61 research outputs found
The Statistics of the Points Where Nodal Lines Intersect a Reference Curve
We study the intersection points of a fixed planar curve with the
nodal set of a translationally invariant and isotropic Gaussian random field
\Psi(\bi{r}) and the zeros of its normal derivative across the curve. The
intersection points form a discrete random process which is the object of this
study. The field probability distribution function is completely specified by
the correlation G(|\bi{r}-\bi{r}'|) = .
Given an arbitrary G(|\bi{r}-\bi{r}'|), we compute the two point
correlation function of the point process on the line, and derive other
statistical measures (repulsion, rigidity) which characterize the short and
long range correlations of the intersection points. We use these statistical
measures to quantitatively characterize the complex patterns displayed by
various kinds of nodal networks. We apply these statistics in particular to
nodal patterns of random waves and of eigenfunctions of chaotic billiards. Of
special interest is the observation that for monochromatic random waves, the
number variance of the intersections with long straight segments grows like , as opposed to the linear growth predicted by the percolation model,
which was successfully used to predict other long range nodal properties of
that field.Comment: 33 pages, 13 figures, 1 tabl
On the Nodal Count Statistics for Separable Systems in any Dimension
We consider the statistics of the number of nodal domains aka nodal counts
for eigenfunctions of separable wave equations in arbitrary dimension. We give
an explicit expression for the limiting distribution of normalised nodal counts
and analyse some of its universal properties. Our results are illustrated by
detailed discussion of simple examples and numerical nodal count distributions.Comment: 21 pages, 4 figure
Short and Long Range Screening of Optical Singularities
Screening of topological charges (singularities) is discussed for paraxial
optical fields with short and with long range correlations. For short range
screening the charge variance in a circular region with radius grows
linearly with , instead of with as expected in the absence of
screening; for long range screening it grows faster than : for a field whose
autocorrelation function is the zero order Bessel function J_{0}, the charge
variance grows as R ln R$. A J_{0} correlation function is not attainable in
practice, but we show how to generate an optical field whose correlation
function closely approximates this form. The charge variance can be measured by
counting positive and negative singularities inside the region A, or more
easily by counting signed zero crossings on the perimeter of A. \For the first
method the charge variance is calculated by integration over the charge
correlation function C(r), for the second by integration over the zero crossing
correlation function Gamma(r). Using the explicit forms of C(r) and of Gamma(r)
we show that both methods of calculation yield the same result. We show that
for short range screening the zero crossings can be counted along a straight
line whose length equals P, but that for long range screening this
simplification no longer holds. We also show that for realizable optical
fields, for sufficiently small R, the charge variance goes as R^2, whereas for
sufficiently large R, it grows as R. These universal laws are applicable to
both short and pseudo-long range correlation functions
Counting nodal domains on surfaces of revolution
We consider eigenfunctions of the Laplace-Beltrami operator on special
surfaces of revolution. For this separable system, the nodal domains of the
(real) eigenfunctions form a checker-board pattern, and their number is
proportional to the product of the angular and the "surface" quantum numbers.
Arranging the wave functions by increasing values of the Laplace-Beltrami
spectrum, we obtain the nodal sequence, whose statistical properties we study.
