2,196 research outputs found
Winding clusters in percolation on the Torus and the Moebius strip
Using a simulation technique introduced recently, we study winding clusters
in percolation on the torus and the Moebius strip for different aspect ratios.
The asynchronous parallelization of the simulation makes very large system and
sample sizes possible. Our high accuracy results are fully consistent with
predictions from conformal field theory. The numerical results for the Moebius
strip and the number distribution of winding clusters on the torus await
theoretical explanation. To our knowledge, this study is the first of its kind.Comment: 20 pages, 9 figures, submitted to J. Stat. Phy
Functional-integral based perturbation theory for the Malthus-Verhulst process
We apply a functional-integral formalism for Markovian birth and death
processes to determine asymptotic corrections to mean-field theory in the
Malthus-Verhulst process (MVP). Expanding about the stationary mean-field
solution, we identify an expansion parameter that is small in the limit of
large mean population, and derive a diagrammatic expansion in powers of this
parameter. The series is evaluated to fifth order using computational
enumeration of diagrams. Although the MVP has no stationary state, we obtain
good agreement with the associated {\it quasi-stationary} values for the
moments of the population size, provided the mean population size is not small.
We compare our results with those of van Kampen's -expansion, and apply
our method to the MVP with input, for which a stationary state does exist.Comment: 24 pages, 15 figure
Comment on: "Superscaling of Percolation on Rectangular Domains"
In [Watanabe et al., Phys. Rev. Lett. 93 190601 (2004)], the authors show
numerically that spanning and percolation probabilities in two-dimensional
systems with different aspect ratios obey a form of "superscaling". In this
comment, we would like to point out some difficulties with their proposed
scaling ansatz and suggest why this remained undetected in their numerical
analysis.Comment: 1 page + references, 1 figur
Data-Driven Prediction of Thresholded Time Series of Rainfall and SOC models
We study the occurrence of events, subject to threshold, in a representative
SOC sandpile model and in high-resolution rainfall data. The predictability in
both systems is analyzed by means of a decision variable sensitive to event
clustering, and the quality of the predictions is evaluated by the receiver
operating characteristics (ROC) method. In the case of the SOC sandpile model,
the scaling of quiet-time distributions with increasing threshold leads to
increased predictability of extreme events. A scaling theory allows us to
understand all the details of the prediction procedure and to extrapolate the
shape of the ROC curves for the most extreme events. For rainfall data, the
quiet-time distributions do not scale for high thresholds, which means that the
corresponding ROC curves cannot be straightforwardly related to those for lower
thresholds.Comment: 19 pages, 10 figure
Order statistics of 1/f^{\alpha} signals
Order statistics of periodic, Gaussian noise with 1/f^{\alpha} power spectrum
is investigated. Using simulations and phenomenological arguments, we find
three scaling regimes for the average gap d_k= between the k-th
and (k+1)-st largest values of the signal. The result d_k ~ 1/k known for
independent, identically distributed variables remains valid for 0<\alpha<1.
Nontrivial, \alpha-dependent scaling exponents d_k ~ k^{(\alpha -3)/2} emerge
for 1<\alpha<5 and, finally, \alpha-independent scaling, d_k ~ k is obtained
for \alpha>5. The spectra of average ordered values \epsilon_k= ~
k^{\beta} is also examined. The exponent {\beta} is derived from the gap
scaling as well as by relating \epsilon_k to the density of near extreme
states. Known results for the density of near extreme states combined with
scaling suggest that \beta(\alpha=2)=1/2, \beta(4)=3/2, and beta(infinity)=2
are exact values. We also show that parallels can be drawn between \epsilon_k
and the quantum mechanical spectra of a particle in power-law potentials.Comment: 8 pages, 5 figure
Analysis of an information-theoretic model for communication
We study the cost-minimization problem posed by Ferrer i Cancho and Sol\'e in
their model of communication that aimed at explaining the origin of Zipf's law
[PNAS 100, 788 (2003)]. Direct analysis shows that the minimum cost is , where determines the relative weights of
speaker's and hearer's costs in the total, as shown in several previous works
using different approaches. The nature and multiplicity of the minimizing
solution changes discontinuously at , being qualitatively
different for , and . Zipf's law
is found only in a vanishing fraction of the minimum-cost solutions at and therefore is not explained by this model. Imposing the further
condition of equal costs yields distributions substantially closer to Zipf's
law, but significant differences persist. We also investigate the solutions
reached by the previously used minimization algorithm and find that they
correctly recover global minimum states at the transition.Comment: 19 pages, 4 figures. Important references and new results adde
The perils of thresholding
The thresholding of time series of activity or intensity is frequently used
to define and differentiate events. This is either implicit, for example due to
resolution limits, or explicit, in order to filter certain small scale physics
from the supposed true asymptotic events. Thresholding the birth-death process,
however, introduces a scaling region into the event size distribution, which is
characterised by an exponent that is unrelated to the actual asymptote and is
rather an artefact of thresholding. As a result, numerical fits of simulation
data produce a range of exponents, with the true asymptote visible only in the
tail of the distribution. This tail is increasingly difficult to sample as the
threshold is increased. In the present case, the exponents and the spurious
nature of the scaling region can be determined analytically, thus demonstrating
the way in which thresholding conceals the true asymptote. The analysis also
suggests a procedure for detecting the influence of the threshold by means of a
data collapse involving the threshold-imposed scale.Comment: 16 pages, 10 figure
Transition from senior secondary to tertiary languages study: student attitudes in three Sydney schools
This paper reports on a small study of attitudes to tertiary language study amongst senior secondary language learners in three independent New South Wales schools. The study examines what elements of preparedness may be the most effective in supporting transition to tertiary study for this sample of languages students. An analysis of survey data indicates that motivation, confidence in language achievement, and the construction of a 'future self' as a language user and learner appear to be useful elements positively supporting transition to tertiary study. Findings from this study point to a relationship between the construction of 'future selves' as language users, and academic performance, motivation, self-esteem and aspiration
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