edgeworth correction by bootstrap in autoregressions we prove that the distribution of least squares estimates in autoregressions can be bootstrapped with accuracy o n 1 2 a s thereby improving the normal approximation error of o n

robustness in quantum measurements conditions are formulated under which a representation of an intrinsic c algebra of often quasilocal observables of an infinite system is appropriate to describe measurement type processes such a representation should allow for the description of robust experiments it should be separable and the pointer observable should be in its weak closure if the pointer values are discrete the existence of such a measurement representation can be proven if the pointer can take continuously many values then the existence can only be proven under the additional assumptions of having an asymptotically abelian system or dealing with type i representations in the constructed measurement representations the pointer observable turns out to be classical the structure of the representation suggests that spontaneous symmetry breaking might be a physical explanation of the emergence of the classical pointer

gleason s theorem for rectangular jbw triples a jbw triple b is said to be rectangular if there exists a w algebra a and a pair p q of centrally equivalent elements of the complete orthomodular lattice of projections in a such that b is isomorphic to the jbw triple paq any weak closed injective operator space provides an example of a rectangular jbw triple the principal order ideal of the complete lattice of centrally equivalent pairs of projections in a w algebra a generated by p q forms a complete lattice that is order isomorphic to the complete lattice of weak closed inner ideals in b and to the complete lattice of structural projections on b although not itself in general orthomodular possesses a complementation that allows for definitions of orthogonality centre and central orthogonality to be given a less familiar notion in lattice theory that is well known in the theory of jordan algebras and jordan triple systems is that of rigid collinearity of a pair e2 f2 and e2 f2 of elements of this is defined and characterized in terms of properties of a w algebra a is sometimes thought of as providing a model for a statistical physical system in this case b or equivalently paq may be thought of as providing a model for a fixed sub system of that represented by a therefore may be considered to represent the set consisting of a particular kind of sub system of that represented by paq central orthogonality and rigid collinearity of pairs of elements of may be regarded as representing two different types of disjointness the former classical disjointness and the latter decoherence of the two sub systems it is therefore natural to consider bounded measures m on that are additive on centrally orthogonal and rigidly collinear pairs of elements using results of j d m wright it is shown that provided that neither of the two hereditary sub w algebras pap and qaq of a has a weak closed ideal of type i2 such measures are precisely those that are the restrictions of bounded sesquilinear functionals m on pap qaq with the property that the action of the centroid z b of b commutes with the adjoint operation when b is a complex hilbert space of dimension greater than two this result reduces to gleason s theorem

quantum logic state space geometry and operator algebras the problem of characterising those quantum logics which can be identified with the lattice of projections in a jbw algebra or a von neumann algebra is considered for quantum logics which satisfy the countable chain condition and which have no typei2 part a characterisation in terms of geometric properties of the quantum state space is given

bootstrapping a regression equation some empirical results abstract the bootstrap like the jackknife is a technique for estimating standard errors the idea is to use monte carlo simulation based on a nonparametric estimate of the underlying error distribution the main object of this article is to present the bootstrap in the context of an econometric equation describing the demand for energy by industry as it turns out the conventional asymptotic formulas for estimating standard errors are too optimistic by factors of nearly three when applied to a particular finite sample problem in a simpler context this finding can be given a mathematical proof

the lattice of weak closed inner ideals in a w algebra the family of centrally equivalent pairs of projections in a w algebra a forms a complete lattice that is order isomorphic to the complete lattice of weak closed inner ideals in a and to the complete lattice of structural projections on a furthermore the set of symmetric elements of is order isomorphic to the complete orthomodular lattice of projections in a although not itself in general orthomodular possesses a complementation that allows for definitions of orthogonality centre and central orthogonality to be given a less familiar notion in lattice theory that is well known in the theory of jordan algebras and jordan triple systems is that of rigid collinearity of a pair e1 f1 and e2 f2 of elements of this is defined and characterized in terms of properties of

occupational segregation in the multidimensional case decomposition and tests of significance a new multidimensional version of the g segregation index is developed and applied to the study of occupational segregation u s current population survey data are used to measure the difference in occupational segregation between races as well as the change between time periods decomposition of the difference change into occupation mix and gender composition components indicates the contribution of each factor because these inequality measures are computed from sample data distributional information required to test hypotheses is lacking two computer intensive methods for estimating the distributional properties are demonstrated the approximate randomization and bootstrap methodologies are used to test for statistically significant differences in segregation between races and for changes over time in addition the components of the decomposition are examined for statistical significance

