Indexed induction and coinduction, fibrationally.

This paper extends the fibrational approach to induction and coinduction pioneered by Hermida and Jacobs, and developed by the current authors, in two key directions. First, we present a sound coinduction rule for any data type arising as the final coalgebra of a functor, thus relaxing Hermida and Jacobs’ restriction to polynomial data types. For this we introduce the notion of a quotient category with equality (QCE), which both abstracts the standard notion of a fibration of relations constructed from a given fibration, and plays a role in the theory of coinduction dual to that of a comprehension category with unit (CCU) in the theory of induction. Second, we show that indexed inductive and coinductive types also admit sound induction and coinduction rules. Indexed data types often arise as initial algebras and final coalgebras of functors on slice categories, so our key technical results give sufficent conditions under which we can construct, from a CCU (QCE) U : E -> B, a fibration with base B/I that models indexing by I and is also a CCU (QCE)

SIMONE WEIL: A SENSE OF GOD

There is a reality outside of the world, that is to say, outside spaceand time, outside man’s mental universe, outside any sphere ofwhatsoever that is accessible to human faculties.Corresponding to this reality, at the center of the human heart, is thelonging for an absolute good, a longing which is always there and isnever appeased by any object in this world.SIMONE WEIL1909-194

The Catholic Church in the Philippine Public Sphere

Whether religion has a place in the public sphere is a complex issue. Many thinkers believed that the rationalization process of modernity would result in secularization and banish religion into the private sphere. Religion has not only survived; it has even taken an active role in the political affairs of the state. This has been the case in countries like the Philippines where the publicity and activism of the Catholic hierarchy in the political public sphere of the country have been sustained and to some extent dominant. Said publicity and activism are carried out in the name of religion and the pursuit of a religious mandate accordingly. Although the reactions to such public involvement have not always been the same, these varying reactions still make sense in light of some theoretical understanding about the specifically political role of religion in the modern society. The aim of this paper is to make a modest contribution to such understanding by reflecting on the place and function of religion in the public sphere. It trains a special focus on the Philippine experience and employs mainly the view of Jürgen Habermas, an “agnostic and secular thinker” but one who has written extensively on the public sphere and recently revised his stance from thinking that religion will be overtaken by the rationalization of society to admitting that religion has something important to contribute in the public sphere

Fibrational induction rules for initial algebras

This paper provides an induction rule that can be used to prove properties of data structures whose types are inductive, i.e., are carriers of initial algebras of functors. Our results are semantic in nature and are inspired by Hermida and Jacobs’ elegant algebraic formulation of induction for polynomial data types. Our contribution is to derive, under slightly different assumptions, an induction rule that is generic over all inductive types, polynomial or not. Our induction rule is generic over the kinds of properties to be proved as well: like Hermida and Jacobs, we work in a general fibrational setting and so can accommodate very general notions of properties on inductive types rather than just those of particular syntactic forms. We establish the correctness of our generic induction rule by reducing induction to iteration. We show how our rule can be instantiated to give induction rules for the data types of rose trees, finite hereditary sets, and hyperfunctions. The former lies outside the scope of Hermida and Jacobs’ work because it is not polynomial; as far as we are aware, no induction rules have been known to exist for the latter two in a general fibrational framework. Our instantiation for hyperfunctions underscores the value of working in the general fibrational setting since this data type cannot be interpreted as a set

Fibrational induction meets effects

This paper provides several induction rules that can be used to prove properties of effectful data types. Our results are semantic in nature and build upon Hermida and Jacobs’ fibrational formulation of induction for polynomial data types and its extension to all inductive data types by Ghani, Johann, and Fumex. An effectful data type μ(TF) is built from a functor F that describes data, and a monad T that computes effects. Our main contribution is to derive induction rules that are generic over all functors F and monads T such that μ(TF) exists. Along the way, we also derive a principle of definition by structural recursion for effectful data types that is similarly generic. Our induction rule is also generic over the kinds of properties to be proved: like the work on which we build, we work in a general fibrational setting and so can accommodate very general notions of properties, rather than just those of particular syntactic forms. We give examples exploiting the generality of our results, and show how our results specialize to those in the literature, particularly those of Filinski and Støvring

