vVe discuss procedures based on non parametric regression for estimating the dominant Lyapunov exponent Al from time-series data generated by a system xt =f(xt _l' x t _2' ... xt_d)+o-et , where XtEIR, and {et } is an iid sequence of random variables. For systems with bounded fluctuations in x t ' '\1 >0 is the defining feature of chaos. vVe show that any consistent estimator of the partial of/...

Radial basis functions are used in the recovery step of nite volume methods for the numerical solution of conservation laws. Being conditionally positive deenite such functions generate optimal recovery splines in the sense of Micchelli and Rivlin in associated native spaces. We analyse the solvability to the recovery problem of point functionals from cell average values with radial basis funct...

Non-rigid registration requires a smoothness or regularization term for making the warp field regular. Standard models in use here include b-splines and thin plate splines. In this paper, we suggest a regularizer which is based on first principles, is symmetric with respect to source and destination, and fulfills a natural semi-group property for warps. We construct the regularizer from a distr...

This paper describes a method for estimating insurance claims or risk premiums allowing for spatial dependence as well as explanatory factors. The concepts are related to those used for graduation of mortality tables using cubic splines but extended to spatial dependence as found in many insurance products. Firstly techniques for measuring spatial dependence are reviewed. Then models with bivar...

Splines can be used to approximate noisy data with a few control points. This paper presents a new curve matching method for deformable shapes using two-dimensional splines. In contrast to the residual error criterion [7], which is based on relative locations of corresponding knot points such that is reliable primarily for dense point sets, we use deformation energy of thin-plate-spline mapping...

........................................................................................................................................ III ABBREVIATIONS ............................................................................................................................. VI LIST OF FIGURES.....................................................................................................

We study a vectorial approximation problem based on thin plate spline with tension involving two positive parameters one for a control of the oscillations and the other one allows a control on the divergence and rotational components of the field. The existence and uniqueness of the solution is proved and the solution is explicitly given. We study the limit problems and the convergence problem ...

Radial basis functions under tension (RBFT) depend on a positive parameter, incorporate the concept of spline with tension and provide a convenient way for the control of the behavior of the interpolating surface. The RBFT involve a function which is not complicated than exponential and may be easily coded. In this paper, we show that the RBFT, as like thin plate spline, may be associated to a ...