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

Time-series regression models to study the short-term effects of environmental factors on health

Time series regression models are especially suitable in epidemiology for evaluating short-term effects of time-varying exposures on health. The problem is that potential for confounding in time series regression is very high. Thus, it is important that trend and seasonality are properly accounted for. Our paper reviews the statistical models commonly used in time-series regression methods, specially allowing for serial correlation, make them potentially useful for selected epidemiological purposes. In particular, we discuss the use of time-series regression for counts using a wide range Generalised Linear Models as well as Generalised Additive Models. In addition, recently critical points in using statistical software for GAM were stressed, and reanalyses of time series data on air pollution and health were performed in order to update already published. Applications are offered through an example on the relationship between asthma emergency admissions and photochemical air pollutants in Madrid for the period 1995-1998, of how these methods are employed.Time-series; Poisson; GLM; GAM; autocorrelation; overdispersion; air pollution

Social complexity from within: how individuals experience the structure and organization of their groups

We argue that the study of social complexity can follow two different approaches, based on how it is seen from the outside or on how it is experienced from within. Recent focus has been on the former with social complexity emerging from the interactions of group members. Here, we take the view from within and deal with the social complexity that individual group members may experience, exploring complexity arising from aspects of the social structure and social organization. We review a variety of sources of social complexity in terms of variation between and within social relationships, variation in opportunities to interact with different group members, and the role of third parties. We then examine how individuals can cope with the social complexity they face. We conclude that a refined view of social relationships at different levels is needed to study the social complexity faced by individual group members and emphasize the potential contribution of the view from within to the study of social complexity and cognition. Animals may experience different degrees of complexity in their social groups. Instead of viewing social complexity as an emergent property of the interactions exchanged by group members, we focus on the social complexity individual group members may experience. We examine how aspects of social structure and social organization, such as the variation between and within social relationships, the variation in opportunities to interact with different group members, and the role of third parties, could create challenges and sources of complexity for individual group members. We then evaluate how emotions and cognitive abilities could be used by animals of different species to navigate the social complexity they experience and make appropriate decisions. We show that there are neglected sources of social complexity related to social relationships that derive from them changing over time and consisting of different components. We conclude by emphasizing that a change in perspective is needed to study how cognition is linked to the social complexity individual group members may experience

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