a local linearization approach to nonlinear filtering the local linearization approach to nonlinear filtering of time series generated from continuous time stochastic dynamical systems is discussed and a simple and powerful method for the nonlinear filtering is introduced some numerical results of applications of the filter are shown

sensitivity of post critical states to changes in design parameters abstract sensitivity of post buckling paths is studied in the context of the general theory of elastic stability of discrete structural systems it is assumed that the sensitivity of the critical state itself has been computed and a formulation is developed to account for sensitivity of the curvature of the post critical states when there are changes in design parameters a linear fundamental path is considered explicit expressions are obtained for the sensitivities and they take the form of perturbation expansions only first order sensitivity of post critical paths has been developed a simple example of an angle section column with deformable cross section illustrates that although a critical state may be insensitive to changes in certain design parameters the post critical response may be highly sensitive in the first example presented an axially loaded angle section column the postbuckling response even changes from stable to unstable depending on the values of the design parameter considered

conditions imposed by tacnodes and cusps the study of linear systems of algebraic plane curves with fixed imposed singularities is a classical subject which has recently experienced important progress the horace method introduced by a hirschowitz has been successfully exploited to prove many h1 vanishing theorems even in higher dimension other specialization techniques which include degenerations of the plane are due to z ran and c ciliberto and r miranda g m greuel c lossen and e shustin use a local specialization procedure together with the horace method to give the first asymptotically proper general existence criterion for singular curves of low degree in this paper we develop a specialization method which allows us to compute the dimension of several linear systems as well as to substantially improve the bounds given by greuel lossen and shustin for curves with tacnodes and cusps

local linearization filters for non linear continuous discrete state space models with multiplicative noise in this paper the local linearization method for the approximate computation of the prediction and filtering estimates of continuous discrete state space models is extended to the general case of non linear non autonomous models with multiplicative noise the approximate prediction and filter estimates are obtained by applying the optimal linear filter to the piecewise linear state space model that emerges from a local linearization of both the non linear state equation and the non linear measurement equation in addition the solutions of the differential equations that describe the evolution of the first two conditional moments between observations are obtained and an algorithm for their numerical computation is also given the performance of the ll filters is illustrated by mean of numerical experiments

a reexamination of diffusion estimators with applications to financial model validation time homogeneous diffusion models have been widely used for describing the stochastic dynamics of the underlying economic variables recently stanton proposed drift and diffusion estimators based on a higher order approximation scheme and kernel regression method he claimed that higher order approximations must outperform lower order approximations and concluded nonlinearity in the instantaneous return function of short term interest rates to examine the impact of higher order approximations we develop general and explicit formulas for the asymptotic behavior of both drift and diffusion estimators we show that these estimators will reduce the numerical approximation errors in asymptotic biases but their asymptotic variances escalate nearly exponentially with the order of approximation simulation studies also confirm our asymptotic results this variance inflation problem arises not only from nonparametric fitting but also from parametric fitting stanton s work also postulates the interesting qu

second order sensitivity analysis in vibration and buckling problems a perturbation approach for the first and second order sensitivity analysis of eigenvalue problems as they arise in buckling and vibration of structural systems is presented a particular feature introduced in the formulation is the dependence of all matrices that model the problem not only on the design parameter but also on a pre critical state thus the sensitivity of the response of the fundamental path in buckling problems or a pre stressed state in vibration problems are introduced in the analysis two techniques are considered in this work the direct and the adjoint methods first and second order sensitivity equations for eigenvalues and eigenvectors are obtained and it is shown that second order sensitivity of an eigenvalue can be accomplished by using only one adjoint problem

adjoint sensitivity analysis for nonlinear dynamic thermoelastic systems an adjoint approach is presented to formulate explicit sensitivities for a general functional associated with a nonlinear dynamic thermoelastic system uncoupled thermoelastic response and small deformation behavior are assumed the formulation uses the lagrange multiplier method to define an adjoint system the convolution operator to incorporate transient effects and domain parameterization to describe shape variations variations of the functional are expressed in explicit form with respect to perturbations of the design fields structural shape material properties applied loads prescribed boundary conditions and initial conditions the functional is defined in terms of the design fields and the implicit response fields displacement temperature strain temperature gradient stress heat flux vector reaction force and reaction surface flux in an example problem the finite element method is used to evaluate the real and adjoint responses and the shape sensitivities for a tank design problem the tank is modeled as a nonlinear quasistatic uncoupled thermoelastic system

