deformed oscillator algebra approach of some quantum superintegrable lissajous systems on the sphere and of their rational extensions we extend the construction of 2d superintegrable hamiltonians with separation of variables in spherical coordinates using combinations of shift ladder and supercharge operators to models involving rational extensions of the two parameter lissajous systems on the sphere these new families of superintegrable systems with integrals of arbitrary order are connected with jacobi exceptional orthogonal polynomials of type i or ii and supersymmetric quantum mechanics moreover we present an algebraic derivation of the degenerate energy spectrum for the one and two parameter lissajous systems and the rationally extended models these results are based on finitely generated polynomial algebras casimir operators realizations as deformed oscillator algebras and finite dimensional unitary representations such results have only been established so far for 2d superintegrable systems separable in cartesian coordinates which are related to a class of polynomial algebras that display a simpler structure we also point out how the structure function of these deformed oscillator algebras is directly related with the generalized heisenberg algebras spanned by the nonpolynomial integrals

two kinds of generalized taub nut metrics and the symmetry of associated dynamical systems a number of researches have been made for the euclidean taub nut metric because the geodesic for this metric describes approximately the motion of well separated monopole monopole interaction from the viewpoint of dynamical systems it is well known also that the taub nut metric admits the kepler type symmetry and hence provides a nontrivial generalization of the kepler problem more specifically speaking because of a u 1 symmetry the geodesic flow system as a hamiltonian system for the taub nut metric is reduced to a hamiltonian system which admits a conserved runge lenz like vector in addition to the angular momentum vector and thereby whose trajectories turn out to be conic sections in particular all the bounded trajectories of the reduced system are closed the taub nut metrics is generalized so that the reduced system may remain to have the property that all of bounded trajectories are closed on the application of bertrand s method to the reduced system two types of systems are found one is called the kepler type system and the other the harmonic oscillator type system correspondingly two types of metrics come out the kepler type metric and the harmonic oscillator type metric furthermore the symmetry of the kepler type system and of the harmonic oscillator type system are studied through forming accidental first integrals thus the generalization of the taub nut metric accomplishes nontrivial generalizations of the kepler problem and the harmonic oscillator

recurrence approach and higher rank cubic algebras for the n dimensional superintegrable systems by applying the recurrence approach and coupling constant metamorphosis we construct higher order integrals of motion for the stackel equivalents of the n dimensional superintegrable kepler coulomb model with non central terms and the double singular oscillators of type n n n we show how the integrals of motion generate higher rank cubic algebra c 3 circle plus l 1 circle plus l 2 with structure constants involving casimir operators of the lie algebras l 1 and l 2 the realizations of the cubic algebras in terms of deformed oscillators enable us to construct finite dimensional unitary representations and derive the degenerate energy spectra of the corresponding superintegrable systems

bounding parameter estimates with nonclassical measurement error abstract the bias introduced by errors in the measurement of independent variables has increasingly been a topic of interest among researchers estimating economic parameters however studies typically use the assumption of classical measurement error that is the variable of interest and its measurement error are uncorrelated and the expected value of the mismeasured variable is equal to the expected value of the true measure these assumptions often arise from convenience rather than conviction when a variable is bounded it is likely that the measurement error and the true value of the variable are negatively correlated we consider the case of a noisily measured variable with a negative covariance between the measurement error and the true value of the variable we show that asymptotically the parameter in a univariate regression is bounded between the ordinary least squares ols estimator and an instrumental variables iv estimator further we demonstrate that the ols bound can be improved in

stable runge kutta integrations for differential systems with semi stable equilibria in this paper the stability of runge kutta methods for differential systems with semi stable equilibria is analyzed in fact a way of circumventing the very severe unconditional stability barrier 3 is proposed the usage of time meshes with step size ratios under some constant greater than one as usual in standard numerical codes is considered in order to recover stability for many implicit methods the main result roughly says that any strongly a stable runge kutta method is stable for this kind of differential systems on this sort of meshes

reverse regression for latent variable models abstract under joint normality of all regressors the errors in variables bounds for linear regression may be extended to probit and related models of censorship and truncation

