The motion of whips and chains

We study the motion of an inextensible string (a whip) fixed at one point in the absence of gravity, satisfying the equations $$\eta_{tt} = \partial_s(\sigma \eta_s), \qquad \sigma_{ss}-\lvert \eta_{ss}\rvert^2 = -\lvert \eta_{st}\rvert^2, \qquad \lvert \eta_s\rvert^2 \equiv 1$$ with boundary conditions $\eta(t,1)=0$ and $\sigma(t,0)=0$. We prove local existence and uniqueness in the space defined by the weighted Sobolev energy $$\sum_{\ell=0}^m \int_0^1 s^{\ell} \lvert \partial_s^{\ell}\eta_t\rvert^2 \, ds + \int_0^1 s^{\ell+1} \lvert \partial_s^{\ell+1}\eta\rvert^2 \, ds,$$ when $m\ge 3$. In addition we show persistence of smooth solutions as long as the energy for $m=3$ remains bounded. We do this via the method of lines, approximating with a discrete system of coupled pendula (a chain) for which the same estimates hold.Comment: 47 pages, 8 figure

Direct generation of photon triplets using cascaded photon-pair sources

Non-classical states of light, such as entangled photon pairs and number states, are essential for fundamental tests of quantum mechanics and optical quantum technologies. The most widespread technique for creating these quantum resources is the spontaneous parametric down-conversion (SPDC) of laser light into photon pairs. Conservation of energy and momentum in this process, known as phase-matching, gives rise to strong correlations which are used to produce two-photon entanglement in various degrees of freedom. It has been a longstanding goal of the quantum optics community to realise a source that can produce analogous correlations in photon triplets, but of the many approaches considered, none have been technically feasible. In this paper we report the observation of photon triplets generated by cascaded down-conversion. Here each triplet originates from a single pump photon, and therefore quantum correlations will extend over all three photons in a way not achievable with independently created photon pairs. We expect our photon-triplet source to open up new avenues of quantum optics and become an important tool in quantum technologies. Our source will allow experimental interrogation of novel quantum correlations, the post-selection free generation of tripartite entanglement without post- selection and the generation of heralded entangled-photon pairs suitable for linear optical quantum computing. Two of the triplet photons have a wavelength matched for optimal transmission in optical fibres, ideally suited for three-party quantum communication. Furthermore, our results open interesting regimes of non-linear optics, as we observe spontaneous down-conversion pumped by single photons, an interaction also highly relevant to optical quantum computing.Comment: 7 pages, 3 figures, 1 table; accepted by Natur

Isolated and Syndromic Retinal Dystrophy Caused by Biallelic Mutations in RCBTB1, a Gene Implicated in Ubiquitination.

Inherited retinal dystrophies (iRDs) are a group of genetically and clinically heterogeneous conditions resulting from mutations in over 250 genes. Here, homozygosity mapping and whole-exome sequencing (WES) in a consanguineous family revealed a homozygous missense mutation, c.973C>T (p.His325Tyr), in RCBTB1. In affected individuals, it was found to segregate with retinitis pigmentosa (RP), goiter, primary ovarian insufficiency, and mild intellectual disability. Subsequent analysis of WES data in different cohorts uncovered four additional homozygous missense mutations in five unrelated families in whom iRD segregates with or without syndromic features. Ocular phenotypes ranged from typical RP starting in the second decade to chorioretinal dystrophy with a later age of onset. The five missense mutations affect highly conserved residues either in the sixth repeat of the RCC1 domain or in the BTB1 domain. A founder haplotype was identified for mutation c.919G>A (p.Val307Met), occurring in two families of Mediterranean origin. We showed ubiquitous mRNA expression of RCBTB1 and demonstrated predominant RCBTB1 localization in human inner retina. RCBTB1 was very recently shown to be involved in ubiquitination, more specifically as a CUL3 substrate adaptor. Therefore, the effect on different components of the CUL3 and NFE2L2 (NRF2) pathway was assessed in affected individuals' lymphocytes, revealing decreased mRNA expression of NFE2L2 and several NFE2L2 target genes. In conclusion, our study puts forward mutations in RCBTB1 as a cause of autosomal-recessive non-syndromic and syndromic iRD. Finally, our data support a role for impaired ubiquitination in the pathogenetic mechanism of RCBTB1 mutations

WiseEye: next generation expandable and programmable camera trap platform for wildlife research