first and second order sensitivity analysis of linear and nonlinear structures this paper employs the principle of virtual work to derive sensitivity derivatives of structural response with respect to stiffness parameters using both direct and adjoint approaches the computations required are based on additional load conditions characterized by imposed initial strains body forces or surface tractions as such they are equally applicable to numerical or analytical solution techniques the relative efficiency of various approaches for calculating first and second derivatives is assessed it is shown that for the evaluation of second derivatives the most efficient approach is one that makes use of both the first order sensitivities and adjoint vectors two example problems are used for demonstrating the various approaches

shape sensitivity analysis and design optimization of linear thermoelastic solids in this study a numerical scheme is developed for shape sensitivity analysis and design optimization of linear quasistatic thermoelastic solids in this scheme the finite element method is used as the analyzer for analyzing stress temperature shape sensitivity and design velocity field based upon the method of material derivatives both the techniques of the direct differentiation method and the adjoint variable method are applied to derive the shape sensitivity equations the shape optimization formulations discussed here include boundary integrals of displacements and heat fluxes as well as domain integrals of stresses and areas numerical results show that the proposed scheme works well in terms of accuracy

variational approach by means of adjoint systems to structural optimization and sensitivity analysis ii structure shape variation abstract for a linear elastic structure the first variation of an arbitrary stress strain and displacement functionals corresponding to variation of shape of external boundaries or interfaces is derived by using the solutions for primary and adjoint systems the application to optimal design is next presented and the relevant optimally conditions are derived from general expressions the path independent integrals used in fracture mechanics are rederived as a particular case of general expressions

an alternative approach to shape design sensitivity analysis a novel method is presented in this paper for calculating shape design sensitivity which is based on the finite difference method fdm by analysing the numerical procedure of the fdm the perturbation of the geometry is replaced by a perturbation load which can be calculated once the stress field of the initial problem and the design boundary perturbation are known the final shape design sensitivity is obtained by solving the perturbation problem which has the same geometry and the kinematical boundary condition as the initial problem but under the perturbation loads therefore the new method does not require the calculation of the matrices of the perturbed structure and is independent of the perturbation step a numerical implementation of the finite difference load method fdlm is described in which the boundary element method is used to evaluate the structural response the numerical examples demonstrate that this new method for shape design sensitivity analysis is very accurate

optimal topological design through insertion and configuration of finite sized heterogeneities in this paper we develop a procedure for optimal topological design by sequentially inserting finite sized non spherical inclusions or holes within a homogeneous domain we propose a new criterion for topology change that results in a trade off problem to achieve the greatest least change in the objective for the least greatest change in the size of the inclusion hole respectively we derive the material derivative of the proposed objective termed as the configurational derivative that describes sensitivity of arbitrary functionals to arbitrary motions of the inclusion hole as well as the domain boundaries we specifically utilize the sensitivity to position orientation and scaling of finite sized heterogeneities to effect topological design we simplify the configurational derivative to the special case of infinitesimally small spherical inclusions or holes and show that the developed derivative is a generalization of the classical topological derivative the computational implementation relies on b spline isogeometric approximations we demonstrate through a series of examples optimal topology achieved through sequential insertion of a heterogeneity of fixed shape and optimization of its configuration location orientation and scale

nonparametric filtering for stochastic nonlinear oscillations this paper proposes a method of nonparametric filtering for stochastic nonlinear oscillations with particular interest in their derivative estimation based on a second order ordinary differential equation a stochastic oscillation is modeled by a two variate stochastic differential equation without specifying the function form of the drift function where the first variable is assumed to be observable but not the other given the discrete time series with observation error the proposed method enables us to estimate the values of the drift function and its derivatives including those of the unobservable variable according to the results of numerical experiments to compare estimation accuracy with a parametric method the proposed method shows better performance in the estimation of nonlinear models

