compared to the planck constant are shown to be expressed quantum mechanically by a family of quantum projection operators with the help of known theorems in microlocal analysis under the conditions of egorov s theorem the conservation of this correspondence under classical quantum dynamics is asserted

exposure misclassification bias in category specific poisson regression coefficients in epidemiologic studies of the association between exposure and disease misclassification of exposure is common and known to induce bias in the effect estimates the nature of the bias is difficult to foretell for this purpose we present a simple method to assess the bias in poisson regression coefficients for a categorical exposure variable subject to misclassification we derive expressions for the category specific coefficients from the regression on the error prone exposure naive coefficients in terms of the coefficients from the regression on the true exposure true coefficients these expressions are similar for crude and adjusted models if we assume that the covariates are measured without error and that it is independence between the misclassification probabilities and covariate values we find that the bias in the naive coefficient for one category of the exposure variable depends on all true category specific coefficients weighted by misclassification probabilities on the other hand misclassification of an exposure variable does not induce bias in the estimates of the coefficients of the perfectly measured covariates similarities with linear regression models are pointed out for selected scenarios of true exposure disease associations and selected patterns of misclassification we illustrate the inconsistency in naive poisson regression coefficients and show that it can be difficult to intuitively characterize the nature of the bias both the magnitude and the direction of the bias may vary between categories of an exposure variable

quantum discord a measure of the quantumness of correlations two classically identical expressions for the mutual information generally differ when the systems involved are quantum this difference defines the quantum discord it can be used as a measure of the quantumness of correlations separability of the density matrix describing a pair of systems does not guarantee vanishing of the discord thus showing that absence of entanglement does not imply classicality we relate this to the quantum superposition principle and consider the vanishing of discord as a criterion for the preferred effectively classical states of a system i e the pointer states

spectral analysis and generation of certain highly oscillatory curves related to chaos part 2 calculation aspects abstract the fourier spectrum of a curve on a given interval as represented by the fourier series is very reflective of the oscillatory behavior of the curve as the weights of the fourier coefficients can indicate the individual prominence of frequencies of oscillations but unfortunately the calculations of the fourier coefficients can often get quite cumbersome in this paper we first review the oscillatory behavior of chaotic maps as time series and discuss certain properties between the exponential growth of total variations and the fourier coefficients then we will discuss some simple techniques that can simplify the calculations of fourier coefficients in the process one can also obtain valuable information about the asymptotic properties of the fourier coefficients

correction of logistic regression relative risk estimates and confidence intervals for systematic within person measurement error errors in the measurement of exposure that are independent of disease status tend to bias relative risk estimates and other measures of effect in epidemiologic studies toward the null value two methods are provided to correct relative risk estimates obtained from logistic regression models for measurement errors in continuous exposures within cohort studies that may be due to either random unbiased within person variation or to systematic errors for individual subjects these methods require a separate validation study to estimate the regression coefficient lambda relating the surrogate measure to true exposure in the linear approximation method the true logistic regression coefficient beta is estimated by beta lambda where beta is the observed logistic regression coefficient based on the surrogate measure in the likelihood approximation method a second order taylor series expansion is used to approximate the logistic function enabling closed form likelihood estimation of beta confidence intervals for the corrected relative risks are provided that include a component representing error in the estimation of lambda based on simulation studies both methods perform well for true odds ratios up to 3 0 for higher odds ratios the likelihood approximation method was superior with respect to both bias and coverage probability an example is provided based on data from a prospective study of dietary fat intake and risk of breast cancer and a validation study of the questionnaire used to assess dietary fat intake

inferences about exposure disease associations using probability of exposure information unconditional and conditional likelihood methods are proposed for modeling odds and odds ratios relating a binary disease variable and an exposure variable that is only known probabilistically e g via measurement of a surrogate exposure variable while adjusting appropriately for a vector of covariables assuming nondifferential errors a probabilistic structure is developed that permits analysis of the marginal relation between disease and the surrogate while maintaining important properties of the marginal relation between disease and true exposure in particular analyses conditioned on marginal totals in surrogate disease tables remove the same nuisance parameters as are removed in a conditional analysis of true exposure disease tables in addition a relation between the probability of exposure poe in the disease and disease free groups is derived permitting the use of information about exposure from populations with structure different from the study population examples are presented illustr

decoherence and linear entropy increase in the quantum baker s map we show that the coarse grained quantum baker s map exhibits a linear entropy increase at an asymptotic rate given by the kolmogorov sinai entropy of the classical chaotic baker s map the starting point of our analysis is a symbolic representation of the map on a string of n qubits i e an n bit register of a quantum computer to coarse grain the quantum evolution we make use of the decoherent histories formalism as a by product we show that the condition of medium decoherence holds asymptotically for the coarse grained quantum baker s map

