Minimizing variational curves restricted to a preassigned set

Minimizing Variational Curves Restricted to a Preassigned Set

Existence of set-interpolating and energy-minimizing curves

We consider existence of curves c : [0, 1] → R which minimize an energy of the form ∫ ‖c‖ (k = 1, 2, . . . , 1 < p < ∞) under side-conditions of the form Gj(c(t1,j), . . . , c (tk,j)) ∈ Mj , where Gj is a continuous function, ti,j ∈ [0, 1], Mj is some closed set, and the indices j range in some index set J . This includes the problem of finding energy minimizing interpolants restricted to surfa...

A Variational Approach to Learning Curves

We combine the replica approach from statistical physics with a variational approach to analyze learning curves analytically. We apply the method to Gaussian process regression. As a main result we derive approximative relations between empirical error measures, the generalization error and the posterior variance.

Minimizing Restricted-Fanout Queries

Sagiv, Y. and Y. Saraiya, Minimizing restricted-fanout queries, Discrete Applied Mathematics 40 ( 1992) 2455264. Conjunctive queries form an important subset of relational algebra. Each conjunctive query has a unique minimum equivalent (up to isomorphism). However, the computation of the minimum equivalent is complete for co-. u% Johnson and Klug have proposed a subclass of conjunctive queries,...

A variational approach to spline curves on surfaces

Given an m-dimensional surface Φ in R, we characterize parametric curves in Φ, which interpolate or approximate a sequence of given points p i ∈ Φ and minimize a given energy functional. As energy functionals we study familiar functionals from spline theory, which are linear combinations of L norms of certain derivatives. The characterization of the solution curves is similar to the well-known ...