Linear stochastic differential equations with functional boundary conditions

We consider linear n-th order stochastic differential equations on [0,1], with linear boundary conditions supported by a finite subset of [0,1]. We study some features of the solution to these problems, and especially its conditional independence properties of Markovian type.Comment: 25 page

Classifying the typefaces of the Gutenberg 42-line bible

We have measured the dissimilarities among several printed characters of a single page in the Gutenberg 42-line bible and we prove statistically the existence of several different matrices from which the metal types where constructed. This is in contrast with the prevailing theory, which states that only one matrix per character was used in the printing process of Gutenberg's greatest work. The main mathematical tool for this purpose is cluster analysis, combined with a statistical test for outliers. We carry out the research with two letters, i and a. In the first case, an exact clustering method is employed; in the second, with more specimens to be classified, we resort to an approximate agglomerative clustering method. The results show that the letters form clusters according to their shape, with significant shape differences among clusters, and allow to conclude, with a very small probability of error, that indeed the metal types used to print them were cast from several different matrices. Mathematics Subject Classification: 62H30Comment: 21 pages, 8 figure

Sistemes electorals

La democràcia parlamentària està basada en l'elecció justa d'un nombre petit d'individus (diputats) per representar un nombre molt més gran de ciutadans. És una idea senzilla, llevat d'un detall: Què vol dir justa? En el nostre país, els candidats a diputat es presenten a les eleccions agrupats en les anomenades candidatures o llistes, que poden ser presentades per partits polítics o per coalicions de partits. Cada elector vota una de les llistes. A partir del nombre de vots obtinguts, cada llista rep una certa quantitat d'escons. La pregunta és, doncs, com determinar, a partir del nombre de vots que rep cada llista, la quantitat d'escons que li corresponen. El sistema que s'utilitza a les eleccions al Parlament de Catalunya i al Congrés dels Diputats espanyol es coneix com a llei de d'Hondt, i els càlculs que requereix són molt fàcils de fer

The Modelling of Random Phenomena

This survey is based on a course given by the author in the Università degli Studi dell'Aquila, as a part of the Intensive Programme Mathematical Models in Life and Social Sciences, in July 2008. It is a fast-paced introduction, aimed at graduate students, to the mathematical modelling of phenomena and experiments in which randomness is present. After the introductory first section, several examples from daily life, industry, biology, and finance are presented, and the necessary tools are introduced alongside, but without much mathematical detail

No-Free-Lunch Theorems in the continuum

No-Free-Lunch Theorems state, roughly speaking, that the performance of all search algorithms is the same when averaged over all possible objective functions. This fact was precisely formulated for the first time in a now famous paper by Wolpert and Macready, and then subsequently refined and extended by several authors, always in the context of a set of functions with discrete domain and codomain. Recently, Auger and Teytaud have shown that for continuum domains there is typically no No-Free-Lunch theorems. In this paper we provide another approach, which is simpler, requires less assumptions, relates the discrete and continuum cases, and that we believe that clarifies the role of the cardinality and structure of the domain

Democràcia : dels vots als escons

La democràcia parlamentària està basada en l'elecció justa d'un nombre petit d'individus (diputats) per representar un nombre molt més gran de ciutadans. És una idea ben clara, llevat que. . . què vol dir justa