367 research outputs found

### Statistical Modelling of Pre-Impact Velocities in Car Crashes

The law wants to determine if any party involved in a car crash is guilty. The Dutch court invokes the expertise of the Netherlands Forensic Institute (NFI) to answer this question. We discuss the present method of the NFI to deter-
mine probabilities on pre-impact car velocities, given the evidence from the crash scene. A disadvantage of this method is that it requires a prior distribution on the velocities of the cars involved in the crash. We suggest a different approach, that of statistical significance testing, which can be carried out without a prior. We explain this method, and apply it to a toy model. Finally, a sensitivity analysis is performed on a simple two-car collision model

### A local limit theorem for the critical random graph

We consider the limit distribution of the orders of the k largest components in the ErdÂżos-RĂ©nyi random graph inside the critical window for arbitrary k. We prove a local limit theorem for this joint distribution and derive an exact expression for the joint probability density function

### Monte Carlo study of the hull distribution for the q=1 Brauer model

We study a special case of the Brauer model in which every path of the model
has weight q=1. The model has been studied before as a solvable lattice model
and can be viewed as a Lorentz lattice gas. The paths of the model are also
called self-avoiding trails. We consider the model in a triangle with boundary
conditions such that one of the trails must cross the triangle from a corner to
the opposite side. Motivated by similarities between this model, SLE(6) and
critical percolation, we investigate the distribution of the hull generated by
this trail (the set of points on or surrounded by the trail) up to the hitting
time of the side of the triangle opposite the starting point. Our Monte Carlo
results are consistent with the hypothesis that for system size tending to
infinity, the hull distribution is the same as that of a Brownian motion with
perpendicular reflection on the boundary.Comment: 21 pages, 9 figure

### Transforming fixed-length self-avoiding walks into radial SLE_8/3

We conjecture a relationship between the scaling limit of the fixed-length
ensemble of self-avoiding walks in the upper half plane and radial SLE with
kappa=8/3 in this half plane from 0 to i. The relationship is that if we take a
curve from the fixed-length scaling limit of the SAW, weight it by a suitable
power of the distance to the endpoint of the curve and then apply the conformal
map of the half plane that takes the endpoint to i, then we get the same
probability measure on curves as radial SLE. In addition to a non-rigorous
derivation of this conjecture, we support it with Monte Carlo simulations of
the SAW. Using the conjectured relationship between the SAW and radial SLE, our
simulations give estimates for both the interior and boundary scaling
exponents. The values we obtain are within a few hundredths of a percent of the
conjectured values

### Exact sampling of self-avoiding paths via discrete Schramm-Loewner evolution

We present an algorithm, based on the iteration of conformal maps, that
produces independent samples of self-avoiding paths in the plane. It is a
discrete process approximating radial Schramm-Loewner evolution growing to
infinity. We focus on the problem of reproducing the parametrization
corresponding to that of lattice models, namely self-avoiding walks on the
lattice, and we propose a strategy that gives rise to discrete paths where
consecutive points lie an approximately constant distance apart from each
other. This new method allows us to tackle two non-trivial features of
self-avoiding walks that critically depend on the parametrization: the
asphericity of a portion of chain and the correction-to-scaling exponent.Comment: 18 pages, 4 figures. Some sections rewritten (including title and
abstract), numerical results added, references added. Accepted for
publication in J. Stat. Phy

