Model bicategories and their homotopy bicategories

We give the definitions of model bicategory and $w$-homotopy, which are natural generalizations of the notions of model category and homotopy to the context of bicategories. For any model bicategory $\mathcal{C}$, denote by $\mathcal{C}_{fc}$ the full sub-bicategory of the fibrant-cofibrant objects. We prove that the 2-dimensional localization of $\mathcal{C}$ at the weak equivalences can be computed as a bicategory \mathcal{H}\mbox{o}(\mathcal{C}) whose objects and arrows are those of $\mathcal{C}_{fc}$ and whose 2-cells are classes of $w$-homotopies up to an equivalence relation. The pseudofunctor \mathcal{C} \stackrel{r}{\longrightarrow} \mathcal{H}\mbox{o}(\mathcal{C}) which yields the localization is constructed by using a notion of fibrant-cofibrant replacement in this context. When considered for a model category, the results in this article give in particular a bicategory whose reflection into categories is the usual homotopy category constructed by Quillen.Comment: 37 pages, many elevator calculus diagrams. This is a "preliminary version

Axiomatizations for downward XPath on Data Trees

We give sound and complete axiomatizations for XPath with data tests by "equality" or "inequality", and containing the single "child" axis. This data-aware logic predicts over data trees, which are tree-like structures whose every node contains a label from a finite alphabet and a data value from an infinite domain. The language allows us to compare data values of two nodes but cannot access the data values themselves (i.e. there is no comparison by constants). Our axioms are in the style of equational logic, extending the axiomatization of data-oblivious XPath, by B. ten Cate, T. Litak and M. Marx. We axiomatize the full logic with tests by "equality" and "inequality", and also a simpler fragment with "equality" tests only. Our axiomatizations apply both to node expressions and path expressions. The proof of completeness relies on a novel normal form theorem for XPath with data tests

Closure properties of synchronized relations

International audienceA standard approach to define k-ary word relations over a finite alphabet A is through k-tape finite state automata that recognize regular languages L over {1,. .. , k} × A, where (i, a) is interpreted as reading letter a from tape i. Accordingly, a word w ∈ L denotes the tuple (u1,...,uk) ∈ (A*)^k in which ui is the projection of w onto i-labelled letters. While this formalism defines the well-studied class of rational relations, enforcing restrictions on the reading regime from the tapes, which we call synchronization, yields various sub-classes of relations. Such synchronization restrictions are imposed through regular properties on the projection of the language L onto {1,..., k}. In this way, for each regular language C ⊆ {1,..., k}*, one obtains a class Rel(C) of relations. Synchronous, Recognizable, and Length-preserving rational relations are all examples of classes that can be defined in this way. We study basic properties of these classes of relations, in terms of closure under intersection, complement, concatenation, Kleene star and projection. We characterize the classes with each closure property. For the binary case (k = 2) this yields effective procedures

A theory of 2-Pro-objects

In [1], Grothendieck develops the theory of pro-objects over a category C . The fundamental property of the category Pro(C) is that there is an embedding C c −→ Pro(C), the category Pro(C) is closed under small cofiltered limits, and these limits are free in the sense that for any category E closed under small cofiltered limits, pre-composition with c determines an equivalence of categories Cat(Pro(C), E)+ 'Cat(C, E), (where the ” + ” indicates the full subcategory of the functors preserving cofiltered limits). In this paper we develop a 2-dimensional theory of pro-objects. Given a 2-category C , we define the 2-category 2-Pro(C) whose objects we call 2-pro-objects. We prove that 2-Pro(C) has all the expected basic properties adequately relativized to the 2-categorical setting, including the universal property corresponding to the one described above. We have at hand the results of Cat -enriched category theory, but our theory goes beyond the Cat -enriched case since we consider the non strict notion of pseudo-limit, which is usually that of practical interest.Fil: Descotte, María Emilia. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Dubuc, Eduardo Julio. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Resynchronizing classes of word relations

A natural approach to defining binary word relations over a finite alphabet A is through two-tape finite state automata, which can be seen as regular language L over {1,2} x A, where (i,a) is interpreted as reading letter a from tape i. Thus, a word w of the language L denotes the pair (u_1,u_2) in A* x A* in which u_i is the projection of w onto i-labelled letters. While this formalism defines the well-studied class of Rational relations (a.k.a. non-deterministic finite state transducers), enforcing restrictions on the reading regime from the tapes, that we call synchronization, yields various sub-classes of relations. Such synchronization restrictions are imposed through regular properties on the projection of the language onto {1,2}. In this way, for each regular language C contained in {1,2}*, one obtains a class Rel(C) of relations, such as the classes of Regular, Recognizable, or length-preserving relations, as well as (infinitely) many other classes. We study the problem of containment for synchronized classes of relations: given C,D subsets of {1,2}*, is Rel(C) contained in Rel(D)? We show a characterization in terms of C and D which gives a decidability procedure to test for class inclusion. This also yields a procedure to re-synchronize languages from {1,2} x A preserving the denoted relation whenever the inclusion holds

Pico hydro turbines for electricity in rural areas

This article discusses the feedback and lessons learned, particularly from a survey carried out following the deployment program of a pico hydro power solution in a very isolated rural area in north Laos. This project is part of the strategic development for the rural electrification of Laos, in which pico hydro power facilities constitute the main avenue of progress for the electrification of isolated villages

A localization of bicategories via homotopies

Given a bicategory C and a family W of arrows of C, we give conditions on the pair (C, W) that allow us to construct the bicategorical localization with respect to W by dealing only with the 2-cells, that is without adding objects or arrows to C. We show that in this case, the 2-cells of the localization can be given by the homotopies with respect to W, a notion defined in this article which is closely related to Quillen’s notion of homotopy for model categories but depends only on a single family of arrows. This localization result has a natural application to the construction of the homotopy bicategory of a model bicategory, which we develop elsewhere, as the pair (Cf c, W) given by the weak equivalences between fibrant-cofibrant objects satisfies the conditions given in the present article.Fil: Descotte, María Emilia. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Dubuc, Eduardo Julio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Szyld, M.. Dalhousie University Halifax; Canad

Thomas Hobbes: Antropología y política en el Leviatán.

La lectura renovada del filósofo inglés Thomas Hobbes (1588-1679) nos ha llevado a reexaminar las tesis fundamentales de su pen­samiento. El tricentenario de su muerte fue una fecha propicia para que se volviera sobre la reflexión de Hobbes en el marco de una Euro­pa que comenzaba a ser traspasada por el espíritu de la modernidad. Seminario, coloquios, ediciones críticas, fueron algunos de los frutos -en 1979- de este regreso al pensador británico