Safety requirements in dynamical systems are commonly enforced with set invariance constraints over a safe region of the state space. Control barrier functions, which Lyapunov-like functions for guaranteeing invariance, an effective tool to enforce such and guarantee safety when system is represented as point In this paper, we introduce extent-compatible control explicitly accounting its volume...

This paper studies non-crossing geometric perfect matchings. Two such perfect matchings are compatible if they have the same vertex set and their union is also non-crossing. Our first result states that for any two perfect matchings M and M ′ of the same set of n points, for some k ∈ O(log n), there is a sequence of perfect matchings M = M0,M1, . . . ,Mk = M , such that each Mi is compatible wi...

We study a model in which a "statistician" takes an action on behalf of an agent, based on a random sample involving other people. The statistician follows a penalized regression procedure: the action that he takes is the dependent variable’s estimated value given the agent’s disclosed personal characteristics. We ask the following question: Is truth-telling an optimal disclosure strategy for t...

Half a century ago, Noam Chomsky introduced the field of linguistics to new mathematical tools drawn largely from recursive function theory. These were exciting tools that imparted mathematical precision, perhaps for the first time in the history of Linguistics, to the enterprise of grammar construction. The cornerstone of Chomsky’s new theoretical edifice, was the grammatical transformation, a...