Non-negativity preserving numerical algorithms for stochastic differential equations

Construction of splitting-step methods and properties of related non-negativity and boundary preserving numerical algorithms for solving stochastic differential equations (SDEs) of Ito-type are discussed. We present convergence proofs for a newly designed splitting-step algorithm and simulation studies for numerous numerical examples ranging from stochastic dynamics occurring in asset pricing theory in mathematical finance (SDEs of CIR and CEV models) to measure-valued diffusion and superBrownian motion (SPDEs) as met in biology and physics.Comment: 23 pages, 7 figures. Figures 6.2 and 6.3 in low resolution due to upload size restrictions. Original resolution at http://gisc.uc3m.es/~moro/profesional.htm

La ciudad no es un árbol estático: comprender las áreas urbanas a través de la óptica de los datos de comportamiento en tiempo real

Cities are the main ground on which our society and culture develop today and will develop in the future. Against the traditional understanding of cities as physical spaces mostly around our neighborhoods, recent use of large-scale mobility datasets has enabled the study of our behavior at unprecedented spatial and temporal scales, much beyond our static residential spaces. Here we show how it is possible to use these datasets to investigate the role that human behavior plays in traditional urban problems like segregation, public health, or epidemics. Apart from measuring or monitoring such problems in a more comprehensive way, the analysis of those large datasets using modern machine learning techniques or causality detection permits to unveil of the behavioral roots behind them. As a result, only by incorporating real-time behavioral data can we design more efficient policies or interventions to improve such critical societal issues in our urban areas.Las ciudades son el principal terreno sobre el que se desarrollan —y se desarrollarán— nuestra sociedad y cultura. Frente a la concepción tradicional de las ciudades como espacio físico, en torno a nuestros barrios, el uso reciente de grandes conjuntos de datos de movilidad ha permitido estudiar el comportamiento humano a escalas espaciales y temporales sin precedentes, más allá de nuestros espacios residenciales. Este artículo muestra cómo es posible utilizar estos conjuntos de datos para investigar el papel que desempeña el comportamiento humano en problemas urbanos tradicionales como la segregación, la salud pública o las epidemias. Además de medir o monitorizar estos problemas de forma exhaustiva, el análisis de estos grandes conjuntos de datos mediante técnicas de aprendizaje automático o detección de causalidad permite desvelar raíces conductuales detrás de esos problemas. Como resultado, solo incorporando datos de comportamiento en tiempo real podemos diseñar políticas o intervenciones más eficientes que contribuyan a mejorar estos problemas sociales críticos en nuestras áreas urbanas

Statistical physics of adaptive correlation of agents in a market

Recent results and interpretations are presented for the thermal minority game, concentrating on deriving and justifying the fundamental stochastic differential equation for the microdynamics.Comment: Invited talk presented at the Conference: Disordered and Complex Systems, King's College London, July 200

Predicting human preferences using the block structure of complex social networks

With ever-increasing available data, predicting individuals' preferences and helping them locate the most relevant information has become a pressing need. Understanding and predicting preferences is also important from a fundamental point of view, as part of what has been called a "new" computational social science. Here, we propose a novel approach based on stochastic block models, which have been developed by sociologists as plausible models of complex networks of social interactions. Our model is in the spirit of predicting individuals' preferences based on the preferences of others but, rather than fitting a particular model, we rely on a Bayesian approach that samples over the ensemble of all possible models. We show that our approach is considerably more accurate than leading recommender algorithms, with major relative improvements between 38% and 99% over industry-level algorithms. Besides, our approach sheds light on decision-making processes by identifying groups of individuals that have consistently similar preferences, and enabling the analysis of the characteristics of those groups

Variational mean-field study of a continuum model of crystalline tensionless surfaces

9 pages, 6 figures.-- PACS nrs.: 64.60.Ht, 64.60.Cn, 68.35.Rh, 81.10.Aj.-- ArXiv pre-print available at: http://arxiv.org/abs/cond-mat/9912013We study analytically the equilibrium and near-equilibrium properties of a model of a d-dimensional surface relaxing via linear surface diffusion and subject to a lattice potential. We employ the variational mean-field formalism introduced by Saito for the study of the sine-Gordon model. In equilibrium, our variational theory predicts a first-order roughening transition between a flat low-temperature phase and a rough high-temperature phase with the properties of the linear molecular-beam epitaxy equation. Moreover, the study of a Gaussian approximation to the Langevin dynamics of the system indicates that the surface shows hysteresis when temperature is continuously tuned. Out of equilibrium, these approximate Langevin dynamics show that the surface mobility can have different behaviors as a function of a driving flux. Some considerations are made regarding different underlying lattices, and connections are drawn to related models or different approaches to the same model we study.This work was partially supported by DGES Grant Nos. PB96-0119 and HB1999-0018, and EPSRC Grant No. GR/M04426.Publicad

The dynamical strength of social ties in information spreading

We investigate the temporal patterns of human communication and its influence on the spreading of information in social networks. The analysis of mobile phone calls of 20 million people in one country shows that human communication is bursty and happens in group conversations. These features have opposite effects in information reach: while bursts hinder propagation at large scales, conversations favor local rapid cascades. To explain these phenomena we define the dynamical strength of social ties, a quantity that encompasses both the topological and temporal patterns of human communication