the evaluation of integrals of the form f t exp t 2 dt application to logistic normal models abstract logistic normal distributions and related functions arise in a variety of statistical applications of current interest including binary measurement error models and the analysis of teratogenicity experiments analytic intractability has led to the development of numerous approximations to the desired forms often with consequences that have not been well studied a method is developed to compute these forms to arbitrary accuracy and comparative calculations are made that show when the common numerical alternative 20 point gaussian quadrature begins to fail by using a simple matrix transformation this method can be used with multiple covariate regression models of the logistic normal form we conducted a simulation study that compares the ability of 20 point gaussian quadrature and our new method to obtain the maximum likelihood estimator of relative risk in the logistic normal measurement error model using standard subroutines to maximize the likelihood equations 27 of 50 trials failed to

efficient regression calibration for logistic regression in main study internal validation study designs with an imperfect reference instrument an extension to the version of the regression calibration estimator proposed by rosner et al for logistic and other generalized linear regression models is given for main study internal validation study designs this estimator combines the information about the parameter of interest contained in the internal validation study with rosner et al s regression calibration estimate using a generalized inverse variance weighted average it is shown that the validation study selection model can be ignored as long as this model is jointly independent of the outcome and the incompletely observed covariates conditional at most upon the surrogates and other completely observed covariates in an extensive simulation study designed to follow a complex multivariate setting in nutritional epidemiology it is shown that with validation study sizes of 340 or more this estimator appears to be asymptotically optimal in the sense that it is nearly unbiased and nearly as efficient as a properly specified maximum likelihood estimator a modification to the regression calibration variance estimator which replaces the standard uncorrected logistic regression coefficient variance with the sandwich estimator to account for the possible misspecification of the logistic regression fit to the surrogate covariates in the main study was also studied in this same simulation experiment in this study the alternative variance formula yielded results virtually identical to the original formula a version of the proposed estimator is also derived for the case where the reference instrument available only in the validation study is imperfect but unbiased at the individual level and contains error that is uncorrelated with other covariates and with error in the surrogate instrument replicate measures are obtained in a subset of study participants in this case it is shown that the validation study selection model can be ignored when sampling into the validation study depends at most only upon perfectly measured covariates two data sets a study of fever in relation to occupational exposure to antineoplastics among hospital pharmacists and a study of breast cancer incidence in relation to dietary intakes of alcohol and vitamin a adjusted for total energy intake from the nurses health study were analysed using these new methods in these data because the validation studies contained less than 200 observations and the events of interest were relatively rare as is typical the potential improvements offered by this new estimator were not apparent

bayesian analysis of misclassified binary data from a matched case control study with a validation sub study bayesian methods are proposed for analysing matched case control studies in which a binary exposure variable is sometimes measured with error but whose correct values have been validated for a random sample of the matched case control sets three models are considered model 1 makes few assumptions other than randomness and independence between matched sets while models 2 and 3 are logistic models with model 3 making additional distributional assumptions about the variation between matched sets with models 1 and 2 the data are examined in two stages the first stage analyses data from the validation sample and is easy to perform the second stage analyses the main body of data and requires mcmc methods all relevant information is transferred between the stages by using the posterior distributions from the first stage as the prior distributions for the second stage with model 3 a hierarchical structure is used to model the relationship between the exposure probabilities of the matched sets which gives the potential to extract more information from the data all the methods that are proposed are generalized to studies in which there is more than one control for each case the bayesian methods and a maximum likelihood method are applied to a data set for which the exposure of every patient was measured using both an imperfect measure that is subject to misclassification and a much better measure whose classifications may be treated as correct to test methods the latter information was suppressed for all but a random sample of matched sets

conditional regression analysis of the exposure disease odds ratio using known probability of exposure values conditional inference methods are proposed for the odds ratio between binary exposure and disease variables when only the probability of exposure is known for each study subject we develop a conditional likelihood approach that removes nuisance parameters and permits inferences to be made about important parameters in log odds ratio regression models we also discuss a heuristic procedure based on estimating the unknown number of truly exposed individuals this procedure provides a simple framework for interpreting our likelihood based statistics and leads to a mantel haenszel type estimator and a goodness of fit test as an example of the use of this methodology we present an analysis of some genetic data of swift et al 1976 cancer research 36 209 215

two derivations of the master equation of quantum brownian motion central to many discussion of decoherence is a master equation for the reduced density matrix of a massive particle experiencing scattering from its surrounding environment such as that of joos and zeh such master equations enjoy a close relationship with spontaneous localization models like the grw model the aim of this paper is to present two derivations of the master equation the first derivation is a pedagogical model designed to illustrate the origins of the master equation as simply as possible focusing on physical principles and without the complications of s matrix theory this derivation may serve as a useful tutorial example for students attempting to learn this subject area the second is the opposite a very general derivation using non relativistic many body field theory it reduces to the equation of the type given by joos and zeh in the one particle sector but correcting certain numerical factors which have recently become significant in connection with experimental tests of decoherence this master equation also emphasizes the role of local number density as the preferred basis for decoherence in this model