In particular we investigate the distribution of the normalized counts
for sequences of eigenfunctions with where . We show that the distribution approaches
a limit as (the classical limit), and study the leading
corrections in the semi-classical limit. With this information, we derive the
central result of this work: the nodal sequence of a mirror-symmetric surface
is sufficient to uniquely determine its shape (modulo scaling).Comment: 36 pages, 8 figure
How do you say ‘hello’? Personality impressions from brief novel voices
On hearing a novel voice, listeners readily form personality impressions of that speaker. Accurate or not, these impressions are known to affect subsequent interactions; yet the underlying psychological and acoustical bases remain poorly understood. Furthermore, hitherto studies have focussed on extended speech as opposed to analysing the instantaneous impressions we obtain from first experience. In this paper, through a mass online rating experiment, 320 participants rated 64 sub-second vocal utterances of the word ‘hello’ on one of 10 personality traits. We show that: (1) personality judgements of brief utterances from unfamiliar speakers are consistent across listeners; (2) a two-dimensional ‘social voice space’ with axes mapping Valence (Trust, Likeability) and Dominance, each driven by differing combinations of vocal acoustics, adequately summarises ratings in both male and female voices; and (3) a positive combination of Valence and Dominance results in increased perceived male vocal Attractiveness, whereas perceived female vocal Attractiveness is largely controlled by increasing Valence. Results are discussed in relation to the rapid evaluation of personality and, in turn, the intent of others, as being driven by survival mechanisms via approach or avoidance behaviours. These findings provide empirical bases for predicting personality impressions from acoustical analyses of short utterances and for generating desired personality impressions in artificial voices
Longitudinal Auxological recovery in a cohort of children with Hyperinsulinaemic Hypoglycaemia
Background: Hypoglycaemia due to hyperinsulinism (HI) is the commonest cause of severe, recurrent hypoglycaemia in childhood. Cohort outcomes of HI remain to be described and whilst previous follow up studies have focused on neurodevelopmental outcomes, there is no information available on feeding and auxology.
Aim: We aimed to describe HI outcomes for auxology, medications, feeding and neurodevelopmental in a cohort up to age 5 years.
Method: We reviewed medical records for all patients with confirmed HI over a three-year period in a single centre to derive a longitudinal dataset.
Results: Seventy patients were recruited to the study. Mean weight at birth was - 1.0 standard deviation scores (SDS) for age and sex, while mean height at 3 months was - 1.5 SDS. Both weight and height trended to the population median over the follow up period. Feeding difficulties were noted in 17% of patients at 3 months and this reduced to 3% by 5 years. At age 5 years, 11 patients (15%) had neurodevelopmental delay and of these only one was severe. Resolution of disease was predicted by lower maximum early diazoxide dose (p = 0.007) and being born SGA (p = 0.009).
Conclusion: In a three-year cohort of HI patients followed up for 5 years, in spite of feeding difficulties and carbohydrate loading in early life, auxology parameters are normal in follow up. A lower than expected rate of neurodevelopmental delay could be attributed to prompt early treatment.This article is freely available via Open Access. Click on the Publisher URL to access it via the publisher's site.The study was supported by the Northern Congenital Hyperinsulinism (NORCHI) charitable fund, by the Manchester Academic Health Sciences Centre and by The University of Manchester MRC Confidence in Concept (CiC) Award (MC_PC_18056). KEC was funded by a Research Councils UK Academic Fellowship (https://www.ukri.org/). SEF has a Sir Henry Dale Fellowship jointly funded by the Wellcome Trust and the Royal Society (105636/Z/14/Z).published version, accepted versio
Different Vocal Parameters Predict Perceptions of Dominance and Attractiveness
Low mean fundamental frequency (F0) in men’s voices has been found to positively influence perceptions of dominance by men and attractiveness by women using standardized speech. Using natural speech obtained during an ecologically valid social interaction, we examined relationships between multiple vocal parameters and dominance and attractiveness judgments. Male voices from an unscripted dating game were judged by men for physical and social dominance and by women in fertile and non-fertile menstrual cycle phases for desirability in short-term and long-term relationships. Five vocal parameters were analyzed: mean F0 (an acoustic correlate of vocal fold size), F0 variation, intensity (loudness), utterance duration, and formant dispersion (Df, an acoustic correlate of vocal tract length). Parallel but separate ratings of speech transcripts served as controls for content. Multiple regression analyses were used to examine the independent contributions of each of the predictors. Physical dominance was predicted by low F0 variation and physically dominant word content. Social dominance was predicted only by socially dominant word content. Ratings of attractiveness by women were predicted by low mean F0, low Df, high intensity, and attractive word content across cycle phase and mating context. Low Df was perceived as attractive by fertile-phase women only. We hypothesize that competitors and potential mates may attend more strongly to different components of men’s voices because of the different types of information these vocal parameters provide
Long-term medical treatment in congenital hyperinsulinism: a descriptive analysis in a large cohort of patients from different clinical centers
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