convergence of dziuk s linearly implicit parametric finite element method for curve shortening flow convergence of dziuk s fully discrete linearly implicit parametric finite element method for curve shortening flow on the plane still remains open since it was proposed in 1991 though the correspo

higher order finite element methods and pointwise error estimates for elliptic problems on surfaces we define higher order analogues to the piecewise linear surface finite element method studied in g dziuk finite elements for the beltrami operator on arbitrary surfaces in partial differential equations and calculus of variations springer verlag berlin 1988 pp 142 155 and prove error estimates in both pointwise and l 2 based norms using the laplace beltrami problem on an implicitly defined surface gamma as a model pde we define lagrange finite element methods of arbitrary degree on polynomial approximations to gamma which likewise are of arbitrary degree then we prove a priori error estimates in the l 2 h 1 and corresponding pointwise norms that demonstrate the interaction between the pde error that arises from employing a finite dimensional finite element space and the geometric error that results from approximating gamma we also consider parametric finite element approximations that are defined on gamma and thus induce no geometric error computational examples confirm the sharpness of our error estimates

gain scheduled and nonlinear systems dynamic analysis by velocity based linearization families a family of velocity based linearizations is proposed for a nonlinear system in contrast to the conventional series expansion linearization a member of the family of velocity based linearizations is valid in the vicinity of any operating point not just an equilibrium operating point the velocity based linearizations facilitate dynamic analysis far from the equilibrium operating points and enable the transient behaviour of the nonlinear system to be investigated using velocity based linearizations stability conditions are derived for both smooth and non smooth nonlinear systems which avoid the restrictions to trajectories lying within an unnecessarily perhaps excessively small neighbourhood about the equilibrium operating points inherent in existing frozen input theory for systems where there is no restriction on the rate of variation the velocity based linearization analysis is global in nature the analysis techniques developed although quite general are motivated by the gain scheduling design

a fully discrete evolving surface finite element method in this paper we consider a time discrete evolving surface finite element method for the advection and diffusion of a conserved scalar quantity on a moving surface in earlier papers using a suitable variational formulation in time dependent sobolev space we proposed and analyzed a finite element method using surface finite elements on evolving triangulated surfaces ima j numer anal 25 2007 pp 385 407 math comp to appear optimal order l 2 gamma t and h 1 gamma t error bounds were proved for linear finite elements in this work we prove optimal order error bounds for a backward euler time discretization

state dependent parameter models of non linear sampled data systems a velocity based linearization approach discrete time models with state dependent parameters are derived for non linear sampled data systems velocity based linearization of the continuous time system followed by integration over the sampling interval is used to represent the sampled data system by a discrete time state space model with state dependent parameters by reconstructing the state a quasi arx model is obtained the parameters of which are functions of past inputs and outputs as the velocity based linearization procedure does not involve suppression of higher order terms the state dependent state space model and the quasi arx description give exact representations of the non linear system

on the variational approximation of combined second and fourth order geometric evolution equations we present a variational formulation of combined motion by minus the laplacian of curvature and mean curvature flow as well as related flows the proposed scheme covers both the closed curve case and the case of curves that are connected via triple or quadruple junction points or intersect the external boundary on introducing a parametric finite element approximation we prove stability bounds and compare our scheme with existing approaches the presented scheme has very good properties with respect to the equidistribution of mesh points and if applicable area conservation

curve shortening flow coupled to lateral diffusion we present and analyze a semi discrete finite element scheme for a system consisting of a geometric evolution equation for a curve and a parabolic equation on the evolving curve more precisely curve shortening flow with a forcing term that depends on a field defined on the curve is coupled with a diffusion equation for that field the scheme is based on ideas of dziuk siam j numer anal 36 6 1808 1830 1999 for the curve shortening flow and dziuk and elliott ima j numer anal 27 2 262 292 2007 for the parabolic equation on the moving curve additional estimates are required in order to show convergence most notably with respect to the length element while in dziuk siam j numer anal 36 6 1808 1830 1999 an estimate of its error was sufficient we here also need to estimate the time derivative of the error which arises from the diffusion equation numerical simulation results support the theoretical findings

