reciprocal transformations of two component hyperbolic systems and their invariants abstract criteria for the equivalence under reciprocal transformations of two component hyperbolic systems are established in terms of reciprocal invariants these results are applied to a 1 1 dimensional isentropic gasdynamics system to determine reciprocal equivalence to the canonical system with a polytropic gas law the four parameter model pressure density relations for which this reciprocal equivalence holds are parameterized in terms of the lagrangian signal speed

minimal representations geometric quantization and unitarity in the framework of geometric quantization we explicitly construct in a uniform fashion a unitary minimal representation pio of every simply connected real lie group go such that the maximal compact subgroup of go has finite center and go admits some minimal representation we obtain algebraic and analytic results about pio we give several results on the algebraic and symplectic geometry of the minimal nilpotent orbits and then quantize these results to obtain the corresponding representations we assume lie go c is simple

geodesic flows bi hamiltonian structure and coupled kdv type systems abstract we show that all the antonowicz fordy type coupled kdv equations have the same symmetry group and similar bi hamiltonian structures it turns out that their configuration space is diff s 1 c s 1 where diff s 1 is the bott virasoro group of orientation preserving diffeomorphisms of the circle and all these systems can be interpreted as equations of a geodesic flow with respect to l 2 metric on the semidirect product space diff s 1 c s 1

inverse regression estimation for censored data an inverse regression methodology for assessing predictor performance in the censored data setup is developed along with inference procedures and a computational algorithm the technique developed here allows for conditioning on the unobserved failure time along with a weighting mechanism that accounts for the censoring the implementation is nonparametric and computationally fast this provides an efficient methodological tool that can be used especially in cases where the usual modeling assumptions are not applicable to the data under consideration it can also be a good diagnostic tool that can be used in the model selection process we have provided theoretical justification of consistency and asymptotic normality of the methodology simulation studies and two data analyses are provided to illustrate the practical utility of the procedure

the hausdorff young inequality on lie groups we prove several results about the best constants in the hausdorff young inequality for noncommutative groups in particular we establish a sharp local central version for compact lie groups and extend known results for the heisenberg group in addition we prove a universal lower bound to the best constant for general lie groups

on quantum gauge theories in two dimensions two dimensional quantum yang mills theory is studied from three points of view i by standard physical methods ii by relating it to the largek limit of three dimensional chern simons theory and two dimensional conformal field theory iii by relating its weak coupling limit to the theory of reidemeister ray singer torsion the results obtained from the three points of view agree and give formulas for the volumes of the moduli spaces of representations of fundamental groups of two dimensional surfaces

geometric quantization and multiplicities of group representations the heisenberg uncertainty principle says that it is impossible to determine simultaneously the position and momentum of a quantum mechanical particle this can be rephrased as follows the smallest subsets of classical phase space in which the presence of a quantum mechanical particle can be detected are its lagrangian submanifolds for this reason it makes sense to regard the lagrangian submanifolds of phase space as being its true points see weinstein 17 now let g be a compact lie group and g x x x a hamiltonian action of g on x see w for definitions it is well known that the fixed points of this action form a symplectic submanifold of x see for instance guillemin and sternberg 5 however what can one say about the fixed points of g we will show that they are also the points of a symplectic manifold xc this manifold is the marsden weinstein reduction of x with respect to the zero orbit in g and will be described in sect 2 it was introduced in a completely different context fl om ours by marsden and weinstein 12 problems in classical mechanics can often be reduced to the study of hamiltonian systems on symplectic manifolds and problems in quantum mechanics to the study of linear operators on hilbert space this fact has inspired a number of efforts to quantize symplectic geometry by devising schemes for associating hilbert space to symplectic manifolds the no go theorems of groenwald and van hove impose some embarrassing limitations on all such schemes however it seems to be a useful idea heuristically to think of every symplectic manifold x a ic 1 as being symbiotically associated with a hilbert space xq a t in such a way that the classical observables on the first space correspond to quantum observables on the second space the heuristics further suggests that if g is a group of symmetries of x la i j it should also be a group of symmetries of xq a tum in this heuristic spirit we will state the main conjecture of this paper

