contextual estimators of mixing probabilities for markov chain random fields abstract this paper discusses the estimation of proportions of classes from an image classification methods are compared with likelihood methods and the importance of contextual information is discussed the joint distribution of classes at neighbouring sites is modelled by a markov chain random field the class attributes are estimated from training sets and unclassified observations the effect of biased class means is reduced with a stochastic model of the bias contextual likelihood methods yield better results than non contextual methods

designing stabilizing controllers for uncertain systems using the riccati equation approach a useful technique for determining a linear feedback control law stabilizes an uncertain system is the riccati equation approach of i r petersen and c v hollot 1986 they consider systems with time varying uncertainty in the system matrix and obtain the constant feedback gains for the linear stabilizing controller in terms of the solutions of a riccati equation the technique is extended to include problems with time varying uncertainty in the input connection matrix several examples are included to demonstrate the efficacy of this result

assessing the performance of an allocation rule the problem of estimating the error rates of a sample based rule on the basis of the same sample used in its construction is considered the apparent error rate is an obvious nonparametric estimate of the conditional error rate of a sample rule but unfortunately it provides too optimistic an assessment attention is focussed on the formation of improved estimates mainly through appropriate bias correction of the apparent error rate in this respect the role of the bootstrap a computer based methodology is highlighted

constant scalar curvature metrics with isolated singularities we extend the results and methods of 6 to prove the existence of constant positive scalar curvature metrics g which are complete and conformal to the standard metric on s where is a disjoint union of submanifolds of dimensions between 0 and n 2 2 the existence of solutions with isolated singularities occupies the majority of the paper their existence was previously established by schoen 12 but the proof we give here based on the techniques of 6 is more direct and provides more information about their geometry when is discrete we also establish that these solutions are smooth points in the moduli spaces of all such solutions introduced and studied in 7 and 8

uniform exact model matching for a class of linear time varying analytic systems abstract the problem of uniform exact model matching is studied via state and output feedback for a class of linear time varying analytic systems the following two major issues are resolved the nessecary and sufficient conditions for the problems to have a solution and the general analytical expressions for the controller matrices a major feature of the proposed approach is that it reduces the uniform exact model matching problem to that of solving a linear nonhomogeneous algebraic matrix equation

analysis of the periodic lyapunov and riccati equations via canonical decomposition a new proof is given of the following result a periodic riccati equation admits a unique positive semidefinite periodic solution and the solution is stabilizing if and only if the underlying system is stabilizable and detectable the proof hinges on the decomposition of the riccati equation induced by the system canonical decomposition the solution structure is therefore naturally pointed out

remarks on cosmological spacetimes and constant mean curvature surfaces we give a general condition which ensures the existence of constant mean curvature cmc cauchy surfaces in cosmological spacetimes however there is an example of a spacetime which does not satisfy this condition and does not admit any cmc cauchy surfaces we discuss conditions under which cmc surfaces may exist

complete embedded minimal n dimensional submanifolds in ℂn a classical problem in the theory of minimal submanifolds of euclidean spaces is to understand whether a minimal submanifold exists with a prescribed behavior at infinity or to determine from the asymptotes the geometry of the whole submanifold beyond the intrinsic interest of these questions they are also of crucial importance when studying the possible singularities of minimal submanifolds in general riemannian manifolds for minimal surfaces i e two dimensional submanifolds the standard tool to solve these problems is given by the weierstrass representation formula which relates the geometry of the minimal surface to complex analytic properties of holomorphic 1 forms on riemann surfaces recently gluing techniques have been developed that provide an abundant number of new examples of minimal hypersurfaces in euclidean space for higher dimensional minimal submanifolds such a link clearly disappears and no complex analysis can be put into play although gluing techniques have been extensively used in the study of minimal hypersurfaces they have not been adapted to handle higher codimensional submanifolds the aim of this paper is to use a gluing technique for minimal submanifolds to make a step toward understanding these questions in higher codimension more precisely we will restrict ourselves to the case of real n dimensional submanifolds of cn there are two main reasons for doing so the first one comes from the fact that when trying to desingularize the intersection for example of a pair of n planes that give the desired asymptotic behavior one needs a model of a minimal submanifold with this behavior at infinity to rescale and to glue into the pair of planes where a neighborhood of the intersection is removed this local model needs to be sufficiently simple to allow a detailed study of the linearized mean curvature operator in our situation this is provided by a generalization of an area minimizing submanifold found by lawlor in 12 while in more general cases such an example is not known the second reason is that among minimal n submanifolds ofcn there is a

continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems we consider a dynamic system containing uncertain elements only the set of possible values of these uncertainties is known based on this information a class of state feedback controls is proposed in order to guarantee uniform ultimate boundedness of every system response within an arbitrarily small neighborhood of the zero state these feedback controls are continuous functions of the state

gluing and wormholes for the einstein constraint equations we establish a general gluing theorem for constant mean curvature solutions of the vacuum einstein constraint equations this allows one to take connected sums of solutions or to glue a handle wormhole onto any given solution away from this handle region the initial data sets we produce can be made as close as desired to the original initial data sets these constructions can be made either when the initial manifold is compact or asymptotically euclidean or asymptotically hyperbolic with suitable corresponding conditions on the extrinsic curvature in the compact setting a mild nondegeneracy condition is required in the final section of the paper we list a number ways this construction may be used to produce new types of vacuum spacetimes

the mass of an asymptotically flat manifold we show that the mass of an asymptotically flat n manifold is a geometric invariant the proof is based on harmonic coordinates and to develop a suitable existence theory results about elliptic operators with rough coefficients on weighted sobolev spaces are summarised some relations between the mass scalar curvature and harmonic maps are described and the positive mass theorem for n dimensional spin manifolds is proved

error analysis of crop acreage estimation using satellite data the problem of crop acreage estimation using satellite data is discussed the bias and variance of a crop estimate in an area segment obtained from the classification of its multispectral sensor data are derived as functions of the means variances and covariances of error rates linear discriminant analysis and class proportion estimation for the two class case have been extended to include a third class of measurement units where these units are mixed on the ground special attention is given to the investigation of mislabeling in training samples and its effect on crop proportion estimation it is shown that the bias and variance of the estimate of a crop acreage proportion increase as the disparity in mislabeling rates of the two classes increases the effect of mixed pixels on the bias and variance of the proportion estimate is also investigated

a riccati equation approach to the design of stabilizing controllers and observers for a class of uncertain linear systems this paper presents a procedure for designing a full state observer and feedback control law which will stabilize a given uncertain linear system the uncertain linear systems under consideration are described by state equations which depend on uncertain parameters these uncertain parameters may be time varying their values however are constrained to lie within known compact bounding sets the design procedure involves solving two algebraic riccati equations a feature of the design procedure presented is the fact that it reduces to the standard lqg design procedure if the system contains no uncertain parameters

initial data engineering we present a local gluing construction for general relativistic initial data sets the method applies to generic initial data in a sense which is made precise in particular the trace of the extrinsic curvature is not assumed to be constant near the gluing points which was the case for previous such constructions no global conditions on the initial data sets such as compactness completeness or asymptotic conditions are imposed as an application we prove existence of spatially compact maximal globally hyperbolic vacuum space times without any closed constant mean curvature spacelike hypersurface

estimating cell populations abstract an important step in the diagnosis of a cervical cytology specimen is estimating the proportions of the various cell types present this is usually done with a cell classifier the error rates of which can be expressed as a confusion matrix we show how to use the confusion matrix to obtain an unbiased estimate of the desired proportions we show that the mean square error of this estimate depends on a befuddlement matrix derived from the confusion matrix and how this in turn leads to a figure of merit for cell classifiers finally we work out the two class problem in detail and present examples to illustrate the theory

on the regularity of solutions to the yamabe equation and the existence of smooth hyperboloidal initial data for einstein s field equations the regularity of the solutions to the yamabe problem is considered in the case of conformally compact manifolds and negative scalar curvature the existence of smooth hyperboloidal initial data for einstein s field equations is demonstrated

estimating the error rate of a prediction rule improvement on cross validation abstract we construct a prediction rule on the basis of some data and then wish to estimate the error rate of this rule in classifying future observations cross validation provides a nearly unbiased estimate using only the original data cross validation turns out to be related closely to the bootstrap estimate of the error rate this article has two purposes to understand better the theoretical basis of the prediction problem and to investigate some related estimators which seem to offer considerably improved estimation in small samples

the boost problem in general relativity we show that any asymptotically flat initial data for the einstein field equations have a development which includes complete spacelike surfaces boosted relative to the initial surface furthermore the asymptotic fall off is preserved along these boosted surfaces and there exists a global system of harmonic coordinates on such a development we also extend former results on global solutions of the constraint equations by virtue of this extension the constraint and evolution parts of the problem fit together exactly several theorems are given which concern the behaviour in the large of general classes of linear and quasilinear differential systems this paper contains in addition a systematic exposition of the functional spaces employed