a state space model of the hemodynamic approach nonlinear filtering of bold signals in this paper a new procedure is presented which allows the estimation of the states and parameters of the hemodynamic approach from blood oxygenation level dependent bold responses the proposed method constitutes an alternative to the recently proposed friston neuroimage 16 2002 513 method and has some advantages over it the procedure is based on recent groundbreaking time series analysis techniques that have been in this case adopted to characterize hemodynamic responses in functional magnetic resonance imaging fmri this work represents a fundamental improvement over existing approaches to system identification using nonlinear hemodynamic models and is important for three reasons first our model includes physiological noise previous models have been based upon ordinary differential equations that only allow for noise or error to enter at the level of observation secondly by using the innovation method and the local linearization filter not only the parameters but also the underlying states of the system generating responses can be estimated these states can include things like a flow inducing signal triggered by neuronal activation de oxyhemoglobine cerebral blood flow and volume finally radial basis functions have been introduced as a parametric model to represent arbitrary temporal input sequences in the hemodynamic approach which could be essential to understanding those brain areas indirectly related to the stimulus hence thirdly by inferring about the radial basis parameters we are able to perform a blind deconvolution which permits both the reconstruction of the dynamics of the most likely hemodynamic states and also to implicitly reconstruct the underlying synaptic dynamics induced experimentally which caused these states variations from this study we conclude that in spite of the utility of the standard discrete convolution approach used in statistical parametric maps spm nonlinear bold phenomena and unspecific input temporal sequences must be included in the fmri analysis

improving quality of sample entropy estimation for continuous distribution probability functions abstract entropy is a one of the key parameters characterizing state of system in statistical physics although the entropy is defined for systems described by discrete and continuous probability distribution function pdf in numerous applications the sample entropy is estimated by a histogram which in fact denotes that the continuous pdf is represented by a set of probabilities such a procedure may lead to ambiguities and even misinterpretation of the results within this paper two possible general algorithms based on continuous pdf estimation are discussed in the application to the shannon and tsallis entropies it is shown that the proposed algorithms may improve entropy estimation particularly in the case of small data sets

nonlinear structural design sensivitity analysis for path dependent problems part 1 general theory abstract two procedures direct differentiation and adjoint structure for design sensitivity analysis of nonlinear structural systems with path dependent effects are described in this paper continuum formulation is used and both geometric and material nonlinearities are included in the derivations incremental nonlinear analysis based on the total lagrangian concept is adopted the reference volume concept is used to unify the shape and nonshape design problems to show the generality of the theory the derived expressions are reduced to some special cases that have been treated previously in the literature in part 2 of the paper a few analytical example problems will be solved to demonstrate the use of the design sensitivity analysis theory the theory has also beendiscretized elsewhere using finite element approximations for implementation into structural analysis programs these developments offer a firm foundation for design optimization of complex structural systems

simultaneous material load shape variations of thermoelastic structures a continuous approach is adopted in order to find the total variation of a general performance criterion the present analysis may find important physical applications in the simultaneous shape optimization and control of large space structures in time by applied thermal and or mechanical loads the adjoint variable method and the material derivative concept are used to find the sensitivity expressions

on krylov subspace approximations to the matrix exponential operator krylov subspace methods for approximating the action of matrix exponentials are analyzed in this paper we derive error bounds via a functional calculus of arnoldi and lanczos methods that reduces the study of krylov subspace approximations of functions of matrices to that of linear systems of equations as a side result we obtain error bounds for galerkin type krylov methods for linear equations namely the biconjugate gradient method and the full orthogonalization method for krylov approximations to matrix exponentials we show superlinear error decay from relatively small iteration numbers onwards depending on the geometry of the numerical range the spectrum or the pseudospectrum the convergence to exp tau a v is faster than that of corresponding krylov methods for the solution of linear equations i tau a x v which usually arise in the numerical solution of stiff ordinary differential equations odes we therefore propose a new class of time integration methods for large systems of nonlinear differential equations which use krylov approximations to the exponential function of the jacobian instead of solving linear or nonlinear systems of equations in every time step

functorial construction of le barz s triangle space with applications we give a new functorial construction of the space of triangles introduced by le barz this description is used to exhibit the space as a composition of smooth blowups to obtain a space of unordered triangles and to study how the space varies in a family