Selective and highly efficient dye scavenging by a pH-responsive molecular hydrogelator

A structurally simple low molecular weight hydrogelator derived from isophthalic acid forms robust pH-responsive hydrogels capable of highly efficient and selective dye adsorption

El uso de recursos tecnológicos como forma de expresión cultural : ha encaminado a creadores y espectadores a tener una percepción alternativa de la realidad

El uso de recursos tecnológicos como forma de expresión cultural ha encaminado a creadores y espectadores a tener una percepción alternativa de la realida

Generic Fibrational Induction

This paper provides an induction rule that can be used to prove properties of data structures whose types are inductive, i.e., are carriers of initial algebras of functors. Our results are semantic in nature and are inspired by Hermida and Jacobs' elegant algebraic formulation of induction for polynomial data types. Our contribution is to derive, under slightly different assumptions, a sound induction rule that is generic over all inductive types, polynomial or not. Our induction rule is generic over the kinds of properties to be proved as well: like Hermida and Jacobs, we work in a general fibrational setting and so can accommodate very general notions of properties on inductive types rather than just those of a particular syntactic form. We establish the soundness of our generic induction rule by reducing induction to iteration. We then show how our generic induction rule can be instantiated to give induction rules for the data types of rose trees, finite hereditary sets, and hyperfunctions. The first of these lies outside the scope of Hermida and Jacobs' work because it is not polynomial, and as far as we are aware, no induction rules have been known to exist for the second and third in a general fibrational framework. Our instantiation for hyperfunctions underscores the value of working in the general fibrational setting since this data type cannot be interpreted as a set.Comment: For Special Issue from CSL 201

Improved fermentation strategies in a bioreactor for enhancing poly(3-hydroxybutyrate) (PHB) production by wild type Cupriavidus necator from fructose

Poly(3-hydroxybutyrate) (PHB) belongs to the family of polyhydroxyalkanoates, biopolymers used for agricultural, industrial, or even medical applications. However, scaling up the production is still an issue due to the myriad of parameters involved in the fermentation processes. The present work seeks, firstly, to scale up poly(3- hydroxybutyrate) (PHB) production by wild type C. necator ATCC 17697 from shaken flasks to a stirred-tank bioreactor with the optimized media and fructose as carbon source. The second purpose is to improve the production of PHB by applying both the batch and fed-batch fermentation strategies in comparison with previous works of wild type C. necator with fructose. Furthermore, thinking of biomedical applications, physicochemical, and cytotoxicity analyses of the produced biopolymer, are presented. Fed-batch fermentation with an exponential feeding strategy enabled us to achieve the highest values of PHB concentration and productivity, 25.7 g/l and 0.43 g/(l h), respectively. The PHB productivity was 3.3 and 7.2 times higher than the one in batch strategy and shaken flask cultures, respectively. DSC, FTIR, 1 H, and 13C NMR analysis led to determine that the biopolymer produced by C. necator ATCC 17697 has a molecular structure and characteristics in agreement with the commercial PHB. Additionally, the biopolymer does not induce cytotoxic effects on the NIH/3T3 cell culture. Due to the improved fermentation strategies, PHB concentration resulted in 40 % higher of the already reported one for wild type C. necator using other fed-batch modes and fructose as a carbon source. Thus the produced PHB could be attractive for biomedical applications, which generate a rising interest in polyhydroxyalkanoates during recent years.Fil: Nygaard, Daiana. Universidad Nacional de San Martín. Escuela de Ciencia y Tecnología; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Yashchuk, Oxana. Universidad Nacional de San Martín. Escuela de Ciencia y Tecnología; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Noseda, Diego Gabriel. Universidad Nacional de San Martín. Instituto de Investigaciones Biotecnológicas. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Biotecnológicas; ArgentinaFil: Araoz, Beatriz. Universidad Nacional de San Martín. Escuela de Ciencia y Tecnología; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Hermida, Élida B.. Universidad Nacional de San Martín. Escuela de Ciencia y Tecnología; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin