robust model predictive control of constrained linear systems with bounded disturbances this paper provides a novel solution to the problem of robust model predictive control of constrained linear discrete time systems in the presence of bounded disturbances the optimal control problem that is solved online includes uniquely the initial state of the model employed in the problem as a decision variable the associated value function is zero in a disturbance invariant set that serves as the origin when bounded disturbances are present and permits a strong stability result namely robust exponential stability of the disturbance invariant set for the controlled system with bounded disturbances to be obtained the resultant online algorithm is a quadratic program of similar complexity to that required in conventional model predictive control

calculation of brs cohomology with spectral sequences a method for finding the general form of the brs cohomology spaceh for the various gauge and supersymmetry theories is presented the method is adapted for use in the space of integrated local polynomials of the gauge fields and ghosts with arbitrary numbers of fields and dervivatives the technique uses the hodge decomposition in a fock space with a euclidean inner product and combines this with spectral sequences to generate simple and soluble equations whose solutions span a simple spacee isomorphic to the complicated spaceh the technique is illustrated for pedagogic purposes by the detailed calculation of the ghost charge zero and one sectors ofh for yang mills theory with gauge groupso 32 in ten dimensions the method is appropriate for supersymmetric theories gravity supergravity and superstrings where higher order terms with many derivatives occur naturally in the effective action

estimators and tests in the analysis of multiple nonindependent 2 x 2 tables with partially missing observations we present methods for the analysis of a k variate binary measure for two independent groups where some observations may be incomplete as in the case of k repeated measures in a comparative trial for the k 2 x 2 tables let theta theta 1 theta k be a vector of association parameters where theta k is a measure of association that is a continuous function of the probabilities pi ik in each group i 1 2 k 1 k such as the log odds ratio or log relative risk the asymptotic distribution of the estimates theta theta 1 theta k is derived under the assumption that theta k theta for all k we describe the maximally efficient linear estimator theta of the common parameter theta tests of contrasts on the theta are presented which provide a test of homogeneity ha theta k theta l for all k not equal to l we then present maximally efficient tests of aggregate association hb theta theta 0 where theta 0 is a given value it is shown that the test of aggregate association hb is asymptotically independent of the preliminary test of homogeneity ha these methods generalize the efficient estimators of gart 1962 biometrics 18 601 610 and the cochran 1954 biometrics 10 417 451 mantel haenszel 1959 journal of the national cancer institute 22 719 748 and radhakrishna 1965 biometrics 21 86 98 tests to nonindependent tables the methods are illustrated with an analysis of repeated morphologic evaluations of liver biopsies obtained in the national cooperative gallstone study

equivariant symplectic geometry of gauge fixing in yang mills theory the faddeev popov gauge fixing in yang mills theory is interpreted as equivariant localization it is shown that the faddeev popov procedure amounts to a construction of a symplectic manifold with a hamiltonian group action the brst cohomology is shown to be equivalent to the equivariant cohomology based on this symplectic manifold with hamiltonian group action the ghost operator is interpreted as a pre symplectic form and the gauge condition as the moment map corresponding to the hamiltonian group action this results in the identification of the gauge fixing action as a closed equivariant form the sum of an equivariant symplectic form and a certain closed equivariant 4 form which ensures convergence an almost complex structure compatible with the symplectic form is constructed the equivariant localization principle is used to localize the path integrals onto the gauge slice the gribov problem is also discussed in the context of equivariant localization principle as a simple illustration of the

batalin vilkovisky formalism in the functional approach to classical field theory we develop the batalin vilkovisky formalism for classical field theory on generic globally hyperbolic spacetimes a crucial aspect of our treatment is the incorporation of the principle of local covariance which amounts to formulate the theory without reference to a distinguished spacetime in particular this allows a homological construction of the poisson algebra of observables in classical gravity our methods heavily rely on the differential geometry of configuration spaces of classical fields

batalin vilkovisky formalism in perturbative algebraic quantum field theory on the basis of a thorough discussion of the batalin vilkovisky formalism for classical field theory presented in our previous publication we construct in this paper the batalin vilkovisky complex in perturbatively renormalized quantum field theory the crucial technical ingredient is an extended notion of the renormalized time ordered product as a binary product equivalent to the pointwise product of classical field theory originally in causal perturbation theory the time ordered product is understood merely as a sequence of multilinear maps on the space of local functionals our extended notion of the renormalized time ordered product denoted by cdot mathcal t rm r is consistent with the old one and we found a subspace of the quantum algebra which is closed with respect to cdot mathcal t rm r on this space the renormalized batalin vilkovisky algebra is then the classical algebra but written in terms of the time ordered product together with an operator which replaces the ill defined graded laplacian of the unrenormalized theory we identify it with the anomaly term of the anomalous master ward identity of brennecke and dutsch contrary to other approaches we do not refer to the path integral formalism and do not need to use regularizations in intermediate steps