least squares continuous sensitivity shape optimization for structural elasticity applications a general first order formulation of the continuous sensitivity equations is introduced that improves the accuracy of the sensitivity boundary conditions in the continuous sensitivity method design or shape parameter gradients are computed from a continuous system of partial differential equations instead of the discretized system which avoids the problematic mesh sensitivity calculations of discrete methods for shape variation problems the first order formulation for both the underlying elasticity and sensitivity equations is amenable to solution by a high order polynomial least squares finite element model the continuous sensitivity boundary value problem which can be posed in local or total derivative form is generally simpler in local sensitivity form for shape variation problems although the local form is not unique and total material sensitivities are generally desired for structural elasticity problems the local sensitivity solution is easily transformed to a material derivative the first order formulation and the transformation to material derivatives are demonstrated for two elasticity example problems the least squares continuous sensitivity solutions are presented and compared with analytic sensitivities and finite difference results and should prove convenient validation benchmarks for other continuous sensitivity applications

variational approach by means of adjoint systems to structural optimization and sensitivity analysis i variation of material parameters within fixed domain abstract for a linear elastic structure the first variation of an arbitrary stress strain and displacement functionals corresponding to variation of material parameters within specified domain is derived by using the solution for primary and adjoint systems this variation is of fundamental importance in sensitivity analysis optimal design and identification problems simple examples of optimal stiffness design and identification of stiffness parameters in beams are presented

dynamic modeling of neuronal responses in fmri using cubature kalman filtering this paper presents a new approach to inverting fitting models of coupled dynamical systems based on state of the art cubature kalman filtering crucially this inversion furnishes posterior estimates of both the hidden states and parameters of a system including any unknown exogenous input because the underlying generative model is formulated in continuous time with a discrete observation process it can be applied to a wide variety of models specified with either ordinary or stochastic differential equations these are an important class of models that are particularly appropriate for biological time series where the underlying system is specified in terms of kinetics or dynamics i e dynamic causal models we provide comparative evaluations with generalized bayesian filtering dynamic expectation maximization and demonstrate marked improvements in accuracy and computational efficiency we compare the schemes using a series of difficult nonlinear toy examples and conclude with a special focus on hemodynamic models of evoked brain responses in fmri our scheme promises to provide a significant advance in characterizing the functional architectures of distributed neuronal systems even in the absence of known exogenous experimental input e g resting state fmri studies and spontaneous fluctuations in electrophysiological studies importantly unlike current bayesian filters e g dem our scheme provides estimates of time varying parameters which we will exploit in future work on the adaptation and enabling of connections in the brain

intersection theory of linear embeddings we study intersection theoretic properties of subschemes defined by ideal sheaves of linear type in particular their behavior with respect to blowups and segre classes

a comparative study of maximum likelihood estimators for nonlinear dynamical system models estimating nonlinear stochastic dynamical system models from discrete observation is discussed nonlinear dynamical system models with observation noise as well as system noise is practically useful for describing the time evolution of dynamic phenomena the models will work only if their parameters are set appropriately then the models must be estimated from real data which are almost always observed at discrete times generally nonlinear models in continuous time are not easy to estimate with linear approximation of a nonlinear dynamical system model it can be transformed into a discrete state space model using the discretized model together with the kalman filter algorithm the parameters of the model can be estimated from discrete observation via maximum likelihood technique what linear approximation is used is critical for performance of estimation this paper considers two linear approximations the first order linear approximation used in the extended kalman filter and a second order linear approximation based on ito s formula applying these linear approximations to van der pol s random oscillation and rayleigh s random oscillation we make a numerical comparison of the performance of the two maximum likelihood estimators by monte carlo experiments in addition it is also important for estimating continuous time models from discrete observation to evaluate how much the performance of estimation is dependent on time interval of discrete observation we examine the influence of time interval on estimation

degree of strata of singular cubic surfaces determinacion de los grados de algunos estratos de una clasificacion de superficies cubicas singulares que son subvariedades del espacio proyectivo de dimension 19 de las que se conoce su dimension y que son irreducibles

