¿Deben las universidades imitar a la industria?

This article shows the risks for the University’s identity in the current knowledge society. The prestigious American mathematician dead in 2005, argues that the universities in the United States have been affected by the dismantling of research industrial laboratories and their transfer to the academic area. According to Mac Lane, this and other factors like a managerialist conception of education, are deforming university research work subordinating it to the logic of short-run outcomes.Este artículo señala los peligros que existen para la identidad de la universidad en la actual era de la sociedad del conocimiento. El prestigioso matemático norteamericano fallecido en 2005 sostiene que las universidades en los Estados Unidos se han visto afectadas por el desmantelamiento de los laboratorios de investigación industriales y su traslado al ámbito académico. De acuerdo a Mac Lane, éste y otros factores como una concepción managerialista de la educación están llevando a la deformación de la investigación universitaria sometiéndola a la lógica de los resultados inmediatos

Interaction laws of monads and comonads

We introduce and study functor-functor and monad-comonad interaction laws as mathematical objects to describe interaction of effectful computations with behaviors of effect-performing machines. Monad-comonad interaction laws are monoid objects of the monoidal category of functor-functor interaction laws. We show that, for suitable generalizations of the concepts of dual and Sweedler dual, the greatest functor resp. monad interacting with a given functor or comonad is its dual while the greatest comonad interacting with a given monad is its Sweedler dual. We relate monad-comonad interaction laws to stateful runners. We show that functor-functor interaction laws are Chu spaces over the category of endofunctors taken with the Day convolution monoidal structure. Hasegawa's glueing endows the category of these Chu spaces with a monoidal structure whose monoid objects are monad-comonad interaction laws

Innocent strategies as presheaves and interactive equivalences for CCS

Seeking a general framework for reasoning about and comparing programming languages, we derive a new view of Milner's CCS. We construct a category E of plays, and a subcategory V of views. We argue that presheaves on V adequately represent innocent strategies, in the sense of game semantics. We then equip innocent strategies with a simple notion of interaction. This results in an interpretation of CCS. Based on this, we propose a notion of interactive equivalence for innocent strategies, which is close in spirit to Beffara's interpretation of testing equivalences in concurrency theory. In this framework we prove that the analogues of fair and must testing equivalences coincide, while they differ in the standard setting.Comment: In Proceedings ICE 2011, arXiv:1108.014

Dependently-Typed Formalisation of Typed Term Graphs

We employ the dependently-typed programming language Agda2 to explore formalisation of untyped and typed term graphs directly as set-based graph structures, via the gs-monoidal categories of Corradini and Gadducci, and as nested let-expressions using Pouillard and Pottier's NotSoFresh library of variable-binding abstractions.Comment: In Proceedings TERMGRAPH 2011, arXiv:1102.226

Bisimilarity and refinement for hybrid(ised) logics

The complexity of modern software systems entails the need for reconfiguration mechanisms governing the dynamic evolution of their execution configurations in response to both external stimulus or internal performance measures. Formally, such systems may be represented by transition systems whose nodes correspond to the different configurations they may assume. Therefore, each node is endowed with, for example, an algebra, or a first-order structure, to precisely characterise the semantics of the services provided in the corresponding configuration. Hybrid logics, which add to the modal description of transition structures the ability to refer to specific states, offer a generic framework to approach the specification and design of this sort of systems. Therefore, the quest for suitable notions of equivalence and refinement between models of hybrid logic specifications becomes fundamental to any design discipline adopting this perspective. This paper contributes to this effort from a distinctive point of view: instead of focussing on a specific hybrid logic, the paper introduces notions of bisimilarity and refinement for hybridised logics, i.e. standard specification logics (e.g. propositional, equational, fuzzy, etc) to which modal and hybrid features were added in a systematic way.FC

The 1982 Nora and Edward Ryerson Lecture at The University of Chicago

http://deepblue.lib.umich.edu/bitstream/2027.42/60187/1/Reprint91MacLane.pd

La vitalitat de les matemàtiques

La recerca matemàtica aborda avui la solució de vells i nous problemes, molts d'ells plantejats pel conjunt de la ciènci

Homology

x, 422 p. ; 24 cm