Bayesian inversion is at the heart of probabilistic programming and more generally machine learning. Understanding inversion is made difficult by the pointful (kernel-centric) point of view usually taken in the literature. We develop a pointless (kernel-free) approach to inversion. While doing so, we revisit some foundational objects of probability theory, unravel their category-theoretical underpinnings and show how pointless Bayesian inversion sits naturally at the centre of this construction. P (d) · P (h | d) = P (d | h) · P (h)(1)
Bisimulation is a concept that captures behavioural equivalence. It has been studied extensively on nonprobabilistic systems and on discrete-time Markov processes and on so-called continuous-time Markov chains. In the latter time is continuous but the evolution still proceeds in jumps. We propose two definitions of bisimulation on continuoustime stochastic processes where the evolution is a flow through time. We show that they are equivalent and we show that when restricted to discrete-time, our concept of bisimulation encompasses the standard discrete-time concept. The concept we introduce is not a straightforward generalization of discrete-time concepts.
Des récits espagnols du XVIe siècle dont l'action se situait à la frontière entre la terre chrétienne et le royaume de Grenade, dernier royaume musulman d'Espagne, à la fin de la Reconquête, ont joué un rôle de premier plan dans la transmission d'un héritage historique multiculturel fait à la fois de coexistence et de conflit. L'anonyme Abencerraje, les Guerras civiles de Granad de Pérez de Hita et la nouvelle «Ozmfn et Daraja» insérée dans le roman picaresque Guzman de Alfarache de Mateo Alemân sont les « romans mauresques » qui ont rénové la prose de fiction en créant un type littéraire, celui du gentilhomme maure, guerrier émérite et amant accompli qui suscite l'admiration et l'amitié du noble chrétien dont il est le captif. La tradition a ainsi entretenu le souvenir d'une cohabitation qu'elle a idéalisée en exaltant les vertus chevaleresques partagées. La « maurophilie » contribue-t-elle au marquage des frontières culturelles ou suggère-t-elle une autre définition identitaire, qui inclut l'Autre sans le réduire ?
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