scalar curvature deformation and a gluing construction for the einstein constraint equations on a compact manifold the scalar curvature map at generic metrics is a local surjection f m we show that this result may be localized to compact subdomains in an arbitrary riemannian manifold the method is extended to establish the existence of asymptotically flat scalar flat metrics on n n 3 which are spherically symmetric hence schwarzschild at infinity i e outside a compact set such metrics provide cauchy data for the einstein vacuum equations which evolve into nontrivial vacuum spacetimes which are identically schwarzschild near spatial infinity

deformation of scalar curvature and volume the stationary points of the total scalar curvature functional on the space of unit volume metrics on a given closed manifold are known to be precisely the einstein metrics one may consider the modified problem of finding stationary points for the volume functional on the space of metrics whose scalar curvature is equal to a given constant in this paper we localize a condition satisfied by such stationary points to smooth bounded domains the condition involves a generalization of the static equations and we interpret solutions and their boundary values of this equation variationally on domains carrying a metric that does not satisfy the condition we establish a local deformation theorem that allows one to achieve simultaneously small prescribed changes of the scalar curvature and of the volume by a compactly supported variation of the metric we apply this result to obtain a localized gluing theorem for constant scalar curvature metrics in which the total volume is preserved finally we note that starting from a counterexample of min oo s conjecture such as that of brendle marques neves counterexamples of arbitrarily large volume and different topological types can be constructed

on elliptic systems in rn on etudie des systemes elliptiques k k d operateurs differentiels dans r n qui peuvent s ecrire sous la forme a a q ou a est un systeme elliptique d operateurs a coefficients constants et q est une perturbation a coefficient variable avec certaines proprietes de decroissance a x

bias associated with the discriminant analysis approach to the estimation of mixing proportions abstract the estimation of the mixing proportion 1 in which the first of two multivariate normal groups occur is considered on the basis of a sample drawn from a mixture of them under the model studied there are also data of known origin available from each of the groups for the formation of a discriminant rule r the bias of the estimator of 1 based on the proportion of the mixture data assigned to the first group by r is investigated also the case where the data of known origin are taken to be correlated is considered

linear time varying system control based on the inversion transformation this paper proposes a new state feedback control design for uniformly controllable linear time varying systems the new design is based on a nonlinear state transformation that converts the stabilization problem of the system state into a destabilization problem of the transformed state such a transformation results in a new control that has two advantages over previous controls 1 in some of the previous control designs forecast of future information of the time varying system matrices over some time interval t t is required to calculate the state feedback gain at any time instant t while in the new control design no such forecast is needed 2 in other previous control designs consecutive time differentiation on the time varying system matrices is required while in the new control design time integration instead of differentiation is applied to the system matrices the new control can therefore be applied to systems with time varying parameters that are piecewise continuous in time

robust static and dynamic output feedback stabilization deterministic and stochastic perspectives three parallel gaps in robust feedback control theory are examined sufficiency versus necessity deterministic versus stochastic uncertainty modeling and stability versus performance deterministic and stochastic output feedback control problems are considered with both static and dynamic controllers the static and dynamic robust stabilization problems involve deterministically modeled bounded but unknown measurable time varying parameter variations while the static and dynamic stochastic optimal control problems feature state control and measurement dependent white noise general sufficiency conditions for the deterministic problems are obtained using lyapunov s direct method while necessary conditions for the stochastic problems are derived as a consequence of minimizing a quadratic performance criterion the sufficiency tests are then applied to the necessary conditions to determine when solutions of the stochastic optimization problems also solve the deterministic robust stability problems as an additional application of the deterministic result the modified riccati equation approach of petersen and hollot is generalized in the static case and extended to dynamic compensation

on ultimate boundedness control of uncertain systems in the absence of matching assumptions this paper describes an approach to ultimate boundedness control under hypotheses less stringent than heretofore required instead of imposing the so called matching conditions of previous authors a certain decomposition of the dynamics is performed the resulting decomposed system has two parts a matched portion and a mismatched portion a certain measure of mismatch m is defined and it is shown that effective control is possible as long as m does not exceed some critical mismatch threshold m it is seen that this threshold depends on the choice of feedback hence it becomes possible to investigate the tradeoffs between the size of the mismatch threshold and the sizes of the feedback gains which achieve the desired ultimate boundedness of solutions

gluing initial data sets for general relativity we establish an optimal gluing construction for general relativistic initial data sets the construction is optimal in two distinct ways first it applies to generic initial data sets and the required generically satisfied hypotheses are geometrically and physically natural second the construction is completely local in the sense that the initial data is left unaltered on the complement of arbitrarily small neighborhoods of the points about which the gluing takes place using this construction we establish the existence of cosmological maximal globally hyperbolic vacuum space times with no constant mean curvature spacelike cauchy surfaces