non self adjoint zakharov shabat operator with a potential of the finite asymptotic values i direct spectral and scattering problems the zakharov and shabat equation for the scattering problem is studied the estimates analytical properties and asymptotic expansions of the jost solution are presented for a general class of the potentials q x not vanishing at infinity the existence of the similarity transformation is also shown for q x vanishing at infinity the continuous part of the spectrum doubly degenerates however nonvanishing finite asymptotic values of q x dissolve the degeneracy completely the expansion theorem is given in c 0 2 r and for a class of q x we prove that the zakharov and shabat equation yields a non self adjoint spectral operator in the hilbert space in the sense of dunford and schwartz

misspecified proportional hazard models summary the properties of an estimator based on a proportional hazards model are investigated when the model is incorrect the estimator from the partial likelihood is shown to be consistent for a parameter that is defined implicitly the results are used to investigate the effects on estimation if the true model is accelerated failure time or if covariates are omitted from the proportional hazards model

a new approach to the converse of noether s theorem the concepts of vector fields and forms along a map are used to establish a condition characterising symmetries of the hamiltonian system associated with a regular lagrangian this condition does not mention any second order differential equation field but is expressed in terms of the geometry of the second order tangent bundle this result is also generalised to the case of lagrangian functions depending on higher order derivatives

non parametric confidence interval estimation for competing risks analysis application to contraceptive data non parametric maximum likelihood estimation of the cause specific failure probability and of its standard error in the presence of competing risks is discussed with reference to some contraceptive use dynamics data from bangladesh the cause specific incidence function provides an intuitively appealing summary curve for failure rates and probabilities such as probabilities of discontinuation of different kinds of contraception based on right censored data of the particular event dinse and larson s formula can be utilized to calculate the standard error of the cause specific probability for the failure type of interest and to construct pointwise confidence intervals the accuracy of these intervals as well as those based on the log log transformation and the arcsine transformation are compared by simulations we find that dinse and larson s formula used in conjuction with a log log transform yields reliable standard error estimates and accurate coverage in samples of small and large size and can be recommended for use in this situation copyright 2002 john wiley sons ltd

on dirac s conjecture for systems having only first class constraints dirac s conjecture is proved for a general class of systems having only first class constraints in other words it is shown for that kind of problem that all the primary or secondary first class constraints generate equivalence transformations between physical states

lagrangian and hamiltonian many time equations the lagrangian and hamiltonian many time equations are derived for a finite dimensional system with an arbitray number of primary and secondary first class constraints assuming that all the secondary constraints are generators of gauge transformations the general form of the lagrangian gauge algebra is given

fluctuations around classical solutions for gauge theories in lagrangian and hamiltonian approach we analyse the dynamics of gauge theories and constrained systems in general under small perturbations around a classical solution in both lagrangian and hamiltonian formalisms we prove that a fluctuations theory described by a quadratic lagrangian has the same constraint structure and number of physical degrees of freedom as the original non perturbed theory assuming the non degenerate solution has been chosen we show that the number of noether gauge symmetries is the same in both theories but that the gauge algebra in the fluctuations theory becomes abelianized we also show that the fluctuations theory inherits all functionally independent rigid symmetries from the original theory and that these symmetries are generated by linear or quadratic generators according to whether the original symmetry is preserved by the background or is broken by it we illustrate these results with examples

regularity and symmetries of nonholonomic systems lagrangian systems with nonholonomic constraints may be considered as singular differential equations defined by some constraints and some multipliers the geometry solutions symmetries and constants of motion of such equations are studied within the framework of linearly singular differential equations some examples are given in particular the well known singular lagrangian of the relativistic particle which with the nonholonomic constraint v2 c2 yields a regular system

on the lagrangian and hamiltonian constraint algorithms for the rarita schwinger field coupled to an external electromagnetic field the complete constraint analysis for the rarita schwinger 3 2 field coupled to an external electromagnetic field is given showing the parallel between the lagrangian and dirac bergman algorithms the analysis confirms the connection between the velo zwanzinger 1969 and johnson sudarshan 1961 pathologies and illustrates that these do not in fact arise because the constraint analysis leading to them is incomplete on the contrary a new tier of constraints occurs for the critical field values reducing the pathology to a field induced change in degrees of freedom