comment on identification in the linear errors in variables model on considere un modele etudie par kapteyn et wansbeek 1983 et on presente des conditions necessaires et suffisantes d identification

two families of superintegrable and isospectral potentials in two dimensions as an extension of the intertwining operator idea an algebraic method which provides a link between supersymmetric quantum mechanics and quantum super integrability is introduced by realization of the method in two dimensions two infinite families of superintegrable and isospectral stationary potentials are generated the method makes it possible to perform darboux transformations in such a way that in addition to the isospectral property they acquire the superintegrability preserving property symmetry generators are second and fourth order in derivatives and all potentials are isospectral with one of the smorodinsky winternitz potentials explicit expressions of the potentials their dynamical symmetry generators and the algebra they obey as well as their degenerate spectra and corresponding normalizable states are presented

numerical bifurcation analysis for odes we discuss numerical methods for the computation and continuation of equilibria and bifurcation points of equilibria of dynamical systems we further consider the computation of cycles as a boundary value problem their continuation and bifurcations homoclinic orbits can also be computed as truncated boundary value problems and numerically continued on curves of homoclinic orbits further bifurcations can be detected and computed we discuss the basic numerical methods the connections between various computational objects and provide references to the literature and software implementations

integrable and superintegrable systems with spin a system of two particles with spin s 0 and s 12 respectively moving in a plane is considered it is shown that such a system with a nontrivial spin orbit interaction can allow an eight dimensional lie algebra of first order integrals of motion the pauli equation is solved in this superintegrable case and reduced to a system of ordinary differential equations when only one first order integral exists

quadratic poisson algebras of two dimensional classical superintegrable systems and quadratic associative algebras of quantum superintegrable systems the integrals of motion of the classical two dimensional superintegrable systems with quadratic integrals of motion close in a restrained quadratic poisson algebra whose the general form is investigated each classical superintegrable problem has a quantum counterpart a quantum superintegrable system the quadratic poisson algebra is deformed into a quantum associative algebra the finite dimensional representations of this algebra are calculated by using a deformed parafermion oscillator technique it is shown that the finite dimensional representations of the quadratic algebra are determined by the energy eigenvalues of the superintegrable system the calculation of energy eigenvalues is reduced to the solution of algebraic equations which are universal that is for all two dimensional superintegrable systems with quadratic integrals of motion

proxies versus omitted variables in regression analysis when some variables to be used in a regression analysis contain measurement error the ols estimator will be inconsistent when these variables are left out ols will also be inconsistent in an appropriate metric the first type of inconsistency is smaller than the second type

combined state adding and state deleting approaches to type iii multi step rationally extended potentials applications to ladder operators and superintegrability type iii multi step rationally extended harmonic oscillator and radial harmonic oscillator potentials characterized by a set of k integers m1 m2 mk such that m1 m2 mk with mi even resp odd for i odd resp even are considered the state adding and state deleting approaches to these potentials in a supersymmetric quantum mechanical framework are combined to construct new ladder operators the eigenstates of the hamiltonians are shown to separate into mk 1 infinite dimensional unitary irreducible representations of the corresponding polynomial heisenberg algebras these ladder operators are then used to build a higher order integral of motion for seven new infinite families of superintegrable two dimensional systems separable in cartesian coordinates the finite dimensional unitary irreducible representations of the polynomial algebras of such systems are directly determined from the ladder operator action on the constituent one dimensional hamiltonian eigenstates and provide an algebr

superintegrability and higher order polynomial algebras we present a method to obtain higher order integrals and polynomial algebras for two dimensional quantum superintegrable systems separable in cartesian coordinates from ladder operators all systems with a second and a third order integral of motion separable in cartesian coordinates were studied the integrals of motion of two of them do not generate a cubic algebra we construct for these hamiltonians a higher order polynomial algebra from their ladder operators we obtain quintic and seventh order polynomial algebras we also give for the polynomial algebras of order 7 realizations in terms of deformed oscillator algebras these realizations and finite dimensional unitary representations allow us to obtain the energy spectrum we also apply the construction to the caged anisotropic harmonic oscillator and a system involving the fourth painleve transcendent