partial identification and inference in censored quantile regression abstract in this paper we study partial identification and inference in a linear quantile regression where the dependent variable is subject to possibly unknown dependent censoring characterized by an archimedean copula an outer set of the identified set for the regression coefficient is characterized via inequality constraints for one parameter ordered families of archimedean copulas we construct a simple confidence set by inverting an asymptotically pivotal statistic a bootstrap confidence set is also constructed sensitivity of the identified set to possible misspecification of the true copula and the finite sample performance of the boostrap confidence set are investigated numerically

estimation of exposure distribution adjusting for association between exposure level and detection limit in environmental exposure studies it is common to observe a portion of exposure measurements to fall below experimentally determined detection limits dls the reverse kaplan meier estimator which mimics the well known kaplan meier estimator for right censored survival data with the scale reversed has been recommended for estimating the exposure distribution for the data subject to dls because it does not require any distributional assumption however the reverse kaplan meier estimator requires the independence assumption between the exposure level and dl and can lead to biased results when this assumption is violated we propose a kernel smoothed nonparametric estimator for the exposure distribution without imposing any independence assumption between the exposure level and dl we show that the proposed estimator is consistent and asymptotically normal simulation studies demonstrate that the proposed estimator performs well in practical situations a colon cancer study is provided for illustration copyright 2017 john wiley sons ltd

a geometric criterion for gelfand pairs associated with nilpotent lie groups abstract in this paper we give a proof to the orbit conjecture of benson jenkins lipsman ratcliff and get a geometric criterion for gelfand pairs associated with nilpotent lie groups our proof is based on an analysis of the condition by using certain operators naturally attached to two step nilpotent lie algebras provided with an inner product a class of nilpotent lie groups considered by lauret is also treated as examples

semiparametric estimation of a proportional hazard model with unobserved heterogeneity the proportional hazard model with unobserved heterogeneity gives the hazard function of a random variable conditional on covariates and a second random variable representing unobserved heterogeneity this paper shows how to estimate the baseline hazard function and the distribution of the unobserved heterogeneity nonparametrically the baseline hazard function and heterogeneity distribution are assumed to satisfy smoothness conditions but are not assumed to belong to known finite dimensional parametric families existing estimators assume that the baseline hazard function or heterogeneity distribution belongs to a known parametric family thus the estimators presented here are more general than existing ones

on the local equivalence in a unidimensional world the physical meaning of some semiunitary irreducible realizations of the unidimensional poincare and galilei groups including time inversion which are characteristic of a unidimensional world is investigated it is shown that in order to achieve this purpose the local equivalence is the most appropriate and it does not coincide with an equivalence of the global kind in this study use has been made of the theory of locally operating realizations developed by hoogland while dealing with the nontrivial factor systems the representation group technics were used

eigenvalue distributions of reduced density matrices given a random quantum state of multiple distinguishable or indistinguishable particles we provide an effective method rooted in symplectic geometry to compute the joint probability distribution of the eigenvalues of its one body reduced density matrices as a corollary by taking the distribution s support which is a convex moment polytope we recover a complete solution to the one body quantum marginal problem we obtain the probability distribution by reducing to the corresponding distribution of diagonal entries i e to the quantitative version of a classical marginal problem which is then determined algorithmically this reduction applies more generally to symplectic geometry relating invariant measures for the coadjoint action of a compact lie group to their projections onto a cartan subalgebra and can also be quantized to provide an efficient algorithm for computing bounded height kronecker and plethysm coefficients

conditional empirical processes consider a sequence i xi yi i 1 of independent d 1 random vectors with common d f h text h left text x y right mathbb p left text x x y y right text left text x y right in mathbb r text d 1