lagrangian and hamiltonian constraint structure coefficients we introduce the notion of lagrangian and hamiltonian constraint structure coefficients these coefficients appear in the process of investigating the consistency condition on constraints in both formulations then we show that for a first class hamiltonian constrained system one can find all the lagrangian coefficients in terms of hamiltonian ones

local symmetries in systems with constraints for arbitrary systems with first class constraints the local gauge transformations are constructed in phase and configuration spaces i e a method for obtaining symmetry transformations in the second noether s theorem is given

nonvanishing boundary condition for the mkdv hierarchy and the gardner equation a kac moody algebra construction for the integrable hierarchy containing the gardner equation is proposed solutions are systematically constructed by employing the dressing method and deformed vertex operators which take into account the nonvanishing boundary value problem for the modified korteweg de vries mkdv hierarchy explicit examples are given and besides the usual kdv like solitons our solutions contemplate the large amplitude table top solitons kinks dark solitons breathers and wobbles

supertransparent potentials for the dirac equation an extension of the classical darboux transformations is applied to the one dimensional dirac equation in order to construct von neumann wigner potentials allowing embedded eigenvalues these potentials lead to a novel type of scattering problem with a trivial s matrix composed of vanishing reflection coefficients and a trivial transmission coefficient related topics like the underlying symmetry of the dirac equation and the connection with positon solutions of nonlinear evolution equations are discussed

new relations between hamiltonian and lagrangian constraints different procedures for obtaining all the lagrangian constraints from the hamiltonian constraints are studied the connection of arbitrary functions in both hamiltonian and lagrangian formalisms is also studied as a consequence the authors give a way to pass directly from the final hamilton dirac equations to the euler lagrange ones

generalized hamiltonian dynamics i formulation on t q tq the dirac bergmann generalized hamiltonian dynamics for a degenerate lagrangian system is formulated on the whitney sum t q tq of the phase space t q and the velocity space tq over the configuration space q the formulation is related to those on t q and tq some ambiguities concerning generalized dynamics that have appeared in the literature are clarified

symmetries and constants of motion for constrained lagrangian systems a presymplectic version of the noether theorem the concept of dynamical symmetry for constrained lagrangian systems is analysed and generalized both the direct and converse noether theorems are proved for singular lagrangians

on the use of cause specific failure and conditional failure probabilities examples from clinical oncology data abstract nonparametric maximum likelihood estimation of the probability of failing from a particular cause by time t in the presence of other acting causes i e the cause specific failure probability is discussed a commonly used incorrect approach is to take 1 minus the kaplan meier km estimator 1 km whereby patients who fail of extraneous causes are treated as censored observations examples showing the extent of bias in using the 1 km approach are presented using clinical oncology data this bias can be quite large if the data are uncensored or if a large percentage of patients fail from extraneous causes prior to the occurrence of failures from the cause of interest each cause specific failure probability is mathematically defined as a function of all of the cause specific hazards therefore nonparametric estimates of the cause specific failure probabilities may not be able to identify categorized covariate effects on the cause specific hazards these effects would be correctly identified

estimation of the proportional hazard in two treatment group clinical trials two easily computed approximate methods of obtaining an estimate of the ratio of the hazard rates for two treatments in survival analysis are compared by simulation with the partial maximum likelihood cml estimator which assumes the cox model with no covariates the two methods studied are the mantel haenszel estimator and the o e method which employs the ratio of the relative death rates for the two treatments uncensored and censored cases are examined for both continuous and tied data with the assumption of either an underlying exponential distribution or a weibull distribution with shape parameter 2 the o e method is biased but within the range of values of the ratio of the hazard rates of interest in clinical trials it is more efficient in terms of mean square error than either cml or the mantel haenszel method for all but the largest trials the mantel haenszel method is minimally biased gives answers very close to those obtained using cml and may be used to provide satisfactory approximate confidence intervals