convergence of a finite volume scheme for coagulation fragmentation equations this paper is devoted to the analysis of a numerical scheme for the coagulation and fragmentation equation a time explicit finite volume scheme is developed based on a conservative formulation of the equation it is shown to converge under a stability condition on the time step while a first order rate of convergence is established and an explicit error estimate is given finally several numerical simulations are performed to investigate the gelation phenomenon and the long time behavior of the solution

bootstrap prediction intervals for autoregression abstract the nonparametric bootstrap is applied to the problem of prediction in autoregression let y t t 0 1 2 be a stationary autoregressive process of known order p ar p given a realization of the series up to time t y 1 y 2 y t a 100 prediction interval for y t k is desired standard forecasting techniques which assume that the error sequence of the process y t is gaussian rely on the fact that the conditional distribution of y t k given the data is gaussian as well as a nonparametric alternative the bootstrap provides an estimate of the conditional distribution of y t k the method is similar to other applications of the bootstrap for linear models because the residuals are resampled the proposed methodology represents a different approach since an alternative representation for ar p series is used allowing for bootstrap replicates generated backward in time it follows that the resulting replicates all have the same conditionally fixed values at the end

bootstrapping regression models the regression and correlation models are considered it is shown that the bootstrap approximation to the distribution of the least squares estimates is valid and some error bounds are given

decoherence functionals for von neumann quantum histories boundedness and countable additivity gell mann and hartle have proposed a significant generalisation of quantum theory in which decoherence functionals perform a key role verifying a conjecture of isham linden schreckenberg the author analysed the structure of bounded finitely additive decoherence functionals for a general von neumann algebra a where a has no type i2 direct summand isham et al had already given a penetrating analysis for the situation where a is finite dimensional the assumption of countable additivity for a decoherence functional may seem more plausible physically than that of boundedness the results of this note are obtained much more generally but when specialised to l h the algebra of all bounded linear operators on a separable hilbert space h give

some asymptotic theory for the bootstrap efron s bootstrap method of distribution approximation is shown to be asymptotically valid in a large number of situations including t statistics the empirical and quantile processes and von mises functionals some counter examples are also given to show that the approximation does not always succeed

the structure of decoherence functionals for von neumann quantum histories gell mann and hartle have proposed a significant generalization of quantum theory in which decoherence functionals perform a key role isham linden schreckenberg have given a penetrating analysis of decoherence functionals for l h where h is finite dimensional dimension greater than 2 in this note their conjecture on the significance of boundedness is verified in particular it is shown that when d is a bounded decoherence functional associated with a von neumann algebra a then provided a has no direct summand of type i2 d can be represented as the difference between semi innerproducts on a

generalized bootstrap for estimating equations we introduce a generalized bootstrap technique for estimators obtained by solving estimating equations some special cases of this generalized bootstrap are the classical bootstrap of efron the delete d jackknife and variations of the bayesian bootstrap the use of the proposed technique is discussed in some examples distributional consistency of the method is established and an asymptotic representation of the resampling variance estimator is obtained

bootstrap bartlett adjustment in seemingly unrelated regression abstract seemingly unrelated regression sur is a method introduced by zellner 1962 for estimating several regression equations simultaneously a common and important problem in econometrics this article considers hypothesis testing in sur using the log likelihood ratio llr test although the asymptotic distribution of this statistic is well known substantial departures occur in samples of the size commonly employed by economists significance levels given by the use of this asymptotic distribution are too low sometimes by an order of magnitude leading to the rejection of too many true null hypotheses a common approach to this problem is to use a bartlett 1937 adjustment to the llr statistic in which the test statistic is multiplied by a factor derived from second order asymptotics before it is referred to the asymptotic 2 q distribution this article proposes that the bartlett adjustment factor be computed using efron s bootstrap 1979 1982 in the cases examined this leads to more accu

piecewise homomorphisms and jordan maps on c algebras and factor von neumann algebras abstract we investigate maps between c algebras that are well behaved with respect to mutually commuting elements we contribute to the mackey gleason problem by showing that any continuous bijection between self adjoint parts of c algebras that preserves triple product a b a b a and is linear on commutative subspaces is already linear this allows us to describe such maps as direct differences of linear jordan isomorphisms we shall show that any weak continuous bijection between positive invertible elements of von neumann factors of dimension at least 9 that preserves products of commuting elements in both directions is of the form a e log a a c where is a linear jordan isomorphism c nonzero real number and is a hermitian continuous functional in a similar way we describe the same type of bicontinuous maps between unitary groups of von neumann factors general form of the above mentioned maps on c algebras is also presented

