Low-temperature statistical mechanics of the QuanTizer problem: fast quenching and equilibrium cooling of the three-dimensional Voronoi Liquid

The Quantizer problem is a tessellation optimisation problem where point configurations are identified such that the Voronoi cells minimise the second moment of the volume distribution. While the ground state (optimal state) in 3D is almost certainly the body-centered cubic lattice, disordered and effectively hyperuniform states with energies very close to the ground state exist that result as stable states in an evolution through the geometric Lloyd's algorithm [Klatt et al. Nat. Commun., 10, 811 (2019)]. When considered as a statistical mechanics problem at finite temperature, the same system has been termed the 'Voronoi Liquid' by [Ruscher et al. EPL 112, 66003 (2015)]. Here we investigate the cooling behaviour of the Voronoi liquid with a particular view to the stability of the effectively hyperuniform disordered state. As a confirmation of the results by Ruscher et al., we observe, by both molecular dynamics and Monte Carlo simulations, that upon slow quasi-static equilibrium cooling, the Voronoi liquid crystallises from a disordered configuration into the body-centered cubic configuration. By contrast, upon sufficiently fast non-equilibrium cooling (and not just in the limit of a maximally fast quench) the Voronoi liquid adopts similar states as the effectively hyperuniform inherent structures identified by Klatt et al. and prevents the ordering transition into a BCC ordered structure. This result is in line with the geometric intuition that the geometric Lloyd's algorithm corresponds to a type of fast quench.Comment: 11 pages, 6 figure

Evidence-based planning and costing palliative care services for children : novel multi-method epidemiological and economic exemplar

Background: Children’s palliative care is a relatively new clinical specialty. Its nature is multi-dimensional and its delivery necessarily multi-professional. Numerous diverse public and not-for-profit organisations typically provide services and support. Because services are not centrally coordinated, they are provided in a manner that is inconsistent and incoherent. Since the first children’s hospice opened in 1982, the epidemiology of life-limiting conditions has changed with more children living longer, and many requiring transfer to adult services. Very little is known about the number of children living within any given geographical locality, costs of care, or experiences of children with ongoing palliative care needs and their families. We integrated evidence, and undertook and used novel methodological epidemiological work to develop the first evidence-based and costed commissioning exemplar. Methods: Multi-method epidemiological and economic exemplar from a health and not-for-profit organisation perspective, to estimate numbers of children under 19 years with life-limiting conditions, cost current services, determine child/parent care preferences, and cost choice of end-of-life care at home. Results: The exemplar locality (North Wales) had important gaps in service provision and the clinical network. The estimated annual total cost of current children’s palliative care was about £5.5 million; average annual care cost per child was £22,771 using 2007 prevalence estimates and £2,437- £11,045 using new 2012/13 population-based prevalence estimates. Using population-based prevalence, we estimate 2271 children with a life-limiting condition in the general exemplar population and around 501 children per year with ongoing palliative care needs in contact with hospital services. Around 24 children with a wide range of life-limiting conditions require end-of-life care per year. Choice of end-of-life care at home was requested, which is not currently universally available. We estimated a minimum (based on 1 week of end-of-life care) additional cost of £336,000 per year to provide end-of-life support at home. Were end-of-life care to span 4 weeks, the total annual additional costs increases to £536,500 (2010/11 prices). Conclusions: Findings make a significant contribution to population-based needs assessment and commissioning methodology in children’s palliative care. Further work is needed to determine with greater precision which children in the total population require access to services and when. Half of children who died 2002-7 did not have conditions that met the globally used children's palliative care condition categories, which need revision in light of findings

A mathematical model for top-shelf vertigo: the role of sedimenting otoconia in BPPV