polynomial lpv approach to robust h control of nonlinear sampled data systems this paper addresses l2 gain analysis and robust h control of nonlinear sampled data systems described by a polynomial linear parameter varying plpv model first conditions for l2 gain analysis of sampled data plpv systems are derived using a modified krasovskii functional in which the distance between the real and measured parameters are considered as uncertainties the resulting conditions are formulated in terms of parameterised linear matrix inequalities plmi second a solution approach for satisfying plmi conditions over the set of whole parameters and uncertainties is proposed using the sum of squares decomposition method third conditions for robust h sampled data controller synthesis for nonlinear systems described by plpv models are derived in terms of parameterised bilinear matrix inequalities pbmi with the maximum allowable sampling period as the parameter to make the resulting bilinear matrix inequality bmi problems tractable an iterative algorithm is developed and utilised to s

identification of state dependent parameter models with support vector regression a support vector regression approach is presented for the identification of state dependent parameter arx models whose parameters are described as functions of past inputs and outputs the problem of identifying the state dependent parameters reduces to a standard support vector regression problem with a kernel function which is defined in terms of the kernels used to represent the individual parameters numerical examples show that the support vector method gives accurate parameter estimates for systems which have a state dependent parameter representation

numerical analysis for a system coupling curve evolution to reaction diffusion on the curve we consider a finite element approximation for a system consisting of the evolution of a closed planar curve by forced curve shortening flow coupled to a reaction diffusion equation on the evolving curve the scheme for the curve evolution is based on a parametric description allowing for tangential motion whereas the discretization for the pde on the curve uses an idea from g dziuk and c m elliott ima j numer anal 27 2007 pp 262 292 we prove optimal error bounds for the resulting fully discrete approximation and present numerical experiments these confirm our estimates and also illustrate the advantage of the tangential motion of the mesh points in practice

system identification using kautz models in this paper the problem of approximating a linear time invariant stable system by a finite weighted sum of given exponentials is considered system identification schemes using laguerre models are extended and generalized to kautz models which correspond to representations using several different possible complex exponentials in particular linear regression methods to estimate this sort of model from measured data are analyzed the advantages of the proposed approach are the simplicity of the resulting identification scheme and the capability of modeling resonant systems using few parameters the subsequent analysis is based on the result that the corresponding linear regression normal equations have a block toeplitz structure several results on transfer function estimation are extended to discrete kautz models for example asymptotic frequency domain variance expressions

variational discretization of axisymmetric curvature flows we present natural axisymmetric variants of schemes for curvature flows introduced earlier by the present authors and analyze them in detail although numerical methods for geometric flows have been used frequently in axisymmetric settings numerical analysis results so far are rare in this paper we present stability equidistribution existence and uniqueness results for the introduced approximations numerical computations show that these schemes are very efficient in computing numerical solutions of geometric flows as only a spatially one dimensional problem has to be solved the good mesh properties of the schemes also allow them to compute in very complex axisymmetric geometries

nonlinear black box models in system identification mathematical foundations we discuss several aspects of the mathematical foundations of the nonlinear black box identification problem we shall see that the quality of the identification procedure is always a result of a certain trade off between the expressive power of the model we try to identify the larger the number of parameters used to describe the model the more flexible is the approximation and the stochastic error which is proportional to the number of parameters a consequence of this trade off is the simple fact that a good approximation technique can be the basis of a good identification algorithm from this point of view we consider different approximation methods and pay special attention to spatially adaptive approximants we introduce wavelet and neuron approximations and show that they are spatially adaptive then we apply the acquired approximation experience to estimation problems finally we consider some implications of these theoretical developments for the practically implemented versions of the spatially adaptive algorithms