the batalin fradkin and vilkovisky formalism for higher order theories the generalized batalin fradkin and vilkovisky bfv formalism was developed as a method for determining the ghost structure for theories such as gravity and supergravity whose hamiltonian formalism has constraints not related to a lie algebra action previously the classical dynamical content of the bfv description of yang mills theory was investigated there it was found that this approach had a homological interpretation derived from the lie algebra cohomology of the gauge group which allowed one to understand the construction in terms of the dirac approach to constrained systems in this paper the dynamical consequences of the generalized bfv formalism are investigated it is found that even though one no longer has a lie algebra structure associated with the constraints one can still develop a homology theory that reproduces the dirac analysis and from which the generalized bfv formalism can be derived some of the consequences of this approach are discussed

estimation of a common effect parameter from sparse follow up data breslow 1981 biometrika 68 73 84 has shown that the mantel haenszel odds ratio is a consistent estimator of a common odds ratio in sparse stratifications for cohort studies however estimation of a common risk ratio or risk difference can be of greater interest under a binomial sparse data model the mantel haenszel risk ratio and risk difference estimators are consistent in sparse stratifications while the maximum likelihood and weighted least squares estimators are biased under poisson sparse data models the mantel haenszel and maximum likelihood rate ratio estimators have equal asymptotic variances under the null hypothesis and are consistent while the weighted least squares estimators are again biased similarly of the common rate difference estimators the weighted least squares estimators are biased while the estimator employing mantel haenszel weights is consistent in sparse data variance estimators that are consistent in both sparse data and large strata can be derived for all the mantel haenszel estimators

local anomalies and local equivariant cohomology the locality conditions for the vanishing of local anomalies in field theory are shown to admit a geometrical interpretation in terms of local equivariant cohomology this interpretation allows us to solve the problem proposed by singer in 31 and consists in defining an adequate notion of local cohomology to deal with the problem of locality in the geometrical approaches to the study of local anomalies based on the atiyah singer index theorem moreover using the relation between local cohomology and the cohomology of jet bundles studied in 19 we obtain necessary and sufficient conditions for the cancellation of local gravitational and mixed anomalies

correspondence robust stabilization of uncertain time varying discrete systems and comments on an improved approach for constrained robust model predictive control this paper addresses the robust stabilizability problem of linear discrete time systems with time varying polytopic uncertainties a state feedback control law is proposed based on the construction of a parameter dependent lyapunov function also it points out that the main results of cuzzola geromel and morari automatica 38 2002 1183 1189 are incorrect and presents the corrected version of these results

estimating a common relative risk application in equal employment abstract to analyze hiring data in equal employment cases the available positions should be stratified in accordance with the qualifications needed for the jobs it is then necessary to combine the results of each stratum to obtain an overall test of equal hiring rates furthermore a summary measure which compares the hiring rate of a minority applicant to that of a majority one is then estimated indeed the relative risk measure is used by the government in assessing an employment practice for possible discriminatory impact sometimes reliable data on the applicants is unavailable but an accurate estimate of the minority fraction i of qualified persons in the appropriate labor market is obtainable from census or other external data usually the number of hires t i in each occupation is small relative to the number of applicants which itself is a small fraction of the large external pool of qualified persons then the number of minority hires x i in each occupation can be regarded as a binom

output feedback robust mpc of uncertain norm bounded linear systems with disturbance the output feedback robust model predictive control mpc for the linear systems with norm bounded uncertainty and disturbance is studied a new state estimator is formulated where both estimator d

estimation for paired binomial data with application to radiation therapy we compare and contrast several different methods for estimating the effect of treatment when responses are paired binomial observations the ratio of binomial probabilities is the parameter of interest while the binomial probabilities are nuisance parameters which may vary between pairs the application is a meta analysis of the treatment of rectal cancer with observations in each study indicating the number of recurrences of the cancer in each of two groups one with radiation therapy and one without the ratio of the probabilities of recurrence in the radiation to non radiation groups is of substantive interest and is modelled as a logistic or complementary log log function of an unknown linear combination of the covariates the three methods we consider are maximum likelihood a bayesian approach and an approach based on estimating equations for the mle and bayesian approach the potentially large number of nuisance parameters are estimated together with the parameters of interest whereas for the estimating equation approach only the parameters of interest are estimated a simulation study is performed to compare the methods and evaluate the impact of overdispersion