measures on the lattice of closed inner ideals in a spin triple two elements j and k of the complete lattice i a of weak closed inner ideals in a jbw triple a are said to be centrally orthogonal if there exists a weak closed ideal i in a such that a2 j a2 i and a2 k a0 i and are said to be rigidly collinear when a2 j a1 k and a2 k a1 j where for j equal to 0 1 or 2 aj i aj j and aj k are the components in the generalized peirce decomposition of a relative to the weak closed inner ideals i j and k respectively a measure m on i a is a mapping from i a to c such that if j and k are either centrally orthogonal or rigidly collinear thenmj k mj mk a complex hilbert space a endowed with a conjugation possesses a triple product and norm with respect to which it forms a jbw triple known as a spin triple in this paper the structure of the complete lattice i a of closed inner ideals in a spin triple a and the measures on it are investigated it is shown that if the dimension of a is greater than 5 then there are no non zero measures on i a when the dimension of a is 5 non zero measures exist and up to multiplication by a constant a unique measure exists that is invariant under automorphisms of a when the dimension of a is 4 then a is triple isomorphic to the w algebra of 2 2 complex matrices in this case results of bunce and wright are used to show that there is an uncountable number of measures on i a the situation when the dimension of a is less than 4 is also described

multiplicative jordan triple isomorphisms on the self adjoint elements of von neumann algebras abstract in this paper we consider multiplicative jordan triple isomorphisms between the sets of self adjoint elements respectively the sets of positive elements of von neumann algebras these transformations are the bijective maps which satisfy the equality aba a b a on their domains we show that all those transformations originate from linear algebra isomorphisms and linear algebra antiisomorphisms in the case when the underlying von neumann algebras do not have commutative direct summands an application of our results concerning non linear maps which preserve the absolute value of products is also presented

contextuality and noncommutative geometry in quantum mechanics observable properties of a classical physical system can be modelled deterministically as functions from the space of pure states to outcome values dually states can be modelled as functions from the algebra of observables to outcome values the probabilistic predictions of quantum physics are contextual in that they preclude this classical assumption of reality noncommuting observables which are not assumed to be jointly measurable cannot be consistently ascribed deterministic values even if one enriches the description of a quantum state here we consider the geometrically dual objects of noncommutative operator algebras of observables as being generalisations of classical deterministic state spaces to the quantum setting and argue that these generalised state spaces represent the objects of study of noncommutative operator geometry by adapting the spectral presheaf of hamilton isham butterfield a formulation of quantum state space that collates contextual data we reconstruct tools of noncommutative geometry in an explicitly geometric fashion in this way we bridge the foundations of quantum mechanics with the foundations of noncommutative geometry a la connes et al to each unital c algebra mathcal a we associate a geometric object a diagram of topological spaces collating quotient spaces of the noncommutative space underlying mathcal a that performs the role of a generalised gel fand spectrum we show how any functor f from compact hausdorff spaces to a suitable target category mathsf c can be applied directly to these geometric objects to automatically yield an extension tilde f acting on all unital c algebras this procedure is used to give a novel formulation of the operator k0 functor via a finitary variant tilde k f of the extension tilde k of the topological k functor we then delineate a c algebraic conjecture that the extension of the functor that assigns to a topological space its lattice of open sets assigns to a unital c algebra the zariski topological lattice of its primitive ideal spectrum i e its lattice of closed two sided ideals we prove the von neumann algebraic analogue of this conjecture

influence analysis of generalized least squares estimators abstract influence analysis and leverage analysis are important and well established adjuncts to ordinary least squares ols regression but analogous regression diagnostics are not generally available for multivariate regression problems this article describes measures of influence and leverage for a generalized least squares gls estimator of the regression coefficients in a class of multivariate linear models for repeated measurements when the covariance matrix of the observation vectors is known the gls estimator can be expressed as an ols estimator calculated from transformed variables in this situation the multivariate regression diagnostics are directly related to the univariate measures when the covariance matrix is unknown however multistage estimation procedures are required we describe measures of influence and leverage for a three step estimator that uses the residuals from an initial ols regression to estimate the covariance matrix of the response vectors these diagnostics account