a convergent evolving finite element algorithm for mean curvature flow of closed surfaces a proof of convergence is given for semi and full discretizations of mean curvature flow of closed two dimensional surfaces the numerical method proposed and studied here combines evolving finite elements whose nodes determine the discrete surface like in dziuk s method and linearly implicit backward difference formulae for time integration the proposed method differs from dziuk s approach in that it discretizes huisken s evolution equations for the normal vector and mean curvature and uses these evolving geometric quantities in the velocity law projected to the finite element space this numerical method admits a convergence analysis in the case of finite elements of polynomial degree at least two and backward difference formulae of orders two to five the error analysis combines stability estimates and consistency estimates to yield optimal order h 1 norm error bounds for the computed surface position velocity normal vector and mean curvature the stability analysis is based on the matrix vector formulation of the finite element method and does not use geometric arguments the geometry enters only into the consistency estimates numerical experiments illustrate and complement the theoretical results

identification of non linear system structure and parameters using regime decomposition abstract an off line algorithm for empirical modeling and identification of non linear dynamic systems is presented the minimal input to the algorithm is a sequence of empirical data and the model order using this information the algorithm searches for an optimal model structure and parameters within a rich non linear model set the model representation is based on the interpolation of a number of simple local models where each local model has a limited range of validity but the local models yield a complete global model when interpolated the method is illustrated using simulated data

input output linearization by velocity based gain scheduling the velocity based analysis framework provides direct support for divide and conquer design approaches such as the gain scheduling control design methodology whereby the design of a non linear system is decomposed into the design of an associated family of linear systems the velocity based gain scheduling approach is quite general and directly supports the design of feedback configurations for which the closed loop dynamics are non linear however the present paper concentrates on the velocity based design of controllers which when combined with a non linear plant attain linear dynamics the resulting approach is a direct generalization to non linear systems of classical frequency domain pole zero inversion which is in many ways complementary to the input output linearization approach in particular the former is dynamic and reduces to open loop inversion in the linear case whilst the latter is essentially static and utilizes full state feedback

analytic framework for blended multiple model systems using linear local models in this paper it is shown that the dynamics of a conventional type of blended multiple model system are only weakly related to the local models from which it is formed a novel class of velocity based blended multiple model systems is proposed for which the dynamics are directly related to the local models indeed the solution to the blended multiple model system locally to a specific operating point is approximated by the weighted linear combination of the solutions to the local models moreover in contrast to conventional blended multiple model systems the velocity based blended multiple model systems employs linear local models thereby providing a degree of continuity with established linear methods and consequently facilitating analysis and design

accuracy analysis for wavelet approximations constructive wavelet networks are investigated as a universal tool for function approximation the parameters of such networks are obtained via some direct monte carlo procedures approximation bounds are given typically it is shown that such networks with one layer of wavelons achieve an l sub 2 error of order o n sup spl rhod where n is the number of nodes d is the problem dimension and spl rho is the number of summable derivatives of the approximated function an algorithm is also proposed to estimate this approximation based on noisy input output data observed from the function under consideration unlike neural network training this estimation procedure does not rely on stochastic gradient type techniques such as the celebrated backpropagation and it completely avoids the problem of poor convergence or undesirable local minima

finite element approximation of level set motion by powers of the mean curvature in this paper we study the level set formulations of certain geometric evolution equations from a numerical point of view specifically we consider the flow by powers greater than one of the mean curvature and the inverse mean curvature flow since the corresponding equations in level set form are quasilinear degenerate and especially possibly singular a regularization method is used in the literature to approximate these equations to overcome the singularities of the equations motivated by the paper 29 which studies the finite element approximation of inverse mean curvature flow we prove error estimates for the finite element approximation of the regularized equations for the flow by powers of the mean curvature we validate the rates with numerical examples additionally the regularization error in the rotational symmetric case for both flows is analyzed numerically all calculations are performed in the 2d case

l 2 estimates for the evolving surface finite element method in this paper we consider the evolving surface nite element method for the advection and di usion of a conserved scalar quantity on a moving surface in an earlier paper using a suitable variational formulation in time dependent sobolev space we proposed and analysed a nite element method using surface nite elements on evolving triangulated surfaces an optimal order h error bound was proved for linear nite elements in this work we prove the optimal error bound in l t uniformly in time