robust constrained predictive control using comparison model this paper proposes a quadratic programming qp approach to robust model predictive control mpc for constrained linear systems having both model uncertainties and bounded disturbances to this end we construct an additional comparison model for worst case analysis based on a robust control lyapunov function rclf for the unconstrained system not necessarily an rclf in the presence of constraints this comparison model enables us to transform the given robust mpc problem into a nominal one without uncertain terms based on a terminal constraint obtained from the comparison model we derive a condition for initial states under which the ultimate boundedness of the closed loop is guaranteed without violating state and control constraints since this terminal condition is described by linear constraints the control optimization can be reduced to a qp problem

b r s algebras analysis of the consistency equations in gauge theory we compute all possible anomalous terms in quantum gauge theory in the natural class of polynomials of differential forms by using the appropriate cohomological and algebraic methods we do it for all dimensions of spacetime and all structure groups with reductive lie algebras

asymptotic efficiency of general noniterative estimators of common relative risk summary gart 1962 presented consistent and efficient estimators of the common relative risk for several 2 x 2 tables together with their associated confidence intervals a theorem on the asymptotic efficiency of general weighted noniterative point estimators is formulated and proved a modification of interval estimators based on log normality is given

higher order brst and anti brst operators and cohomology for compact lie algebras after defining cohomologically higher order brst and anti brst operators for a compact simple algebra g the associated higher order laplacians are introduced and the corresponding supersymmetry algebra is analyzed these operators act on the states generated by a set of fermionic ghost fields transforming under the adjoint representation in contrast with the standard case for which the laplacian is given by the quadratic casimir the higher order laplacians w are not in general given completely in terms of the casimir racah operators and may involve the ghost number operator the higher order version of the hodge decomposition is exhibited the example of su 3 is worked out in detail including the expression of its higher order laplacian w

cohomology in connection space family index theorem and abelian gauge structure using the natural connection form on a principal bundle p m g and the bundle a a g g a systematic derivation of the double cohomological series constituted by the exterior differential d on space time m and arbitrary horizontal and vertical variations in connection space is given the relationship between these cohomologies and the family index theorem is clarified the formalism is then used to analyze abelian gauge structure inside non abelian gauge theory the pertinent functional u 1 connection form curvature form and three form curvature are identified and computed and are related to the vacuum anomalous commutation relation and jacobi identity respectively some of the results differ from those obtained by wu and zee nucl phys b 258 157 1985 and niemi and semenoff phys rev lett 55 227 1985 and the results of this paperrecover theirs under certain conditions finally the generalization of the formalism to a nontrivial principal bundle by introduction of a fixed backg

universal connections gauge anomalies and lie group cohomology the geometric interpretation due to thierry mieg 1980 of the ghost field as certain components of an ehresmann connection on the total space of a principal bundle and of the brs transformation as part of the exterior derivative on the total space is discussed and amended to incorporate the spacetime dependence of the ghost field using this interpretation it is shown that non trivial solutions to the wess zumino consistency condition for gauge anomalies are related to non trivial de rham cohomology of the lie group

estimation of the hazards ratio in two grouped samples a simple estimator of the hazards ratio of two grouped samples is proposed if the number of time grouping intervals is fixed the following asymptotics hold unbiasedness and full efficiency when the true hazards ratio is 1 and the probability of failure in each interval is small under the latter condition the estimator is equivalent to mhp estimator mantel haenszel estimator for a poisson model simulations show that this estimator performs better than others when grouping is coarse an asymptotically unbiased estimator of its variance is proposed

on heterogeneity tests based on efficient scores summary for cases in which a parameter may be estimated from several independent data sets mather 1935 proposed a heterogeneity test based on the efficient scores for the individual data sets evaluated at the overall maximum likelihood estimator following fisher 1946 a modification of the heterogeneity score test is presented wherein a consistent but inefficient estimator of the parameter of interest is substituted for the overall maximum likelihood estimator the modified test is also derived using the c q theory of neyman 1959 using the modified procedure we derive a test for a common odds ratio in several 2 x 2 tables based on the mantel haenszel estimator

brs cohomology and topological anomalies the occurrence of non abelian anomalies in gauge theories and gravitation first discovered via perturbative techniques is now completely explained from the mathematical point of view by means of the family index theorem of atiyah and singer here we make contact between this approach and brs cohomology by showing that they yield the same non abelian anomalies provided a certain restriction to local functionals is not introduced from the very beginning in particular this solves the unicity problem for this kind of anomalies local brs cohomology is still relevant for the abelian case

robust constrained model predictive control using linear matrix inequalities abstract the primary disadvantage of current design techniques for model predictive control mpc is their inability to deal explicitly with plant model uncertainty in this paper we present a new approach for robust mpc synthesis that allows explicit incorporation of the description of plant uncertainty in the problem formulation the uncertainty is expressed in both the time and frequency domains the goal is to design at each time step a state feedback control law that minimizes a worst case infinite horizon objective function subject to constraints on the control input and plant output using standard techniques the problem of minimizing an upper bound on the worst case objective function subject to input and output constraints is reduced to a convex optimization involving linear matrix inequalities lmis it is shown that the feasible receding horizon state feedback control design robustly stabilizes the set of uncertain plants several extensions such as application to systems with time delays problems involving constant set point tracking trajectory tracking and disturbance rejection which follow naturally from our formulation are discussed the controller design is illustrated with two examples