the multi form generalised gleason theorem arising from investigations of decoherence functionals in the histories approach to quantum mechanics the following result is given by the methods of 14 let a1 and a2 be von neumann algebras without type i2 direct summands and let p ej j 1 2 be their lattices of projections let m colon p a1 p a2 be a bounded quantum bi measure then there is a unique bounded bilinear functional m on a1 a2 which extends m in this note we use a different approach to establish a generalisation of this result to k fold vector valued quantum multi measures this tool is needed for further investigations of decoherence functionals in quantum theory

numerical simulation of a transport fragmentation coagulation model in this paper we deal with numerical analysis of a transport fragmentation coagulation equation with power fragmentation rates and separable coagulation kernels for numerical simulations the model is rewritten in a conservative form and semi discretized in space using a laguerre pseudo spectral method some error estimates are derived and efficiency of the numerical scheme is considered the paper is concluded with several computational examples

convergence analysis of sectional methods for solving breakage population balance equations ii the cell average technique this work presents the convergence of the cell average technique kumar et al in powder technol 179 205 228 2007 for solving breakage population balance equation similarly to our paper kumar and warnecke numerische math 2008 of this series we study convergence on four different types of meshes a second order convergence is proved for uniform locally uniform and non uniform smooth meshes finally the scheme is analyzed on random mesh and it is found that the scheme is only first order accurate nevertheless we obtain for locally uniform as well as for random mesh one order higher accuracy than the fixed pivot technique discussed by the authors in the first paper all mathematical observations of convergence analysis are also validated numerically and numerical results are compared with the results of the first part

active lattices determine aw algebras abstract we prove that operator algebras that have enough projections are completely determined by those projections their symmetries and the action of the latter on the former this includes all von neumann algebras and all aw algebras we introduce active lattices which are formed from these three ingredients more generally we prove that the category of aw algebras is equivalent to a full subcategory of active lattices crucial ingredients are an equivalence between the category of piecewise aw algebras and that of piecewise complete boolean algebras and a refinement of the piecewise algebra structure of an aw algebra that enables recovering its total structure

continental scale relationship between bankfull width and drainage area for single thread alluvial channels we explore the bankfull width wbf versus drainage area ada relationship across a range of climatic and geologic environments and ask 1 is the relationship between ln wbf and ln ada best described by a linear function and 2 can a reliable relationship be developed for predicting wbf with ada as the only independent variable the principal data set for this study was compiled from regional curve studies and other reports that represent 1018 sites 1 m wbf 110 m and 0 50 km2 ada 22 000 km2 in the continental united states two additional data sets were used for validation after dividing the data into small medium and large size basins which respectfully correspond to ada 4 95 km2 4 95 km2 ada 337 km2 and ada 337 km2 regression lines from each data set were compared using one way analysis of covariance ancova a second ancova was performed to determine if mean annual precipitation p is an extraneous factor in the wbf versus ada relationship the ancova results reveal that using ada alone does not yield a reliable wbf versus ada relationship that is applicable across a wide range of environments and that p is a significant extraneous factor in the relationship considering data for very small basins ada 0 49 km2 and very large basins ada 1 0 105 km2 we conclude that a two segment linear model is the most probable form of the ln wbf versus ln ada relationship this study provides useful information for building complex multivariate models for predicting wbf

quantum logics and convex geometry the main result is a representation theorem which shows that for a large class of quantum logics a quantum logic q is isomorphic to the lattice of projective faces in a suitable convex setk as an application we extend our earlier results 4 which subject to countability conditions gave a geometric characterization of those quantum logics which are isomorphic to the projection lattice of a von neumann algebra or aj b w algebra

stochastic equation of fragmentation and branching processes related to avalanches we give a stochastic model for the fragmentation phase of an avalanche we construct a fragmentation branching process related to the avalanches on the set of all fragmentation sizes introduced by bertoin a fractal property of this process is emphasized we also establish a specific stochastic differential equation of fragmentation it turns out that specific branching markov processes on finite configurations of particles with sizes bigger than a strictly positive threshold are convenient for describing the continuous time evolution of the number of the resulting fragments the results are obtained by combining analytic and probabilistic potential theoretical tools

measures on projections and physical states it is shown that a finitely additive measure on the projections of a von neumann algebra withouti2 andii1 summands is the restriction of a state a definition of a physical state is proposed and it is shown that such a physical state on a simplec algebra with unit is a state