a notion of rank for unitary representations of reductive groups based on kirillov s orbit method we introduce a new notion of rank for unitary representations of semisimple groups over a local field of characteristic zero the theory is based on kirillov s method of orbits for nilpotent groups over local fields when the semisimple group is a classical group we prove that the new theory is essentially equivalent to howe s theory of n rank see ho4 l2 sc therefore our results provide a systematic generalization of the notion of a small representation in the sense of howe to exceptional groups however unlike previous works that used ad hoc methods to study different types of classical groups and some exceptional ones see we ls our definition is simultaneously applicable to both classical and exceptional groups the most important result of this article is a general purity result for unitary representations which demonstrates how similar partial results in these authors works should be formulated and proved for an arbitrary semisimple group in the language of kirillov s theory the purity result is a crucial step toward studying small representations of exceptional groups new results concerning small unitary representations of exceptional groups will be published in a forthcoming paper s

on the use of nonparametric regression techniques for fitting parametric regression models a new method for fitting parametric regression models is proposed it consists of applying the least squares ls principle on the pairs xi rh xi i 1 n where x denotes the explanatory variable and mn x is a location estimate of the conditional distribution of the response variable y given that x x consistency and asymptotic normality of the estimators are established under general conditions these conditions are shown to be satisfied when the data are incomplete due to random censoring or truncation usable expressions for the asymptotic variance covariance matrix of the parameters are provided in these incomplete data cases as an extra bonus this regression method allows the use of ordinary residual plots as a data analytic aide this is illustrated on two real data sets a simulation study examines the small sample behavior of the estimators and their estimated asymptotic variance extension of the method to more complicated models is discussed

the stratonovich weyl correspondence for one dimensional kinematical groups the stratonovich weyl correspondence is a restatement of the moyal quantization where the phase space is a manifold and where a group of transformations acts on it transitively the first and most important step is to define a mapping from the manifold into the set of self adjoint operators on a hilbert space under suitable conditions this mapping is called a stratonovich weyl kernel the construction of this mapping is discussed on coadjoint orbits of the one dimensional galilei poincare and newton hooke groups as well as the two dimensional euclidean group

the irreducible unitary representations of the extended poincare group in 1 1 dimensions we prove that the extended poincare group in 1 1 dimensions p is non nilpotent solvable exponential and therefore that it belongs to type i we determine its first and second cohomology groups in order to work out a classification of the two dimensional relativistic elementary systems moreover all irreducible unitary representations of p are constructed by the orbit method the most physically interesting class of irreducible representations corresponds to the anomaly free relativistic particle in 1 1 dimensions which cannot be fully quantized however we show that the corresponding coadjoint orbit of p determines a covariant maximal polynomial quantization by unbounded operators which is enough to ensure that the associated quantum dynamical problem can be consistently solved thus providing a physical interpretation for this particular class of representations

degenerate principal series representations and their holomorphic extensions let x h l be an irreducible real bounded symmetric domain realized as a real form in an hermitian symmetric domain d g k the intersection s of the shilov boundary of d with x defines a distinguished subset of the topological boundary of x and is invariant under h it can be realized as s h p for certain parabolic subgroup p of h we study the spherical representations of h induced from p we find formulas for the spherical functions in terms of the macdonald hypergeometric function this generalizes the earlier result of faraut koranyi for hermitian symmetric spaces d we consider a class of h invariant integral intertwining operators from the representations on l2 s to the holomorphic representations of g restricted to h we construct a new class of complementary series for the groups h so n m su n m with n m 2 and sp n m with n m 1 we realize them as discrete components in the branching rule of the analytic continuation of the holomorphic discrete series of g su n m su n m su n m and su 2n 2m respectively

nearest neighbor estimation of a bivariate distribution under random censoring we consider the problem of estimating the bivariate distribution of the random vector x y when y may be subject to random censoring the censoring variable c is allowed to depend on x but it is assumed that y and c are conditionally independent given x x the estimate of the bivariate distribution is obtained by averaging estimates of the conditional distribution of y given x x over a range of values of x the weak convergence of the centered estimator multiplied by n 1 2 is obtained and a closed form expression for the covariance function of the limiting process is given it is shown that the proposed estimator is optimal in the beran sense this is similar to an optimality property the product limit estimator enjoys using the proposed estimator of the bivariate distribution an extension of the least squares estimator to censored data polynomial regression is obtained and its asymptotic normality established