asymptotic analysis of fundamental solutions of dirac operators on even dimensional euclidean spaces abstract we analyze the short distance asymptotic behavior of some quantities formed out of fundamental solutions of dirac operators minimally coupled to finite dimensional matrix valued gauge potentials on even dimensional euclidean spaces the analysis gives a mathematically rigorous proof as well as a mathematically self consistent description to the so called abelian chiral anomaly in quantum gauge field theories

a path integral for turbulence in incompressible fluids in this paper a classical path integral is formulated for incompressible fluids that evolve according to the navier stokes equation the path integral propagates probability distributions deterministically on the space gvol of solenoidal velocity fields we construct a set of isp 2 charges associated with the geometry of gvol and its poisson structure and a pair of supersymmetry charges connected with the hamiltonian these charges generate exact symmetries of the classical path integral when the viscosity is set equal to zero when the effect of dissipation is included the charges associated with the poisson structure and the hamiltonian are no longer conserved charges that generate kolmogorov scaling and galilean transformations are also constructed the classical path integral is formulated in terms of vorticity as well

cyclomonotonicity and stabilizability properties of solutions of the difference periodic riccati equation the kalman filter associated with a discrete time linear t periodic system is tested the problem considered is that of selecting an initial covariance matrix such that the periodic filter based on the first t values of the kalman filter gain is stabilizing sufficient conditions are given that hinge on the cyclomonotonicity of the solution of the periodic riccati equation potential applications are found in filter design quasi linearization techniques for the periodic riccati equation and the design of receding horizon control strategies for periodic and multirate systems when specialized to time invariant systems the results give rise to new sufficient conditions for the cyclomonotonicity of the solutions of the time invariant riccati equation and the existence of periodic stabilizing feedback

a class of asymptotically efficient noniterative estimators of a common odds ratio summary a new class of noniterative estimators of a common odds ratio is presented it is shown that the principle of construction leads to asymptotically optimal estimators that is estimators which are consistent asymptotically normally distributed and asymptotically efficient

receding horizon output feedback control for constrained uncertain systems using periodic invariance in this article we consider a receding horizon output feedback control rhoc method for linear discrete time systems with polytopic model uncertainties and input constraints first we derive a set of estimator gains and then we obtain on the basis of the periodic invariance a series of state feedback gains stabilising the augmented output feedback system with these estimator gains these procedures are formulated as linear matrix inequalities an rhoc strategy is proposed based on these state feedback and state estimator gains in conjunction with their corresponding periodically invariant sets the proposed rhoc strategy enhances the performance in comparison with the case in which static periodic gains are used and increases the size of the stabilisable region by introducing a degree of freedom to steer the augmented state into periodically invariant sets

gravitational anomalies and the family s index theorem we discuss the use of the family s index theorem in the study of gravitational anomalies the geometrical framework required to apply the family s index theorem is presented and the relation to gravitational anomalies is discussed we show how physics necessitates the introduction of the notion oflocal cohomology which is distinct from the ordinary topological cohomology the recent results of alvarez gaume and witten are derived by using the family s index theorem

a linear programming approach to constrained robust predictive control a receding horizon predictive control algorithm for systems with model uncertainty and input constraints is developed the proposed algorithm adopts the receding horizon dual mode i e free control moves and invariant set paradigm the approach is novel in that it provides a convenient way of combining predictions of control moves which are optimal in the sense of worst case performance with large target invariant sets thus the proposed algorithm has a large stabilizable set of states corresponding to a cautious state feedback law while enjoying the good performance of a tightly tuned but robust control law unlike earlier approaches which are based on qp or semidefinite programming here computational complexity is reduced through the use of lp

the anomaly structure of theories with external gravity the cohomology problem of the overall local symmetry group of theories with external gravity including diffeomorphisms local lorentz and gauge transformations is studied in order to determine all possible anomalies to this end the nontrivial cohomology classes of the coupled system of two coboundary operators are classified in the abstract using this result and a technical assumption the nontrivial cohomology classes of the coboundary operator associated with diffeomorphisms are determined these possible anomalies split in any dimension into two distinct families both are calculated the second only in four dimensions using known results about gauge and local lorentz anomalies the possible anomalies of the overall local symmetry group are determined