bootstrapping improved estimators for linear regression models abstract since stein 1955 proved that the least squares ls estimator for the linear regression model is inadmissible and james and stein 1961 demonstrated a superior estimator under squared error loss a number of better estimators have been proposed one reason these estimators have not been used in empirical work is that it is difficult to derive their sampling distributions this study shows that nonparametric bootstrapping provides good estimates of the sampling distribution of mundlak s 1981 restricted principal components estimator and a new stein rule estimator which shrinks mundlak s towards ls a monte carlo study of the bootstrap is performed for a range of increasingly collinear designs with 100 observations and 10 regressors using a squared error loss function the stein rule estimator performed much better than ls over most of the designs the nonparametric bootstrap generated reasonable estimates of the estimator s risk as well as standard errors of the individual components

boundedness of completely additive measures with application to 2 local triple derivations we prove a jordan version of dorofeev s boundedness theorem for completely additive measures and use it to show that every not necessarily linear nor continuous 2 local triple derivation on a continuous jbw triple is a triple derivation 2 local triple derivations are well understood on von neumann algebras jbw triples which are properly defined in section i are intimately related to infinite dimensional holomorphy and include von neumann algebras as special cases in particular continuous jbw triples can be realized as subspaces of continuous von neumann algebras which are stable for the triple product xy z zy x and closed in the weak operator topology

measures on projections in w factors soit 7b a un facteur de von neumann fini agissant dans un espace de hilbert complexe et 7b l la logique de toutes les projections dans 7b a 7b l c note la mesure finie additive bornee sur 7b l si le type du facteur 7b a est different de i 2 alors il existe une fonctionnelle lineaire f 7b a c etendant

b h has a pure state that is not multiplicative on any masa assuming the continuum hypothesis we prove that h has a pure state whose restriction to any masa is not pure this resolves negatively old conjectures of kadison and singer and of anderson

isomorphisms of ordered structures of abelian c subalgebras of c algebras abstract the aim of this note is to study the interplay between the jordan structure of c algebra and the structure of its abelian c subalgebras let abel a be a system of unital c subalgebras of a unital c algebra a ordered by set theoretic inclusion we show that any order isomorphism abel a abel b can be uniquely written in the form c c s a i c s a where is a partially linear jordan isomorphism between self adjoint parts of unital c algebras a and b as a corollary we obtain that for certain class of c algebras including von neumann algebras ordered structure of abelian subalgebras completely determines the jordan structure the results extend hitherto known results for abelian c algebras and may be relevant to foundations of quantum theory

quasi states and quasi measures abstract it is shown that in general non linear quasi states will exist on c x where x is a compact hausdorff space we introduce the concept of a quasi measure in x and establish the connection between quasi states and quasi measures

the effect of estimating weights in weighted least squares abstract in weighted least squares it is typical that the weights are unknown and must be estimated most packages provide standard errors assuming that the weights are known this is fine for sufficiently large sample sizes but what about for small to moderate sample sizes the investigation of this article into the effect of estimating weights proceeds under the assumption typical in practice that one has a parametric model for the variance function in this context generalized least squares consists of a an initial estimate of the regression parameter b a method for estimating the variance function and c the number of iterations in reweighted least squares by means of expansions for the covariance it is shown that each of a c can matter in problems of small to moderate size a few conclusions may be of practical interest first estimated standard errors assuming that the weights are known can be too small in practice the investigation indicates that a simple bootstrap operation resul

automorphisms of hilbert space effect algebras abstract we consider bijections of the hilbert space effect algebra that preserve the algebraic structures in one direction and have some other properties it is shown that if e h e h is conditionally multiplicative and conditionally additive then is implemented by a unitary or antiunitary operator on h we also show that 2 local ortho order automorphisms on e h are of the same form if dim h 3

dye s theorem and gleason s theorem for aw algebras abstract we prove that any map between projection lattices of a w algebras a and b where a has no type i 2 direct summand that preserves orthocomplementation and suprema of arbitrary elements is a restriction of a normal jordan homomorphism between a and b this allows us to generalize dye s theorem from von neumann algebras to a w algebras we show that mackey gleason bunce wright theorem can be extended to homogeneous a w algebras of type i the interplay between dye s theorem and gleason s theorem is shown as an application we prove that jordan homomorphisms are commutatively determined another corollary says that jordan parts of a w algebras can be reconstructed from posets of their abelian subalgebras