Benign Paroxysmal Positional Vertigo (BPPV) is a mechanical disorder of the vestibular system in which calcite particles called otoconia interfere with the mechanical functioning of the fluid-filled semicircular canals normally used to sense rotation. Using hydrodynamic models, we examine the two mechanisms proposed by the medical community for BPPV: cupulolithiasis, in which otoconia attach directly to the cupula (a sensory membrane), and canalithiasis, in which otoconia settle through the canals and exert a fluid pressure across the cupula. We utilize known hydrodynamic calculations and make reasonable geometric and physical approximations to derive an expression for the transcupular pressure $\Delta P_c$ exerted by a settling solid particle in canalithiasis. By tracking settling otoconia in a two-dimensional model geometry, the cupular volume displacement and associated eye response (nystagmus) can be calculated quantitatively. Several important features emerge: 1) A pressure amplification occurs as otoconia enter a narrowing duct; 2) An average-sized otoconium requires approximately five seconds to settle through the wide ampulla, where $\Delta P_c$ is not amplified, which suggests a mechanism for the observed latency of BPPV; and 3) An average-sized otoconium beginning below the center of the cupula can cause a volumetric cupular displacement on the order of 30 pL, with nystagmus of order $2^\circ$/s, which is approximately the threshold for sensation. Larger cupular volume displacement and nystagmus could result from larger and/or multiple otoconia.Comment: 15 pages, 5 Figures updated, to be published in J. Biomechanic

Fluorodeoxyglucose positron emission tomography in the evaluation of germ cell tumours at relapse

Differentiation of active disease from fibrosis/mature teratoma in patients with residual masses or identifying of sites of recurrence in patients with raised markers following treatment of their testicular cancer remains a problem.18F-fluorodeoxyglucose positron emission tomography (FDG-PET) has the potential to identify active disease and thereby influence further management in these patients. We performed a retrospective study of the use of FDG-PET in detecting residual/recurrent testicular carcinoma in 55 patients (seventy FDG-PET scans). Forty-seven scans were for the assessment of residual masses (18 had raised markers) and 23 scans were for the investigation of raised markers in the presence of normal CT scans. True positive results were based on positive histology or clinical follow-up. FDG-PET had a positive predictive value (PPV) of 96% and a negative predictive value (NPV) of 90% in patients with residual masses. This PPV was equivalent to that of markers (94%) but FDG-PET had the advantage of identifying the site of that recurrence. The NPV was higher than that of markers. In patients with raised markers alone the PPV of FDG-PET was 92% but the NPV was only 50%. However, subsequent FDG-PET imaging was frequently the first imaging modality to identify the site of disease. FDG-PET effected a management change in 57% of cases. FDG-PET scanning detected viable tumour in residual masses and identified sites of disease in suspected recurrence. © 2000 Cancer Research Campaig

The MGB Challenge: Evaluating Multi-genre Broadcast Media Recognition

This paper describes the Multi-Genre Broadcast (MGB) Challenge at ASRU 2015, an evaluation focused on speech recognition, speaker diarization, and "lightly supervised" alignment of BBC TV recordings. The challenge training data covered the whole range of seven weeks BBC TV output across four channels, resulting in about 1,600 hours of broadcast audio. In addition several hundred million words of BBC subtitle text was provided for language modelling. A novel aspect of the evaluation was the exploration of speech recognition and speaker diarization in a longitudinal setting - i.e. recognition of several episodes of the same show, and speaker diarization across these episodes, linking speakers. The longitudinal tasks also offered the opportunity for systems to make use of supplied metadata including show title, genre tag, and date/time of transmission. This paper describes the task data and evaluation process used in the MGB challenge, and summarises the results obtained

Phase diagram and critical properties in the Polyakov--Nambu--Jona-Lasinio model

We investigate the phase diagram of the so-called Polyakov--Nambu--Jona-Lasinio model at finite temperature and nonzero chemical potential with three quark flavours. Chiral and deconfinement phase transitions are discussed, and the relevant order-like parameters are analyzed. The results are compared with simple thermodynamic expectations and lattice data. A special attention is payed to the critical end point: as the strength of the flavour-mixing interaction becomes weaker, the critical end point moves to low temperatures and can even disappear.Comment: Talk given at the 9th International Conference on Quark Confinement and the Hadron Spectrum - QCHS IX, Madrid, Spain, 30 August - September 201

Superpotentials for M-theory on a G_2 holonomy manifold and Triality symmetry

For $M$-theory on the $G_2$ holonomy manifold given by the cone on {\bf S^3}\x {\bf S^3} we consider the superpotential generated by membrane instantons and study its transformations properties, especially under monodromy transformations and triality symmetry. We find that the latter symmetry is, essentially, even a symmetry of the superpotential. As in Seiberg/Witten theory, where a flat bundle given by the periods of an universal elliptic curve over the $u$-plane occurs, here a flat bundle related to the Heisenberg group appears and the relevant universal object over the moduli space is related to hyperbolic geometry.Comment: 58 pages, latex; references adde