continuous time histories observables probabilities phase space structure and the classical limit the continuous time histories program stems from the consistent histories approach to quantum theory and aims to provide a fully covariant formalism for quantum mechanics in this paper we examine some structural points of the formalism we demonstrate a general construction of history hilbert spaces and identify a large class of time averaged observables we pay particular attention to the construction of the decoherence functional the object that encodes probability information in the continuous time limit and its relation to the temporal structure of the theory phase space observables are introduced through the study of general representations of the history group which is the analog of the canonical group in the formalism we can also define a closed time path ctp generating functional for each observable which encodes the information of its correlation functions the phase space version of the ctp generating functional leads to the implementation of wigner weyl transforms that gives a description of quantum theory solely in terms of phase space histories these results allow the identification of an algorithm for going to the classical stochastic limit for a generic quantum system

chaotic oscillations of a linear hyperbolic pde with a general nonlinear boundary condition abstract this article establishes a theorem that guarantees the occurrence of chaotic oscillations in a system governed by a linear hyperbolic partial differential equation pde with a nonlinear boundary condition nbc compared with the nbcs in all previous related literature such an nbc is more general both the left end and the right end of the system parameter interval for the occurrence of chaotic oscillations are precisely characterized the chaotic results obtained are further applied to two specific nbcs and the telegraph equation finally numerical examples verify the effectiveness of theoretical prediction

a bell inequality analog in quantum measure theory one obtains bell s inequalities if one posits a hypothetical joint probability distribution or measure whose marginals yield the probabilities produced by the spin measurements in question the existence of a joint measure is in turn equivalent to a certain causality condition known as screening off we show that if one assumes more generally a joint quantal measure or decoherence functional one obtains instead an analogous inequality weaker by a factor of the proof of this tsirel son inequality is geometrical and rests on the possibility of associating a hilbert space to any strongly positive quantal measure these results lead both to a question does a joint measure follow from some quantal analog of screening off and to the observation that non contextual hidden variables are viable in histories based quantum mechanics even if they are excluded classically

estimation and inference for logistic regression with covariate misclassification and measurement error in main study validation study designs abstract in epidemiological studies continuous covariates often are measured with error and categorical covariates often are misclassified using the logistic regression model to represent the relationship between the binary outcome and the perfectly measured and classified covariates the model for the observed main study data is derived this derivation relies on the assumption that the error in the continuous covariates is multivariate normally distributed and uses a chain of logistic regression models to describe the misclassification processes these model assumptions are empirically verified in the validation study where the misclassified and mismeasured covariates are validated using perfectly measured and classified data the full data likelihood including contributions from both the main study and the validation study is maximized to obtain the maximum likelihood estimates for the parameters of the underlying logistic regression model and of the measurement error model and reclassification mo

adjusting for errors in classification and measurement in the analysis of partly and purely categorical data abstract this article examines a method of adjusting subgroup means when there are errors both in the allocation of elements to the subgroups and in the measurement of the response the advantages with the method are that it is simple it is also applicable when there are many subgroups and it requires no distributional assumptions for the response variable the method is compared to the maximum likelihood method for a dichotomous response and an example from the swedish level of living survey is given

quantum equilibrium and the origin of absolute uncertainty what is randomness probability certainty knowledge these are old and difficult questions and we shall not focus on them here nonetheless we shall obtain sharp striking conclusions concerning the relationship between these concepts

rapid fluctuations of chaotic maps on rn the iterates f n of a chaotic map f display heightened oscillations or fluctuations as n i ff is a chaotic interval map in one dimension then it is now known that the total variation of f n on that interval grows exponentially with respect to n g chen t huang y huang chaotic behavior of interval maps and total variations of iterates internat j bifur chaos 14 2004 2161 2186 however the characterization of chaotic behavior of maps in multi dimensional spaces is generally much more challenging here we generalize the definition of bounded variations for vector valued maps in terms of the hausdorff measure and then use it to study what we call rapid fluctuations on fractal sets in multi dimensional chaotic discrete dynamical systems the relations among rapid fluctuations strict turbulence and positive entropy are established for lipschitz continuous systems on general n dimensional euclidean spaces applications to planar monotone or competitive systems and triangular systems on the square are also given

linearly positive histories probabilities for a robust family of sequences of quantum events non negative probabilities that obey the sum rules may be assigned to a much wider family of sets of histories than decohering histories the resulting linearly positive histories avoid the highly restrictive decoherence conditions and yet give the same probabilities when those conditions apply thus linearly positive histories are a broad extension of decohering histories moreover the resulting theory is manifestly time reversal invariant