on the bundle of connections and the gauge orbit manifold in yang mills theory in an appropriate mathematical framework we supply a simple proof that the quotienting of the space of connections by the group of gauge transformations in yang mills theory is ac principal fibration the underlying quotient space the gauge orbit space is seen explicitly to be ac manifold modelled on a hilbert space

yang mills cohomology in four dimensions the local polynomial cohomology space of the yang mills brs operator in four dimensions is computed in order to simplify the analysis without omitting the physically interesting cases the investigation is limited to polynomials whose fadeev popov charge and uv naive dimensions have upper bounds furthermore the results are used to compute a la stora the local functional yang mills anomalies from which the uniqueness of the adler bardeen jackiw anomaly follows

the c algebra of bosonic strings we give a rigorous definition of witten sc string algebra to this end we present a new construction ofc algebras associated to special geometric situations kahler foliations and generalize this later construction to the string case through this we get a natural geometrical interpretation of the string of semi infinite forms as well as the fermionic algebra structure using the non commutative geometric concepts for investigating the string algebra we get a natural fredholm module representation of dimension 26

local brst cohomology in the antifield formalism ii application to yang mills theory yang mills models with compact gauge group coupled to matter fields are considered the general tools developed in a companion paper are applied to compute the local cohomology of the brst differentials modulo the exterior space time derivatived for all values of the ghost number in the space of polynomials in the fields the ghosts the antifields sources for the brst variations and their derivatives new solutions to the consistency conditionssa db 0 depending non trivially on the antifields are exhibited for a semi simple gauge group however these new solutions arise only at ghost number two or higher thus at ghost number zero or one the inclusion of the antifields does not bring in new solutions to the consistency conditionsa db 0 besides the already known ones the analysis does not use power counting and is purely cohomological it can be easily extended to more general actions containing higher derivatives of the curvature or chern simons terms

on exterior variational calculus exterior variational calculus is introduced through examples in field theory a very simple technique is provided to decide whether or not lagrangians exist for given sets of field equations and when they do to find them some applications are made to gauge and chiral fields

stability of periodically time varying systems this paper proposes a novel approach to stability analysis of discrete time nonlinear periodically time varying systems the contributions are as follows firstly a relaxation of standard lyapunov conditions is derived this leads to a less conservative lyapunov function that is required to decrease at each period rather than at each time instant secondly for linear periodic systems with constraints it is shown that compared to standard lyapunov theory the novel concept of periodic lyapunov functions allows for the calculation of a larger estimate of the region of attraction an example illustrates the effectiveness of the developed theory

geometrical structure of faddeev popov fields and invariance properties of gauge theories let pn be the trivial principal bundle with structural group g and base space pn 1 p1 being the usual fiber bundle of gauge theories in order to give a geometrical interpretation to the faddeev popov fields as well as to the becchi rouet and stora transformations we need to use the fiber bundle p3 the gauge fields and the faddeev popov ghost and antighost fields appear as part of certain 1 forms defined on the base space p2 the anticommuting character of the ghost and antighost fields is essentially due to their identification with 1 forms the becchi rouet and stora transformations are identified with generalized infinitesimal gauge transformations on p3 of parameters related to the ghost fields we obtain a further invariance of the action given by a similar generalized infinitesimal gauge transformation on p3 related to the antighost fields

on the asymptotic inefficiency of certain noniterative estimators of a common relative risk or odds ratio nurminen 1981 gives conditions for the asymptotic efficiency of general weighted mean estimators his application is a noniterative estimator of a common relative risk for binomial variates this summary estimator and by implication the mantel haenszel summary odds ratio estimator are asserted to be asymptotically efficient we examine conditions for the asymptotic efficiency in the unconditional sample space of the mantelhaenszel estimator for a common odds ratio the estimator of a common relative risk considered by nurminen and tarone s 1981 estimator of a common relative risk for binomial variables contrary to nurminen we find that except for a few degenerate cases these estimators are inefficient whenever the common odds ratio or common relative risk is not equal to 1

constrained robust feedback model predictive control for uncertain systems with polytopic description for the constrained uncertain systems with polytopic description a new design method of robust feedback model predictive control is proposed by using a sequence of feedback control laws and designing the parameter dependent lyapunov function for each model the design method provides more degrees of freedom and then can improve the control performance and enlarge the feasible region based on the characteristic property of the design method an offline design algorithm is developed to reduce the mpc controller s online computation burden the numerical examples verify the effectiveness of the results presented in this article

stabilizing tube based model predictive control terminal set and cost construction for lpv systems abstract this paper presents a stabilizing tube based mpc synthesis for lpv systems we employ terminal constraint sets which are required to be controlled periodically contractive periodically or finite step contractive sets are easier to compute and can be of lower complexity than true contractive ones lowering the required computational effort both off line and on line under certain assumptions on the tube parameterization recursive feasibility of the scheme is proven subsequently asymptotic stability of the origin is guaranteed through the construction of a suitable terminal cost based on a novel lyapunov like metric for compact convex sets containing the origin a periodic variant on the well known homothetic tube parameterization that satisfies the necessary assumptions and yields a tractable lpv mpc algorithm is derived the resulting mpc algorithm requires the on line solution of a single linear program with linear complexity in the prediction horizon the properties of the approach are demonstrated by a numerical example