supersymmetry as a method of obtaining new superintegrable systems with higher order integrals of motion the main result of this article is that we show that from supersymmetry we can generate new superintegrable hamiltonians we consider a particular case with a third order integral and apply mielnik s construction in supersymmetric quantum mechanics we obtain a new superintegrable potential separable in cartesian coordinates with a quadratic and quintic integrals and also one with a quadratic integral and an integral of order of 7 we also construct a superintegrable system written in terms of the fourth painleve transcendent with a quadratic integral and an integral of order of 7

new ladder operators for a rational extension of the harmonic oscillator and superintegrability of some two dimensional systems new ladder operators are constructed for a rational extension of the harmonic oscillator associated with type iii hermite exceptional orthogonal polynomials and characterized by an even integer m the eigenstates of the hamiltonian separate into m 1 infinite dimensional unitary irreducible representations of the corresponding polynomial heisenberg algebra these ladder operators are used to construct a higher order integral of motion for two superintegrable two dimensional systems separable in cartesian coordinates the polynomial algebras of such systems provide for the first time an algebraic derivation of the whole spectrum through their finite dimensional unitary irreducible representations

differential systems with semi stable equilibria and numerical methods in this paper the long time stability of numerical methods for a class of nonlinear autonomous differential systems possessing a semi stable equilibrium is considered the local dynamics of the class under the h assumptions is reviewed some interesting differential systems of stiff type are seen to belong to this class it is also shown that the implicit euler method is the only one of practical interest which is unconditionally stable

nonparametric identification and semiparametric estimation of classical measurement error models without side information virtually all methods aimed at correcting for covariate measurement error in regressions rely on some form of additional information e g validation data known error distributions repeated measurements or instruments in contrast we establish that the fully nonparametric classical errors in variables model is identifiable from data on the regressor and the dependent variable alone unless the model takes a very specific parametric form this parametric family includes but is not limited to the linear specification with normally distributed variables as a well known special case this result relies on standard primitive regularity conditions taking the form of smoothness constraints and nonvanishing characteristic functions assumptions our approach can handle both monotone and nonmonotone specifications provided the latter oscillate a finite number of times given that the very specific unidentified parametric functional form is arguably the exception rather than the rule this identification r

regressor diagnostics for the classical errors in variables model abstract a series of diagnostics are developed which can be used to probe the sensitivity of regression coefficient estimates to measurement error in each regressor when all the regressors may be measured with error the diagnostics are based on the large sample properties of the classical errors in variables model the diagnostics provide information about the bounds on the measurement error variances of the regressors needed to bound any coefficient to a desired interval algorithms to compute the diagnostics are provided and the use of the diagnostics is illustrated in an example

measurement error in multiple equations tobin s q and corporate investment saving and debt abstract we characterize the sharp identification regions for the coefficients in a system of linear equations that share an explanatory variable measured with classical error we demonstrate the identification gain from analyzing the equations jointly we derive the sharp identification regions under any configuration of three auxiliary assumptions these restrict the noise to signal ratio the coefficients of determination and the signs of the correlations among the cross equation disturbances for inference we implement results on intersection bounds the application studies the effects of cash flow on the investment saving and debt of firms when tobin s q serves as a proxy for marginal q

errors in variables in linear systems this paper extends the simple errors in variable bound to the setting of systems of equations both diagonal and nondiagonal measurement error covariance matrices are considered in the nondiagonal case the analogue of the simple errors in variable interval of estimates is an ellipsoid with diagonal equal to the line segment connecting the direct least squares with a two stage least squares estimate for the diagonal case the set of estimates under some conditions must lie within the convex hull of 2k points

an efficient family of strongly a stable runge kutta collocation methods for stiff systems and daes part i stability and order results for each integer s 3 a new uniparametric family of stiffly accurate strongly a stable s stage runge kutta methods is obtained these are collocation methods with a first internal stage of explicit type the methods are based on interpolatory quadrature rules with precision degree equal to 2s 4 and all of them have two prefixed nodes c 1 0 and c s 1 the amount of implicitness of our s stage method is similar to that involved with the s stage lobattoiiia method or with the s 1 stage radauiia method the new family of runge kutta methods proves to be of interest for the numerical integration of stiff systems and differential algebraic equations in fact on several stiff test problems taken from the current literature two methods selected in our 4 stage family seem to be slightly more efficient than the 3 stage radauiia method and also more robust than the 4 stage lobattoiiia method