variance estimation for epidemiologic effect estimates under misclassification this paper presents basic methods for construction of variance estimators for epidemiologic effect estimates when adjusting for misclassification methods are described for differential and non differential misclassification and for external and internal estimates of classification rates the methods take account of sampling variability in both the observed data and the estimated classification rates the methods are illustrated in a case control analysis of the association of antibiotic use during pregnancy with sudden infant death syndrome

the classical limit for a class of quantum baker s maps we show that the class of quantum baker s maps defined by schack and caves have the proper classical limit provided the number of momentum bits approaches infinity this is done by deriving a semi classical approximation to the coherent state propagator

the action operator for continuous time histories we define the action operator for the consistent histories formalism as the quantum analog of the classical action functional for the simple harmonic oscillator case we conclude that the action operator is the generator of time transformations and is associated with the two types of time evolution of the standard quantum theory the wave packet reduction and the unitary time evolution we construct the corresponding classical histories and demonstrate the relevance with the quantum histories finally we show the relation of the action operator to the decoherence functional

on state dependent implication in quantum mechanical distant correlations let be an arbitrary given composite system state statistical operator it is shown that same subsystem events imply each other state dependently according to if and only if they act equally in the range of the corresponding subsystem state reduced statistical operator opposite subsystem events imply each other in the same way if and only if they are twin events i e if is a pure state it is shown that the anti unitary correlation operator also plays a decisive role in the latter implication

a quantum measure of coherence and incompatibility the well known two slit interference is understood as a special relation between an observable localization at the slits and a state being on both slits the relation between an observable and a quantum state is investigated in the general case it is assumed that the amount of coherence equals that of the incompatibility between an observable and a state on these grounds an argument is presented that leads to a natural quantum measure of coherence called coherence or incompatibility information its properties are studied in detail making use of the mixing property of relative entropy derived in this paper a precise relation between the measure of coherence of an observable and that of its coarsening is obtained and discussed from the intuitive point of view convexity of the measure is proved and thus the fact that it is an information entity is established a few more detailed properties of the coherence information are derived with a view to investigating the final state entanglement in general repeatable measurement and more importantly general bipartite entanglement in follow ups of this study

corrected score estimation in the proportional hazards model with misclassified discrete covariates we consider cox proportional hazards regression when the covariate vector includes error prone discrete covariates along with error free covariates which may be discrete or continuous the misclassification in the discrete error prone covariates is allowed to be of any specified form building on the work of nakamura and his colleagues we present a corrected score method for this setting the method can handle all three major study designs internal validation design external validation design and replicate measures design both functional and structural error models and time dependent covariates satisfying a certain localized error condition we derive the asymptotic properties of the method and indicate how to adjust the covariance matrix of the regression coefficient estimates to account for estimation of the misclassification matrix we present the results of a finite sample simulation study under weibull survival with a single binary covariate having known misclassification rates the performance of the method described here was similar to that of related methods we have examined in previous works specifically our new estimator performed as well as or in a few cases better than the full weibull maximum likelihood estimator we also present simulation results for our method for the case where the misclassification probabilities are estimated from an external replicate measures study our method generally performed well in these simulations the new estimator has a broader range of applicability than many other estimators proposed in the literature including those described in our own earlier work in that it can handle time dependent covariates with an arbitrary misclassification structure we illustrate the method on data from a study of the relationship between dietary calcium intake and distal colon cancer

on the relationship between complex potentials and strings of projection operators it is of interest in a variety of contexts and in particular in the arrival time problem to consider the quantum state obtained through unitary evolution of an initial state regularly interspersed with periodic projections onto the positive x axis pulsed measurements echanobe del campo and muga have given a compelling but heuristic argument that the state thus obtained is approximately equivalent to the state obtained by evolving in the presence of a certain complex potential of step function form in this paper with the help of the path decomposition expansion of the associated propagators we give a detailed derivation of this approximate equivalence the propagator for the complex potential is known so the bulk of the derivation consists of an approximate evaluation of the propagator for the free particle interspersed with periodic position projections this approximate equivalence may be used to show that to produce significant reflection the projections must act at time spacing less than e where e is the energy scale of the initial state

a topos formulation of history quantum theory topos theory has been suggested by doring and isham as an alternative mathematical structure with which to formulate physical theories in particular it has been used to reformulate standard quantum mechanics in such a way that a novel type of logic is used to represent propositions in this paper we extend this formulation to include temporally ordered collections of propositions as opposed to single time propositions that is to say we have developed a quantum history formalism in the language of topos theory where truth values can be assigned to temporal propositions we analyze the extent to which such truth values can be derived from the truth values of the constituent single time propositions