kullback leibler information and its applications in multi dimensional adaptive testing this paper first discusses the relationship between kullback leibler information kl and fisher information in the context of multi dimensional item response theory and is further interpreted for the two dimensional case from a geometric perspective this explication should allow for a better understanding of the various item selection methods in multi dimensional adaptive tests mat which are based on these two information measures the kl information index ki method is then discussed and two theorems are derived to quantify the relationship between ki and item parameters due to the fact that most of the existing item selection algorithms for mat bear severe computational complexity which substantially lowers the applicability of mat two versions of simplified kl index ski built from the analytical results are proposed to mimic the behavior of ki while reducing the overall computational intensity

on the parametric finite element approximation of evolving hypersurfaces in r 3 we present a variational formulation of motion by minus the laplacian of curvature and mean curvature flow as well as related second and fourth order flows of a closed hypersurface in r 3 on introducing a parametric finite element approximation we prove stability bounds and compare our scheme with existing approaches the presented scheme has very good properties with respect to the distribution of mesh points and if applicable volume conservation

flow by mean curvature of convex surfaces into spheres the motion of surfaces by their mean curvature has been studied by brakke 1 from the viewpoint of geometric measure theory other authors investigated the corresponding nonparametric problem 2 5 9 a reason for this interest is that evolutionary surfaces of prescribed mean curvature model the behavior of grain boundaries in annealing pure metal in this paper we take a more classical point of view consider a compact uniformly convex w dimensional surface m mo without boundary which is smoothly imbedded in r let mo be represented locally by a diffeomorphism

orthogonal least squares methods and their application to non linear system identification abstract identification algorithms based on the well known linear least squares methods of gaussian elimination cholesky decomposition classical gram schmidt modified gram schmidt householder transformation givens method and singular value decomposition are reviewed the classical gram schmidt modified gram schmidt and householder transformation algorithms are then extended to combine structure determination or which terms to include in the model and parameter estimation in a very simple and efficient manner for a class of multivariate discrete time non linear stochastic systems which are linear in the parameters

linearly implicit full discretization of surface evolution stability and convergence of full discretizations of various surface evolution equations are studied in this paper the proposed discretization combines a higher order evolving surface finite element method for space discretization with higher order linearly implicit backward difference formulae for time discretization the stability of the full discretization is studied in the matrix vector formulation of the numerical method the geometry of the problem enters into the bounds of the consistency errors but does not enter into the proof of stability numerical examples illustrate the convergence behaviour of the full discretization

convergence of finite elements on an evolving surface driven by diffusion on the surface for a parabolic surface partial differential equation coupled to surface evolution convergence of the spatial semidiscretization is studied in this paper the velocity of the evolving surface is not given explicitly but depends on the solution of the parabolic equation on the surface various velocity laws are considered elliptic regularization of a direct pointwise coupling a regularized mean curvature flow and a dynamic velocity law a novel stability and convergence analysis for evolving surface finite elements for the coupled problem of surface diffusion and surface evolution is developed the stability analysis works with the matrix vector formulation of the method and does not use geometric arguments the geometry enters only into the consistency estimates numerical experiments complement the theoretical results

estimating difficulty from polytomous categorical data a comprehensive analysis of difficulty for multiple choice items requires information at different levels the test the items and the alternatives this paper introduces a new parameterization of the nominal categories model ncm for analyzing difficulty at these three levels the new parameterization is referred to as the ne ncm and is statistically equivalent to the ncm the ne ncm is applied to a sample of responses from a logical analysis test the results suggest that the individuals execute a self terminated response process that is mostly determined by working memory load

parametric approximation of isotropic and anisotropic elastic flow for closed and open curves deckelnick and dziuk math comput 78 266 645 671 2009 proved a stability bound for a continuous in time semidiscrete parametric finite element approximation of the elastic flow of closed curves in mathbb r d d geq2 we extend these ideas in considering an alternative finite element approximation of the same flow that retains some of the features of the formulations in barrett et al j comput phys 222 1 441 462 2007 siam j sci comput 31 1 225 253 2008 ima j numer anal 30 1 4 60 2010 in particular an equidistribution mesh property for this new approximation we obtain also a stability bound for a continuous in time semidiscrete scheme apart from the isotropic situation we also consider the case of an anisotropic elastic energy in addition to the evolution of closed curves we also consider the isotropic and anisotropic elastic flow of a single open curve in the plane and in higher codimension that satisfies various boundary conditions