correcting for omitted variables and measurement error bias in regression with an application to the effect of lead on iq abstract ordinary least squares ols regression estimates are biased in general when relevant variables are omitted from the regression equation or when included variables are measured with error the errors in variables bias can be corrected using auxiliary information about unobservable measurement errors in this article we demonstrate how auxiliary information can also be used to correct for omitted variables bias we illustrate our methods with an application to four published studies of the effect on iq of childhood exposure to lead each of the published studies used ols methods or equivalent none of the studies includes a father iq variable and none accounts for the biasing effect of measurement error in the right side variables for each of the studies we demonstrate that bias corrected estimates of the effect of lead on iq are much reduced in size and are not significantly different from 0 our methods can be used in other applications involving omitted variables or errors of measurement

estimation of average treatment effects with misclassification this paper considers identification and estimation of the effect of a mismeasured binary regressor in a nonparametric or semiparametric regression or the conditional average effect of a binary treatment or policy on some outcome where treatment may be misclassified failure to account for misclassification is shown to result in attenua tion bias in the estimated treatment effect an identifying assumption that overcomes this bias is the existence of an instrument for the binary regressor that is conditionally independent of the treatment effect a discrete instrument suffices for nonparametric identification this paper provides conditions for identification and estimation of the av erage effect conditioned on covariates of a binary treatment program or pol icy on a scalar outcome when treatment may be misclassified more generally what is provided is an estimator of the effect of a binary regressor in a con ditional mean regression which may also include other regressors when the binary regressor is observed with error this equals the conditional average treatment effect given a weak unconfoundedness assumption misclassification occurs when a binary variable the treatment indicator is measured with error that is some units are reported to have received treat ment when they actually have not and vice versa for example in a returns to schooling analysis the outcome could be wages the binary variable could be attaining a college degree and misclassification could arise from school tran script reporting errors see e g kane and rouse 1995 and kane rouse and staiger 1999 bollinger 1996 considers misclassification of union status in wage equations if treatment is a job training program misclassification may arise if individuals assigned to the program fail to attend or if those not as signed obtain training elsewhere similarly for medical treatment individuals assigned a drug might fail to take it and those assigned a placebo might obtain treatment from another source more generally misclassification describes any binary variable that is sometimes mismeasured this paper first shows that misclassification causes attenuation bias in esti mated treatment effects analogous to the attenuation bias of classically mis measured variables in linear regression models additional assumptions on

generalized kaluza klein monopole quadratic algebras and ladder operators we present a generalized kaluza klein monopole system we solve this quantum superintegrable system on a euclidean taub nut manifold using the separation of variables of the corresponding schr odinger equation in spherical and parabolic coordinates we present the integrals of motion of this system the quadratic algebra generated by these integrals the realization in terms of a deformed oscillator algebra using the daskaloyannis construction and the energy spectrum the structure constants and thecasimir operator are functions not only of the hamiltonian but also of other two integrals commuting with all generators of the quadratic algebra and forming an abelian subalgebra we present another algebraic derivation of the energy spectrum of this system using the factorization method and ladder operators

nonlinear errors in variables estimation of some engel curves abstract the most common solution to the errors in variables problem for the linear regression model is the use of instrumental variable estimation however this methodology cannot be applied in the nonlinear regression framework in this paper we develop consistent estimators for nonlinear regression specifications when errors in variables are present we apply our methodology to estimation of engel curves on household data first we find that the lesser working specification of budget shares regressed on the log of income or expenditure should be generalized to higher order terms in log income also we find that errors in variables in either reported income or expenditure should be accounted for lastly and perhaps most interesting we find rather strong support for the gorman rank restriction on the matrix of coefficients for the polynomial terms in income