popescu rohrlich boxes in quantum measure theory two results are proved at the quantal level in sorkin s hierarchy of measure theories one is a strengthening of an existing bound on the correlations in the epr bohm set up under the assumption that the probabilities admit a strongly positive joint quantal measure it is also proved that any set of no signalling probabilities for two distant experimenters with a choice of two alternative experiments each and two possible outcomes per experiment admits a joint quantal measure though one that is not necessarily strongly positive

more on the state dependent implication in quantum mechanics the mixing structure of a given quantum state statistical operator is considered that is the pure states and associated weights of which it consists its influence on the state dependent quantum logical implication determined by is also studied it is found that it has no influence at all except through the null projector it is shown that the latter when it determines the state dependent implication in a certain sense carries with it all the boolean mathematical structure of projectors in the given boolean subalgebra of quantum logic where is the domain of definition of the state dependent implication

expected estimating equations for missing data measurement error and misclassification with application to longitudinal nonignorable missing data missing data measurement error and misclassification are three important problems in many research fields such as epidemiological studies it is well known that missing data and measurement error in covariates may lead to biased estimation misclassification may be considered as a special type of measurement error for categorical data nevertheless we treat misclassification as a different problem from measurement error because statistical models for them are different indeed in the literature methods for these three problems were generally proposed separately given that statistical modeling for them are very different the problem is more challenging in a longitudinal study with nonignorable missing data in this article we consider estimation in generalized linear models under these three incomplete data models we propose a general approach based on expected estimating equations eees to solve these three incomplete data problems in a unified fashion this eee approach can be easily implemented and its asymptotic covariance can be obtained by sandwich estimation intensive simulation studies are performed under various incomplete data settings the proposed method is applied to a longitudinal study of oral bone density in relation to body bone density

a new characterization of nonisotropic chaotic vibrations of the one dimensional linear wave equation with a van der pol boundary condition the one dimensional linear wave equation with a van der pol nonlinear boundary condition is one of the simplest models that may cause isotropic or nonisotropic chaotic vibrations trans amer math soc 350 1998 4265 4311 internat j bifur chaos 8 1998 423 445 internat j bifur chaos 8 1998 447 470 j math phys 39 1998 6459 6489 internat j bifur chaos 12 2002 535 559 in this paper we characterize nonisotropic chaotic vibration by means of the total variation theory we obtain the classification results on the growth of the total variation of the snapshots on the spatial interval in the long time horizon with respect to two parameters entering different regimes in r2

local polynomial regression and simulation extrapolation summary the paper introduces a new local polynomial estimator and develops supporting asymptotic theory for nonparametric regression in the presence of covariate measurement error we address the measurement error with cook and stefanski s simulation extrapolation simex algorithm our method improves on previous local polynomial estimators for this problem by using a bandwidth selection procedure that addresses simex s particular estimation method and considers higher degree local polynomial estimators we illustrate the accuracy of our asymptotic expressions with a monte carlo study compare our method with other estimators with a second set of monte carlo simulations and apply our method to a data set from nutritional epidemiology simex was originally developed for parametric models although simex is in principle applicable to nonparametric models a serious problem arises with simex in nonparametric situations the problem is that smoothing parameter selectors that are developed for data without measurement error are no longer appropriate and can result in considerable undersmoothing we believe that this is the first paper to address this difficulty

a partial differential equation with infinitely many periodic orbits chaotic oscillations of a forced beam this paper delineates a class of time periodically perturved evolution equations in a banach space whose associated poincar e map contains a smale horseshoe this implies that such systems possess periodic orbits with arbitrarily high period the method uses techniques originally due to melnikov and applies to systems of the form x f0 x f1 x t where x f0 x is hamiltonian and has a homoclinic orbit we give an example from structural mechanics sinusoidally forced vibrations of a buckled beam

quantumness of bipartite states in terms of conditional entropies quantum discord as defined by olliver and zurek 2002 phys rev lett 88 017901 as the difference of two natural quantum extensions of the classical mutual information plays an interesting role in characterizing quantumness of correlations inspired by this idea we will study quantumness of bipartite states arising from different quantum analogs of the classical conditional entropy our approach is intrinsic in contrast to the olliver zurek method that involves extrinsic local measurements for this purpose we introduce two alternative variants of quantum conditional entropies via conditional density operators which in turn are intuitive quantum extensions of equivalent classical expressions for the conditional probability the significance of these quantum conditional entropies in characterizing quantumness of bipartite states is illustrated through several examples

logical reformulation of quantum mechanics i foundations the basic rules of quantum mechanics are reformulated they deal primarily with individual systems and do not assume that every ket may represent a physical state the customary kinematic and dynamic rules then allow to construct consistent boolean logics describing the history of a system following essentially griffiths proposal logical implication is defined within these logics the multiplicity of which reflects the complementary principle only one interpretative rule of quantum mechanics is necessary in such a framework it states that these logics providebona fide foundations for the description of a quantum system and for reasoning about it one attempts to build up classical physics including classical logic on these quantum foundations the resulting theory of measurement needs not to statea priori that the eigenvalues of an observable have to be the results of individual measurements nor to assume wave packet reduction both these properties can be obtained as consequences of the basic rules one also needs not to postulate that every observable is measurable even in principle a proposition calculus is obtained allowing in principle the replacement of the discussion of problems concerned with the practical interpretation of experiments by due calculations

