Difference Minimizing Theory

Elasticity-based Matching by Minimizing the Symmetric Difference of Shapes

We consider the problem of matching two shapes assuming these shapes are related by an elastic deformation. Using linearized elasticity theory and the finite element method we seek an elastic deformation that is caused by simple external boundary forces and accounts for the difference between the two shapes. Our main contribution is in proposing a cost function and an optimization procedure to ...

Minimizing the symmetric difference distance in conic spline approximation

We show that the complexity (the number of elements) of an optimal parabolic or conic spline approximating a smooth curve with nonvanishing curvature to within symmetric difference distance ε is c1 ε −1/4 + O(1), if the spline consists of parabolic arcs and c2 ε −1/5 +O(1), if it is composed of general conic arcs of varying type. The constants c1 and c2 are expressed in the affine curvature of ...

Model Theory of Difference Fields

The purpose of this course is to learn the fundamental results about the model theory of difference fields, as developed in Chatzidakis and Hrushovski [10]. The goal is to get to a level that will allow reading that paper. In this section we give some basic definitions, and mention some of the applications of this theory. A more detailed description of the content of the course can be found in ...

Stability Theory for Difference Approximations

are given, u1 and u11 are defined according to the partition of A, i.e. u1 = (wU), • • -, um)', ulL = (w<!+1), • • -, uM)', and *S is a given constant rectangular matrix. It is well known that the above problem is correctly posed in L2 (see for example Thomée [4]). The present treatment of the case when A is a constant matrix can be extended, as in [1], to the case when A depends on (x, t) in a...

Introduction to difference algebra and model theory of difference fields