interlacing families ii mixed characteristic polynomials and the kadison singer problem we use the method of interlacing polynomials introduced in our previous article to prove two theorems known to imply a positive solution to the kadison singer problem the rst is weaver s conjecture ks 2 which is known to imply kadison singer via a projection paving conjecture of akemann and anderson the second is a formulation due to casazza et al of anderson s original paving conjecture s for which we are able to compute explicit paving bounds the proof involves an analysis of the largest roots of a family of polynomials that we call the mixed characteristic polynomials of a collection of matrices

analysis of least absolute deviation summary we develop a unified l 1 based analysis of variance type method for testing linear hypotheses like the classical l2 based analysis of variance the method is coordinate free in the sense that it is invariant under any linear transformation of the covariates or regression parameters moreover it allows singular design matrices and heterogeneous error terms a simple approximation using stochastic perturbation is proposed to obtain cut offvalues for the resulting test statistics both test statistics and distributional approximations can be computed using standard linear programming an asymptotic theory is derived for the method special cases of one and multi way analysis of variance and analysis of covariance models are worked out in detail the main results of this paper can be extended to general quantile regression extensive simulations show that the method works well in practical settings the method is also applied to a dataset from general social surveys

numerical simulation and convergence analysis of a finite volume scheme for solving general breakage population balance equations this paper presents a finite volume scheme fvs for solving general breakage population balance equations bpbes in particular the number density based bpbe is transformed to the form of a mass conservation law then it becomes easy to apply the well known fvss that have an important property of mass conservation following kumar and warnecke for fixed pivot fp method 16 and cell average technique cat 15 the stability and the convergence analysis of the semi discretized fvs are studied unlike the cat and the fp method the fvs is second order consistent independently of the type of meshes we also observe that fvs gives second order convergence rate on four different types of uniform and non uniform meshes with non decreasing behavior of mesh width nevertheless one order better accuracy than the fp method is achieved on locally uniform meshes it is also noticed that on non uniform random meshes the fvs shows one order and two orders higher accuracy than the cat and the fp method respectively the mathematical results of convergence analysis are validated numerically by taking three test problems the numerical simulations are also compared with the results obtained by the cat and the fp method

from the discrete to the continuous coagulation fragmentation equations the connection between the discrete and the continuous coagulation fragmentation models is investigated a weak stability principle relying on a priori estimates and weak compactness in l 1 is developed for the continuous model we approximate the continuous model by a sequence of discrete models and writing the discrete models as modified continuous ones we prove the convergence of the latter towards the former with the help of the above mentioned stability principle another application of this stability principle is the convergence of an explicit time and size discretization of the continuous coagulation fragmentation model

transition probabilities of normal states determine the jordan structure of a quantum system let x1d516 m1 x1d516 m2 be a bijection not assumed affine nor continuous between the sets of normal states of two quantum systems modelled on the self adjoint parts of von neumann algebras m1 and m2 respectively this paper concerns with the situation when preserves or partially preserves one of the following three notions of transition probability on the normal state spaces the transition probability pu introduced by uhlmann rep math phys 9 273 279 1976 the transition probability pr introduced by raggio lett math phys 6 233 236 1982 and an asymmetric transition probability p0 as introduced in this article it is shown that the two systems are isomorphic i e m1 and m2 are jordan isomorphic if preserves all pairs with zero uhlmann respectively raggio or asymmetric transition probability in the sense that for any normal states and we have p 0 if and only if p 0 where p stands for pu respectively pr or p0 furthermore as an extension of wi

bootstrap standard error estimates for linear regression standard errors of parameter estimates are widely used in empirical work the bootstrap often can provide a convenient means of estimating standard errors the conditions under which bootstrap standard error estimates are theoretically justified have not received much attention however this article establishes conditions for the consistency of the moving blocks bootstrap estimators of the variance of the least squares estimator in linear dynamic models with dependent data we discuss several applications of this result in particular the use of bootstrap standard error estimates for bootstrapping studentized statistics a simulation study shows that inference based on bootstrap standard error estimates may be considerably more accurate in small samples than inference based on closed form asymptotic estimates