complex probabilities on r n as real probabilities on c n and an application to path integrals we establish a necessary and sufficient condition for averages over complex valued weight functions on r n to be represented as statistical averages over real non negative probability weights on c n using this result we show that many path integrals for time ordered expectation values of bosonic degrees of freedom in real valued time can be expressed as statistical averages over ensembles of paths with complex valued coordinates and then speculate on possible consequences of this result for the relation between quantum and classical mechanics

can a quantum state over time resemble a quantum state at a single time the standard formalism of quantum theory treats space and time in fundamentally different ways in particular a composite system at a given time is represented by a joint state but the formalism does not prescribe a joint state for a composite of systems at different times if there were a way of defining such a joint state this would potentially permit a more even handed treatment of space and time and would strengthen the existing analogy between quantum states and classical probability distributions under the assumption that the joint state over time is an operator on the tensor product of single time hilbert spaces we analyse various proposals for such a joint state including one due to leifer and spekkens one due to fitzsimons jones and vedral and another based on discrete wigner functions finding various problems with each we identify five criteria for a quantum joint state over time to satisfy if it is to play a role similar to the standard joint state for a composite system that it is a hermitian operator on the tensor product of the single time hilbert spaces that it represents probabilistic mixing appropriately that it has the appropriate classical limit that it has the appropriate single time marginals that composing over multiple time steps is associative we show that no construction satisfies all these requirements if hermiticity is dropped then there is an essentially unique construction that satisfies the remaining four criteria

contrary quantum histories and contrary inferences abstract in the context of the quantum histories approach to quantum mechanics we define a contrary relation between quantum histories generalizing the standard definition of contrary quantum properties using this contrary relation we study the possibility of inferring contrary quantum histories we consider the quantum histories approach with three different consistency conditions weak medium and global consistency conditions for the first two conditions we show that it is possible to infer contrary histories from different families of histories in accordance with previous results for global consistency condition we prove that it is not possible to infer contrary histories

chaotic vibrations of the one dimensional wave equation due to a self excitation boundary condition part i controlled hysteresis the study of nonlinear vibrations oscillations in mechanical and electronic systems has always been an important research area while important progress in the development of mathematical chaos theory has been made for finite dimensional second order nonlinear odes arising from nonlinear springs and electronic circuits the state of understanding of chaotic vibrations for analogous infinite dimensional systems is still very incomplete the 1 dimensional vibrating string satisfying wtt wxx 0 on the unit interval x 0 1 is an infinite dimensional harmonic oscillator consider the boundary conditions at the left end x 0 the string is fixed while at the right end x 1 a nonlinear boundary condition wx wt w3 t 0 takes effect this nonlinear boundary condition behaves like a van der pol oscillator causing the total energy to rise and fall within certain bounds regularly or irregularly we formulate the problem into an equivalent first order hyperbolic system and use the method of characteristics to derive a nonlinear reflection relation caused by the nonlinear boundary condition since the solution of the first order hyperbolic system depends completely on this nonlinear relation and its iterates the problem is reduced to a discrete iteration problem of the type un 1 f un where f is the nonlinear reflection relation we say that the pde system is chaotic if the mapping f is chaotic as an interval map algebraic asymptotic and numerical techniques are developed to tackle the cubic nonlinearities we then define a rotation number following j p keener 11 and obtain denseness of orbits and periodic points by either directly constructing a shift sequence or by applying results of m i malkin 17 to determine the chaotic regime of for the nonlinear reflection relation f thereby rigorously proving chaos nonchaotic cases for other values of are also classified such cases correspond to limit cycles in nonlinear second order odes numerical simulations of chaotic and nonchaotic vibrations are illustrated by computer graphics received by the editors july 20 1995 and in revised form october 16 1996 1991 mathematics subject classification primary 35l05 35l70 58f39 70l05 the first and third authors work was supported in part by nsf grant dms 9404380 texas arp grant 010366 046 and texas a m university interdisciplinary research initiative iri 96 39 work completed while the first author was on sabbatical leave at the institute of applied mathematics national tsing hua university hsinchu 30043 taiwan r o c the second author s work was supported in part by grant nsc 83 0208 m 007 003 from the national council of science of the republic of china c 1998 american mathematical society

