Scaling behavior of random knots.

Using numerical simulations we investigate how overall dimensions of random knots scale with their length. We demonstrate that when closed non-self-avoiding random trajectories are divided into groups consisting of individual knot types, then each such group shows the scaling exponent of approximately 0.588 that is typical for self-avoiding walks. However, when all generated knots are grouped together, their scaling exponent becomes equal to 0.5 (as in non-self-avoiding random walks). We explain here this apparent paradox. We introduce the notion of the equilibrium length of individual types of knots and show its correlation with the length of ideal geometric representations of knots. We also demonstrate that overall dimensions of random knots with a given chain length follow the same order as dimensions of ideal geometric representations of knots.

Geometric stopping of a random walk and its applications to valuing equity-linked death benefits

We study discrete-time models in which death benefits can depend on a stock price index, the logarithm of which is modeled as a random walk. Examples of such benefit payments include put and call options, barrier options, and lookback options. Because the distribution of the curtate-future-lifetime can be approximated by a linear combination of geometric distributions, it suffices to consider curtate-future-lifetimes with a geometric distribution. In binomial and trinomial tree models, closed-form expressions for the expectations of the discounted benefit payment are obtained for a series of options. They are based on results concerning geometric stopping of a random walk, in particular also on a version of the Wiener-Hopf factorization.

Priming psychic and conjuring abilities of a magic demonstration influences event interpretation and random number generation biases

Magical ideation and belief in the paranormal is considered to represent a trait-like character; people either believe in it or not. Yet, anecdotes indicate that exposure to an anomalous event can turn skeptics into believers. This transformation is likely to be accompanied by altered cognitive functioning such as impaired judgments of event likelihood. Here, we investigated whether the exposure to an anomalous event changes individuals' explicit traditional (religious) and non-traditional (e.g., paranormal) beliefs as well as cognitive biases that have previously been associated with non-traditional beliefs, e.g., repetition avoidance when producing random numbers in a mental dice task. In a classroom, 91 students saw a magic demonstration after their psychology lecture. Before the demonstration, half of the students were told that the performance was done respectively by a conjuror (magician group) or a psychic (psychic group). The instruction influenced participants' explanations of the anomalous event. Participants in the magician, as compared to the psychic group, were more likely to explain the event through conjuring abilities while the reverse was true for psychic abilities. Moreover, these explanations correlated positively with their prior traditional and non-traditional beliefs. Finally, we observed that the psychic group showed more repetition avoidance than the magician group, and this effect remained the same regardless of whether assessed before or after the magic demonstration. We conclude that pre-existing beliefs and contextual suggestions both influence people's interpretations of anomalous events and associated cognitive biases. Beliefs and associated cognitive biases are likely flexible well into adulthood and change with actual life events.

Exit times in non-Markovian drifting continuous-time random-walk processes

By appealing to renewal theory we determine the equations that the mean exit time of a continuous-time random walk with drift satisfies both when the present coincides with a jump instant or when it does not. Particular attention is paid to the corrections ensuing from the non-Markovian nature of the process. We show that when drift and jumps have the same sign the relevant integral equations can be solved in closed form. The case when holding times have the classical Erlang distribution is considered in detail.

Pseudo-aneurismas: relato de dois casos e revisão da literatura

Pseudo-aneurismas são uma afecção arterial rara. Os autores destacam a raridade da ocorrência de pseudo-aneurisma da artéria carótida comum pós-traumático e a associação de pseudo-aneurisma com osteocondroma femoral. Enfatizam a importância dos métodos por imagem, em especial a angiotomografia, no diagnóstico de afecções vasculares, como na ocorrência de pseudo-aneurismas. Realizam, ainda, revisão bibliográfica pertinente ao assunto.

Monotonic continuous-time random walks with drift and stochastic reset events

In this paper we consider a stochastic process that may experience random reset events which suddenly bring the system to the starting value and analyze the relevant statistical magnitudes. We focus our attention on monotonic continuous-time random walks with a constant drift: The process increases between the reset events, either by the effect of the random jumps, or by the action of the deterministic drift. As a result of all these combined factors interesting properties emerge, like the existence (for any drift strength) of a stationary transition probability density function, or the faculty of the model to reproduce power-law-like behavior. General formulas for two extreme statistics, the survival probability, and the mean exit time, are also derived. To corroborate in an independent way the results of the paper, Monte Carlo methods were used. These numerical estimations are in full agreement with the analytical predictions.