non parametric inference of adverse events under informative censoring in long term treatments or in treatments associated with frequent severe adverse events aes such as those for oncology it is important to know the probability of occurrence of aes over time and their severity however some patients discontinue treatment and drop out of the clinical trial assumption that the drop outs are non informative is not always true and are not validated by data we propose a method of applying competing risk analysis by defining events of occurrence of ae and drop out prior to ae we focus on one ae at a time we distinguish obvious non informative censoring from other censorings that may not be non informative therefore our approach does not need an independent assumption for drop outs the cumulative incidence function estimator cife for the ae by severity can be obtained by treating the degree of severity as a competing risk within the ae we also propose a non parametric estimator of cif for sequential occurrence of the same ae by forming a subset of subjects with prior occurrence s of the same ae and by applying wang and wells estimator we give a very simple formulation of the cumulative joint incidence function estimator cjife for subjects who drop out of the clinical trial after having suffered from the ae at least one time we evaluate the performance of pepe s variance estimator for cjife with small samples by simulations we find that it works well with a sample size more than 100 a useful graphical presentation for cifes and cjife is shown

a hamiltonian approach to lagrangian noether transformations it is proven that each lagrangian noether symmetry rigid or gauge can be easily obtained from a kind of hamiltonian generator which is a conserved quantity satisfying a simple condition this yields a procedure to construct lagrangian gauge transformations it is also shown that some regularity conditions are needed in order to assure the existence of hamiltonian gauge generators the authors present an example which has no such generators though noether gauge transformations can be constructed for it they apply this method to obtain the covariant gauge transformations of the bosonic string from its hamiltonian constraints

gauge invariance of systems with first class constraints the infinitesimal canonical transformations which map solutions of the total hamiltonian equations of motion into each other are investigated for that the generating function of such transformations should satisfy certain conditions in general is a function which depends on the coordinates the momenta and the lagrange multipliers however it is shown that the requirement of independence of the function on the lagrange multipliers is sufficient for the existence of gauge invariant transformations in the lagrange formalism it is shown that the condition that the poisson brackets between and all the primary first class constraints are a linear combination of the latter ones provides the independence of the function the existence of such a independent function is proven for some systems in particular this is proven for the relevant case of systems having primary and secondary first class constraints the authors suggest the possibility that for some specific systems a independen

existence theorem for gauge algebra a general gauge action is defined by postulating a minimum of its properties necessary for the existence of loop expansion in the quantum theory the structure of the general gauge algebra is derived from these postulates the proof of existence of the structure functions lacking in previous works is given the question of uniqueness is also completely cleared up some unsolved problems are discussed in connection with the covariant quantization conjecture

the impact of time dependent bias in proportional hazards modelling in the clinical literature time dependent exposure status has regularly been analysed as if known at time origin although statisticians agree that such an analysis yields biased results when analysing the effect on the time until some endpoint of interest this paper is the first to study in detail the bias arising in a proportional hazards analysis we show that the biased hazard ratio estimate will always be less than the unbiased one this leads to either an inflated or a damped effect of exposure depending on the sign of the correct log hazard ratio estimate we find an explicit formula of the asymptotic bias based on generalized rank estimators and we investigate the role of censoring which may prevent an individual from being considered as being baseline exposed in the biased analysis we illustrate our results with data on hospital infection status and different censoring patterns

on the legendre transformation for singular lagrangians and related topics the authors study the concept of projectability by the legendre transformation fl tq to t q induced by a singular lagrangian and the restrictions on this concept when submanifolds of tq are considered the fl projectability of the characteristic vector fields and constraint functions relative to such a submanifold is analysed thus giving a way of characterising the submanifolds of tq according to their behaviour under fl by means of the study of the tangency of the fields belonging to ker fl the application of some of the results to the theory of constrained systems is discussed

graphical representation of survival curves associated with a binary non reversible time dependent covariate the use of time dependent covariates has allowed for incorporation into analysis of survival data intervening events that are binary and non reversible for example heart transplant initial response to chemotherapy we can represent this type of intervening event as a three state stochastic process with a starting state s an intervening state i and an absorbing state d which usually represents death in this paper we present three procedures for calculating survivorship functions which attempt to display the prognostic significance of the time dependent covariate the first method compares survival from baseline for the two possible paths through the stochastic process the second method compares overall survival to survival with state i removed from the process and the third method compares survival for those already in state i at a landmark time x to those in state s at time x who will never enter state i we develop discrete hazard estimates for the survival curves associated with the three methods two examples illustrate how these methods can yield different results and in which situations one might employ each of the three methods extensions to applications with reversible binary time dependent covariates and models with both baseline and time dependent covariates are suggested

noether s theorem and gauge transformations application to the bosonic string and cp n 12 model new results on the theory of constrained systems are applied to characterize the generators of noether s symmetry transformations as a byproduct an algorithm to construct gauge transformations in hamiltonian formalism is derived this is illustrated with two relevant examples