continuous quasi states on c algebras a quasi state on d is a positive quasi linear functional p on d that satisfies the normalization condition sup p a ia e d a 0 ia i 1 1 if d is unital with unit 1 this is equivalent to the condition p l 1 in this paper we are concerned with the question of when positive quasilinear functionals on c algebras are linear in view of the condition iii and since positive quasi linear functionals are scalar multiples of quasistates this reduces to the question of additivity of quasi states on the self adjoint elements of a c algebra this question and its various forms depending both on the nature of quasi states and on the structure of the underlying algebra were considered before 1 3 4 6 7 9 13 17 181 substantial progress had been made in a number of cases one of the most remarkable advances was the pioneering work of gleason 6 in which the question was settled in the allirmative for quasistates on b x the algebra of all bounded operators acting on a hilbert space 2 with the property of being completely additive on orthogonal projections provided the dimension of y is different from 2 in the twodimensional case the answer is in general negative one can construct discontinuous quasi states by simple geometrical arguments so that one cannot expect all quase states to be linear on c algebras that admit two dimensional irreducible representations following gleason s result contributions to the problem were made by aarnes l and gunson 7 and in recent years the general problem for von neumann algebras was 111

wigner type theorem on transition probability preserving maps in semifinite factors abstract the wigner s theorem which is one of the cornerstones of the mathematical formulation of quantum mechanics asserts that every symmetry of quantum system is unitary or anti unitary this classical result was first given by wigner in 1931 thereafter it has been proved and generalized in various ways by many authors recently g p geher extended wigner s and molnar s theorems and characterized the transformations on the grassmann space of all rank n projections which preserve the transition probability the aim of this paper is to provide a new approach to describe the general form of the transition probability preserving not necessarily bijective maps between grassmann spaces as a byproduct we are able to generalize the results of molnar and g p geher

jauch piron states in w algebraic quantum mechanics a state on a w algebra m is said to fulfill the jauch piron condition if p q 1 for projections p q m implies p q 1 here p q denotes the infimum of p and q in the projection lattice of m the jauch piron condition is a compatibility condition between the algebraic and the lattice theoretic approach for the description of physical systems normal i e weakly continuous states always fulfill the jauch piron condition it is argued that states not fulfilling this condition should be regarded as unphysical it is shown that a state on a finite factor m is singular if and only if projections e f m exist such that e f 1 and e f 0 in particular any pure state on m fulfilling the jauch piron condition is normal which implies that the underlying factor m is of type i furthermore the following result is proved let be a pure jauch piron state on w algebra m with separable predual and without any commutative summand then is normal and a central projection z0 m exists such

weak 2 local derivations on b h are linear derivations abstract we prove that for every separable complex hilbert space h every weak 2 local derivation on b h is a linear derivation we also establish that every non necessarily linear nor continuous weak 2 local derivation on a finite dimensional c algebra is a linear derivation

jackknife bootstrap and other resampling methods in regression analysis motivated by a representation for the least squares estimator we propose a class of weighted jackknife variance estimators for the least squares estimator by deleting any fixed number of observations at a time they are unbiased for homoscedastic errors and a special case the delete one jackknife is almost unbiased for heteroscedastic errors the method is extended to cover nonlinear parameters regression m estimators nonlinear regression and generalized linear models interval estimators can be constructed from the jackknife histogram three bootstrap methods are considered two are shown to give biased variance estimators and one does not have the bias robustness property enjoyed by the weighted delete one jackknife a general method for resampling residuals is proposed it gives variance estimators that are bias robust several bias reducing estimators are proposed some simulation results are reported

s map and tracial states the notion of s map introduced in quantum logics to define conditional expectations for non compatible events is studied in projection lattices of von neumann algebras it is shown that every tracial state gives rise to an s map and conversely every s map defines a tracial state

the mackey gleason problem let a be a von neumann algebra with no direct summand of type i 2 and let p a be its lattice of projections let x be a banach space let m p a x be a bounded function such that m p q m p m q whenever p and q are orthogonal projections the main theorem states that m has a unique extension to a bounded linear operator from a to x in particular each bounded complex valued finitely additive quantum measure on p a has a unique extension to a bounded linear functional on a

physical symmetries of quantum histories gell mann and hartle have proposed a significant generalisation of quantum theory in which decoherence functionals play a key role physical symmetries of quantum history systems are shown under mild physical assumptions to correspond to isometric jordan automorphisms of the underlying von neumann algebra unitary representations of groups of symmetries of quadratic forms over operator algebras are discussed and related to symmetries of decoherence functionals

on peak phenomena for non commutative h a non commutative extension of amar and lederer s peak set result is given as its simple applications it is shown that any non commutative h algebra h m has unique predual and moreover some restriction in some of the results of blecher and labuschagne are removed making them hold in full generality

