a simple flexible and effective covariate adaptive treatment allocation procedure we present a method for allocating treatment when subjects arrive in sequence based on the theory of propensity scores more commonly used in observational studies the method balances both discrete and continuous covariates without assuming a model for the outcome although we allow for a number of possible specifications we explore some specific instances in depth the proposed method is compared with previously suggested sequential randomization and allocation procedures with relationships to some well known methods highlighted through simulations the deterministic version is shown to achieve both covariate balance and near optimum efficiency with minimal assumptions we also investigate the properties of selected randomized versions with respect to both optimality and selection bias we conclude with an application to a pilot study on weight loss the proposed method is shown to be robust to the number of covariates balanced and the marginal and joint distributions of those covariates

differential geometry palatini gravity and reduction the present article deals with a formulation of the so called vacuum palatini gravity as a general variational principle in order to accomplish this goal some geometrical tools related to the geometry of the bundle of connections of the frame bundle lm are used a generalization of lagrange poincare reduction scheme to these types of variational problems allows us to relate it with the einstein hilbert variational problem relations with some other variational problems for gravity found in the literature are discussed

semidirect products and reduction in mechanics this paper shows how to reduce a hamiltonian system on the cotangent bundle of a lie group to a hamiltonian system in the dual of the lie algebra of a semidirect product the procedure simplifies unifies and extends work of greene guillemin holm holmes kupershmidt marsden morrison ratiu sternberg and others the heavy top compressible fluids magnetohydrodynamics elasticity the maxwell vlasov equations and multifluid plasmas are presented as examples starting with lagrangian variables our method explains in a direct way why semidirect products occur so frequently in examples it also provides a framework for the systematic introduction of clebsch or canonical variables

the lie poisson structure of integrable classical non linear sigma models the canonical structure of classical non linear sigma models on riemannian symmetric spaces which constitute the most general class of classical non linear sigma models known to be integrable is shown to be governed by a fundamental poisson bracket relation that fits into ther s matrix formalism for non ultralocal integrable models first discussed by maillet the matricesr ands are computed explicitly and being field dependent satisfy fundamental poisson bracket relations of their own which can be expressed in terms of a new numerical matrixc it is proposed that all these poisson brackets taken together are representation conditions for a new kind of algebra which for this class of models replaces the classical yang baxter algebra governing the canonical structure of ultralocal models the poisson brackets for the transition matrices are also computed and the notorious regularization problem associated with the definition of the poisson brackets for the monodromy matrices is discussed

using mixed integer programming for matching in an observational study of kidney failure after surgery this article presents a new method for optimal matching in observational studies based on mixed integer programming unlike widely used matching methods based on network algorithms which attempt to achieve covariate balance by minimizing the total sum of distances between treated units and matched controls this new method achieves covariate balance directly either by minimizing both the total sum of distances and a weighted sum of specific measures of covariate imbalance or by minimizing the total sum of distances while constraining the measures of imbalance to be less than or equal to certain tolerances the inclusion of these extra terms in the objective function or the use of these additional constraints explicitly optimizes or constrains the criteria that will be used to evaluate the quality of the match for example the method minimizes or constrains differences in univariate moments such as means variances and skewness differences in multivariate moments such as correlations between covari

hamiltonian formulation of the kdv equation we consider the canonical formulation of whitham s variational principle for the kdv equation this lagrangian is degenerate and we have found it necessary to use dirac s theory of constrained systems in constructing the hamiltonian earlier discussions of the hamiltonian structure of the kdv equation were based on various different decompositions of the field which is avoided by this new approach

optimum biased coin designs for sequential treatment allocation with covariate information randomized optimum designs of biased coin type are compared with other strategies for the sequential allocation of two or more treatments in a clinical trial the emphasis is on the variance of estimated treatment contrasts this variance which depends on the design strategy employed may be interpreted as the number of patients on whom information is lost simulations provide clear plots of the evolution of this loss during the course of the clinical trial

finite sample properties and asymptotic efficiency of monte carlo tests on donne une approche unifiee qui couvre le cas d une distribution nulle arbitraire afin d etudier les proprietes statistiques des tests de monte carlo

covariate imbalance and random allocation in clinical trials a model is developed to estimate the effect of covariate imbalance on the size of a test of treatment efficacy in randomized clinical trials comparing two treatments when dispersion parameters are known it is concluded that tests of homogeneity on the covariates should not be performed that covariate imbalance is just as much a problem for large studies as for small ones in terms of effect on size and that the effect of correlation between covariates and measures of efficacy is more complex than has previously been suggested the best way to adjust for covariate imbalance is by an analysis of covariance

