The JNR Property and the Borel Structure of a Banach Space

Research partially supported by a grant of Caja de Ahorros del Mediterraneo.In this paper we study the property of having a countable cover by sets of small local diameter (SLD for short). We show that in the context of Banach spaces (JNR property) it implies that the Banach space is Cech-analytic. We also prove that to have the JNR property, to be σ- fragmentable and to have the same Borel sets for the weak and the norm topologies, they all are topological invariants of the weak topology. Finally, by means of “good” injections into c0 (Γ), we give a great class of Banach spaces with the JNR property

El silencio en la historia de las ideas: Introducción y tentativas taxonómicas

Resumen: En el presente trabajo se examina la noción de silencio mediante el escrutinio de sus diferentes tipos al trasluz de múltiples criterios de clasificación y perspectivas metodológicas y disciplinares: fenomenológica, epistemológica, axiológica, sociológica e histórica. Mediante el análisis de la versatilidad del silencio se pretende sostener que una historia conceptual (Begriffsgeschichte) crítica de éste constituye un requisito imprescindible para avanzar en el conocimiento acerca del ser humano y sus producciones sociales, culturales e históricas.Palabras clave: silencio, historia conceptual, cultura, memoria, expresión.Abstract: This paper examines the notion of silence by scrutinizing different types of silence that can be distinguished from multiple classificatory criteria and from a plurality of methodological and disciplinary perspectives: phenomenological, epistemological, axiological, sociological, and historical. The aim of this analysis of the versatility of silence is to argue that a conceptual history (Begriffsgeschichte) critical of silence is an essential requirement for making progress in our understanding of human beings and their social, cultural and historical productions.Keywords: silence, conceptual history, culture, memory, expression. 

EXPERIENCIA Y POLÍTICA EN LA HISTORIA CONCEPTUAL

My contribution is an attempt to examine the political background of Reinhart Koselleck’s Begriffsgeschichte, both in its metodological and theoretical aspects. This author has indicated the elective affinities between a conceptual history attached to the textual specific sources, from one side, and an epistemology of history with trascendental and extra-textual ambitions, from the other. A halfway position corresponds to the historical semantics, paradigmatically applied to the transition from Absolutism to the French Revolution. Habermas and the Cambridge School (Pocock and Skinner) have confronted the ideologically partial description of this step, and the metodology employed for it. According to Habermas, satanization of publicity and public opinion as casus belli, wich excludes both of them as principle of political rationality, reveals the schmittian filiation of Koselleck. The trascendental doctrine of history, the Historik, is conservative because it masks the interest of finding a continuity with the most fateful past of Germany. Pocock denounces the extrapolation of a methodology valid only for the German national culture, that is, the germanization of all the conceptual history. In front of the accelerated times of modernity, in wich the two main metahistoric categories —experience space and horizont of expectation— achieve, because their maximum assimetry, the greatest visibility, Koselleck aims to slow cautiously that frenetic rhythm with a balance between tradition and future. But Koselleck does not profit the potential of criticism and self-criticism implied in his contributions because his lack of will to questioning, in his own case, the dynamic tensions between concept and structure or the versatility of the notion of praxis (as hermeneutic application of sense, or as intervention at long-term in the world). The Begriffsgeschichte contains all the ingredients to the reflection on a public use of history or historic reason. In its public use, he would plead for a retrospective inquire on the meaning of an imputation of responsibilities, in a prospective search to come to a reciprocal understanding among the citizens.Mi contribución pretende examinar el trasfondo político de la Begriffsgeschichte de Reinhart Koselleck tanto en su vertiente metodológica como teórica. Este autor ha indicado las afinidades electivas entre una historia conceptual apegada a las fuentes textuales concretas, por un lado, y una epistemología de la historia con ambiciones trascendentales y extratextuales, por otro. El punto intermedio lo ocupa la semántica histórica, aplicada paradigmáticamente al tránsito del Absolutismo a la Revolución Francesa. Habermas y la Escuela de Cambridge (Pocock y Skinner) se han enfrentado a la descripción ideológicamente parcial de ese paso y a la metodología empleada. Según Habermas, la satanización de la publicidad y de la opinión pública como casus belli, que la excluye como principio de racionalidad política, desvela la filiación schmittiana de Koselleck. La doctrina trascendental de la historia, la Histórica, es conservadora al enmascarar intereses continuistas con el pasado más aciago de Alemania. Pocock denunciará la extrapolación de una metodología sólo válida para la cultura nacional alemana, esto es, la germanización de la historia conceptual. Frente al tiempo acelerado de la modernidad, en la que, por su máxima asimetría alcanzan una óptima visibilidad las dos principales categorías metahistóricas, espacio de experiencia y horizonte de expectativa, Koselleck quiere ralentizar prudentemente ese ritmo frenético mediante un equilibrio entre tradición y porvenir. Pero Koselleck no rentabiliza el potencial de crítica y de autocrítica ínsito en sus aportaciones por su falta de voluntad de problematizar en su propio caso las tensiones dinámicas entre concepto y estructura o la versatilidad de la noción de praxis (ya como aplicación hermenéutica del sentido, ya como intervención a largo plazo en el mundo). La Begriffsgeschichte alberga todos los ingredientes para estimular la reflexión sobre un uso público de la historia o de la razón histórica. En su uso público abogaría por indagar, retrospectivamente, el significado de una imputación de responsabilidades en aras, prospectivamente, del entendimiento recíproco de los ciudadanos