smoothing spline models for the analysis of nested and crossed samples of curves abstract we introduce a class of models for an additive decomposition of groups of curves stratified by crossed and nested factors generalizing smoothing splines to such samples by associating them with a corresponding mixed effects model the models are also useful for imputation of missing data and exploratory analysis of variance we prove that the best linear unbiased predictors blups from the extended mixed effects model correspond to solutions of a generalized penalized regression where smoothing parameters are directly related to variance components and we show that these solutions are natural cubic splines the model parameters are estimated using a highly efficient implementation of the em algorithm for restricted maximum likelihood reml estimation based on a preliminary eigenvector decomposition variability of computed estimates can be assessed with asymptotic techniques or with a novel hierarchical bootstrap resampling scheme for nested mixed effects models our methods are applied to me

some multiplicative preservers on b h abstract in this paper we describe the form of those continuous multiplicative maps on b h h being a separable complex hilbert space of dimension not less than 3 which preserve the rank or the corank furthermore we characterize those continuous presup semigroup endomorphisms of b h which are spectrum non increasing

a generalization of wigner s unitary antiunitary theorem to hilbert modules let h be a hilbert c module over a matrix algebra a it is proved that any function t h h which preserves the absolute value of the generalized inner product is of the form tf f uf f h where is a phase function and u is an a linear isometry the result gives a natural extension of wigner s classical unitary antiunitary theorem for hilbert modules

the bootstrap and identification of prognostic factors via cox s proportional hazards regression model this paper describes the use of the bootstrap 1 2 a new computer based statistical methodology to help validate a regression model resulting from the fitting of cox s proportional hazards model3 to a set of censored survival data as an example we define a prognostic model for outcome in childhood acute lymphocytic leukemia with the cox model and use of a training set of 224 patients to validate the accuracy of the model we use a bootstrap resampling technique to mimic the population under study in two stages first we select the important prognostic factors via a stepwise regression procedure with 100 bootstrap samples secondly we estimate the corresponding regression parameters for these important factors with 400 bootstrap samples the bootstrap result suggests that the model constructed from the training set is reasonable

pseudospectral laguerre approximation of transport fragmentation equations we develop a laguerre type pseudo spectral scheme for solving transport fragmentation equations the method converges rapidly for certain type of fragmentation problems and works under mild restrictions on the growth rate of the coefficients of the equation rigorous stability and convergence analyses are provided numerical simulations illustrate the performance of the scheme

quantum measurable cardinals abstract we investigate states on von neumann algebras which are not normal but enjoy various forms of infinite additivity and show that these exist on b h if and only if the cardinality of an orthonormal basis of h satisfies various large cardinal conditions for instance there is a singular countably additive pure state on b l 2 if and only if is ulam measurable and there is a singular additive pure state on b l 2 if and only if is measurable the proofs make use of farah and weaver s theory of quantum filters 12 we can generalize some of these characterizations to arbitrary von neumann algebras applications to ueda s peak set theorem for von neumann algebras are discussed in the final section

quantum measures and states on jordan algebras a problem of mackey for von neumann algebras has been settled by the conjunction of the early work of gleason and the recent advances of christensen and yeadon we show that mackey s conjecture holds in much greater generality leta be a jbw algebra and letl be the lattice of all projections ina a quantum measure onl is a countably additive map m froml into the real numbers our results imply thatm always has a unique extension to a bounded linear functional ona provided thata has no typei2 direct summand

flexible functional forms and global curvature conditions empirically estimated flexible functional forms frequently fail to satisfy the appropriate theoretical curvature conditions lau and gallant and golub have worked out methods for imposing the appropriate curvature conditions locally but those local techniques frequently fail to yield satisfactory results we develop two methods for imposing curvature conditions globally in the context of cost function estimation the first method adopts lau s technique to a generalization of a functional form first proposed by mcfadden using this generalized mcfadden functional form it turns out that imposing the appropriate curvature conditions at one data point imposes the conditions globally the second method adopts a technique used by mcfadden and barnett which is based on the fact that a non negative sum of concave functions will be concave our various suggested techniques are illustrated using the u s manufacturing data utilized by berndt and khaled

joint system quantum descriptions arising from local quantumness bipartite correlations generated by non signalling physical systems that admit a finite dimensional local quantum description cannot exceed the quantum limits i e they can always be interpreted as distant measurements of a bipartite quantum state here we consider the effect of dropping the assumption of finite dimensionality remarkably we find that the same result holds provided that we relax the tensor structure of space like separated measurements to mere commutativity we argue why an extension of this result to tensor representations seems unlikely