Funding: The work was supported by the RCUK Digital Economy programme to the dot.rural Digital Economy Hub; award reference: EP/G066051/1. The work of S. Newey and RJI was part funded by the Scottish Government's Rural and Environment Science and Analytical Services (RESAS). Details published as an Open Source Toolkit, PLOS Journals at: http://dx.doi.org/10.1371/journal.pone.0169758Peer reviewedPublisher PD

Uncovering the Oppenheimer Siddur: using scientific analysis to reveal the production process of a medieval illuminated Hebrew manuscript

The aim of this research was to use non-invasive scientifc analysis to uncover evidence of the planning process and relationship between pigments used in text copying and artwork production in the Oppenheimer Siddur (Oxford Bodleian Library MS Opp. 776), an illuminated 15th-century Hebrew prayer book. In many medieval Hebrew illuminated manuscripts, the authorship of the artwork is unknown. This manuscript’s colophon states that it was copied by its scribe-owner for personal family use but does not confrm who was responsible for the artwork. Prior deductive analysis suggested that the scribe-owner may also have been the manuscript’s artist, based on common motifs and an apparent shared colour palette appearing in both texts and artwork. Visual examination using high resolution digital images also identifed points of contact between pigments used in the manuscript’s texts and artwork, raising questions about the pigment application sequence, and concurrent versus sequential text copying and artwork production. An in-house developed remote spectral imaging system (PRISMS) with 10 flters spanning the spectral range from 400 to 880 nm was modifed for close-range application to image two of the folios to examine the sequence of production, identify the pigments and compare the materials used for the illumination and the text. Optical microscopy and Fourier Transform Infrared spectroscopy in the attenuated total refection mode (FTIR-ATR) were used directly on the folios to complement the spectral imaging data in binding media and pigment identifcation. The results revealed close matches in refectance spectra for the colorants and inks used in both text copying and illuminations, suggesting that the same mixture of colorants and inks have been used. The spectral imaging in the near infrared bands revealed a hidden underdrawing, indicating a design change during production of the manuscript, and the outlining of letters prior to coloured pigment being applied. The pigment use, the variation in the binder for diferent pigments and some elements of its production were found to be consistent with those described in historical sources. The evidence from this study supports the hypothesis that the scribe applied pigments for the manuscript’s artwork at the same time he did some of the scribal work which has implications for understandings of Jewish medieval visual cultures

One-dimensional symmetry and Liouville type results for the fourth order Allen-Cahn equation in RN^N

In this paper, we prove an analogue of Gibbons' conjecture for the extended fourth order Allen-Cahn equation in R N , as well as Liouville type results for some solutions converging to the same value at infinity in a given direction. We also prove a priori bounds and further one-dimensional symmetry and rigidity results for semilinear fourth order elliptic equations with more general nonlinearities

Assessment of Left Ventricular Geometrical Patterns and Function among Hypertensive Patients at a Tertiary Hospital, Northern Tanzania.

With hypertension, the cardiovascular system changes to adapt to the varying neuro-humoral and hemodynamic changes and this may lead to the development of different left ventricular geometric patterns, each carrying a different risk profile for major adverse cardiovascular events. Using a consecutive sampling technique, a cross-sectional, prospective, hospital based study was done and two hundred and twenty seven (227) hypertensive patients were studied. The distribution of different abnormal LV geometrical patterns was 19.8%, 28.2%, 22% for concentric remodelling, concentric hypertrophy and eccentric hypertrophy respectively. With echocardiographic criteria, the proportion of patients with left ventricular hypertrophy (LVH) was higher when left ventricular mass (LVM) was indexed to height(2.7) than to body surface area (70.0% vs. 52.9%). Duration of hypertension markedly influenced the type of LV geometry with normal LV geometry predominating in early hypertension and abnormal geometrical patterns predominating in late hypertension. The left ventricular fractional shortening decreased with duration of hypertension and was common in patients with eccentric hypertrophy. Age of the patient, systolic blood pressure, duration of hypertension and body mass index were found to be independent predictors left ventricular hypertrophy. About 70% of hypertensive patients had abnormal geometry existing in different patterns. Eccentric hypertrophy had more of clinical and echocardiographic features suggestive of reduced left ventricular systolic function. Hypertensive patients should be recognized as a heterogeneous population and therefore stratifying them into their respective LV geometrical patterns is useful as way of assessing their risk profile as well as instituting appropriate management