technical communique extended invariance and its use in model predictive control the use of time invariant linear state feedback control laws for the definition of terminal invariant regions can be conservative thereby reducing the efficacy of predictive control in terms of size of stabilisable sets and closed loop performance this difficulty which is particularly pronounced in the case of nonlinear and or uncertain dynamics can be remedied through the use of time varying control laws and terminal invariant sets in existing mpc schemes however these have to be computed online thereby rendering implementation impracticable for anything other than low dimensional systems here the definition of invariance is extended to apply over n predicted control moves thereby enabling the use of pre determined offline time varying state feedback gains more importantly this extension allows for the use of local uncertainty or linear difference inclusion sets and thus affords significant improvements e g in terms of the size of terminal regions

brst anti brst and their geometry we continue the comparison between the field theoretical and geometrical approaches to the gauge field theories of various types by deriving their becchi rouet stora tyutin brst and anti brst transformation properties and comparing them with the geometrical properties of the bundles and gerbes in particular we provide the geometrical interpretation of the so called curci ferrari conditions that are invoked for the absolute anticommutativity of the brst and anti brst symmetry transformations in the context of non abelian one form gauge theories as well as the abelian gauge theory that incorporates a two form gauge field we also carry out the explicit construction of the three form gauge fields and compare it with the geometry of 2 gerbes

finite sample properties of some old and some new estimators of a common odds ratio from multiple 2 2 tables abstract a simulation study was used to determine the finite sample properties of various estimators of a common odds ratio from multiple 2 2 tables the maximum likelihood mantel haenszel and woolf estimators plus four variants of each were considered the original woolf estimator and one of its variants are dismissed on the grounds that they often cannot be calculated in terms of minimum bias maximum likelihood is the recommended procedure after adding 25 to each cell

likelihood ratio tests with three way tables likelihood ratio lr tests for association and for interaction are examined for three way contingency tables particularly the widely used 2 2 k table mutual information identities are used to characterize the information decomposition and the logical relationship between the omnibus lr test for conditional independence across k strata and its two independent components lr tests for interaction and for uniform association the latter two tests are logically connected to formulating a natural two step test for conditional independence the proposed two step test with reduced nominal levels is suggested instead of the breslow day test and the cochran mantel haenszel test this yields efficient interval estimation for both the interaction parameter and the common odds ratio compared with using the mantel haenszel estimate this allows the development of power analysis for testing general hypotheses of varied interactions using an invariant pythagorean law of relative entropy

approximate tests and interval estimation of the common relative risk in the combination of 2 2 tables consider i pairs of mutually independent binomial variates xoi and x1i with corresponding parameters poi and p1i and sample sizes noi and n1 where i 1 i we assume that the relative risk is constant that is b pt izpoi i 1 i further let qji 1 pji and we assume throughout that 0 pji qji 1 for i 1 i and j 0 1 we consider asymptotic results as noi s and n1j s become large but i is fixed extending the results of cochran 1954 for the common odds ratio radhakrishna 1965 derived an asymptotically efficient test of the hypothesis b 1 recently for i 1 koopman 1984 heuristically derived a useful approximate method for finding confidence limits for 0 in the present paper we use the methods of score statistics particularly as given by bartlett 1953a 1953b 1955 to derive for the general case the asymptotically efficient tests of b 1 and of its homogeneity over the i tables as well as approximate confidence limits for the common 0 the test of 0 1 is identical with that of radhakrishna and koopman s limits are a special case of these more general results thus this rather simple theory gives a coherent structured methodology for analysing ratios of binomial probabilities parallel to that usually employed for common odds ratios see for example gart 1970 1971

new formulation of the classical path integral with reparametrization invariance a classical path integral cpi provides a functional integral representation of the kernel which propagates phase space density distributions in this paper a new formulation of the cpi is developed in which time and energy are promoted to dynamical variables the reparametrization invariance inherent in this formalism is handled by means of the batalin fradkin vilkovisky method the path integral action possesses a set of isp 2 symmetries connected with reparametrization invariance and an additional set of isp 2 symmetries connected with the symplectic geometry of the extended phase space supersymmetry is also present in the cpi action this formulation of the cpi allows us to study the dependence on energy of the dynamical evolution of hamiltonian systems it naturally incorporates the constraints onto the energy surface a classical path integral cpi provides a functional integral representation of the kernel which propagates phase space density distributions in this paper a new formulation of the cpi is developed in which time and energy are promoted to dynamical variables the reparametrization invariance inherent in this formalism is handled by means of the batalin fradkin vilkovisky method the path integral action possesses a set of isp 2 symmetries connected with reparametrization invariance and an additional set of isp 2 symmetries connected with the symplectic geometry of the extended phase space supersymmetry is also present in the cpi action this formulation of the cpi allows us to study the dependence on energy of the dynamical evolution of hamiltonian systems it naturally incorporates the constraints onto the energy surface

