Probability of Incipient Spanning Clusters in Critical Two-Dimensional Percolation

The probability of simultaneous occurence of at least k spanning clusters has been studied by Monte Carlo simulations on the 2D square lattice at the bond percolation threshold Pc=1/2. The calculated probabilities for free boundary conditions and periodic boundary conditions are in a very good coincidence with the exact formulae developed recently by Cardy.Comment: Contribution to Lattice 97, LaTeX, 3 pages, 4 figures (1-eps, 3- LaTeX

Enhancing Engagement and Early Literacy Through Music: Perspectives from Head Start Teachers

Early literacy and engagement are critical outcomes that can be fostered by early childhood educators in their classrooms through intentional implementation of age-appropriate and contextually relevant learning experiences. This study examines the implementation of a music intervention model developed to enhance engagement and early literacy development of young children within inclusive early childhood settings. The intervention, which incorporated daily music activities embedded in a Head Start classroom’s daily routines, was implemented for six months by the classroom teachers. Qualitative data on the children’s actions allowed for an in-depth exploration of the role of music as the mediator for engaging teaching moments that allow learning to evolve as an integral part of children’s routines. Further, the perspectives of Head Start teachers’ on the use of the music as an engaging context to promote engagement and early literacy development were explored. Finally, possible challenges of implementing such a music intervention model in the classroom and the role of music as an asset-building strategy that can meet the educators’ goals and the children’s needs are discussed. Keywords: music, early literacy, inclusion, preschool, engagement DOI: 10.7176/JEP/11-14-02 Publication date:May 31st 202

Exact Results for the Roughness of a Finite Size Random Walk

We consider the role of finite size effects on the value of the effective Hurst exponent H. This problem is motivated by the properties of the high frequency daily stock-prices. For a finite size random walk we derive some exact results based on Spitzer's identity. The conclusion is that finite size effects strongly enhance the value of H and the convergency to the asymptotic value (H=1/2) is rather slow. This result has a series of conceptual and practical implication which we discuss.Comment: 5 pages, 3 figure

Disarmament and Development: An Idea Whose Time Should Have Come

SUMMARY In 1982 the General Assembly advised governments ‘to start to plan and prepare for a conversion process which could be implemented in a disarmament situation’. But to make the required decisions and actions, drastic changes were needed in the behaviour of political leaders, particularly those of the dominant military powers. So far, efforts to create a political constituency for disarmament and development have not been successful. Only the Swedish government has undertaken a study, resulting in the report, In Pursuit of Disarmament . Although this study does not necessarily establish a model that can be replicated in other countries, it does show that the UN's recommendations can in principle be put into effect. SOMMAIRE Désarmement et développement: II n'est jamais trop tard pour y penser En 1982 l'Assemblée Générale conseillait aux gouvernements 'de commencer à planifier et à préparer un procédé de conversion qui pourrait être rendu effectif dans une situation de désarmement. ‘Mais afin de prendre les décisions correctes et d'agir en conséquence, il faudrait des changements radicaux dans l'attitude des chefs politiques, particulièrement ceux des puissances militaires dominantes’. Jusqu'à présent les efforts dirigés à la création d'une circonscription électorale politique en faveur du désarmement et du développement n'ont pas abouti. Seul le gouvernement Suédois a entrepris une étude, figurant dans mon rapport, In Pursuit of Disarmament . Quoique cette étude n'établit pas nécessairement un modèle qui pourrait être adapté dans d'autres pays, il montre que les recommendations des Nations Unies peuvent en principe être mise en pratique. RESUMEN Desarme y desarrollo: una idea cuyo turno debiera haber llegado En 1982, la Asamblea General le recomendó a los gobiernos ‘que empezaran a planificar y a prepararse para un proceso de conversión a implementarse en una situación de desarme’. El comportamiento de los dirigentes políticos, especialmente de aquellos dé las potencias militares dominantes tiene que cambiar drásticamente si se quiere adoptar las decisiones y llevar a cabo acciones necesarias. Hasta ahora, los esfuerzos desplegados para crear un entorno político favorable al desarme y el desarrollo no han tenido éxito. Sólo el gobierno sueco ha realizado un estudio que culminó en mi informe En Búsqueda del Desarme . A pesar de que este estudio no establece necesariamente un modelo que se pueda copiar en otros países, demuestra que las recomendaciones de las Naciones Unidas pueden, en principio, ponerse en práctica