consistent histories and the interpretation of quantum mechanics the usual formula for transition probabilities in nonrelativistic quantum mechanics is generalized to yield conditional probabilities for selected sequences of events at several different times called consistent histories through a criterion which ensures that within limits which are explicitly defined within the formalism classical rules for probabilities are satisfied the interpretive scheme which results is applicable to closed isolated quantum systems is explicitly independent of the sense of time i e past and future can be interchanged has no need for wave function collapse makes no reference to processes of measurement though it can be used to analyze such processes and can be applied to sequences of microscopic or macroscopic events or both as long as the mathematical condition of consistency is satisfied when applied to appropriate macroscopic events it appears to yield the same answers as other interpretative schemes for standard quantum mechanics though from a different point of view which avoids the conceptual difficulties which are sometimes thought to require reference to conscious observers or classical apparatus

a bayesian approach to prospective binary outcome studies with misclassification in a binary risk factor misclassification in a binary exposure variable within an unmatched prospective study may lead to a biased estimate of the disease exposure relationship it usually gives falsely small credible intervals because uncertainty in the recorded exposure is not taken into account when there are several other perfectly measured covariates interrelationships may introduce further potential for bias bayesian methods are proposed for analysing binary outcome studies in which an exposure variable is sometimes misclassified but its correct values have been validated for a random subsample of the subjects this bayesian approach can model relationships between explanatory variables and between exploratory variables and the probabilities of misclassification three logistic regressions are used to relate disease to true exposure misclassified exposure to true exposure and true exposure to other covariates credible intervals may be used to make decisions about whether certain parameters are unnecessary and hence whether the model can be reduced in complexity in the disease exposure model for parameters representing coefficients related to perfectly measured covariates the precision of posterior estimates is only slightly lower than would be found from data with no misclassification for the risk factor which has misclassification the estimates of model coefficients obtained are much less biased than those with misclassification ignored

effects of exposure misclassification on regression analyses of epidemiologic follow up study data in epidemiologic studies subjects are often misclassified as to their level of exposure ignoring this misclassification error in the analysis introduces bias in the estimates of certain parameters and invalidates many hypothesis tests for situations in which there is misclassification of exposure in a follow up study with categorical data we have developed a model that permits consideration of any number of exposure categories and any number of multiple category covariates when used with logistic and poisson regression procedures this model helps assess the potential for bias when misclassification is ignored when reliable ancillary information is available the model can be used to correct for misclassification bias in the estimates produced by these regression procedures

covariate measurement error in logistic regression abstract in a logistic regression model when covariates are subject to measurement error the naive estimator obtained by regressing on the observed covariates is asymptotically biased this document introduces a bias adjusted estimator and two estimators appropriate for normally distributed measurement errors a functional maximum likelihood estimator and an estimator which exploits the consequences of sufficiency the four proposals are studied asymptotically under conditions which are appropriate when the measurement error is small a small monte carlo study illustrates the superiority of the measurement error estimators in certain situations additional keywords mathematical models

semiparametric efficient estimation of a conditional density with missing or mismeasured covariates summary pepe and fleming and carroll and wand have recently proposed estimators in a parametric model for the density of a random variable y conditional on a vector of covariates x v when data on one of the regressors x is missing for some study subjects we propose a new class of estimators that remains consistent and asymptotically normal even when the probability that x is missing depends on the observed v and y includes an estimator whose asymptotic variance attains the semiparametric variance bound for the model and when the data are missing completely at random includes an estimator that is asymptotically equivalent to the inefficient estimators proposed by pepe and fleming and by carroll and wand the optimal estimator in our class depends on the unknown probability law generating the data when the vector v of non missing regressors has at most two continuous components we propose an adaptive semiparametric efficient estimator and compare the performance of the proposed semiparametric efficient estimator with the estimators proposed by pepe and fleming and carroll and wand in a small simulation study when v has many continuous components we propose an alternative class of adaptive estimators that should have high efficiency

existence of chaotic oscillations in second order linear hyperbolic pdes with implicit boundary conditions abstract this paper establishes rigorously mathematical theorems that guarantee the existence of chaotic oscillations in the systems of second order linear hyperbolic pdes it separately considers the systems with nonlinear explicit boundary conditions ebcs and nonlinear implicit boundary conditions ibcs as well as those with such ibcs subjected to small perturbations where ibcs include ebcs as special cases but the latter cannot in general be expressed by the former numerical examples are demonstrated to illustrate the effectiveness of theoretical results

spectral analysis and generation of certain highly oscillatory curves related to chaos abstract highly oscillatory phenomena are omnipresent in applications two important underlying sources are stochastic fluctuations and deterministic randomness in this paper we will present heuristics theorems and a few illustrations on the fourier spectrum and deterministic random time series based upon our understanding of certain rapid oscillations in chaos