lie algebra cohomology and group structure of gauge theories we explicitly construct the adjoint operator of coboundary operator and obtain the hodge decomposition theorem and the poincare duality for the lie algebra cohomology of the infinite dimensional gauge transformation group we show that the adjoint of the coboundary operator can be identified with the brst adjoint generator q for the lie algebra cohomology induced by brst generator q we also point out an interesting duality relation poincare duality with respect to gauge anomalies and wess zumino witten topological terms we consider the consistent embedding of the brst adjoint generator q into the relativistic phase space and identify the noncovariant symmetry recently discovered in qed with the brst adjoint nother charge q

the evaluation map in field theory sigma models and strings ii in this paper we examine specifically the role of the evaluation map in sigma models and strings we discuss the difference between sigma models and field theory as far as anomaly cancellation is concerned the introduction of the wess zumino terms in different sigma models is considered anomalies in string theory are discussed with special attention to the conformal anomalies and to the sigma model anomalies for the imbedded or immersed world sheet of the string conformal anomalies in two dimensions are connected to holomorphic and gravitational anomalies in order to have the cancellation of the sigma model anomalies of the string certain topological conditions must be satisfied by the ambient manifold the role of the evaluation map in the calculations of global anomalies is also discussed both for field theories and for sigma models in particular global anomalies are connected with the differential characters of cheeger and simons we show that the absence of global anomalies in sigma models is guaranteed by the absence of torsion in suitable homology groups of the target space

chiral anomalies and the generalised index theorem shows that the generalised atiyah singer index theorem 1968 describes not only the u 1 anomaly but also the non abelian anomaly these anomalies are determined in arbitrary even dimensions without ambiguity of coefficients the index theorem reveals new kinds of anomalies the relationship between these anomalies and the topology of yang mills fields is discussed

a jackknife estimator of a combined odds ratio a jackknife estimator of a common odds ratio is derived in the situation of stratified contingency tables it is based on pseudovalues that are constructed by omitting each single observation in each cell by means of monte carlo experiments this estimator is compared with the estimators of woolf mantel and haenszel and another jackknife estimator by breslow and liang of the common odds ratio in the situations considered this estimator has lower bias and mean squared error than the other three proposals the accompanying jackknife variance behaves in general similarly to the estimated variances of the woolf estimator and the mantel haenszel estimator

on the algebraic structure of covariant anomalies and covariant schwinger terms the algebraic structure of covariant anomalies and covariant schwinger terms in an anomalous yang mills theory is investigated a cohomological characterization is formulated and geometrically interpreted a new method of determining covariant anomalies and covariant schwinger terms based on the brs anti brs complex is presented

brst symmetries for the tangent gauge group for any principal bundle p one can consider the subspace of the space of connections on its tangent bundle tp given by the tangent bundle ta of the space of connections a on p the tangent gauge group acts freely on ta appropriate brst operators are introduced for quantum field theories that include as fields elements of ta as well as tangent vectors to the space of curvatures as the simplest application the brst symmetry of the so called bf yang mills theory is described and the relevant gauge fixing conditions are analyzed a brief account on the topological bf theories is also included and the relevant batalin vilkovisky operator is described

approximate interval estimation of the ratio of binomial parameters a review and corrections for skewness various methods for finding confidence intervals for the ratio of binomial parameters are reviewed and evaluated numerically it is found that the method based on likelihood scores koopman 1984 biometrics 40 513 517 miettinen and nurminen 1985 statistics in medicine 4 213 226 performs best in achieving the nominal confidence coefficient but it may distribute the tail probabilities quite disparately using general theory of bartlett 1953 biometrika 40 306 317 1955 biometrika 42 201 203 we correct this method for asymptotic skewness following gart 1985 biometrika 72 673 677 we extend this correction to the case of estimating the common ratio in a series of two by two tables computing algorithms are given and applied to numerical examples parallel methods for the odds ratio and the ratio of poisson parameters are noted