an algorithm for evolutionary surfaces an algorithm is presented which allows to split the calculation of the mean curvature flow of surfaces with or without boundary into a series of poisson problems on a series of surfaces this gives a new method to solve plateau s problem forh surfaces

hinging hyperplanes for regression classification and function approximation a hinge function y h x consists of two hyperplanes continuously joined together at a hinge in regression prediction classification pattern recognition and noiseless function approximation use of sums of hinge functions gives a powerful and efficient alternative to neural networks with computation times several orders of magnitude less than is obtained by fitting neural networks with a comparable number of parameters a simple and effective method for finding good hinges is presented

nonlinear regulation the piecewise linear approach this paper approaches nonlinear control problems through the use of discrete time piecewise linear systems these are systems whose next state and output maps are both described by pl maps i e by maps which are affine on each of the components of a finite polyhedral partition various results on state and output feedback observers and inverses standard for linear systems are proved for pl systems many of these results are then used in the study of more general both discrete and continuous time systems using suitable approximations

inference of disjoint linear and nonlinear sub domains of a nonlinear mapping this paper investigates new ways of inferring nonlinear dependence from measured data the existence of unique linear and nonlinear sub spaces which are structural invariants of general nonlinear mappings is established and necessary and sufficient conditions determining these sub spaces are derived the importance of these invariants in an identification context is that they provide a tractable framework for minimising the dimensionality of the nonlinear modelling task specifically once the linear nonlinear sub spaces are known by definition the explanatory variables may be transformed to form two disjoint sub sets spanning respectively the linear and nonlinear sub spaces the nonlinear modelling task is confined to the latter sub set which will typically have a smaller number of elements than the original set of explanatory variables constructive algorithms are proposed for inferring the linear and nonlinear sub spaces from noisy data

reporting of subscores using multidimensional item response theory recently there has been increasing interest in reporting subscores this paper examines reporting of subscores using multidimensional item response theory mirt models e g reckase in appl psychol meas 21 25 36 1997 c r rao and s sinharay eds handbook of statistics vol 26 pp 607 642 north holland amsterdam 2007 beguin glas in psychometrika 66 471 488 2001 a mirt model is fitted using a stabilized newton raphson algorithm haberman in the analysis of frequency data university of chicago press chicago 1974 sociol methodol 18 193 211 1988 with adaptive gauss hermite quadrature haberman von davier lee in ets research rep no rr 08 45 ets princeton 2008 a new statistical approach is proposed to assess when subscores using the mirt model have any added value over i the total score or ii subscores based on classical test theory haberman in j educ behav stat 33 204 229 2008 haberman sinharay puhan in br j math stat psychol 62 79 95 2008 the mirt based methods are applied to several operational data sets the results show that the subscores based on mirt are slightly more accurate than subscore estimates derived by classical test theory

parametric approximation of willmore flow and related geometric evolution equations we present various variational approximations of willmore flow in mathbb r d d 2 3 as well as the classic willmore flow we also consider variants that are a volume preserving and b volume and area preserving the latter evolution law is the so called helfrich flow in addition we consider motion by gaus curvature the presented fully discrete schemes are easy to solve as they are linear at each time level and they have good properties with respect to the distribution of mesh points finally we present numerous numerical experiments including simulations for energies appearing in the modeling of biological cell membranes

a simple mesh generator in matlab creating a mesh is the first step in a wide range of applications including scientific computing and computer graphics an unstructured simplex mesh requires a choice of meshpoints vertex nodes

fully implicit linearly implicit and implicit explicit backward difference formulae for quasi linear parabolic equations quasi linear parabolic equations are discretised in time by fully implicit backward difference formulae bdf as well as by implicit explicit and linearly implicit bdf methods up to order five under appropriate stability conditions for the various methods considered we establish optimal order a priori error bounds by energy estimates which become applicable via the nevanlinna odeh multiplier technique

