72,088 research outputs found
Intermittency in Dynamics of Two-Dimensional Vortex-like Defects
We examine high-order dynamical correlations of defects (vortices,
disclinations etc) in thin films starting from the Langevin equation for the
defect motion. We demonstrate that dynamical correlation functions of
vorticity and disclinicity behave as where is the
characteristic scale and is the fugacity. As a consequence, below the
Berezinskii-Kosterlitz-Thouless transition temperature are
characterized by anomalous scaling exponents. The behavior strongly differs
from the normal law occurring for simultaneous correlation
functions, the non-simultaneous correlation functions appear to be much larger.
The phenomenon resembles intermittency in turbulence.Comment: 30 pages, 11 figure
Statistical Methods in Topological Data Analysis for Complex, High-Dimensional Data
The utilization of statistical methods an their applications within the new
field of study known as Topological Data Analysis has has tremendous potential
for broadening our exploration and understanding of complex, high-dimensional
data spaces. This paper provides an introductory overview of the mathematical
underpinnings of Topological Data Analysis, the workflow to convert samples of
data to topological summary statistics, and some of the statistical methods
developed for performing inference on these topological summary statistics. The
intention of this non-technical overview is to motivate statisticians who are
interested in learning more about the subject.Comment: 15 pages, 7 Figures, 27th Annual Conference on Applied Statistics in
Agricultur
Dynamic phenomena arising from an extended Core Group model
In order to obtain a reasonably accurate model for the spread of a particular infectious disease through a population, it may be necessary for this model to possess some degree of structural complexity. Many such models have, in recent years, been found to exhibit a phenomenon known as backward bifurcation, which generally implies the existence of two subcritical endemic equilibria. It is often possible to refine these models yet further, and we investigate here the influence such a refinement may have on the dynamic behaviour of a system in the region of the parameter space near R0 = 1. We consider a natural extension to a so-called core group model for the spread of a sexually transmitted disease, arguing that this may in fact give rise to a more realistic model. From the deterministic viewpoint we study the possible shapes of the resulting bifurcation diagrams and the associated stability patterns. Stochastic versions of both the original and the extended models are also developed so that the probability of extinction and time to extinction may be examined, allowing us to gain further insights into the complex system dynamics near R0 = 1. A number of interesting phenomena are observed, for which heuristic explanations are provided
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