An analytic solution to the Busemann-Petty problem on sections of convex bodies

We derive a formula connecting the derivatives of parallel section functions of an origin-symmetric star body in R^n with the Fourier transform of powers of the radial function of the body. A parallel section function (or (n-1)-dimensional X-ray) gives the ((n-1)-dimensional) volumes of all hyperplane sections of the body orthogonal to a given direction. This formula provides a new characterization of intersection bodies in R^n and leads to a unified analytic solution to the Busemann-Petty problem: Suppose that K and L are two origin-symmetric convex bodies in R^n such that the ((n-1)-dimensional) volume of each central hyperplane section of K is smaller than the volume of the corresponding section of L; is the (n-dimensional) volume of K smaller than the volume of L? In conjunction with earlier established connections between the Busemann-Petty problem, intersection bodies, and positive definite distributions, our formula shows that the answer to the problem depends on the behavior of the (n-2)-nd derivative of the parallel section functions. The affirmative answer to the Busemann-Petty problem for n\le 4 and the negative answer for n\ge 5 now follow from the fact that convexity controls the second derivatives, but does not control the derivatives of higher orders.Comment: 13 pages, published versio

Considerations in relation to off-site emergency procedures and response for nuclear accidents

The operation of nuclear facilities has, fortunately, not led to many accidents with off-site consequences. However, it is well-recognised that should a large release of radioactivity occur, the effects in the surrounding area and population will be significant. These effects can be mitigated by developing emergency preparedness and response plans prior to the operation of the nuclear facility that can be exercised regularly and implemented if an accident occurs. This review paper details the various stages of a nuclear accident and the corresponding aspects of an emergency preparedness plan that are relevant to these stages, both from a UK and international perspective. The paper also details how certain aspects of emergency preparedness have been affected by the accident at Fukushima Dai-ichi and as a point of comparison how emergency management plans were implemented following the accidents at Three Mile Island 2 and Chernobyl. In addition, the UK’s economic costing model for nuclear accidents COCO-2, and the UK’s Level-3 Probabilistic Safety Assessment code “PACE” are introduced. Finally, the factors that affect the economic impact of a nuclear accident, especially from a UK standpoint, are described

The associations of sedentary time and breaks in sedentary time with 24-hour glycaemic control in type 2 diabetes

The aim of this study was to investigate the associations of accelerometer-assessed sedentary time and breaks in sedentary time with 24-h events and duration of hypoglycaemia (7.8 mmol/l) and above target glucose (>9 mmol/l). Thirty-seven participants with type 2 diabetes (age, 62.8 ± 10.5 years; body mass index, 29.6 ± 6.8 kg/m2) in Glasgow, United Kingdom were enrolled between February 2016 and February 2017. Participants wore an activity monitor (activPAL3) recording the time and pattern of sedentary behaviour and a continuous glucose monitoring (CGM, Abbott FreeStyle Libre) for up to 14 days. Linear regression analyses were used to investigate the associations. Participants spent 3.7%, 64.7%, 32.1% and 19.2% of recording h/day in hypoglycaemia, euglycaemia, hyperglycaemia and above target, respectively. There was a negative association between sedentary time and time in euglycaemia (β = -0.44, 95% CI -0.86; -0.03, p = 0.04). There was a trend towards a positive association between sedentary time and time in hyperglycaemia (β = 0.36, 95% CI -0.05; 0.78, p = 0.08). Breaks in sedentary time was associated with higher time in euglycaemia (β = 0.38, 95% CI 0.00; 0.75, p = 0.04). To conclude, in individuals with type 2 diabetes, more time spent in unbroken and continuous sedentary behaviour was associated with poorer glucose control. Conversely, interrupting sedentary time with frequent breaks appears to improve glycaemic control. Therefore, this should be considered as a simple adjunct therapy to improve clinical outcomes in type 2 diabetes

Open Access, Open Science, Open Society

Open Access’ main goal is not the subversion of publishers’ role as driving actors in an oligopolistic market characterised by reduced competition and higher prices. OA’s main function is to be found somewhere else, namely in the ability to subvert the power to control science’s governance and its future directions (Open Science), a power that is more often found within the academic institutions rather than outside. By decentralising and opening-up not just the way in which scholarship is published but also the way in which it is assessed, OA removes the barriers that helped turn science into an intellectual oligopoly even before an economic one. The goal of this paper is to demonstrate that Open Access is a key enabler of Open Science, which in turn will lead to a more Open Society. Furthermore, the paper argues that while legislative interventions play an important role in the top-down regulation of Open Access, legislators currently lack an informed and systematic vision on the role of Open Access in science and society. In this historical phase, other complementary forms of intervention (bottom-up) appear much more “informed” and effective. This paper, which intends to set the stage for future research, identifies a few pieces of the puzzle: the relationship between formal and informal norms in the field of Open Science and how these impact on intellectual property rights, the protection of personal data, the assessment of science and the technology employed for the communication of science

Advanced operational models of the apple X undulator

Athos is a new soft X-ray beamline at SwissFEL, where the Apple X type undulators will be equipped. These devices are flexible to produce light in different polarization modes. An adequate magnetic field model is required for the operation of undulator. The undulator deflection parameter K and its gradient are calculated starting from the Fourier series of the magnetic field. In the classical parallel and anti-parallel operational modes - respectively elliptical and linear modes, the variation of the magnetic field as well as its parameters are evaluated by computer modeling. The results are compared to the magnetic measurements of the first Apple X prototype.peer-reviewe