randomization matching and propensity scores in the design and analysis of experimental studies with measured baseline covariates in many experimental situations researchers have information on a number of covariates prior to randomization this information can be used to balance treatment assignment with respect to these covariates as well as in the analysis of the outcome data in this paper we investigate the use of propensity scores in both of these roles we also introduce a randomization procedure in which the balance of all measured covariates is approximately indexed by the variance of the empirical propensity scores and randomization is restricted to those permutations with the least variable propensity scores this procedure is compared with recently proposed methods in terms of resulting covariate balance and estimation efficiency properties of the estimators resulting from each procedure are compared with estimates which incorporate the propensity score in the analysis stage simulation results show that analytical adjustment for the propensity score yields results on par with those obtained through restricted randomization procedures and can be used in conjunction with such procedures to further improve inferential efficiency

stratification and weighting via the propensity score in estimation of causal treatment effects a comparative study estimation of treatment effects with causal interpretation from observational data is complicated because exposure to treatment may be confounded with subject characteristics the propensity score the probability of treatment exposure conditional on covariates is the basis for two approaches to adjusting for confounding methods based on stratification of observations by quantiles of estimated propensity scores and methods based on weighting observations by the inverse of estimated propensity scores we review popular versions of these approaches and related methods offering improved precision describe theoretical properties and highlight their implications for practice and present extensive comparisons of performance that provide guidance for practical use

non realizability and ending laminations proof of the density conjecture we give a complete proof of the bers sullivan thurston density conjecture in the light of the ending lamination theorem it suffices to prove that any collection of possible ending invariants is realized by some algebraic limit of geometrically finite hyperbolic manifolds the ending invariants are either riemann surfaces or filling laminations supporting masur domain measured laminations and satisfying some mild additional conditions with any set of ending invariants we associate a sequence of geometrically finite hyperbolic manifolds and prove that this sequence has a convergent subsequence we derive the necessary compactness theorem combining the rips machine with non existence results for certain small actions on real trees of free products of surface groups and free groups we prove then that the obtained algebraic limit has the desired conformal boundaries and the property that none of the filling laminations is realized by a pleated surface in order to be able to apply the ending lamination theorem we have to prove that this algebraic limit has the desired topological type and that these non realized laminations are ending laminations that this is the case is the main novel technical result of this paper loosely speaking we show that a filling masur domain lamination which is not realized is an ending lamination

matching on the fly sequential allocation with higher power and efficiency we propose a dynamic allocation procedure that increases power and efficiency when measuring an average treatment effect in fixed sample randomized trials with sequential allocation subjects arrive iteratively and are either randomized or paired via a matching criterion to a previously randomized subject and administered the alternate treatment we develop estimators for the average treatment effect that combine information from both the matched pairs and unmatched subjects as well as an exact test simulations illustrate the method s higher efficiency and power over several competing allocation procedures in both simulations and in data from a clinical trial

on neoclassical schottky groups the goal of this paper is to describe a theoretical construction of an infinite collection of non classical schottky groups we first show that there are infinitely many non classical noded schottky groups on the boundary of schottky space and we show that infinitely many of these are sufficiently complicated we then show that every schottky group in an appropriately defined relative conical neighborhood of any sufficiently complicated noded schottky group is necessarily non classical finally we construct two examples the first is a noded riemann surface of genus 3 that cannot be uniformized by any neoclassical schottky group i e classical noded schottky group the second is an explicit example of a sufficiently complicated noded schottky group in genus 3

the geometry of the bundle of connections a generalized symplectic structure on the bundle of connections p colon c p rightarrow m of an arbitrary principal g bundle pi colon p rightarrow m is defined by means of a p ast mathrm ad p valued differential 2 form omega 2 on c p which is related to the generalized contact structure on j 1 p the hamiltonian properties of omega 2 are also analyzed

harmonic maps into lie groups classical solutions of the chiral model on considere deux aspects de la structure algebrique de 7b m l espace des applications harmoniques d un domaine a 2 dimensions simplement connexe dans un groupe de lie reel g r la forme reelle d un groupe complexe g on construit une representation du groupe boucle 7b a s 1 g r sur 7b m correspondant a l algebre de lie de kacmoody des deformations infinitesimales on decrit l action sur 7b m et l action d un sous groupe sur l espace des applications harmoniques dans des gaussmanniens dans une seconde partie on se restreint a une theorie qui s applique seulement quand est un domaine riemannien a 2 dimensions simplement connexe et le groupe est g r u n