calibrating parametric subject specific risk estimation for modern evidence based medicine decisions on disease prevention or management strategies are often guided by a risk index system for each individual the system uses his her baseline information to estimate the risk of experiencing a future disease related clinical event such a risk scoring scheme is usually derived from an overly simplified parametric model to validate a model based procedure one may perform a standard global evaluation via for instance a receiver operating characteristic analysis in this article we propose a method to calibrate the risk index system at a subject level specifically we developed point and interval estimation procedures for t year mortality rates conditional on the estimated parametric risk score the proposals are illustrated with a dataset from a large clinical trial with post myocardial infarction patients

survival analysis using auxiliary variables via non parametric multiple imputation we develop an approach based on multiple imputation that estimates the marginal survival distribution in survival analysis using auxiliary variables to recover information for censored observations to conduct the imputation we use two working survival models to define a nearest neighbour imputing risk set one model is for the event times and the other for the censoring times based on the imputing risk set two non parametric multiple imputation methods are considered risk set imputation and kaplan meier imputation for both methods a future event or censoring time is imputed for each censored observation with a categorical auxiliary variable we show that with a large number of imputes the estimates from the kaplan meier imputation method correspond to the weighted kaplan meier estimator we also show that the kaplan meier imputation method is robust to mis specification of either one of the two working models in a simulation study with time independent and time dependent auxiliary variables we compare the multiple imputation approaches with an inverse probability of censoring weighted method we show that all approaches can reduce bias due to dependent censoring and improve the efficiency we apply the approaches to aids clinical trial data comparing zdv and placebo in which cd4 count is the time dependent auxiliary variable

su 3 mean field hamiltonian the su 3 mean field approximation describes collective nuclear rotation in a density matrix formalism the densities q i l 2 are 3 3 hermitian matrices in the su 3 dual space where q is the expectation of the quadrupole moment and l is the expectation of the angular momentum the mean field approximation restricts these densities to a level surface of the su 3 casimirs each level surface is a coadjoint orbit of the canonical transformation group su 3 for each density the su 3 mean field hamiltonian h is an element of the su 3 lie algebra a model su 3 energy functional and the symplectic structure on the coadjoint orbit determine uniquely the su 3 mean field hamiltonian the densities in time dependent su 3 mean field theory obey the dynamical equation i h on a coadjoint orbit the cranked mean field hamiltonian is h h i where is the angular velocity of the rotating principal axis frame a rotating equilibrium density in the body fixed frame is a self consistent solution to the equation h 0

mean field theory for su 4 so 6 algebraic mean field theory constructs a group theoretical model of quantum systems that have a weak dynamical symmetry but may break dynamical symmetry the strong defining condition for dynamical symmetry is that states belong to one irreducible representation space weak dynamical symmetry demands that the densities corresponding to the states have a constant value for each casimir quantum phase transitions and other complex systems exhibit weak dynamical symmetry furthermore mean field theory often yields analytic formulae for expectations and energy spectra that are not feasible in representation theory this paper develops mean field theory on any coadjoint orbit of su 4 densities the simple lie algebra su 4 so 6 is a 15 dimensional algebra that contains the subalgebra usp 4 so 5 and the angular momentum algebra su 2 the su 4 dual space consists of density matrices which are defined by the expectations of the su 4 generators a coadjoint orbit is a common level surface in the dual space of the three su 4 casimirs a lax pair determines the dynamics of these densities on each coadjoint orbit analytic solutions are reported for rotating su 4 densities in equilibrium for a particular energy function