Percolation in the Harmonic Crystal and Voter Model in three dimensions

We investigate the site percolation transition in two strongly correlated systems in three dimensions: the massless harmonic crystal and the voter model. In the first case we start with a Gibbs measure for the potential, $U=\frac{J}{2} \sum_{} (\phi(x) - \phi(y))^2$, $x,y \in \mathbb{Z}^3$, $J > 0$ and $\phi(x) \in \mathbb{R}$, a scalar height variable, and define occupation variables $\rho_h(x) =1,(0)$ for $\phi(x) > h (<h)$. The probability $p$ of a site being occupied, is then a function of $h$. In the voter model we consider the stationary measure, in which each site is either occupied or empty, with probability $p$. In both cases the truncated pair correlation of the occupation variables, $G(x-y)$, decays asymptotically like $|x-y|^{-1}$. Using some novel Monte Carlo simulation methods and finite size scaling we find accurate values of $p_c$ as well as the critical exponents for these systems. The latter are different from that of independent percolation in $d=3$, as expected from the work of Weinrib and Halperin [WH] for the percolation transition of systems with $G(r) \sim r^{-a}$ [A. Weinrib and B. Halperin, Phys. Rev. B 27, 413 (1983)]. In particular the correlation length exponent $\nu$ is very close to the predicted value of 2 supporting the conjecture by WH that $\nu= \frac{2}{a}$ is exact.Comment: 8 figures. new version significantly different from the old one, includes new results, figures et

Percolation and Magnetization in the Continuous Spin Ising Model

In the strong coupling limit the partition function of SU(2) gauge theory can be reduced to that of the continuous spin Ising model with nearest neighbour pair-interactions. The random cluster representation of the continuous spin Ising model in two dimensions is derived through a Fortuin-Kasteleyn transformation, and the properties of the corresponding cluster distribution are analyzed. It is shown that for this model, the magnetic transition is equivalent to the percolation transition of Fortuin-Kasteleyn clusters, using local bond weights. These results are also illustrated by means of numerical simulations

Universality of ac-conduction in anisotropic disordered systems: An effective medium approximation study

Anisotropic disordered system are studied in this work within the random barrier model. In such systems the transition probabilities in different directions have different probability density functions. The frequency-dependent conductivity at low temperatures is obtained using an effective medium approximation. It is shown that the isotropic universal ac-conduction law, $\sigma \ln \sigma=u$, is recovered if properly scaled conductivity ($\sigma$) and frequency ($u$) variables are used.Comment: 5 pages, no figures, final form (with corrected equations

Efficient data processing and quantum phenomena: Single-particle systems

We study the relation between the acquisition and analysis of data and quantum theory using a probabilistic and deterministic model for photon polarizers. We introduce criteria for efficient processing of data and then use these criteria to demonstrate that efficient processing of the data contained in single events is equivalent to the observation that Malus' law holds. A strictly deterministic process that also yields Malus' law is analyzed in detail. We present a performance analysis of the probabilistic and deterministic model of the photon polarizer. The latter is an adaptive dynamical system that has primitive learning capabilities. This additional feature has recently been shown to be sufficient to perform event-by-event simulations of interference phenomena, without using concepts of wave mechanics. We illustrate this by presenting results for a system of two chained Mach-Zehnder interferometers, suggesting that systems that perform efficient data processing and have learning capability are able to exhibit behavior that is usually attributed to quantum systems only.Comment: http://www.compphys.net/dl

Monte Carlo Renormalization Group for Entanglement Percolation

We use a large cell Monte Carlo Renormalization procedure, to compute the critical exponents of a system of growing linear polymers. We simulate the growth of non-intersecting chains in large MC cells. Dense regions where chains get in each others' way, give rise to connected clusters under coarse graining. At each time step, the fraction of occupied bonds is determined in both the original and the coarse grained configurations, and averaged over many realizations. Our results for the fractal dimension on three dimensional lattices are consistent with the percolation value.Comment: 5 pages, 5 figure

The time resolution of the St. Petersburg paradox

A resolution of the St. Petersburg paradox is presented. In contrast to the standard resolution, utility is not required. Instead, the time-average performance of the lottery is computed. The final result can be phrased mathematically identically to Daniel Bernoulli's resolution, which uses logarithmic utility, but is derived using a conceptually different argument. The advantage of the time resolution is the elimination of arbitrary utility functions.Comment: 20 pages, 1 figur