asymptotic properties of multistate random walks ii applications to inhomogeneous periodic and random lattices the previously developed formalism for the calculation of asymptotic properties of multistate random walks is used to study random walks on several inhomogeneous periodic lattices where the periodically repeated unit cell contains a number of inequivalent sites as well as on lattices with a random distribution of inequivalent sites we concentrate on the question whether the random walk properties depend on the spatial arrangement of the sites in the unit cell or only on the number density of the different types of sites specifically we consider lattices with periodic and random arrangements of columns and lattices with periodic and random arrangements of anisotropic scatterers

fluid space times and conharmonic symmetries the conharmonic curvature tensor is considered as an invariant of the conharmonic transformation defined by ishii and the necessary and sufficient conditions for the conharmonic curvature tensor in a perfect fluid space time to be divergence free has been obtained conharmonic motion conharmonic collineation and conharmonic curvature collineation are introduced as subcases of conformal motion conformal collineation and weyl conformal collineation respectively and relations of conharmonic symmetries with inheriting symmetries are investigated in the case of an existing conharmonic killing vector along the flow vector along the anisotropy vector and perpendicular to both in an anisotropic fluid space time it is found that no equation of state is singled out unless the conharmonic killing vector is also a curvature inheritance vector conditions are obtained for the symmetries of the anisotropic fluid space time admitting a conharmonic killing vector to be inherited in the case of a conharmonic sym

gaussian map filtering using kalman optimization this paper deals with the update step of gaussian map filtering in this framework we seek a gaussian approximation to the posterior probability density function pdf whose mean is given by the maximum a posteriori map estimator we propose two novel optimization algorithms which are quite suitable for finding the map estimate although they can also be used to solve general optimization problems these are based on the design of a sequence of pdfs that become increasingly concentrated around the map estimate the resulting algorithms are referred to as kalman optimization ko methods we also provide the important relations between these ko methods and their conventional optimization algorithms coas counterparts i e newton s and levenberg marquardt algorithms our simulations indicate that ko methods are more robust than their coa equivalents

special conformal killing vector space times and symmetry inheritance viscous heat conducting fluid and anisotropic fluid space times admitting a special conformal killing vector sckv are studied and some general theorems concerning the inheritance of the symmetry associated with the sckv are proved in particular for viscous fluid space times it is shown that i if the sckv maps fluid flow lines into fluid flow lines then all physical components of the energy momentum tensor inherit the sckv symmetry or ii if the lie derivative along a sckv of the shear viscosity term ab is zero then again we have symmetry inheritance all space times admitting a sckv and satisfying the dominant energy condition are found apart from the vacuum pp wave solutions which are the only vacuum solutions that can admit a sckv the energy momentum tensor associated with these space times is shown to admit at least one null eigenvector and can represent either a viscous fluid with heat conduction or an anisotropic fluid no perfect fluid space times can admit a sckv these sckv space t

invariant conformal vectors in space times admitting a group of g3 of motions acting on spacelike orbits s2 the paper deals with four dimensional space times admitting locally a three dimensional group of motions g3 acting on two dimensional spacelike orbits s2 the local existence problem for conformal vectors invariant under g3 is shown to be equivalent to the local existence problem for killing vectors of a given two dimensional pseudo riemannian metric g this problem is explicitly solved in terms of the gaussian curvature r of g and two of its scalar differential concomitants the results are applied to the case of dust filled space times where an exhaustive list of metrics has been obtained by using the algebraic computing language smp the metrics are either homogeneous self similar or friedmann models

ricci collineation vectors in fluid space times the properties of fluid space times that admit a ricci collineation vector rcv parallel to the fluid unit four velocity vector ua are briefly reviewed these properties are expressed in terms of the kinematic quantities of the timelike congruence generated by ua the cubic equation derived by oliver and davis ann inst henri poincare 30 339 1979 for the equation of state p p of a perfect fluid space time that admits an rcv which does not degenerate to a killing vector is solved for physically realistic fluids necessary and sufficient conditions for a fluid space time to admit a spacelike rcv parallel to a unit vector na orthogonal to ua are derived in terms of the expansion shear and rotation of the spacelike congruence generated by na perfect fluid space times are studied in detail and analogues of the results for timelike rcvs parallel to ua are obtained properties of imperfect fluid space times for which the energy flux vector qa vanishes and na is a spacelike eigenvector of the aniso

