Hurst's Rescaled Range Statistical Analysis for Pseudorandom Number Generators used in Physical Simulations

The rescaled range statistical analysis (R/S) is proposed as a new method to detect correlations in pseudorandom number generators used in Monte Carlo simulations. In an extensive test it is demonstrated that the RS analysis provides a very sensitive method to reveal hidden long run and short run correlations. Several widely used and also some recently proposed pseudorandom number generators are subjected to this test. In many generators correlations are detected and quantified.Comment: 12 pages, 12 figures, 6 tables. Replaces previous version to correct citation [19

Driving sandpiles to criticality and beyond

A popular theory of self-organized criticality relates driven dissipative systems to systems with conservation. This theory predicts that the stationary density of the abelian sandpile model equals the threshold density of the fixed-energy sandpile. We refute this prediction for a wide variety of underlying graphs, including the square grid. Driven dissipative sandpiles continue to evolve even after reaching criticality. This result casts doubt on the validity of using fixed-energy sandpiles to explore the critical behavior of the abelian sandpile model at stationarity.Comment: v4 adds referenc

The dimension of loop-erased random walk in 3D

We measure the fractal dimension of loop-erased random walk (LERW) in 3 dimensions, and estimate that it is 1.62400 +- 0.00005. LERW is closely related to the uniform spanning tree and the abelian sandpile model. We simulated LERW on both the cubic and face-centered cubic lattices; the corrections to scaling are slightly smaller for the face-centered cubic lattice.Comment: 4 pages, 4 figures. v2 has more data, minor additional change

The Outcome of the ArtFrame Project, a Domain-Specific BIBFRAME Exploration

The presentation consists of three parts. Jason Kovari’s presentation examines the larger context of the various domain-specific explorations of BIBFRAME extension development, with particular focus on the overlap between art works and rare materials held in libraries. Melanie Wacker and Amber Billey then discuss the specifics of the ARTFRAME project including its initial goals, timeline, community outreach, outcome, as well as tools used and lessons learned throughout the project. Finally, Marie-Chantal L’Ecuyer-Coelho explores the contributions of ARLIS/NA's CAC as a community partner to the ARTFRAME project, highlighting its role in the process of delineating the requirements of art descriptive metadata, and developing an ontology extension suited to the specific characteristics of art objects

Montessori’s teleological approach to education and its implications

Teleology is a fundamental aspect of Montessori education. Understanding its implications helps us appreciate Montessori’s deep affinity with Aristotelian thought and how her pedagogy differs from the New Education movement inspired by Jean-Jacques Rousseau. The teleological approach has several implications in education: for example, when it comes to understanding concepts such as meaningful learning, active learning, learning stimuli, and progress. To understand the teleological approach in the Montessori method, this article discusses some of its fundamental pillars, such as the prepared environment, control of error, the absorbent mind, sustained attention, the development of personality, purposeful repetition, perfective activity, the joy of learning and the rational nature’s inclination towards its end. According to Montessori, human activity is naturally oriented towards an end and is ordered by reason. The end of education is the child himself since education consists in perfecting the agent, bringing his potential into action. The child’s eagerness to develop his personality occurs through the spontaneous activity of his absorbent mind and through purposeful repetition, which generates positive habits. The absorbent character of his mind urges him to know, absorbing his surrounding environment. Hence, the prepared environment and control of error are crucial. Perfective activity, performed with the right and strictly necessary amount of stimuli, helps the child find rest in meaningful voluntary activities done without obstacles. The resulting pleasure should not be understood as a mere experience; it should rather be seen in relation to a natural activity directed towards its end.La teleología es un elemento central de la educación Montessori. Entender las implicaciones del enfoque teleológico en Montessori ayuda a entender sus diferencias con el movimiento de la Educación Nueva, inspirado en Jean-Jacques Rousseau, así como su profunda afinidad con el pensamiento aristotélico. El enfoque teleológico tiene varias implicaciones en la educación, como, por ejemplo, en lo que se refiere a los conceptos de aprendizaje significativo, de aprendizaje activo, de estímulos para el aprendizaje y de progreso. Para entender el enfoque teleológico en Montessori, hablaremos de algunos de los pilares fundamentales de esa pedagogía, como, por ejemplo, el ambiente preparado, el control del error, la mente absorbente, la atención sostenida, el desarrollo de la personalidad, la repetición con propósito, la actividad perfectiva, el placer de aprender y la inclinación de la naturaleza racional hacia su fin. Para Montessori, la actividad humana está naturalmente orientada hacia un fin y ordenada por la razón. El fin de la educación es el niño mismo, ya que esta consiste en perfeccionar al agente, llevando al acto en el niño lo que en él solo está en potencia. El afán del niño por edificar su personalidad ocurre a través de la actividad espontánea de su mente absorbente y de la repetición con propósito, que genera hábitos positivos. El carácter absorbente de la mente del niño le urge a conocer, empapándose de su entorno. De ahí que el ambiente preparado y el control del error resulten cruciales. La actividad perfectiva, realizada con la cantidad justa y necesaria de estímulos, hace que el niño encuentre des- canso en los actos voluntarios realizados con sentido y sin trabas. El placer que resulta no se entiende como mera experiencia, sino en relación con una actividad natural encaminada hacia su fin