log linear models for doubly sampled categorical data fitted by the em algorithm abstract double sampling experiments can be expressed as incomplete multiway contingency tables and analyzed by using techniques appropriate for fitting log linear models the framework described can be applied to experiments with any number of factors and measurement devices maximum likelihood estimation via the em algorithm leads to straightforward expressions for covariances of estimates of the parameters and functions of the parameters

the classification of decoherence functionals an analog of gleason s theorem gell mann and hartle have proposed a significant generalization of quantum theory with a scheme whose basic ingredients are histories and decoherence functionals within this scheme it is natural to identify the space up of propositions about histories with an orthoalgebra or lattice this raises the important problem of classifying the decoherence functionals in the case where up is the lattice of projectors p v in some hilbert space v in effect one seeks the history analog of gleason s famous theorem in standard quantum theory in the present article the solution to this problem for the case where v is finite dimensional is presented in particular it is shown that every decoherence functional d p v can be written in the form d trv v x for some operator x on the tensor product space v v

decoherent histories and realism we reconsider the decoherent histories approach to quantum mechanics and analyze some problems related to its interpretation which we believe have not been adequately clarified by its proponents we put forward some assumptions which in our opinion are necessary for a realistic interpretation of the probabilities that the formalism attaches to decoherent histories we prove that such assumptions unless one limits the set of the decoherent families which can be taken into account lead to a logical contradiction the line of reasoning we follow is conceptually different from other arguments which have been presented and which have been rejected by the supporters of the decoherent histories approach the conclusion is that the decoherent histories approach to be considered as an interesting realistic alternative to the orthodox interpretation of quantum mechanics requires the identification of a mathematically precise criterion to characterize an appropriate set of decoherent families which does not give rise to any problem

regression calibration in semiparametric accelerated failure time models summary in large cohort studies it often happens that some covariates are expensive to measure and hence only measured on a validation set on the other hand relatively cheap but error prone measurements of the covariates are available for all subjects regression calibration rc estimation method prentice 1982 biometrika 69 331 342 is a popular method for analyzing such data and has been applied to the cox model by wang et al 1997 biometrics 53 131 145 under normal measurement error and rare disease assumptions in this article we consider the rc estimation method for the semiparametric accelerated failure time model with covariates subject to measurement error asymptotic properties of the proposed method are investigated under a two phase sampling scheme for validation data that are selected via stratified random sampling resulting in neither independent nor identically distributed observations we show that the estimates converge to some well defined parameters in particular unbiased estimation is feasible under additive normal measurement error models for normal covariates and under berkson error models the proposed method performs well in finite sample simulation studies we also apply the proposed method to a depression mortality study

chaotic semigroups from second order partial differential equations abstract we give general conditions on given parameters to ensure devaney and distributional chaos for the solution c 0 semigroup corresponding to a class of second order partial differential equations we also provide a critical parameter that led us to distinguish between stability and chaos for these semigroups in the case of chaos we prove that the c 0 semigroup admits a strongly mixing measure with full support we also give concrete examples of partial differential equations such as the telegraph equation whose solutions satisfy these properties

logistic regression for two stage case control data summary samples of diseased cases and nondiseased controls are drawn at random from the population at risk after classification according to the exposure of interest subsamples of cases and controls are selected for purposes of covariable ascertainment a modification of the usual logistic regression analysis yields consistent estimates of covariable adjusted relative risks and their standard errors by balancing the numbers of exposed and nonexposed for whom covariable inforniation is ascertained within case and control samples some efficiency may be gained over the usual single stage design particularly when the exposure is rare and the relative risks associated with the covariables are large the procedure may be useful also when covariable information is missing for a large part of the sample

nonisotropic spatiotemporal chaotic vibrations of the one dimensional wave equation with a mixing transport term and general nonlinear boundary condition nonisotropic spatiotemporal chaotic vibrations can happen for a linear wave equation with a mixing transport term on the unit interval and with a nonlinear van der pol boundary condition at one end when the parameter s enters some regime chen et al int j bifurcation chaos appl sci eng 12 535 2002 in this paper on the one hand the equation with general nonlinear boundary conditions is considered on the other hand parameter range for the route to chaos is more precisely classified the results obtained here generalize and sharpen those both in the above paper and the earlier work of li l l and huang y j math anal appl 361 69 2010 two examples and their corresponding numerical simulations of chaotic space time profiles are also illustrated

about the notion of truth in quantum mechanics the meaning of truth in quantum mechanics is considered in order to respond to some objections raised by b d espagnat against a logical interpretation of quantum mechanics recently proposed by the author a complete answer is given it is shown that not only can factual data be said to be true but also some of their logical consequences so that the definition of truth given by heisenberg is both extended and refined some nontrue but reliable propositions may also be used but they are somewhat arbitrary because of the complementarity principle for instance the propositions expressing wave packet reduction can be either true or reliable according to the case under study separability is also discussed as far as the true properties of an individual system are concerned quantum mechanics is separable