euler poincare reduction for discrete field theories in this note we develop a theory of euler poincare reduction for discrete lagrangian field theories we introduce the concept of euler poincare equations for discrete field theories as well as a natural extension of the moser veselov scheme and show that both are equivalent the resulting discrete field equations are interpreted in terms of discrete differential geometry an application to the theory of discrete harmonic mappings is also briefly discussed

estimation of propensity scores using generalized additive models propensity score matching is often used in observational studies to create treatment and control groups with similar distributions of observed covariates typically propensity scores are estimated using logistic regressions that assume linearity between the logistic link and the predictors we evaluate the use of generalized additive models gams for estimating propensity scores we compare logistic regressions and gams in terms of balancing covariates using simulation studies with artificial and genuine data we find that when the distributions of covariates in the treatment and control groups overlap sufficiently using gams can improve overall covariate balance especially for higher order moments of distributions when the distributions in the two groups overlap insufficiently gam more clearly reveals this fact than logistic regression does we also demonstrate via simulation that matching with gams can result in larger reductions in bias when estimating treatment effects than matching with logistic regression

reduction of polysymplectic manifolds the aim of this paper is to generalize the classical marsden weinstein reduction procedure for symplectic manifolds to polysymplectic manifolds in order to obtain quotient manifolds which inherit the polysymplectic structure this generalization allows us to reduce polysymplectic hamiltonian systems with symmetries such as those appearing in certain kinds of classical field theories as an application of this technique an analogue to the kirillov kostant souriau theorem for polysymplectic manifolds is obtained and some other mathematical examples are also analyzed our procedure corrects some mistakes and inaccuracies in previous papers gunther 1987 j differ geom 25 23 53 munteanu et al 2004 j math phys 45 1730 51 on this subject

su n and so n invariant chiral fields one and two dimensional subspaces applying the harmonic map ansatz we find new classes of su n and so n chiral fields we write the corresponding one dimensional subgroups of su n and so n chiral fields in terms of one and two harmonic maps and the corresponding two dimensional subgroups in terms of su 2 and so 3 chiral fields in other words we reduce the su n and so n chiral equations to harmonic maps in one and two dimensional spaces

rerandomization to improve covariate balance in experiments randomized experiments are the gold standard for estimating causal effects yet often in practice chance imbalances exist in covariate distributions between treatment groups if covariate data are available before units are exposed to treatments these chance imbalances can be mitigated by first checking covariate balance before the physical experiment takes place provided a precise definition of imbalance has been specified in advance unbalanced randomizations can be discarded followed by a rerandomization and this process can continue until a randomization yielding balance according to the definition is achieved by improving covariate balance rerandomization provides more precise and trustworthy estimates of treatment effects

k symplectic formalism on lie algebroids in this paper we introduce a geometric description of lagrangian and hamiltonian classical field theories on lie algebroids in the framework of k symplectic geometry we discuss the relation between the lagrangian and hamiltonian descriptions through a convenient notion of legendre transformation the theory is a natural generalization of the standard one in addition other interesting examples are studied in particular systems with symmetry and poisson sigma models

stratification for the propensity score compared with linear regression techniques to assess the effect of treatment or exposure stratifying and matching by the propensity score are increasingly popular approaches to deal with confounding in medical studies investigating effects of a treatment or exposure a more traditional alternative technique is the direct adjustment for confounding in regression models this paper discusses fundamental differences between the two approaches with a focus on linear regression and propensity score stratification and identifies points to be considered for an adequate comparison the treatment estimators are examined for unbiasedness and efficiency this is illustrated in an application to real data and supplemented by an investigation on properties of the estimators for a range of underlying linear models we demonstrate that in specific circumstances the propensity score estimator is identical to the effect estimated from a full linear model even if it is built on coarser covariate strata than the linear model as a consequence the coarsening property of the propensity score adjustment for a one dimensional confounder instead of a high dimensional covariate may be viewed as a way to implement a pre specified richly parametrized linear model we conclude that the propensity score estimator inherits the potential for overfitting and that care should be taken to restrict covariates to those relevant for outcome

constrained randomization in a therapeutic efficacy trial the use of valid constrained randomization is presented for a therapeutic efficacy trial the construction and evaluation of randomization schemes are studied for two treatment replicates per block and for hypothesized linear gradients two different isomorphism classes of designs are compared using the variance of the mean squared error criterion the results indicate that valid constrained randomization schemes can be constructed that are superior to ordinary randomization a mastitis efficacy trial provided the specific problem to be solved