invariant sets techniques for youla kucera parameter synthesis this article addresses an invariant sets approach for youla kucera parameter synthesis using linear matrix inequality lmi techniques given a linear discrete time observer based system affected by bounded disturbances and constraints the proposed technique furnishes the best youla parameter in terms of finding an invariant ellipsoidal set satisfying the constraints and having the maximal ellipsoidal projection on the state space compared with the results obtained for an observer based design the synthesis of a youla parameter provides a larger ellipsoidal projection and an improved sensitivity function the price to pay for these achievements in terms of robustness is usually a slow closed loop performance with degraded complementary sensitivity function in order to obtain a compromise between robustness and performance two methods are proposed the first method imposes a new bound on the lyapunov function decreasing speed and the second refers to the pole placement concept the aforementioned appro

brief paper mpc of constrained discrete time linear periodic systems a framework for asynchronous control strong feasibility stability and optimality via periodic invariance state feedback model predictive control mpc of discrete time linear periodic systems with time dependent state and input dimensions is considered the states and inputs are subject to periodically time dependent hard convex polyhedral constraints first periodic controlled and positively invariant sets are characterized and a method to determine the maximum periodic controlled and positively invariant sets is derived the proposed periodic controlled invariant sets are then employed in the design of least restrictive strongly feasible reference tracking mpc problems the proposed periodic positively invariant sets are employed in combination with well known results on optimal unconstrained periodic linear quadratic regulation lqr to yield constrained periodic lqr control laws that are stabilizing and optimal one motivation for systems with time dependent dimensions is efficient control law synthesis for discrete time systems with asynchronous inputs for which a novel modeling framework resulting in low dimensional models is proposed the presented methods are applied to a multirate nano positioning system

some remarks on brs transformations anomalies and the cohomology of the lie algebra of the group of gauge transformations we show that ghosts in gauge theories can be interpreted as maurer cartan forms in the infinite dimensional group of gauge transformations we examine the cohomology of the lie algebra of and identify the coboundary operator with the brs operator we describe the anomalous terms encountered in the renormalization of gauge theories triangle anomalies as elements of these cohomology groups

algebraic characterization of gauge anomalies on a nontrivial bundle we discuss the algebraic way of solving the descent equations corresponding to the brst consistency condition for the gauge anomalies and the chern simons terms on a nontrivial bundle the method of decomposing the exterior space time derivative as a brst commutator is extended to the present case

a comparative study of conditional maximum likelihood estimation of a common odds ratio the finite sample properties of various point estimators of a common odds ratio from multiple 2 x 2 tables have been considered in a number of simulation studies however the conditional maximum likelihood estimator has received only limited attention that omission is partially rectified here for cases of relatively small numbers of tables and moderate to large within table sample sizes the conditional maximum likelihood estimator is found to be superior to the unconditional maximum likelihood estimator and equal or superior to the mantel haenszel estimator in both bias and precision

cohomology classes associated to anomalies one of the proposed settings for the description of anomalies in the setting of gauge field theories is a local bicomplex associated to a principal fiber bundle g p m it is a bigraded algebra with two differentials which is invariantly defined i e independent of local coordinates of m i denote it by s m briefly s m p q consists of local p multilinear operators from the gauge algebra into q forms on m which depend on a connection a in a local manner local means that the operators decrease supports the gauge algebra is the lie algebra of the gauge group which consists of diffeomorphisms of p that respect the action of g and cover the identity diffeomorphism of m

the asymptotic relative efficiency of the mantel haenszel estimator in the increasing number of strata case the asymptotic relative efficiency are of the mantel haenszel estimator of a common odds ratio at is determined for the case in which the number of strata increases indefinitely for fixed withinstratum sample sizes the are remains above 90 over a very wide range of cases and above 93 for 2 a 5 these results support consideration of the relatively easily calculated mantel haenszel estimator rather than the conditional maximum likelihood estimator in these increasing strata cases

brief an improved approach for constrained robust model predictive control in this paper we present a new technique to address constrained robust model predictive control the main advantage of this new approach with respect to other well known techniques is the reduced conservativeness specifically the technique described in this paper can be applied to polytopic uncertain systems and is based on the use of several lyapunov functions each one corresponding to a different vertex of the uncertainty s polytope

constrained robust model predictive control based on periodic invariance in this paper a receding horizon control method for input state constrained systems with polyhedral uncertainties is proposed the dual mode prediction strategy is adopted to deal with the constraints and periodically invariant sets are used to derive a target invariant set of the dual mode prediction strategy the proposed control method is shown to have novel characteristics earlier approaches do not have i e i the convex hull of all the periodically invariant sets are invariant in the sense that there are feasible feedback gains guaranteeing invariance for any elements of the convex hull and it provides larger target sets than other methods based on ordinary invariant sets ii a particular convex hull of periodically invariant sets that is computable off line can be used as an invariant target set in this case the number of on line variables is only equal to the period of invariance and thus the proposed algorithm is computationally very efficient these on line variables provide interpolation between different feedback gains to yield best performance