We extract a quantitative variant of uniqueness from the usual hypotheses of the implicit functions theorem. This leads not only to an a priori proof of continuity, but also to an ...
We consider a general class of regularization methods which learn a vector of parameters on the basis of linear measurements. It is well known that if the regularizer is a nondecr...
Andreas Argyriou, Charles A. Micchelli, Massimilia...
imps is an Interactive Mathematical Proof System intended as a general purpose tool for formulating and applying mathematics in a familiar fashion. The logic of imps is based on a...
William M. Farmer, Joshua D. Guttman, F. Javier Th...
: The bene ts of the object, logic or relational, functional, and constraint paradigms can be obtained from our previous combination of the object and functional paradigms in hidde...
A function f is continuous iff the pre-image f −1[V ] of any open setV is open again. Dual to this topological7 property, f is called open iff the image f [U] of any open set U ...