analysis of kalman filter approximations for nonlinear measurements a theoretical analysis is presented of the correction step of the kalman filter kf and its various approximations for the case of a nonlinear measurement equation with additive gaussian noise the kf is based on a gaussian approximation to the joint density of the state and the measurement the analysis metric is the kullback leibler divergence of this approximation from the true joint density the purpose of the analysis is to provide a quantitative tool for understanding and assessing the performance of the kf and its variants in nonlinear scenarios this is illustrated using a numerical example

incorporation of space time symmetries in einstein s field equations in the search for exact solutions to einstein s field equations the main simplification tool is the introduction of space time symmetries motivated by this fact we develop a method to write the field equations for general matter in a form that fully incorporates the character of the symmetry the method is being expressed in a covariant formalism using the framework of a double congruence the basic notion on which it is based is that of the geometrization of a general symmetry as a special application of our general method we consider the case of a space like conformal killing vector field on the space time manifold regarding special types of matter fields new perspectives in general relativity are discussed

fourier hermite kalman filter in this note we shall present a new class of gaussian filters called fourier hermite kalman filters fourier hermite kalman filters are based on expansion of nonlinear functions with the fourier hermite series in same way as the traditional extended kalman filter is based on the taylor series the first order truncation of the fourier hermite series gives the previously known statistically linearized filter

square root quadrature kalman filtering the quadrature kalman filter qkf is a recursive nonlinear filtering algorithm developed in the kalman filtering framework it computes the mean and covariance of all conditional densities using the gauss hermite quadrature rule in this correspondence we develop a square root extension of the quadrature kalman filter using matrix triangularizations the square root quadrature kalman filter sqkf propagates the mean and the square root of the covariance although equivalent to the qkf algebraically the sqkf exhibits excellent numerical characteristics but at the expense of increased computational complexity we also present possible refinements of the generic sqkf

the iterated kalman filter update as a gauss newton method it is shown that the iterated kalman filter ikf update is an application of the gauss newton method for approximating a maximum likelihood estimate an example is presented in which the iterated kalman filter update and maximum likelihood estimate show correct convergence behavior as the observation becomes more accurate whereas the extended kalman filter update does not

diffusion in lattices with anisotropic scatterers we study diffusion in lattices with periodic and random arrangements of anisotropic scatterers we show using both analytical techniques based upon our previous work on asymptotic properties of multistate random walks and computer calculation that the diffusion constant for the random arrangement of scatterers is bounded above and below at an arbitrary density by the diffusion constant for an appropriately chosen periodic arrangement of scatterers at the same density we also investigate the accuracy of the low density expansion for the diffusion constant up to second order in the density for a lattice with randomly distributed anisotropic scatterers comparison of the analytical results with numerical calculations shows that the accuracy of the density expansion depends crucially on the degree of anisotropy of the scatterers finally we discuss a monotonicity law for the diffusion constant with respect to variation of the transition rates in analogy with the rayleigh monotonicity law for the effective resistance of electric networks as an immediate corollary we obtain that the diffusion constant averaged over all realizations of the random arrangement of anisotropic scatterers at density is a monotone function of the density

comment on a new method for the nonlinear transformation of means and covariances in filters and estimators with authors reply the above paper julier et al ieee trans automat contr vol 45 pp 477 82 2000 generalizes the kalman filter to nonlinear systems by transforming approximations of the probability distributions through the nonlinear process and measurement functions this comment derives exactly the same estimator by linearizing the process and measurement functions by a statistical linear regression through some regression points in contrast with the extended kalman filter which uses an analytic linearization in one point this insight allows one 1 to understand predict the performance of the estimator for specific applications and 2 to make adaptations to the estimator i e the choice of the regression points and their weights in those cases where the original formulation does not assure good results in reply the authors state that the commenters conclusion is unnecessarily narrow interpretation of results

a new method for the nonlinear transformation of means and covariances in filters and estimators this paper describes a new approach for generalizing the kalman filter to nonlinear systems a set of samples are used to parametrize the mean and covariance of a not necessarily gaussian probability distribution the method yields a filter that is more accurate than an extended kalman filter ekf and easier to implement than an ekf or a gauss second order filter its effectiveness is demonstrated using an example

posterior linearization filter principles and implementation using sigma points this paper is concerned with gaussian approximations to the posterior probability density function pdf in the update step of bayesian filtering with nonlinear measurements in this setting sigma point approximations to the kalman filter kf recursion are widely used due to their ease of implementation and relatively good performance in the update step these sigma point kfs are equivalent to linearizing the nonlinear measurement function by statistical linear regression slr with respect to the prior pdf in this paper we argue that the measurement function should be linearized using slr with respect to the posterior rather than the prior to take into account the information provided by the measurement the resulting filter is referred to as the posterior linearization filter plf in practice the exact plf update is intractable but can be approximated by the iterated plf iplf which carries out iterated slrs with respect to the best available approximation to the posterior the iplf can be seen as an approximate recursive kullback leibler divergence minimization procedure we demonstrate the high performance of the iplf in relation to other gaussian filters in two numerical examples

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

geometrization of a general collineation geometrization of a general collineation means to express the collineation as necessary and sufficient conditions on the kinematic quantities shear vorticity expansion of the congruence of the vector field generating the collineation it is shown that the generic form of a collineation is l gab 2 gab hab where hab is a traceless symmetric tensor a general theorem concerning the geometrization of the generic collineation is presented and its applications are discussed

weak convergence of a random walk in a random environment let i x i 1 d x z d satisfy i x 0 and 1 x d x 1 define a markov chain onz d by specifying that a particle atx takes a jump of 1 in thei th direction with probability 1 2 i x and a jump of 1 in thei th direction with probability 1 2 i x if the i x are chosen from a stationary ergodic distribution then for almost all the corresponding chain converges weakly to a brownian motion

cubature kalman filters in this paper we present a new nonlinear filter for high dimensional state estimation which we have named the cubature kalman filter ckf the heart of the ckf is a spherical radial cubature rule which makes it possible to numerically compute multivariate moment integrals encountered in the nonlinear bayesian filter specifically we derive a third degree spherical radial cubature rule that provides a set of cubature points scaling linearly with the state vector dimension the ckf may therefore provide a systematic solution for high dimensional nonlinear filtering problems the paper also includes the derivation of a square root version of the ckf for improved numerical stability the ckf is tested experimentally in two nonlinear state estimation problems in the first problem the proposed cubature rule is used to compute the second order statistics of a nonlinearly transformed gaussian random variable the second problem addresses the use of the ckf for tracking a maneuvering aircraft the results of both experiments demonstrate the improved performance of the ckf over conventional nonlinear filters

curvature inheritance symmetry in riemannian spaces with applications to fluid space times katzin et al g h katzin j levine and w r davis j math phys 10 617 1969 introduced curvature collineations cc defined by a vector satisfying l rbcda 0 where rbcda is the riemann curvature tensor of a riemannian space vn and l denotes the lie derivative they proved that a cc is related to a special conformal motion which implies the existence of a covariant constant vector field unfortunately recent study indicates that the existence of a covariant constant vector restricts vn to a very rare special case with limited physical use in particular for a fluid space time with special conformal motion either stiff or unphysical equations of state are singled out moreover perfect fluid space times do not admit special conformal motions this information was not available in 1969 when cc symmetry was introduced in this paper cc is generalized to another symmetry called curvature inheritance ci satisfying l rbcda 2 rbcda where is a scalar function we prove that a proper

spacelike conformal killing vectors and spacelike congruences necessary and sufficient conditions are derived for space time to admit a spacelike conformal motion with symmetry vector parallel to a unit spacelike vector field na these conditions are expressed in terms of the shear and expansion of the spacelike congruence generated by na and in terms of the four velocity of the observer employed at any given point of the congruence it is shown that either the expansion or the rotation of this spacelike congruence must vanish if dna dp 0 where p denotes arc length measured along the integral curves of na and also that there exist no proper spacelike homothetic motions with constant expansion propagation equations for the projection tensor and the rotation tensor are derived and it is proved that every isometric spacelike congruence is rigid fluid space times are studied in detail a relation is established between spacelike conformal motions and material curves in the fluid if a fluid space time admits a spacelike conformal killing vector parallel to na and

bounds for effective parameters of heterogeneous media by analytic continuation we give a mathematical formulation of a method for obtaining bounds on effective parameters developed by d bergman and g w milton this method in contrast to others used before does not rely on a variational principle but exploits the properties of the effective parameter as an analytic function of the component parameters the method is at present restricted to two component media