transfer of tail information in censored regression models consider a heteroscedastic regression model y m x sigma x varepsilon where the functions m and sigma are smooth and varepsilon is independent of x the response variable y is subject to random censoring but it is assumed that there exists a region of the covariate x where the censoring of y is light under this condition it is shown that the assumed nonparametric regression model can be used to transfer tail information from regions of light censoring to regions of heavy censoring crucial for this transfer is the estimator of the distribution of varepsilon based on nonparametric regression residuals whose weak convergence is obtained the idea of transferrring tail information is applied to the estimation of the conditional distribution of y given x x with information on the upper tail borrowed from the region of light censoring and to the estimation of the bivariate distribution p x leq x y leq y with no regions of undefined mass the weak convergence of the two estimators is obtained by products of this investigation include the uniform consistency of the conditional kaplan meier estimator and its derivative the location and scale estimators and the estimators of their derivatives

on the variation in the cohomology of the symplectic form of the reduced phase space is called the momentum mapping of the hamiltonian t action given 1 1 the condition 1 2 just means that t acts along the fibers of j for the basic definitions and properties of non commutative hamiltonian group actions see am the results of this paper can easily be extended to hamiltonian actions of arbitrary compact connected lie groups by applying our results to the action of its maximal toms and using the equivariance of the momentum mapping for some more details see the remarks at the end of sect 2 we will assume throughout this paper that the momentum map is proper that is j i u is compact for each compact subset u of t now let r be a regular value of j that is t j tmm t is surjective for all meye j 1 4 then ye is a smooth submanifold of m compact because

weak and strong uniform consistency of kernel regression estimates we study the estimation of a regression function by the kernel method under mild conditions on the window the bandwidth and the underlying distribution of the bivariate observations x i y i we obtain the weak and strong uniform convergence rates on a bounded interval these results parallel those of silverman 1978 on density estimation and extend those of schuster and yakowitz 1979 and collomb 1979 on regression estimation

vector coherent state representations induced representations and geometric quantization i scalar coherent state representations coherent state theory is shown to reproduce three categories of representations of the spectrum generating algebra for an algebraic model i classical realizations which are the starting point for geometric quantization ii induced unitary representations corresponding to prequantization and iii irreducible unitary representations obtained in geometric quantization by choice of a polarization these representations establish an intimate relation between coherent state theory and geometric quantization in the context of induced representations

superintegrability of geodesic motion on the sausage model reduction of the eta deformed sigma model on ads 5 x s 5 to the two dimensional squashed sphere s 2 eta can be viewed as a special case of the fateev sausage model where the coupling constant v i

locally weighted censored quantile regression censored quantile regression offers a valuable supplement to cox proportional hazards model for survival analysis existing work in the literature often requires stringent assumptions such as unconditional independence of the survival time and the censoring variable or global linearity at all quantile levels moreover some of the work uses recursive algorithms making it challenging to derive asymptotic normality to overcome these drawbacks we propose a new locally weighted censored quantile regression approach that adopts the redistribution of mass idea and employs a local reweighting scheme its validity only requires conditional independence of the survival time and the censoring variable given the covariates and linearity at the particular quantile level of interest our method leads to a simple algorithm that can be conveniently implemented with r software applying recent theory of m estimation with infinite dimensional parameters we establish the consistency and asymptotic normality of the pr

calibration plots for risk prediction models in the presence of competing risks a predicted risk of 17 can be called reliable if it can be expected that the event will occur to about 17 of 100 patients who all received a predicted risk of 17 statistical models can predict the absolute risk of an event such as cardiovascular death in the presence of competing risks such as death due to other causes for personalized medicine and patient counseling it is necessary to check that the model is calibrated in the sense that it provides reliable predictions for all subjects there are three often encountered practical problems when the aim is to display or test if a risk prediction model is well calibrated the first is lack of independent validation data the second is right censoring and the third is that when the risk scale is continuous the estimation problem is as difficult as density estimation to deal with these problems we propose to estimate calibration curves for competing risks models based on jackknife pseudo values that are combined with a nearest neighborhood smoother and a cross validation approach to deal with all three problems

on almost sure convergence of conditional empirical distribution functions on etudie la convergence presque sure d une distribution empirique conditionnelle de type noyau a la fois en norme sup et en norme sup ponderee

sp 3 r coadjoint orbit theory the algebraic mean field method is applied to the symplectic lie algebra sp 3 r that describes geometrical collective states in atomic nuclei the expectations of sp 3 r generators define a symplectic density matrix the mean field approximation restricts the densities to a manifold that is a coadjoint orbit of the transformation group sp 3 r and a level surface of the symplectic casimir functions compared to representation theory mean field theory is technically simpler but yields similar predictions for physical properties of collective states the critical points of the energy functional on a coadjoint orbit surface define rotational bands the deformation kinetic energy and kelvin circulation of principal axis symplectic rotors are determined as a function of the angular momentum illustrative applications of coadjoint orbit theory are reported for the yrast rotational bands of a light 20ne and a heavy 166er deformed isotope

semiparametric estimation of a panel data proportional hazards model with fixed effects this paper considers a panel duration model that has a proportional hazards specification with fixed effects the paper shows how to estimate the baseline and integrated baseline hazard functions without assuming that they belong to known finite dimensional families of functions existing estimators assume that the baseline hazard function belongs to a known parametric family therefore the estimators presented here are more general than existing ones this paper also presents a method for estimating the parametric part of the proportional hazards model with dependent right censoring under which the partial likelihood estimator is inconsistent the paper presents some monte carlo evidence on the small sample performance of the new estimators

application of a reciprocal transformation to a two phase stefan problem a reciprocal transformation is employed to reduce a two phase stefan problem in nonlinear heat conduction to a form which admits a class of exact solutions analogous to the classical newmann solution

smoothed cox regression nonparametric regression was shown by beran and mckeague and utikal to provide a flexible method for analysis of censored failure times and more general counting processes models in the presence of covariates we discuss application of kernel smoothing towards estimation in a generalized cox regression model with baseline intensity dependent on a covariate under regularity conditions we show that estimates of the regression parameters are asymptotically normal at rate root n and we also discuss estimation of the baseline cumulative hazard function and related parameters

addendum to on the variation in the cohomology of the symplectic form of the reduced phase space here we have used the notation rlx for the inner product of the vector field x with the form a and ix m x j m for the x component of a in an earlier paper 4 it was shown that the push forward j dm of the liouville measure dm on m under the momentum mapping j is a piecewise polynomial measure on moreover in case x has isolated isolated zeros on m an explicit formula for the integral

stochastic calculus as a tool in survival analysis a review this paper gives a brief survey of the uses of stochastic calculus in survival analysis the role played by martingale central limit theory in deriving asymptotic distributions of estimators and test statistics is described the nelson aalen estimator the kaplan meier estimator cox s proportional hazards model aalen s additive risk model and a goodness of fit test for cox s model are discussed sketches of the proofs of the main results are included

doubly robust learning for estimating individualized treatment with censored data individualized treatment rules recommend treatments based on individual patient characteristics in order to maximize clinical benefit when the clinical outcome of interest is survival time estimation is often complicated by censoring we develop nonparametric methods for estimating an optimal individualized treatment rule in the presence of censored data to adjust for censoring we propose a doubly robust estimator which requires correct specification of either the censoring model or survival model but not both the method is shown to be fisher consistent when either model is correct furthermore we establish the convergence rate of the expected survival under the estimated optimal individualized treatment rule to the expected survival under the optimal individualized treatment rule we illustrate the proposed methods using simulation study and data from a phase iii clinical trial on non small cell lung cancer

e factor of representations of classical groups abstract we let g be the isometry group of a nondegenerate symmetric or skew symmetric form h on a space v over some local or global field k i e g u v h we let lg be the l group of go the identity component of g and r be the natural representation of this group we develop here a theory of l functions and e factors attached to this r in particular we develop a theory of local and global zeta integrals for such g we use very special intertwining operators therein we require an analysis of the proper normalization of such operators with such techniques we determine the correct e factors associated to local representations the issue of the correct local l factor is discussed

height zeta functions of equivariant compactifications of unipotent groups we prove manin s conjecture for bi equivariant compactifications of unipotent groups 2015 wiley periodicals inc