partial identification of probability distributions with misclassified data abstract this paper addresses the problem of data errors in discrete variables when data errors occur the observed variable is a misclassified version of the variable of interest whose distribution is not identified inferential problems caused by data errors have been conceptualized through convolution and mixture models this paper introduces the direct misclassification approach the approach is based on the observation that in the presence of classification errors the relation between the distribution of the true but unobservable variable and its misclassified representation is given by a linear system of simultaneous equations in which the coefficient matrix is the matrix of misclassification probabilities formalizing the problem in these terms allows one to incorporate any prior information into the analysis through sets of restrictions on the matrix of misclassification probabilities such information can have strong identifying power the direct misclassification approach fully exploits it to derive identification regions for any real functional of the distribution of interest a method for estimating the identification regions and construct their confidence sets is given and illustrated with an empirical analysis of the distribution of pension plan types using data from the health and retirement study

bounding the effects of measurement error in regressions involving dichotomous variables abstract in a multiple regression involving dichotomous independent variables the effects of measurement error in the dichotomous variables is analyzed unlike the case of classical i e white noise measurement error the measurement error in a dichotomous variable must be correlated with the true variable and any other variables correlated with the true variable nonetheless it is shown that the results for the classical errors in variables model can be used to analyze the implications of measurement error in dichotomous variables it is shown how the bounding procedure developed by klepper and leamer 1984 for the classical errors in variables model can be adapted to bound the coefficients when the regression contains mismeasured dichotomous variables the classical results are also used to analyze the inconsistency in least squares regression coefficient estimators computed from data on the mismeasured variables

equidistant prototypes embedding for single sample based face recognition with generic learning and incremental learning abstract we develop a parameter free face recognition algorithm which is insensitive to large variations in lighting expression occlusion and age using a single gallery sample per subject we take advantage of the observation that equidistant prototypes embedding is an optimal embedding that maximizes the minimum one against the rest margin between the classes rather than preserving the global or the local structure of the training data our method called linear regression analysis lra applies a least square regression technique to map gallery samples to the equally distant locations regardless of the true structure of training data further a novel generic learning method which maps the intraclass facial differences of the generic faces to the zero vectors is incorporated to enhance the generalization capability of lra using this novel method learning based on only a handful of generic classes can largely improve the face recognition performance even when the generic data are collected from a different database and camera set up the incremental learning based on the greville algorithm makes the mapping matrix efficiently updated from the newly coming gallery classes training samples or generic variations although it is fairly simple and parameter free lra combined with commonly used local descriptors such as gabor representation and local binary patterns outperforms the state of the art methods for several standard experiments on the extended yale b cmu pie ar and feret databases

linear dynamic errors in variables models some structure theory abstract this paper gives a survey of some recent results on problems of identifiability or more general of the relation between the observations and certain system characteristics for linear dynamic errors in variables models for a large part of the paper the noise components are assumed to be mutually uncorrelated after the general problem statement a rather complete analysis of the single input single output case is given also the case of three variables and the case where the number of inputs is equal to the number of outputs are discussed in detail finally the use of higher order cummulant spectra for identifiability is investigated

bayesian moment based inference in a regression model with misclassification error we present a bayesian analysis of a regression model with a binary covariate that may have classification measurement error prior research demonstrates that the regression coefficient is only partially identified we take a bayesian approach which adds assumptions in the form of priors on the unknown misclassification probabilities the approach is intermediate between the frequentist bounds of previous literature and strong assumptions which achieve point identification and thus preferable in many settings we present two simple algorithms to sample from the posterior distribution when the likelihood function is not fully parametric but only satisfies a set of moment restrictions we focus on how varying amounts of information contained in a prior distribution on the misclassification probabilities change the posterior of the parameters of interest while the priors add information to the model they do not necessarily tighten the identified set however the information is sufficient to tighten bayesian inferences we also consider the case where the mismeasured binary regressor is endogenous we illustrate the use of our bayesian approach in a simulated data set and an empirical application investigating the association between narcotic pain reliever use and earnings

generalized deformed oscillator and nonlinear algebras the harmonic oscillator is deformed arbitrarily and the properties of the deformed oscillator algebra are studied the eigenstates and eigenvalues of the deformed oscillator are calculated this generalized deformed oscillator algebra is used to create nonlinear deformation of the classical su 2 algebra the deformed boson realizations of an arbitrary nonlinear su 2 algebra are calculated the algebra of the q deformed oscillator is a special case of the generalized deformed oscillator algebra