the central role of the propensity score in observational studies for causal effects abstract the results of observational studies are often disputed because of nonrandom treatment assignment for example patients at greater risk may be overrepresented in some treatment group this paper discusses the central role of propensity scores and balancing scores in the analysis of observational studies the propensity score is the estimated conditional probability of assignment to a particular treatment given a vector of observed covariates both large and small sample theory show that adjustment for the scalar propensity score is sufficient to remove bias due to all observed covariates applications include matched sampling on the univariate propensity score which is equal percent bias reducing under more general conditions than required for discriminant matching multivariate adjustment by subclassification on balancing scores where the same subclasses are used to estimate treatment effects for all outcome variables and in all subpopulations and visual representation of multivariate adjustment by a two dimensional plot author

on the geometry of spontaneous symmetry breaking given a principal bundle p x with a structure group g and an associated higgs bundle with a standard fiber g h the case of a matter bundle e whose standard fiber admits action only of an exact symmetry subgroup h of g is examined in the presence of a fixed higgs field x matter fields are represented by sections of a matter bundle eh associated with the corresponding reduced subbundle ph of p the totality of matter fields and higgs fields is described by sections of the bundle e which is the composite bundle eh x where eh is the bundle associated with the principal h bundle p the bundle e fails to be associated with a principal bundle to construct a connection e j1e on e the canonical jet bundle morphism j1eh j1 j1e is used

reduced classical field theories k cosymplectic formalism on lie algebroids in this paper we introduce a geometric description of lagrangian and hamiltonian classical field theories on lie algebroids in the framework of k cosymplectic geometry we discuss the relation between lagrangian and hamiltonian descriptions through a convenient notion of legendre transformation the theory is a natural generalization of the standard one in addition other interesting examples are studied mainly on reduction of classical field theories

classical field theory on lie algebroids variational aspects the variational formalism for classical field theories is extended to the setting of lie algebroids given a lagrangian function we study the problem of finding critical points of the action functional when we restrict the fields to being morphisms of lie algebroids in addition to the standard case our formalism includes as particular examples the case of systems with symmetry covariant euler poincare and lagrange poincare cases sigma models or chern simons theories

variance reduction in randomised trials by inverse probability weighting using the propensity score in individually randomised controlled trials adjustment for baseline characteristics is often undertaken to increase precision of the treatment effect estimate this is usually performed using covariate adjustment in outcome regression models an alternative method of adjustment is to use inverse probability of treatment weighting iptw on the basis of estimated propensity scores we calculate the large sample marginal variance of iptw estimators of the mean difference for continuous outcomes and risk difference risk ratio or odds ratio for binary outcomes we show that iptw adjustment always increases the precision of the treatment effect estimate for continuous outcomes we demonstrate that the iptw estimator has the same large sample marginal variance as the standard analysis of covariance estimator however ignoring the estimation of the propensity score in the calculation of the variance leads to the erroneous conclusion that the iptw treatment effect estimator has the same variance as an unadjusted estimator thus it is important to use a variance estimator that correctly takes into account the estimation of the propensity score the iptw approach has particular advantages when estimating risk differences or risk ratios in this case non convergence of covariate adjusted outcome regression models frequently occurs such problems can be circumvented by using the iptw adjustment approach 2013 the authors statistics in medicine published by john wiley sons ltd

optimum biased coin designs for sequential clinical trials with prognostic factors patients in a clinical trial arrive sequentially and are assigned to one of t treatments this assignment should maintain a balance between the numbers receiving each treatment yet should be sufficiently random to avoid any suspicion of conscious or unconscious cheating to balance these requirements efron 1971 introduced biased coin designs for the comparison of two treatments in which allocation of the treatment is determined probabilistically but with a bias towards the underrepresented treatment one disadvantage of efron s scheme is that it does not include balance over covariates or prognostic factors which may affect the response of the patient to the treatment biased coin schemes which do force balance over both treatments and prognostic factors are given by pocock simon 1975 and efron 1980 the properties of the designs have been elucidated by numerical studies and they are now being increasingly used in clinical trials reviews of the literature and discussions of the practical implications of the designs are given by pocock 1979 and simon 1979 however the designs suffer from the disadvantage that they rely on arbitrary functions to achieve the desired balance the procedures thus lack a firm theoretical framework an alternative approach in the presence of prognostic factors begg iglewicz 1980 uses optimum design theory to suggest a deterministic design criterion which is then modified for computational convenience in this paper i use optimum design theory to provide a procedure of the biased coin type for an arbitrary number of treatments in the presence or absence of prognostic factors this has the theoretical advantage of obviating dependence on a series of arbitrary functions the necessary optimum design theory is presented in 2 and in 3 applied to biased coin experiments the simplest case that of two treatments in the absence of prognostic factors is studied in 4 the extension to three or more treatments is in 5 followed in 6 by the allowance for prognostic factors although in the biased coin designs allocation of treatments is made probabilistically the results of the paper can be used for the sequential construction of da optimum designs in which randomization is not introduced by the experimenter all the designs mentioned so far are sequential but not adaptive in the useful distinction made by pericchi 1981 they are data dependent but not outcomedependent each allocation depends on the previous allocations and prognostic factors