the wavelet transform time frequency localization and signal analysis two different procedures for effecting a frequency analysis of a time dependent signal locally in time are studied the first procedure is the short time or windowed fourier transform the second is the wavelet transform in which high frequency components are studied with sharper time resolution than low frequency components the similarities and the differences between these two methods are discussed for both schemes a detailed study is made of the reconstruction method and its stability as a function of the chosen time frequency density finally the notion of time frequency localization is made precise within this framework by two localization theorems

orthogonal least squares learning algorithm for radial basis function networks the radial basis function network offers a viable alternative to the two layer neural network in many applications of signal processing a common learning algorithm for radial basis function networks is based on first choosing randomly some data points as radial basis function centers and then using singular value decomposition to solve for the weights of the network such a procedure has several drawbacks and in particular an arbitrary selection of centers is clearly unsatisfactory the authors propose an alternative learning procedure based on the orthogonal least squares method the procedure chooses radial basis function centers one by one in a rational way until an adequate network has been constructed in the algorithm each selected center maximizes the increment to the explained variance or energy of the desired output and does not suffer numerical ill conditioning problems the orthogonal least squares learning strategy provides a simple and efficient means for fitting radial basis function networks this is illustrated using examples taken from two different signal processing applications

multidimensional cat item selection methods for domain scores and composite scores theory and applications multidimensional computer adaptive testing mcat can provide higher precision and reliability or reduce test length when compared with unidimensional cat or with the paper and pencil test this study compared five item selection procedures in the mcat framework for both domain scores and overall scores through simulation by varying the structure of item pools the population distribution of the simulees the number of items selected and the content area the existing procedures such as volume segall in psychometrika 61 331 354 1996 kullback leibler information veldkamp van der linden in psychometrika 67 575 588 2002 minimize the error variance of the linear combination van der linden in j educ behav stat 24 398 412 1999 and minimum angle reckase in multidimensional item response theory springer new york 2009 are compared to a new procedure minimize the error variance of the composite score with the optimized weight proposed for the first time in this study the intent is to find an item selection procedure that yields higher precisions for both the domain and composite abilities and a higher percentage of selected items from the item pool the comparison is performed by examining the absolute bias correlation test reliability time used and item usage three sets of item pools are used with the item parameters estimated from real live cat data results show that volume and minimum angle performed similarly balancing information for all content areas while the other three procedures performed similarly with a high precision for both domain and overall scores when selecting items with the required number of items for each domain the new item selection procedure has the highest percentage of item usage moreover for the overall score it produces similar or even better results compared to those from the method that selects items favoring the general dimension using the general model segall in psychometrika 66 79 97 2001 the general dimension method has low precision for the domain scores in addition to the simulation study the mathematical theories for certain procedures are derived the theories are confirmed by the simulation applications

a stable numerical method for the dynamics of fluidic membranes we develop a finite element scheme to approximate the dynamics of two and three dimensional fluidic membranes in navier stokes flow local inextensibility of the membrane is ensured by solving a tangential navier stokes equation taking surface viscosity effects of boussinesq scriven type into account in our approach the bulk and surface degrees of freedom are discretized independently which leads to an unfitted finite element approximation of the underlying free boundary problem bending elastic forces resulting from an elastic membrane energy are discretized using an approximation introduced by dziuk numer math 111 55 80 2008 the obtained numerical scheme can be shown to be stable and to have good mesh properties finally the evolution of membrane shapes is studied numerically in different flow situations in two and three space dimensions the numerical results demonstrate the robustness of the method and it is observed that the conservation properties are fulfilled to a high precision

orthogonal parameter estimation algorithm for non linear stochastic systems an orthogonal parameter estimation algorithm is derived which allows each parameter in a linear in the parameters non linear difference equation model to be estimated sequentially and quite independently of the other parameters in the model the algorithm can be applied for any persistently exciting input and provides both unbiased estimates in the presence of correlated noise and an indication of which terms to include in the model several simulated examples are included to demonstrate the effectiveness of the algorithm

