Relative entropy as a measure of inhomogeneity in general relativity

We introduce the notion of relative volume entropy for two spacetimes with preferred compact spacelike foliations. This is accomplished by applying the notion of Kullback-Leibler divergence to the volume elements induced on spacelike slices. The resulting quantity gives a lower bound on the number of bits which are necessary to describe one metric given the other. For illustration, we study some examples, in particular gravitational waves, and conclude that the relative volume entropy is a suitable device for quantitative comparison of the inhomogeneity of two spacetimes.Comment: 15 pages, 7 figure

Semiclassical Analysis of the Wigner 12j12j Symbol with One Small Angular Momentum

We derive an asymptotic formula for the Wigner $12j$ symbol, in the limit of one small and 11 large angular momenta. There are two kinds of asymptotic formulas for the $12j$ symbol with one small angular momentum. We present the first kind of formula in this paper. Our derivation relies on the techniques developed in the semiclassical analysis of the Wigner $9j$ symbol [L. Yu and R. G. Littlejohn, Phys. Rev. A 83, 052114 (2011)], where we used a gauge-invariant form of the multicomponent WKB wave-functions to derive asymptotic formulas for the $9j$ symbol with small and large angular momenta. When applying the same technique to the $12j$ symbol in this paper, we find that the spinor is diagonalized in the direction of an intermediate angular momentum. In addition, we find that the geometry of the derived asymptotic formula for the $12j$ symbol is expressed in terms of the vector diagram for a $9j$ symbol. This illustrates a general geometric connection between asymptotic limits of the various $3nj$ symbols. This work contributes the first known asymptotic formula for the $12j$ symbol to the quantum theory of angular momentum, and serves as a basis for finding asymptotic formulas for the Wigner $15j$ symbol with two small angular momenta.Comment: 15 pages, 14 figure

Survival of South African children with cerebral palsy

Background. The South African (SA) public healthcare sector has experienced a surge in birth injury claims in recent years, particularly in respect of cerebral palsy (CP). The lump sum settlements in these matters are a function of the expected survival curve of the individual concerned. It is known from international studies that the life expectancy of children with CP is shorter than that of the general population, and depends on the pattern and severity of their disabilities. However, empirical estimates of survival for children with CP in SA are not available.Objectives. To construct survival curves according to the pattern of gross motor skills for CP children in SA and compare these with international studies.Methods. We collected data on mortality and functional status for 339 CP children on whose behalf claims for medical negligence had been instituted. Motor disabilities were classified according to the five-level Gross Motor Function Classification System (GMFCS). Children who were unable to walk unaided were further classified according to more basic motor skills, including the ability to lift their heads or chests in the prone position, rolling and sitting. Mortality rates were calculated and survival curves were estimated using the Kaplan-Meier method.Results. No deaths were observed among 119 children in GMFCS levels I - IV. Among the 220 children in GMFCS V, there were 20 observed deaths. The proportions surviving to ages 10 and 15 years were 85% (standard error (SE) 5%) and 55% (SE 11%), respectively. The former is comparable to what has been reported for children in California and Sweden, but the survival to age 15 is lower. Among 82 children who could not lift their heads in the prone position, there were 11 observed deaths for a mortality rate of 48.5 (95% confidence interval (CI) 24.2 - 86.9) deaths per 1 000 person-years. Among 72 children who could lift their heads but not their chests, there were 6 observed deaths for a mortality rate of 33.5 (95% CI 12.3 - 73.0) deaths per 1 000 person-years. These mortality rates are 22% and 15% higher than the corresponding figures documented for children with comparable abilities and disabilities in California.Conclusions. Life expectancy of children with CP in SA is lower than that of children with comparably severe disabilities in high-income countries

The Wahlquist metric cannot describe an isolated rotating body

It is proven that the Wahlquist perfect fluid space-time cannot be smoothly joined to an exterior asymptotically flat vacuum region. The proof uses a power series expansion in the angular velocity, to a precision of the second order. In this approximation, the Wahlquist metric is a special case of the rotating Whittaker space-time. The exterior vacuum domain is treated in a like manner. We compute the conditions of matching at the possible boundary surface in both the interior and the vacuum domain. The conditions for matching the induced metrics and the extrinsic curvatures are mutually contradictory.Comment: 13 pages, 0 figure

Automatic wheeze detection based on auditory modelling

Automatic wheeze detection has several potential benefits compared with reliance on human auscultation: it is experience independent, an automated historical record can easily be kept, and it allows quantification of wheeze severity. Previous attempts to detect wheezes automatically have had partial success but have not been reliable enough to become widely accepted as a useful tool. In this paper an improved algorithm for automatic wheeze detection based on auditory modelling is developed, called the frequency- and duration-dependent threshold algorithm. The mean frequency and duration of each wheeze component are obtained automatically. The detected wheezes are marked on a spectrogram. In the new algorithm, the concept of a frequency- and duration-dependent threshold for wheeze detection is introduced. Another departure from previous work is that the threshold is based not on global power but on power corresponding to a particular frequency range. The algorithm has been tested on 36 subjects, 11 of whom exhibited characteristics of wheeze. The results show a marked improvement in the accuracy of wheeze detection when compared with previous algorithms

Easy on that trigger dad: a study of long term family photo retrieval

We examine the effects of new technologies for digital photography on people's longer term storage and access to collections of personal photos. We report an empirical study of parents' ability to retrieve photos related to salient family events from more than a year ago. Performance was relatively poor with people failing to find almost 40% of pictures. We analyze participants' organizational and access strategies to identify reasons for this poor performance. Possible reasons for retrieval failure include: storing too many pictures, rudimentary organization, use of multiple storage systems, failure to maintain collections and participants' false beliefs about their ability to access photos. We conclude by exploring the technical and theoretical implications of these findings

Gravitating Opposites Attract

Generalizing previous work by two of us, we prove the non-existence of certain stationary configurations in General Relativity having a spatial reflection symmetry across a non-compact surface disjoint from the matter region. Our results cover cases such that of two symmetrically arranged rotating bodies with anti-aligned spins in $n+1$ ($n \geq 3$) dimensions, or two symmetrically arranged static bodies with opposite charges in 3+1 dimensions. They also cover certain symmetric configurations in (3+1)-dimensional gravity coupled to a collection of scalars and abelian vector fields, such as arise in supergravity and Kaluza-Klein models. We also treat the bosonic sector of simple supergravity in 4+1 dimensions.Comment: 13 pages; slightly amended version, some references added, matches version to be published in Classical and Quantum Gravit

Entanglement and chaos in the kicked top

The standard kicked top involves a periodically kicked angular momentum. By considering this angular momentum as a collection of entangled spins, we compute the bipartite entanglement dynamics as a function of the dynamics of the classical counterpart. Our numerical results indicate that the entanglement of the quantum top depends on the specific details of the dynamics of the classical top rather than depending universally on the global properties of the classical regime. These results are grounded on linking the entanglement rate to averages involving the classical angular momentum, thereby explaining why regular dynamics can entangle as efficiently as the classically chaotic regime. The findings are in line with previous results obtained with a 2-particle top model, and we show here that the standard kicked top can be obtained as a limiting case of the 2-particle top