confidence intervals from randomization tests an efficient method of constructing confidence intervals that correspond to randomization tests is described the method is based on the robbins monro search process and conducts a separate search for each endpoint of the confidence interval each search requires only slightly more permutations than the number needed for a randomization test diagnostics to monitor searches are suggested and the method is illustrated with examples

reduction in principal bundles covariant lagrange poincare equations a general reduction theory for field theoretical lagrangians on principal fiber bundles is presented the reduced variational problem as well as the associated equations are formulated the link between the solutions of the original problem and that of the reduced problem is discussed and an obstruction to the reconstruction of the solutions is isolated the important case of semidirect products is discussed in detail and several concrete examples are presented

symmetry reduction of variational bicomplexes and the principle of symmetric criticality consider a system of differential equations a 0 which is invariant under a lie group g of point transformations acting on the space e of independent and dependent variables by a method due to lie the g invariant solutions of these differential equations are found by solving a reduced system of differential equations a 0 on the space e of invariants of g in this paper we explore the relationship between the g invariant conservation laws and variational principles for the system of equations a 0 and the conservation laws and variational principles for the reduced equations a 0 this problem translates into one of constructing a certain cochain map qx between the g invariant variational bicomplex for the infinite jet space on e and the free variational bicomplex for e we prove that such a cochain map exists locally if and only if the relative lie algebra cohomology condition h f tooo 0 is satisfied where q is the orbit dimension of g r the lie algebra of vector fields on e which generate the infinitesimal action of g and toc o the linear isotropy subalgebra of t at eo as a simple consequence we prove that the vanishing of hq t tooo is the only local obstruction to palais principle of symmetric criticality 1 introduction when a system of partial differential equations is invari ant under a lie group g of point transformations one can construct a reduced system of partial or ordinary differential equations whose local solutions cor respond precisely to the local g invariant solutions of the original system of equations this simple and effective construction pioneered by lie himself is still one of the most powerful and extensively used techniques for finding exact solutions of many nonlinear partial differential equations 4 15 23 in this paper we explore the relationship between the g invariant conservation laws and variational principles for a system of partial differential equations and the con servation laws and variational principles of the reduced system of equations for the g invariant solutions since conservation laws and variational principles for differential equations are naturally represented by certain cohomology classes in the variational bicomplex associated to the given system of partial differential equations 1 22 our problem translates into that of constructing a cochain map between certain variational bicomplexes remarkably and contrary to the usual spirit of symmetry reduction these cochain maps do not always exist even lo cally we are able to completely classify the local obstructions to the existence of such cochain maps

the hamilton pontryagin principle and multi dirac structures for classical field theoriesa we introduce a variational principle for field theories referred to as the hamilton pontryagin principle and we show that the resulting field equations are the euler lagrange equations in implicit form second we introduce multi dirac structures as a graded analog of standard dirac structures and we show that the graph of a multisymplectic form determines a multi dirac structure we then discuss the role of multi dirac structures in field theory by showing that the implicit euler lagrange equations for fields obtained from the hamilton pontryagin principle can be described intrinsically using multi dirac structures finally we show a number of illustrative examples including time dependent mechanics nonlinear scalar fields maxwell s equations and elastostatics

optimal a priori balance in the design of controlled experiments summary we develop a unified theory of designs for controlled experiments that balance baseline covariates a priori before treatment and before randomization using the framework of minimax variance and a new method called kernel allocation we show that any notion of a priori balance must go hand in hand with a notion of structure since with no structure on the dependence of outcomes on baseline covariates complete randomization no special covariate balance is always minimax optimal restricting the structure of dependence either parametrically or non parametrically gives rise to certain covariate imbalance metrics and optimal designs this recovers many popular imbalance metrics and designs previously developed ad hoc including randomized block designs pairwise matched allocation and rerandomization we develop a new design method called kernel allocation based on the optimal design when structure is expressed by using kernels which can be parametric or non parametric relying on modern optimization methods kernel allocation which ensures nearly perfect covariate balance without biasing estimates under model misspecification offers sizable advantages in precision and power as demonstrated in a range of real and synthetic examples we provide strong theoretical guarantees on variance consistency and rates of convergence and develop special algorithms for design and hypothesis testing