an algebraic framework generalizing the concept of transfer functions to nonlinear systems an algebraic point of view in nonlinear control systems built up by introducing a differential field of meromorphic functions and a vector space of differential forms is in this paper extended by introducing skew polynomials such polynomials act as operators over a vector space of differential forms the left skew polynomial ring defined over the field of meromorphic functions is embedded to its quotient field to provide a basis for a symbolic computation of nonlinear systems members of such a quotient field are suggested as the transfer functions of nonlinear systems whereby the concept of the transfer functions is generalized to nonlinear systems the theory is applied to nonlinear control systems and argues the invariance of introduced transfer functions of nonlinear systems to static state transformations the existence of input output descriptions for state space representations availability of transfer function algebra for nonlinear systems etc

on the hinge finding algorithm for hingeing hyperplanes this correspondence concerns the estimation algorithm for hinging hyperplane hh models a piecewise linear model for approximating functions of several variables suggested in breiman 1993 the estimation algorithm is analyzed and it is shown that it is a special case of a newton algorithm applied to a sum of squared error criterion this insight is then used to suggest possible improvements of the algorithm so that convergence to a local minimum can be guaranteed in addition the way of updating the parameters in the hh model is discussed in breiman a stepwise updating procedure is proposed where only a subset of the parameters are changed in each step this connects closely to some previously suggested greedy algorithms and these greedy algorithms are discussed and compared to a simultaneous updating of all parameters

convergence of a finite element method for non parametric mean curvature flow convergence for the spatial discretization by linear finite elements of the non parametric mean curvature flow is proved under natural regularity assumptions on the continuous solution asymptotic convergence is also obtained for the time derivative which is proportional to mean curvature an existence result for the continuous problem in adequate spaces is included

gain scheduled controller design an analytic framework directly incorporating non equilibrium plant dynamics a velocity based linearization framework is employed to develop a novel rigorous approach to gain scheduling design the proposed approach enables knowledge concerning the plant dynamics at non equilibrium operating points to be incorporated directly into the controller design since the velocity based linearization framework supports the analysis of the transient response performance considerations can be accommodated the approach retains continuity with linear methods which is central to the existing conventional gain scheduling methodology and since a single type of linearization is employed throughout the design procedure is both straightforward and conceptually appealing

nonlinear black box modeling in system identification a unified overview a nonlinear black box structure for a dynamical system is a model structure that is prepared to describe virtually any nonlinear dynamics there has been considerable recent interest in this area with structures based on neural networks radial basis networks wavelet networks and hinging hyperplanes as well as wavelet transform based methods and models based on fuzzy sets and fuzzy rules this paper describes all these approaches in a common framework from a user s perspective it focuses on what are the common features in the different approaches the choices that have to be made and what considerations are relevant for a successful system identification application of these techniques it is pointed out that the nonlinear structures can be seen as a concatenation of a mapping form observed data to a regression vector and a nonlinear mapping from the regressor space to the output space these mappings are discussed separately the latter mapping is usually formed as a basis function expansion the basis functions are typically formed from one simple scalar function which is modified in terms of scale and location the expansion from the scalar argument to the regressor space is achieved by a radial or a ridge type approach basic techniques for estimating the parameters in the structures are criterion minimization as well as two step procedures where first the relevant basis functions are determined using data and then a linear least squares step to determine the coordinates of the function approximation a particular problem is to deal with the large number of potentially necessary parameters this is handled by making the number of used parameters considerably less than the number of offered parameters by regularization shrinking pruning or regressor selection

multidimensional adaptive testing with optimal design criteria for item selection several criteria from the optimal design literature are examined for use with item selection in multidimensional adaptive testing in particular it is examined what criteria are appropriate for adaptive testing in which all abilities are intentional some should be considered as a nuisance or the interest is in the testing of a composite of the abilities both the theoretical analyses and the studies of simulated data in this paper suggest that the criteria of a optimality and d optimality lead to the most accurate estimates when all abilities are intentional with the former slightly outperforming the latter the criterion of e optimality showed occasional erratic behavior for this case of adaptive testing and its use is not recommended if some of the abilities are nuisances application of the criterion of as optimality or ds optimality which focuses on the subset of intentional abilities is recommended for the measurement of a linear combination of abilities the criterion of c optimality yielded the best results the preferences of each of these criteria for items with specific patterns of parameter values was also assessed it was found that the criteria differed mainly in their preferences of items with different patterns of values for their discrimination parameters