### Congenital and neonatal malaria in a rural Kenyan district hospital: An eight-year analysis

<p>Abstract</p> <p>Background</p> <p>Malaria remains a significant burden in sub-Saharan Africa. However, data on burden of congenital and neonatal malaria is scarce and contradictory, with some recent studies reporting a high burden. Using prospectively collected data on neonatal admissions to a rural district hospital in a region of stable malaria endemicity in Kenya, the prevalence of congenital and neonatal malaria was described.</p> <p>Methods</p> <p>From 1<sup>st </sup>January 2002 to 31<sup>st </sup>December 2009, admission and discharge information on all neonates admitted to Kilifi District Hospital was collected. At admission, blood was also drawn for routine investigations, which included a full blood count, blood culture and blood slide for malaria parasites.</p> <p>Results</p> <p>Of the 5,114 neonates admitted during the eight-year surveillance period, blood slide for malaria parasites was performed in 4,790 (93.7%). 18 (0.35%) neonates with <it>Plasmodium falciparum </it>malaria parasitaemia, of whom 11 were admitted within the first week of life and thus classified as congenital parasitaemia, were identified. 7/18 (39%) had fever. Parasite densities were low, â‰¤50 per ÎĽl in 14 cases. The presence of parasitaemia was associated with low haemoglobin (Hb) of <10 g/dl (Ď‡<sup>2 </sup>10.9 P = 0.001). The case fatality rate of those with and without parasitaemia was similar. <it>Plasmodium falciparum </it>parasitaemia was identified as the cause of symptoms in four neonates.</p> <p>Conclusion</p> <p>Congenital and neonatal malaria are rare in this malaria endemic region. Performing a blood slide for malaria parasites among sick neonates in malaria endemic regions is advisable. This study does not support routine treatment with anti-malarial drugs among admitted neonates with or without fever even in a malaria endemic region.</p

### Note on SLE and logarithmic CFT

It is discussed how stochastic evolutions may be linked to logarithmic
conformal field theory. This introduces an extension of the stochastic Loewner
evolutions. Based on the existence of a logarithmic null vector in an
indecomposable highest-weight module of the Virasoro algebra, the
representation theory of the logarithmic conformal field theory is related to
entities conserved in mean under the stochastic process.Comment: 10 pages, LaTeX, v2: version to be publishe

### Geometric Exponents, SLE and Logarithmic Minimal Models

In statistical mechanics, observables are usually related to local degrees of
freedom such as the Q < 4 distinct states of the Q-state Potts models or the
heights of the restricted solid-on-solid models. In the continuum scaling
limit, these models are described by rational conformal field theories, namely
the minimal models M(p,p') for suitable p, p'. More generally, as in stochastic
Loewner evolution (SLE_kappa), one can consider observables related to nonlocal
degrees of freedom such as paths or boundaries of clusters. This leads to
fractal dimensions or geometric exponents related to values of conformal
dimensions not found among the finite sets of values allowed by the rational
minimal models. Working in the context of a loop gas with loop fugacity beta =
-2 cos(4 pi/kappa), we use Monte Carlo simulations to measure the fractal
dimensions of various geometric objects such as paths and the generalizations
of cluster mass, cluster hull, external perimeter and red bonds. Specializing
to the case where the SLE parameter kappa = 4p'/p is rational with p < p', we
argue that the geometric exponents are related to conformal dimensions found in
the infinitely extended Kac tables of the logarithmic minimal models LM(p,p').
These theories describe lattice systems with nonlocal degrees of freedom. We
present results for critical dense polymers LM(1,2), critical percolation
LM(2,3), the logarithmic Ising model LM(3,4), the logarithmic tricritical Ising
model LM(4,5) as well as LM(3,5). Our results are compared with rigourous
results from SLE_kappa, with predictions from theoretical physics and with
other numerical experiments. Throughout, we emphasize the relationships between
SLE_kappa, geometric exponents and the conformal dimensions of the underlying
CFTs.Comment: Added reference

### LERW as an example of off-critical SLEs

Two dimensional loop erased random walk (LERW) is a random curve, whose
continuum limit is known to be a Schramm-Loewner evolution (SLE) with parameter
kappa=2. In this article we study ``off-critical loop erased random walks'',
loop erasures of random walks penalized by their number of steps. On one hand
we are able to identify counterparts for some LERW observables in terms of
symplectic fermions (c=-2), thus making further steps towards a field theoretic
description of LERWs. On the other hand, we show that it is possible to
understand the Loewner driving function of the continuum limit of off-critical
LERWs, thus providing an example of application of SLE-like techniques to
models near their critical point. Such a description is bound to be quite
complicated because outside the critical point one has a finite correlation
length and therefore no conformal invariance. However, the example here shows
the question need not be intractable. We will present the results with emphasis
on general features that can be expected to be true in other off-critical
models.Comment: 45 pages, 2 figure

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