El secreto de la amistad: la dialéctica de la ilustración en Lessing

[Resumen] Mi contribución examina la relación de atracción y repulsión entre la historia conceptual (Begriffsgeschichte) y la Ilustración, y más concretamente, con motivo de una nueva edición española en 2007 de Crítica y crisis. Un estudio sobre la patogénesis del mundo burgués, analiza la exégesis que Reinhart Koselleck propone de la Filosofía de la Historia de G. E. Lessing. La tentativa del historiador de Bielefeld de convertir al bibliotecario de Wolfenbüttel en un conspirador político, en un catalizador de la Revolución, debe ser matizada y corregida merced a un escrutinio del significado del arcano, que revela una tensión incancelable entre política y amistad, entre ciudadanía y masonería esencial. La tesis de la derivación belicista y terrorista de la Ilustración (el caso de Lessing es ejemplar) no está fundada rigurosamente.[Sommaire] Ma contribution examine la relation d’attraction et de répulsion entre l’histoire conceptuelle (Begriffsgeschichte) et Les Lumières, et plus concrètement, à propos d’une nouvelle édition espagnole en 2007 de Crítica y crisis. Un estudio sobre la patogénesis del mundo burgués. Elle analyse l’exégèse que Reinhart Koselleck propose à propos de la Philosophie de l’histoire de G. E. Lessing. La tentative de l’historien de Bielefeld de convertir le bibliothécaire de Wolfenbüttel en conspirateur politique, en catalyseur de la Révolution, doit être nuancée et corrigée grâce à un scrutin du signifié du arcane, qui révèle une tension permanente entre politique et amitié, entre citoyenneté et franc-maçonnerie essentielle. La thèse de la dérivation belliciste et terroriste des Lumières (le cas de Lessing est exemplaire) n’est pas fondée avec rigueur.[Abstract] My contribution examines the attraction-repulsion relation between conceptual history (Begriffsgeschichte) and the Enlightenment; particularly, on the occasion of a new Spanish translation in 2007 of Crítica y crisis. Un estudio sobre la patogénesis del mundo burgués, it analyses the exegesis proposed by Reinhart Koselleck of G. E. Lessing’s philosophy of history. The attempt by the Bielefeld historian to transform the Wolfenbüttel librarian into a political conspirator, a catalyst of the Revolution, should be corrected and given some nuances through a study of the meaning of arcanum, which reveals an unremovable tension between politics and friendship, between citizenship and essential freemasonry. The thesis of a belicist and terrorist derivation of the Enlightenment (Lessing’s case is exemplary) is not rigorously founded