gunther s formalism k symplectic formalism in classical field theory skinner rusk approach and the evolution operator the first aim of this paper is to extend the skinner rusk formalism on classical mechanics for first order field theories the second is to generalize the definition and properties of the evolution k operator on classical mechanics for first order field theories using in both cases gunther s formalism k symplectic formalism

gauge symmetry in lagrangian formulation and schwinger models a systematic method is presented for processing the equations of motion of a singular lagrangian that in principle has all dynamical degrees of freedom together with the lagrangian constraints and a number of identities between the equations of motion then using these identities one can find the complete set of gauge transformations of the system different types of schwinger model are considered as examples and the related gauge transformations are derived

geometric lagrangian approach to first order systems and applications the geometric theory of presymplectic systems is developed to study both the lagrangian and hamiltonian formulations of a system described by a lagrangian linear in the velocities the results are used to study some related problems for second order differential equations and regular lagrangians

variational calculus with constraints on general algebroids variational calculus on a vector bundle e equipped with a structure of a general algebroid is developed together with the corresponding analogs of euler lagrange equations constrained systems are introduced in the variational and geometrical settings the constrained euler lagrange equations are derived for analogs of holonomic vakonomic and nonholonomic constraints this general model covers the majority of first order lagrangian systems which are present in the literature and reduces to the standard variational calculus and the euler lagrange equations in classical mechanics for e tm

darboux transformations for the korteweg de vries equation a darboux transformation converting the jost solution relating to the n 1 soliton solution of the kdv equation to that to the n soliton solution is shown to be written in the form of a pole expansion and is then found explicitly for arbitrary n multisoliton solutions of the kdv equation are thus generated in practice by algebraic recursive procedures

lattice solitary wave solutions of discrete nonlinear wave equations using a direct method it is shown that the real exponential approach to the solutions of nonlinear evolution and wave equations can also he applied to discrete systems as examples the lattice solitary wave and kink solutions of the discrete modified kdv dmkdv equation and some modified versions of this equation are derived using this approach

origin of the lagrangian constraints and their relation with the hamiltonian formulation the theory of presymplectic systems is used for the study of mechanical systems described by singular lagrangians in order to clarify the geometric meaning of the euler lagrange equations for such systems the two different types of primary constraint functions arising in the lagrangian formulation are analyzed by means of the relation between the image under the vertical endomorphism of the kernel of the presymplectic form l and its vertical part the connection with the hamiltonian dirac theory is also studied and the theory is illustrated with several examples

full and partial gauge fixing gauge fixing may be done in different ways we show that using the chain structure to describe a constrained system enables us to use either a full gauge in which all gauged degrees of freedom are determined or a partial gauge in which some first class constraints remain as subsidiary conditions to be imposed on the solutions of the equations of motion we also show that the number of constants of motion depends on the level in a constraint chain in which the gauge fixing condition is imposed the relativistic point particle electromagnetism and the polyakov string are discussed as examples and full or partial gauges are distinguished

hamilton jacobi theory for constrained systems we extend the hamilton jacobi formulation to constrained dynamical systems the discussion covers both the case of first class constraints alone and that of first and second class constraints combined the hamilton dirac equations are recovered as characteristic of the system of partial differential equations satisfied by the hamilton jacobi function

generating survival times to simulate cox proportional hazards models with time varying covariates simulations and monte carlo methods serve an important role in modern statistical research they allow for an examination of the performance of statistical procedures in settings in which analytic and mathematical derivations may not be feasible a key element in any statistical simulation is the existence of an appropriate data generating process one must be able to simulate data from a specified statistical model we describe data generating processes for the cox proportional hazards model with time varying covariates when event times follow an exponential weibull or gompertz distribution we consider three types of time varying covariates first a dichotomous time varying covariate that can change at most once from untreated to treated e g organ transplant second a continuous time varying covariate such as cumulative exposure at a constant dose to radiation or to a pharmaceutical agent used for a chronic condition third a dichotomous time varying covariate with a subject being able to move repeatedly between treatment states e g current compliance or use of a medication in each setting we derive closed form expressions that allow one to simulate survival times so that survival times are related to a vector of fixed or time invariant covariates and to a single time varying covariate we illustrate the utility of our closed form expressions for simulating event times by using monte carlo simulations to estimate the statistical power to detect as statistically significant the effect of different types of binary time varying covariates this is compared with the statistical power to detect as statistically significant a binary time invariant covariate copyright 2012 john wiley sons ltd

