Nonexistence of an integral of the 6th degree in momenta for the Zipoy-Voorhees metric

We prove nonexistence of a nontrivial integral that is polynomial in momenta of degree less than 7 for the Zipoy-Voorhees spacetime with the parameter $\delta=2$Comment: 7 pages, no figure

Coherence properties of the microcavity polariton condensate

A theoretical model is presented which explains the dominant decoherence process in a microcavity polariton condensate. The mechanism which is invoked is the effect of self-phase modulation, whereby interactions transform polariton number fluctuations into random energy variations. The model shows that the phase coherence decay, g1(t), has a Kubo form, which can be Gaussian or exponential, depending on whether the number fluctuations are slow or fast. This fluctuation rate also determines the decay time of the intensity correlation function, g2(t), so it can be directly determined experimentally. The model explains recent experimental measurements of a relatively fast Gaussian decay for g1(t), but also predicts a regime, further above threshold, where the decay is much slower.Comment: 5 pages, 1 figur

Harmonic Maa{\ss}-Jacobi forms of degree 1 with higher rank indices

We define and investigate real analytic weak Jacobi forms of degree 1 and arbitrary rank. En route we calculate the Casimir operator associated to the maximal central extension of the real Jacobi group, which for rank exceeding 1 is of order 4. In ranks exceeding 1, the notions of H-harmonicity and semi-holomorphicity are the same.Comment: 28 page

Spacetime Encodings II - Pictures of Integrability

I visually explore the features of geodesic orbits in arbitrary stationary axisymmetric vacuum (SAV) spacetimes that are constructed from a complex Ernst potential. Some of the geometric features of integrable and chaotic orbits are highlighted. The geodesic problem for these SAV spacetimes is rewritten as a two degree of freedom problem and the connection between current ideas in dynamical systems and the study of two manifolds sought. The relationship between the Hamilton-Jacobi equations, canonical transformations, constants of motion and Killing tensors are commented on. Wherever possible I illustrate the concepts by means of examples from general relativity. This investigation is designed to build the readers' intuition about how integrability arises, and to summarize some of the known facts about two degree of freedom systems. Evidence is given, in the form of orbit-crossing structure, that geodesics in SAV spacetimes might admit, a fourth constant of motion that is quartic in momentum (by contrast with Kerr spacetime, where Carter's fourth constant is quadratic).Comment: 11 pages, 10 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

Geodesics around Weyl-Bach's Ring Solution

We explore some of the gravitational features of a uniform ring both in the Newtonian potential theory and in General Relativity. We use a spacetime associated to a Weyl static solution of the vacuum Einstein's equations with ring like singularity. The Newtonian motion for a test particle in the gravitational field of the ring is studied and compared with the corresponding geodesic motion in the given spacetime. We have found a relativistic peculiar attraction: free falling particle geodesics are lead to the inner rim but never hit the ring.Comment: 8 figures, 14 pages. LaTeX w/ subfigure, graphic

Bucking the trend: the diversity of Anthropocene ‘winners’ among British moths

An appreciation of how some species are becoming more common despite unprecedented anthropogenic pressures could offer key insights for mitigating the global biodiversity crisis.  Research to date has largely focused on declining species, while species that are becoming more common have received relatively little attention. Macro-moths in Great Britain are well-studied and species-rich, making them an ideal group for addressing this knowledge gap. Here, we examine changes in 51 successful species between 1968 and 2016 using 4.5 million occurrence records and a systematic monitoring dataset. We employ 3D graphical analysis to visualise long-term multidimensional trends in prevalence (abundance and range) and use vector autoregression models to test whether past values of local abundance are useful for predicting changes in the extent of occurrence. The responses of Anthropocene winners are heterogeneous, suggesting multiple drivers are responsible. Changes in range and local abundance frequently occur intermittently through time, demonstrating the value of long-term, continuous monitoring. There is significant diversity among the winners themselves, which include widespread generalists, habitat specialists, and recent colonists. We offer brief discussion of possible causal factors and the wider ecosystem implications of these trends