Multidimensional Quasi-Monte Carlo Malliavin Greeks

We investigate the use of Malliavin calculus in order to calculate the Greeks of multidimensional complex path-dependent options by simulation. For this purpose, we extend the formulas employed by Montero and Kohatsu-Higa to the multidimensional case. The multidimensional setting shows the convenience of the Malliavin Calculus approach over different techniques that have been previously proposed. Indeed, these techniques may be computationally expensive and do not provide flexibility for variance reduction. In contrast, the Malliavin approach exhibits a higher flexibility by providing a class of functions that return the same expected value (the Greek) with different accuracies. This versatility for variance reduction is not possible without the use of the generalized integral by part formula of Malliavin Calculus. In the multidimensional context, we find convenient formulas that permit to improve the localization technique, introduced in Fourni\'e et al and reduce both the computational cost and the variance. Moreover, we show that the parameters employed for variance reduction can be obtained \textit{on the flight} in the simulation. We illustrate the efficiency of the proposed procedures, coupled with the enhanced version of Quasi-Monte Carlo simulations as discussed in Sabino, for the numerical estimation of the Deltas of call, digital Asian-style and Exotic basket options with a fixed and a floating strike price in a multidimensional Black-Scholes market.Comment: 22 pages, 6 figure

Importance Functions for RESTART Simulation of General Jackson Networks

RESTART is an accelerated simulation technique that allows the evaluation of extremely low probabilities. In this method a number of simulation retrials are performed when the process enters regions of the state space where the chance of occurrence of the rare event is higher. These regions are defined by means of a function of the system state called the importance function. Guidelines for obtaining suitable importance functions and formulas for the importance function of two-stage networks were provided in previous papers. In this paper, we obtain effective importance functions for RESTART simulation of Jackson networks where the rare set is defined as the number of customers in a particular (‘target’) node exceeding a predefined threshold. Although some rough approximations and assumptions are used to derive the formulas of the importance functions, they are good enough to estimate accurately very low probabilities for different network topologies within short computational time

El enfoque teleológico de la educación Montessori y sus implicaciones

La teleología es un elemento central de la educación Montessori. Entender las implicaciones del enfoque teleológico en Montessori ayuda a entender sus diferencias con el movimiento de la Educación Nueva, inspirado en Jean-Jacques Rousseau, así como su profunda afinidad con el pensamiento aristotélico. El enfoque teleológico tiene varias implicaciones en la educación, como, por ejemplo, en lo que se refiere a los conceptos de aprendizaje significativo, de aprendizaje activo, de estímulos para el aprendizaje y de progreso. Para entender el enfoque teleológico en Montessori, hablaremos de algunos de los pilares fundamentales de esa pedagogía, como, por ejemplo, el ambiente preparado, el control del error, la mente absorbente, la atención sostenida, el desarrollo de la personalidad, la repetición con propósito, la actividad perfectiva, el placer de aprender y la inclinación de la naturaleza racional hacia su fin. Para Montessori, la actividad humana está naturalmente orientada hacia un fin y ordenada por la razón. El fin de la educación es el niño mismo, ya que esta consiste en perfeccionar al agente, llevando al acto en el niño lo que en él solo está en potencia. El afán del niño por edificar su personalidad ocurre a través de la actividad espontánea de su mente absorbente y de la repetición con propósito, que genera hábitos positivos. El carácter absorbente de la mente del niño le urge a conocer, empapándose de su entorno. De ahí que el ambiente preparado y el control del error resulten cruciales. La actividad perfectiva, realizada con la cantidad justa y necesaria de estímulos, hace que el niño encuentre descanso en los actos voluntarios realizados con sentido y sin trabas. El placer que resulta no se entiende como mera experiencia, sino en relación con una actividad natural encaminada hacia su fin