biometrika centenary survival analysis although papers relating to survival analysis have appeared in biometrika since the very first issue the current emphasis on the topic in this journal is fairly new especially as it relates to applications in biostatistics this survey traces the development of survival analysis throughout the twentieth century as reflected in the pages of biometrika focusing primarily on work published since 1980

recursive construction of the generator for lagrangian gauge symmetries we obtain for a subclass of structure functions characterizing a first class hamiltonian system recursive relations from which the general form of the local symmetry transformations can be constructed in terms of the independent gauge parameters we apply this to a non trivial hamiltonian system involving two primary constraints as well as two secondary constraints of the nambu goto type we also illustrate for a pure chern simons theory how this formalism can be extended to a system with first and second class constraints

an explicit expression of the dark n soliton solution of the mkdv equation by means of the darboux transformation a darboux transformation is developed for generating dark multi soliton solutions of the mkdv equation the darboux matrices are found explicitly in recursive manner and a system of linear algebraic equations is derived for determining the dark n soliton solutions by means of the binet cauchy formula an explicit expression of the dark n soliton solution is obtained

on the noether identities for a class of systems with singular lagrangians a straightforward method for obtaining the generators of lagrangian gauge transformations within the lagrangian formalism is presented this procedure can be carried out completely without the need of developing the dirac hamilton formalism singular lagrangians which may generate lagrangian constraints are considered it is assumed that the consistency conditions on the lagrangian constraints do not generate new independent equations for the accelerations from the structure of these consistency conditions the noether identities are explicitly constructed and the lagrangian generators of gauge transformations are obtained it is shown that in the generic case of systems having chains of lagrangian constraints up to a level k k 2 the variations q under which the action is invariant depend on q dq dt and higher time derivatives up to dkq dtk the relation between this lagrangian approach and the standard dirac hamiltonian approach is discussed

bootstrap confidence bands for sojourn distributions in multistate semi markov models with right censoring transient semi markov processes have traditionally been used to describe the transitions of a patient through the various states of a multistate survival model a survival distribution in this context is a sojourn through the states until passage to a fatal absorbing state or certain endpoint states using complete sojourn data this paper shows how such survival distributions and associated hazard functions can be estimated nonparametrically and also how nonparametric bootstrap pointwise confidence bands can be constructed for them when patients are subject to independent right censoring from each state during the sojourn limitations to the estimability of such survival distributions that result from random censoring with bounded support are clarified the methods are applicable to any sort of sojourn through any finite state process of arbitrary complexity involving feedback into previously occupied states copyright 2012 oxford university press

dynamical structure of irregular constrained systems hamiltonian systems with functionally dependent constraints irregular systems for which the standard dirac procedure is not directly applicable are discussed they are classified according to their behavior in the vicinity of the constraint surface into two fundamental types if the irregular constraints are multilinear type i then it is possible to regularize the system so that the hamiltonian and lagrangian descriptions are equivalent when the constraints are power of a linear function type ii regularization is not always possible and the hamiltonian and lagrangian descriptions may be dynamically inequivalent it is shown that the inequivalence between the two formalisms can occur if the kinetic energy is an indefinite quadratic form in the velocities it is also shown that a system of type i can evolve in time from a regular configuration into an irregular one without any catastrophic changes irregularities have important consequences in the linearized approximation to nonlinear theories

comparing the small sample performance of several variance estimators under competing risks we examine several variance estimators for cumulative incidence estimators that have been proposed over time some of which are derived from asymptotic martingale or counting process theory and some of which are developed from the moments of the multinomial distribution there is little published work comparing these variance estimators largely because the variance estimators are algebraically complex and difficult to interpret and all but one have yet to be programmed for a standard statistical package through simulation and application to real data we compare the performance of six variance estimators in relation to each other and the bootstrap in order to confirm earlier reports of their performance and to provide future direction toward their application we find that the multinomial moment based estimators have performance close to that of the bootstrap and are quite accurate for estimating the variance even in samples of 20 subjects all but one of the martingale theory based estimators tend to perform poorly in small samples tending to either overestimate or underestimate the empirical variance in samples of fewer than 100 subjects