sensitivity analysis for coupled thermoelastic systems abstract this paper presents an adjoint approach derived from the reciprocal theorem for the sensitivity analysis of linear dynamic thermoelastic systems the variation of a general response functional is expressed in explicit form with respect to variations of the design fields which consist of the material properties applied loads prescribed boundary initial conditions and the structural shape the functional is dependent on these design quantities as well as the following implicity defined response fields displacement temperature stress strain heat flux temperature gradient reaction forces and reaction surface flux the formulation incorporates the reciprocal relation between variations of the real system design and response fields and an adjoint state here convolution is employed in lieu of time mappings used in other transient adjoint sensitivity derivations specializations of the formulation to uncoupled combined quasi static uncoupled and steady state thermoelasticity are also presented the finite element method is used to demonstrate the application of the formulation to a problem in automobile engine design

enumerating stationary multiple points given a map f x y an r fold point off is a point xi of x such that there exist points x2 x of x which all have the same image underf we say that an r fold point is strict if x x are all distinct points of x and stationary if some of the xi have coalesced to lie infinitely near the infinitely near points determine tangent directions along the iibref f x in the sense that they constitute ramification points of f this paper enlarges on the work of 9 to develop under appropriate hypotheses enumerative formulas for loci of arbitrary stationary r fold points in terms of invariants of the map multiple point theory has a long and rich history we may trace work back to clebsch 1864 who gave a formula for the number of nodes of a plane curve in terms of the degree and genus of the curve perhaps the most famous example of a stationary multiple point result is the riemann hurwitz formula let f x y be a finite separable surjective map between smooth projective curves the riemann hurwitz theorem gives a formula for deg r where r is the ramification divisor of j it may be easily seen that deg r is simply a weighted number of stationary doublepoints off modern multiple point theory is concerned with developing formulas for general classes of maps the subject has been of considerable interest in differential geometry and topology as well as in algebraic geometry surveys of the work in these fields can be found in lo 9 introduction or 8 chap v pp 365 3911 in algebraic geometry multiple point theory has presently culiminated in two basic approaches the hilbert scheme see lo for a survey and the method of iteration we shall only be concerned with the latter technique in the body of this work both approaches share a 149 oool 8708 87 7 50

first order design sensitivities for transient conduction problems by an adjoint method an adjoint approach is presented for the design sensitivity analysis of transient conduction problems variations of a general design functional are expressed in explicit form with respect to all design quantities i e material properties shape applied thermal loads including convection and initial conditions the methodology incorporates the mutual energy between the real and adjoint thermal problems and a geometric mapping to describe shape variations finite element implementation of the method is discussed and an example is provided some potential difficulties that might be encountered when using the adjoint method with the finite element method are addressed these involve the application of impulse loadings and dirac temperature fields in the adjoint loadings

variational approach to first and second order sensitivity analysis of elastic structures for a linear elastic structure the first variations of arbitrary stress strain and displacement functionals were explicitly expressed in terms of variations of material stiffness parameters within specified domain in references 1 and 2 by using the solutions for primary and adjoint systems in this paper explicit expressions for second variations are derived for the case when the material stiffness or compliance variations depend on a set of parameters these expressions arc obtained in terms of variations of stiffness or compliance parameters by using the solutions of two additional sets of adjoint systems furthermore the variation of local stress strain or displacement is considered several illustrative examples are provided for the first and second order sensitivity analysis of beams

strongly cohen macaulay schemes and residual intersections this paper studies the local properties of closed subschemes y in cohen macaulay schemes x such that locally the defining ideal of y in x has the property that its koszul homology is cohen macaulay whenever this occurs y is said to be strongly cohen macaulay in x this paper proves several facts about such embeddings chiefly with reference to the residual intersections of y in x the main result states that any residual intersection of y in x is again cohen macaulay introduction our purpose in this paper is to investigate a property of a closed subscheme y in a noetherian cohen macaulay scheme x which we call strong cohen macaulayness this is a local property which we first describe for a local ring let x spec r where r is a cohen macaulay local ring and let y spec r i

sensitivity analysis for non linear constrained elastostatic systems adjoint and direct differentiation methods are used to formulate design sensitivities for non linear constrained elastostatic systems variations of a general response functional are expressed in explicit form with respect to all design field variations including shape the response functional is expressed over the undeformed configuration however the displacement gradient is included so that field quantities that are defined over the deformed configuration such as cauchy stress may be modelled the finite element method is used to evaluate the sensitivities in an example problem