Pseudo-Próspero de Aquitania, Sobre la providencia de Dios. Introducción, texto latino revisado, traducción y comentario de Raúl Villegas Marín, Publicacions i edicions de la Universitat de Barcelona, Barcelona 2010, 346 pp. ISBN 9788447534869

El primer tercio del siglo V representó un momento muy convulso en la historia del Imperio Romano. Algunas zonas, como la Galia, se vieron inmersas en una crisis provocada principalmente por las devastaciones que poblaciones bárbaras estaban llevando a cabo, desde inicios de la centuria, en casi todo su territorio. El foedus pactado por el Imperio con los visigodos, por el cual éstos se establecían en Aquitania (418), lejos de representar una solución no hizo sino aumentar los problemas de convivencia entre galorromanos y germanos. El pesimismo cundió entre la población autóctona: la teología eusebiana que presentaba al Dios cristiano como garante de los bienes materiales a través de su culto ―siguiendo la tradicional ideología del do ut des― había fallado, y muchas conciencias cristianas se hundieron en la angustia al preg

Prevalence of alcohol-impaired drivers based on random breath tests in a roadside survey

Sobriety checkpoints are not usually randomly located by traffic authorities. As such, information provided by non-random alcohol tests cannot be used to infer the characteristics of the general driving population. In this paper a case study is presented in which the prevalence of alcohol-impaired driving is estimated for the general population of drivers. A stratified probabilistic sample was designed to represent vehicles circulating in non-urban areas of Catalonia (Spain), a region characterized by its complex transportation network and dense traffic around the metropolis of Barcelona. Random breath alcohol concentration tests were performed during spring 2012 on 7,596 drivers. The estimated prevalence of alcohol-impaired drivers was 1.29 PER CENT, which is roughly a third of the rate obtained in non-random tests. Higher rates were found on weekends (1.90 PER CENT on Saturdays, 4.29 PER CENT on Sundays) and especially at night. The rate is higher for men (1.45 PER CENT) than for women (0.64 PER CENT) and the percentage of positive outcomes shows an increasing pattern with age. In vehicles with two occupants, the proportion of alcohol-impaired drivers is estimated at 2.62 PER CENT, but when the driver was alone the rate drops to 0.84 PER CENT, which might reflect the socialization of drinking habits. The results are compared with outcomes in previous surveys, showing a decreasing trend in the prevalence of alcohol-impaired drivers over time.

The pseudo-high-risk prevention strategy

Key Messages: A fundamental failure of high-risk prevention strategies is their inability to prevent disease in the large part of the population at a relatively small average risk and from which most cases of diseases originate. The development of individual predictive medicine and the widening of high-risk categories for numerous (chronic) conditions lead to the application of pseudo-high-risk prevention strategies. Widening the criteria justifying individual preventive interventions and the related pseudo-high-risk strategies lead to treating, individually, ever healthier and larger strata of the population. The pseudo-high-risk prevention strategies raise similar problems compared with high-risk strategies, however on a larger scale and without any of the benefit of population-based strategies. Some 30 years ago, the strengths and weaknesses of population-based and high-risk prevention strategies were brilliantly delineated by Geoffrey Rose in several seminal publications (Table 1).1,2 His work had major implications not only for epidemiology and public health but also for clinical medicine. In particular, Rose demonstrated the fundamental failure of high-risk prevention strategies, that is, by missing a large number of preventable cases.

Persistent random walk model for transport trough thin slabs

We present a model for transport in multiply scattering media based on a three-dimensional generalization of the persistent random walk. The model assumes that photons move along directions that are parallel to the axes. Although this hypothesis is not realistic, it allows us to solve exactly the problem of multiple scattering propagation in a thin slab. Among other quantities, the transmission probability and the mean transmission time can be calculated exactly. Besides being completely solvable, the model could be used as a benchmark for approximation schemes to multiple light scattering.