non self adjoint zakharov shabat operator with a potential of the finite asymptotic values ii inverse problem the inverse spectral and scattering problem of the zakharov shabat zs operator is studied the similarity transformation between zs operators is examined when their potentials q x have the common nonvanishing asymptotic values q at the infinity the marchenko equation is derived from the parseval equation we give the necessary as well as the sufficient condition of the scattering data for the potential of the specified class

equivalence between the lagrangian and hamiltonian formalism for constrained systems the equivalence between the lagrangian and hamiltonian formalism is studied for constraint systems a procedure to construct the lagrangian constraints from the hamiltonian constraints is given those hamiltonian constraints that are first class with respect to the hamiltonian constraints produce lagrangian constraints that are fl projectable

interacting crumpled manifolds in this paper we study the effect of a interaction on a polymerized membrane of arbitrary internal dimension d depending on the dimensionality of the membrane and embedding space different physical scenarios are observed we emphasize the difference of polymers from membranes for the latter nontrivial contributions appear at the two loop level we also exploit a massive scheme inspired by calculations in fixed dimensions for scalar field theories despite the fact that these calculations are only amenable numerically we found that in the limit of d 2 each diagram can be evaluated analytically this property extends in fact to any order in perturbation theory allowing for a summation of all orders this is a novel and quite surprising result finally an attempt to go beyond d 2 is presented applications to the case of selfavoiding membranes are mentioned

dirac and reduced quantization a lagrangian approach and application to coset spaces a lagrangian treatment of the quantization of first class hamiltonian systems with constraints and hamiltonian linear and quadratic in the momenta respectively is performed the first reduce and then quantize and the first quantize and then reduce dirac s methods are compared a source of ambiguities in this latter approach is pointed out and its relevance on issues concerning self consistency and equivalence with the first reduce method is emphasized one of the main results is the relation between the propagator obtained a la dirac and the propagator in the full space as an application of the formalism developed quantization on coset spaces of compact lie groups is presented in this case it is shown that a natural selection of a dirac quantization allows for full self consistency and equivalence finally the specific case of the propagator on a two dimensional sphere s2 viewed as the coset space su 2 u 1 is worked out

explicit form of the gauge transformation generator in terms of constraints we study the conditions that a gauge transformation generator should satisfy then considering a special class of constrained systems we have derived the explicit form of the gauge generator in terms of first class constraints of the system we have shown that the generator derived can be demonstrated by two different known methods and satisfies the conditions required in both methods

reduced phase space quotienting procedure for gauge theories we present a reduction procedure for gauge theories based on quotienting out the kernel of the presymplectic form in configuration velocity space local expressions for a basis of this kernel are obtained using phase space procedures the obstructions to the formulation of the dynamics in the reduced phase space are identified and circumvented we show that this reduction procedure is equivalent to the standard dirac method as long as the dirac conjecture holds that the dirac hamiltonian containing the primary first class constraints with their lagrange multipliers can be enlarged to an extended dirac hamiltonian which includes all first class constraints without any change of the dynamics the quotienting procedure is always equivalent to the extended dirac theory even when it differs from the standard dirac theory the differences occur when there are ineffective constraints and in these situations we conclude that the standard dirac method is preferable at least for classical theories an example is given to illustrate these features as well as the possibility of having phase space formulations with an odd number of physical degrees of freedom

a note on semi markov models for partially censored data summary a recharacterization of the semi markov model described by lagakos sommer zelen 1978 permits the nonparametric maximum likelihood estimators to be expressed in terms of familiar and easily computable quantities such as event specific hazard estimators and kaplan meier 1958 survival estimators in addition to simplifying the calculation and clarifying the interpretation of the previously derived estimators this reformulation also facilitates the estimation of covariance terms and suggests a simple test of equality among the outcome specific distributions of sojourn times in a particular state

higher order conditions for singular lagrangian dynamics for a kth order singular lagrangian the presymplectic equation plus the different mth order differential equation conditions that can be considered in the lagrangian space yield different dynamics which are studied this leads to a new classification of the constraints this study is also performed in the intermediate formalisms which can be defined between the lagrangian and the hamiltonian ones the corresponding classification schemes are then related

