Let ρ be an unknown Borel measure defined on the space Z := X × Y with X ⊂ IR and Y = [−M,M ]. Given a set z ofm samples zi = (xi, yi) drawn according to ρ, the problem of estimating a regression function fρ using these samples is considered. The main focus is to understand what is the rate of approximation, measured either in expectation or probability, that can be obtained under a given prior...

The marriage of art and mathematics has been widespread and productive, but almost nowhere more productive than in the world of origami. In this paper I will discuss how mathematical ideas led to the development of powerful tools for origami design and will present a step-by-step illustration of the design and realization of a representational origami figure using mathematical design algorithms...

1. Chronological remarks. The main source for our knowledge of ancient astronomy is Ptolemy. His Mathematical composition, commonly known as the Almagest, quotes observations of his own ranging from 127 to 142 A.D. [35; 36; 37]. This work seems to be the earliest of a whole series of fundamental works, such as his Geography [41 ], the Tetrabiblos [39; 40], and so on, whose influence on mediaeva...