recurrence approach and higher order polynomial algebras for superintegrable monopole systems we revisit the mic harmonic oscillator in flat space with monopole interaction and derive the polynomial algebra satisfied by the integrals of motion and its energy spectrum using the ad hoc recurrence approach we introduce a superintegrable monopole system in a generalized taub newman unti tamburino nut space the schrodinger equation of this model is solved in spherical coordinates in the framework of stackel transformation it is shown that wave functions of the quantum system can be expressed in terms of the product of laguerre and jacobi polynomials we construct ladder and shift operators based on the corresponding wave functions and obtain the recurrence formulas by applying these recurrence relations we construct higher order algebraically independent integrals of motion we show that the integrals form a polynomial algebra we construct the structure functions of the polynomial algebra and obtain the degenerate energy spectra of the model

nonparametric identification of a binary random factor in cross section data suppose v and u are two independent mean zero random variables where v has an asymmetric distribution with two mass points and u has a symmetric distribution we show that the distributions of v and u are nonparametrically identifled just from observing the sum v u and provide a rate root n estimator we apply these results to the world income distribution to measure the extent of convergence over time where the values v can take on correspond to country types i e wealthy versus poor countries we also extend our results to include covariates x showing that we can nonparametrically identify and estimate cross section regression models of the form y g x d u where d is an unobserved

bounding mean regressions when a binary regressor is mismeasured in this paper i examine identification and estimation of mean regression models when a binary regressor is mismeasured i prove that bounds for the model parameters are identified and provide simple estimators which are consistent and asymptotically normal when stronger prior information about the probability of misclassification is available the bounds can be made tighter again a simple estimator for these cases is provided all results apply to parametric and nonparametric models the paper concludes with a short empirical example

symmetries and degeneracies of a charged oscillator in the field of a magnetic monopole the constants of motion responsible for the level degeneracy of a charged spin 0 particle subjected to harmonic and centrifugal forces and to the field of a magnetic monopole are obtained operators closing onto the su 2 su 2 algebra are constructed in terms of these conserved quantities the space of states decomposes into su 2 su 2 irreducible modules whose dimensions coincide with the degree of degeneracy of the various energy levels

minimum distance estimation of the errors in variables model using linear cumulant equations abstract we consider a multiple mismeasured regressor errors in variables model we develop closed form minimum distance estimators from any number of estimating equations which are linear in the third and higher cumulants of the observable variables using the cumulant estimators alters qualitative inference relative to ordinary least squares in two applications related to investment and leverage regressions the estimators perform well in monte carlos calibrated to resemble the data from our applications although the cumulant estimators are asymptotically equivalent to the moment estimators from erickson and whited 2002 the finite sample performance of the cumulant estimators exceeds that of the moment estimators

the rank of reduced dispersion matrices psychometricians working in factor analysis and econometricians working in regression with measurement error in all variables are both interested in the rank of dispersion matrices under variation of the diagonal elements psychometricians concentrate on cases in which low rank can be attained preferably rank one the spearman case econometricians cocentrate on cases in which the rank cannot be reduced below the number of variables minus one the frisch case in this paper we give an extensive historial discussion of both fields we prove the two key results in a more satisfactory and uniform way we point out various small errors and misunderstandings and we present a methodological comparison of factor analysis and regression on the basis of our results

bounding parameters in a linear regression model with a mismeasured regressor using additional information this paper discusses a linear regression model with a mismeasured regressor in which the measurement error is correlated with both the latent variable and the regression error we use a linear structure to capture the correlation between the measurement error and the latent variable this paper shows that the variance of the latent variable is very useful for revealing information on the parameters which otherwise cannot be obtained with such a nonclassical measurement error the main result is that the finite bounds on the parameters can be found using the variance of the latent variable regardless of how severely the measurement error and the regression error are correlated if the mismeasured regressor contains enough information on the latent one this paper also discusses the special but interesting case of the latent variable being dichotomous in this case the mean of the latent variable may even reveal information on the correlation between the measurement error and the regression error all the bounds developed in the paper are tight