asymptotically efficient two step estimators of the hazards ratio for follow up studies and survival data summary asymptotically efficient estimators of a common hazard rate ratio for follow up studies and the proportional hazards ratio for survival studies are obtained by a single iteration of the mantelhaenszel estimator appropriate for each setting estimators of their variance are also developed the two step estimator for survival data and its variance estimator are shown by simulation to be minimally biased and the estimator is shown to be efficient relative to the cox partial likelihood estimator in small samples

higher order lagrangian systems geometric structures dynamics and constraints in order to study the connections between lagrangian and hamiltonian formalisms constructed from a perhaps singular higher order lagrangian some geometric structures are constructed intermediate spaces between those of lagrangian and hamiltonian formalisms partial ostrogradski s transformations and unambiguous evolution operators connecting these spaces are intrinsically defined and some of their properties studied equations of motion constraints and arbitrary functions of lagrangian and hamiltonian formalisms are thoroughly studied in particular all the lagrangian constraints are obtained from the hamiltonian ones once the gauge transformations are taken into account the true number of degrees of freedom is obtained both in the lagrangian and hamiltonian formalisms and also in all the intermediate formalisms herein defined

an alternative explicit construction of n soliton solutions in 1 1 dimensions using the special riemann problem technique of zakharov et al sov phys jetp 47 1017 1978 an explicit n step backlund transformation is derived for a class of 1 1 dimensional nonlinear evolution equations thus providing an alternative explicit expression of their n soliton solutions which no longer involves computations of the intermediate solutions nor leaves any expansion of n n determinants and their differentiation to be done

dynamical selection of critical exponents in renormalized field theories there are in general one or few fixed points that are accessible by the renormalization group flow they can be identified from the fixed point equations exceptionally an infinite family of fixed points exists parameterized by a scaling exponent itself a function of a nonrenormalizing parameter here we report a different scenario with an infinite family of fixed points of which seemingly only one is chosen by the renormalization group flow this dynamical selection takes place in systems with an attractive interaction v as in standard 4 theory but where the potential v at large goes to zero as e g the attraction by a defect

the difficulty of symplectic analysis with second class systems using the basic concepts of the chain by chain method we show that the symplectic analysis which was claimed to be equivalent to the usual dirac method fails when second class constraints are present we propose a modification in symplectic analysis that solves the problem

non parametric estimation of the case fatality ratio with competing risks data an application to severe acute respiratory syndrome sars for diseases with some level of associated mortality the case fatality ratio measures the proportion of diseased individuals who die from the disease in principle it is straightforward to estimate this quantity from individual follow up data that provides times from onset to death or recovery in particular in a competing risks context the case fatality ratio is defined by the limiting value of the sub distribution function f1 t pr t t and j 1 associated with death as t where t denotes the time from onset to death j 1 or recovery j 2 when censoring is present however estimation of f1 is complicated by the possibility of little information regarding the right tail of f1 requiring use of estimators of f1 t or f1 t f1 t f2 t where t is large with f2 t pr t t and j 2 being the analogous sub distribution function associated with recovery with right censored data the variability of such estimators increases as t increases suggesting the possibility of using estimators at lower values of t where bias may be increased but overall mean squared error be smaller these issues are investigated here for non parametric estimators of f1 and f2 the ideas are illustrated on case fatality data for individuals infected with severe acute respiratory syndrome sars in hong kong in 2003 copyright 2006 john wiley sons ltd

non abelianizable first class constraints we study the necessary and sufficient conditions on abelianizable first class constraints the necessary condition is derived from topological considerations on the structure of the gauge group the sufficient condition is obtained by applying the implicit function theorem in calculus and studying the local structure of gauge orbits since the sufficient condition is necessary for the existence of proper gauge fixing conditions we conclude that in the case of a finite set of non abelianizable first class constraints the faddeev popov determinant is vanishing for any choice of subsidiary constraints this result is explicitly examined for the so 3 gauge invariant model

singular lagrangians some geometric structures along the legendre map new geometric structures that relate the lagrangian and hamiltonian formalisms defined upon a singular lagrangian are presented several vector fields are constructed in velocity space that give new and precise answers to several topics such as the projectability of a vector field to a hamiltonian vector field the computation of the kernel of the presymplectic form of a lagrangian formalism the construction of the lagrangian dynamical vector fields and the characterization of dynamical symmetries