Using Learned Conditional Distributions as Edit Distance

International audienc

A log square average case algorithm to make insertions in fast similarity search

To speed up similarity based searches many indexing techniques have been proposed in order to address the problem of efficiency. However, most of the proposed techniques do not admit fast insertion of new elements once the index is built. The main effect is that changes in the environment are very costly to be taken into account. In this work, we propose a new technique to allow fast insertions of elements in a family of static tree-based indexes. Unlike other techniques, the resulting index is exactly equal to the index that would be obtained by building it from scratch. Therefore there is no performance degradation in search time. We show that the expected number of distance computations (and the average time complexity) is bounded by a function that grows with log2(n) where n is the size of the database. In order to check the correctness of our approach some experiments with artificial and real data are carried out.This work has been supported in part by Grants TIN2009-14205-C04-01 from the Spanish CICYT (Ministerio de Ciencia e Innovación), the IST Programme of the European Community, under the Pascal Network of Excellence, IST-2002-506778, and the program CONSOLIDER INGENIO 2010 (CSD2007-00018)

Learning Multipicity Tree Automata

International audienceIn this paper, we present a theoretical approach for the problem of learning multiplicity tree automata. These automata allows one to define functions which compute a number for each tree. They can be seen as a strict generalization of stochastic tree automata since they allow to define functions over any field K. A multiplicity automaton admits a support which is a non deterministic automaton. From a grammatical inference point of view, this paper presents a contribution which is original due to the combination of two important aspects. This is the first time, as far as we now, that a learning method focuses on non deterministic tree automata which computes functions over a field. The algorithm proposed in this paper stands in Angluin's exact model where a learner is allowed to use membership and equivalence queries. We show that this algorithm is polynomial in time in function of the size of the representation

Recognition of pen-based music notation with finite-state machines

This work presents a statistical model to recognize pen-based music compositions using stroke recognition algorithms and finite-state machines. The series of strokes received as input is mapped onto a stochastic representation, which is combined with a formal language that describes musical symbols in terms of stroke primitives. Then, a Probabilistic Finite-State Automaton is obtained, which defines probabilities over the set of musical sequences. This model is eventually crossed with a semantic language to avoid sequences that does not make musical sense. Finally, a decoding strategy is applied in order to output a hypothesis about the musical sequence actually written. Comprehensive experimentation with several decoding algorithms, stroke similarity measures and probability density estimators are tested and evaluated following different metrics of interest. Results found have shown the goodness of the proposed model, obtaining competitive performances in all metrics and scenarios considered.This work was supported by the Spanish Ministerio de Educación, Cultura y Deporte through a FPU Fellowship (Ref. AP2012–0939) and the Spanish Ministerio de Economía y Competitividad through the TIMuL Project (No. TIN2013-48152-C2-1-R, supported by UE FEDER funds)

Recognition of online handwritten music symbols

Paper submitted to MML 2013, 6th International Workshop on Machine Learning and Music, Prague, September 23, 2013.An effective way of digitizing a new musical composition is to use an e-pen and tablet application in which the user's pen strokes are recognized online and the digital score is created with the sole effort of the composition itself. This work aims to be a starting point for research on the recognition of online handwritten music notation. To this end, different alternatives within the two modalities of recognition resulting from this data are presented: online recognition, which uses the strokes marked by a pen, and offline recognition, which uses the image generated after drawing the symbol. A comparative experiment with common machine learning algorithms over a dataset of 3800 samples and 32 different music symbols is presented. Results show that samples of the actual user are needed if good classification rates are pursued. Moreover, algorithms using the online data, on average, achieve better classification results than the others