simulation of stochastic differential equations through the local linearization method a comparative study a new local linearization ll scheme for the numerical integration of nonautonomous multidimensional stochastic differential equations sdes with additive noise is introduced the numerical scheme is based on the local linearization of the sde s drift coefficient by means of a truncated ito taylor expansion a comparative study with the other ll schemes is presented which shows some advantanges of the new scheme over other ones

a tutorial on particle filters for online nonlinear non gaussian bayesian tracking increasingly for many application areas it is becoming important to include elements of nonlinearity and non gaussianity in order to model accurately the underlying dynamics of a physical system moreover it is typically crucial to process data on line as it arrives both from the point of view of storage costs as well as for rapid adaptation to changing signal characteristics in this paper we review both optimal and suboptimal bayesian algorithms for nonlinear non gaussian tracking problems with a focus on particle filters particle filters are sequential monte carlo methods based on point mass or particle representations of probability densities which can be applied to any state space model and which generalize the traditional kalman filtering methods several variants of the particle filter such as sir asir and rpf are introduced within a generic framework of the sequential importance sampling sis algorithm these are discussed and compared with the standard ekf through an illustrative example

solutions to shape and topology eigenvalue optimization problems using a homogenization method a solution strategy to find the shape and topology of structures that maximize a natural frequency is presented the methodology is based on a homogenization method and the representation of the shape of the structure as a material property the problem is formulated as a reinforcement problem in which a given structure is reinforced using a prescribed amount of material two dimensional plane elasticity problems are considered examples are presented for illustration

linear estimation of continuous discrete linear state space models with multiplicative noise this paper deals with the estimation of the state variable of continuous discrete linear state space models with multiplicative noise specifically the optimal minimum variance linear filter for that class of models is constructed moreover the solutions of the differential equations that describe the evolution of the two first conditional moments between observations are obtained and an algorithm for their numerical computation is also given the performance of the linear filter is illustrated by means of numerical experiments

variational method for design sensitivity analysis in nonlinear structural mechanics this paper describes a unified variational theory of design sensitivity analysis of linear and nonlinear structures for shape nonshape and material selection problems the concepts of reference volume and adjoint structure are used to develop the unified viewpoint a general formula for design sensitivity analysis is derived several analytical linear and nonlinear examples are used to interpret various terms of the formula and demonstrate its use such analytical examples give insight into the application of the general formula to more complex problems that must be treated numerically adjoint state fields are also interpreted as sensitivities for the functional related to the primary structure

the enumerative geometry of projective algebraic surfaces and the complexity of aspect graphs the aspect graph is a popular viewer centered representation that enumerates all the topologically distinct views of an object building the aspect graph requires partitioning viewpoint space in view equivalent cells by a certain number of visual event surfaces if the object is piecewise smooth algebraic then all visual event surfaces are either made of lines having specified contacts with the object or made of lines supporting the points of contacts of planes having specified contacts with the object in this paper we present a general framework for studying the enumerative properties of line and plane systems the context is that of enumerative geometry and intersection theory in particular we give exact results for the degrees of all visual event surfaces coming up in the construction of aspect graphs of piecewise smooth algebraic bodies we conclude by giving a bound on the number of topologically distinet views of such objects

on a class of conservation rules associated with sensitivity analysis in linear elasticity abstract considering arbitrary stress strain or displacement functionals specified over a domain of an elastic homogeneous and isotropic body their invariance is proved for the case of translation rotation and scale change of an arbitrary domain within the body the assosciated class of path independent integrals is derived it is shown that sensitivity analysis with respect to translation rotation or expansion of defects can be performed by using these path independent integrals

the space of triangles vanishing theorems and combinatorics abstract we consider compactifications of pn 3 ij the space of triples of distinct points in projective space one such space is a singular variety of configurations of points and lines another is the smooth compactification of fulton and macpherson and a third is the triangle space of schubert and semple we compute the sections of line bundles on these spaces and show that they are equal as gl n representations to the generalized schur modules associated to bad generalized young diagrams with three rows borel weil theorem on the one hand this yields weyl type character and dimension formulas for the schur modules on the other a combinatorial picture of the space of sections cohomology vanishing theorems play a key role in our analysis