Mohammed Ben Alhocain, in an Arab manuscript of the 10th century, stated that the principal object of the theory of rational right triangles is to find a square that when increased or diminished by a certain number, m becomes a square [Dickson LE (1971) History of the Theory of Numbers (Chelsea, New York), Vol 2, Chap 16]. In modern language, this object is to find a rational point of infinite ...

This paper deals with the problem of estimating an appropriate hand posture to grasp an object, from 2D object’s visual cues in a many-to-many (objects,grasp) configuration. A statistical learning protocol implementing vector-valued regression is adopted for both classifying the most likely grasp type and estimating the hand posture. An extensive experimental evaluation on a publicly available ...

We show that the full version of the so-called ‘rural hospital theorem’ generalizes to many-to-many matching problems where agents on both sides of the problem have substitutable and weakly separable preferences. We also show that when agents’ preferences satisfy substitutability, the domain of weakly separable pref-

In this note, I extend the work of Echenique (forthcoming) to show that a model of many-to-many matching with contracts may be embedded into a model of many-tomany matching with wage bargaining whenever (1) all agents’ preferences are substitutable and (2) the matching with contracts model is unitary, in the sense that every contractual relationship between a given firm–worker pair is specified...