Random set theory and problems of modeling

The three- or four-dimensional world in which we live is full of objects to be measured and summarized. Very often a parsimonious finite collection of measurements is enough for scientific investigation into an object’s genesis and evolution. There is a growing need, however, to describe and model objects through their form as well as their size. The purpose of this article is to show the potentials and limitations of a probabilistic and statistical approach. Collections of objects (the data) are assimilated to a random set (the model), whose parameters provide description and/or explanation

On The Performance Characteristics Of Electron Ring accelerators

On the basis of our present understanding of the physical phenomena involved in an electron ring accelerator (ERA), a theoretical study is made of the performance which might be expected for an ERA. Rigorous upper bounds are obtained on the rate of energy gain, from which it is shown that, in order to prevent azimuthal instability, parameters must be selected such that (for reasonable fields, injector properties, etc., but with no safety factors) the proton energy gain is less than 80 MeV/m. Numerical examples and approximate formulas are given for the properties of rings satisfying the stability conditions for both azimuthal oscillations and ion-electron oscillations. It is found that for reasonable fields and injector properties, but without safety factors, the useable proton energy gain is less than 45 MeV/m

RF Losses in Helical Resonators

Recently, increased interest has been shown in the use of helically loaded wave guides for the acceleration of heavy ions. These structures seem especially suited to this purpose in that they allow lo phase velocities for relatively small transverse dimensions

The effect of FTO variation on increased osteoarthritis risk is mediated through body mass index : a mendelian randomisation study

Objective: Variation in the fat mass and obesity-associated (FTO) gene influences susceptibility to obesity. A variant in the FTO gene has been implicated in genetic risk to osteoarthritis (OA). We examined the role of the FTO polymorphism rs8044769 in risk of knee and hip OA in cases and controls incorporating body mass index (BMI) information. Methods: 5409 knee OA patients, 4355 hip OA patients and up to 5362 healthy controls from 7 independent cohorts from the UK and Australia were genotyped for rs8044769. The association of the FTO variant with OA was investigated in case/control analyses with and without BMI adjustment and in analyses matched for BMI category. A mendelian randomisation approach was employed using the FTO variant as the instrumental variable to evaluate the role of overweight on OA. Results: In the meta-analysis of all overweight (BMI≥25) samples versus normal-weight controls irrespective of OA status the association of rs8044769 with overweight is highly significant (OR[CIs] for allele G=1.14 [01.08 to 1.19], p=7.5×10−7). A significant association with knee OA is present in the analysis without BMI adjustment (OR[CIs]=1.08[1.02 to 1.14], p=0.009) but the signal fully attenuates after BMI adjustment (OR[CIs]=0.99[0.93 to 1.05], p=0.666). We observe no evidence for association in the BMI-matched meta-analyses. Using mendelian randomisation approaches we confirm the causal role of overweight on OA. Conclusions: Our data highlight the contribution of genetic risk to overweight in defining risk to OA but the association is exclusively mediated by the effect on BMI. This is consistent with what is known of the biology of the FTO gene and supports the causative role of high BMI in OA

Coherent Electromagnetic Effects in High-Current Particle Accelerators: [Part] 3. Electromagnetic-Coupling Instabilities in a Coasting Beam

The electromagnetic interaction of an intense relativistic coasting beam with itself, including the effect of a confining nonperfect vacuum tank, or a quiescent rf cavity, is investigated theoretically. It is shown that the resonances that may occur between harmonics of the particle circulation frequencies and the electromagnetic modes of the cavities can lead to a longitudinal instability of the beam. A criterion for stability of the beam against such longitudinal bunching is obtained as a restriction on the shunt impedance of the rf cavity, or the Q of the vacuum tank. This criterion contains the energy spread and intensity of the coasting beam, as well as the parameters of the accelerator. Numerical examples are given which indicate that in general the resonances with the vacuum tank will not cause instabilities, while those with an rf cavity can be prevented from causing instabilities by choosing the shunt impedance at a sufficiently low but still convenient value