Quasi-Isometric Embeddings of Symmetric Spaces

We prove a rigidity theorem that shows that, under many circumstances, quasi-isometric embeddings of equal rank, higher rank symmetric spaces are close to isometric embeddings. We also produce some surprising examples of quasi-isometric embeddings of higher rank symmetric spaces. In particular, we produce embeddings of $SL(n,\mathbb R)$ into $Sp(2(n-1),\mathbb R)$ when no isometric embeddings exist. A key ingredient in our proofs of rigidity results is a direct generalization of the Mostow-Morse Lemma in higher rank. Typically this lemma is replaced by the quasi-flat theorem which says that maximal quasi-flat is within bounded distance of a finite union of flats. We improve this by showing that the quasi-flat is in fact flat off of a subset of codimension $2$.Comment: Exposition improved, outlines of proofs added to introduction. Typos corrected, references added. Also some discussion of the reducible case adde

Coarse differentiation of quasi-isometries I: spaces not quasi-isometric to Cayley graphs

In this paper, we prove that certain spaces are not quasi-isometric to Cayley graphs of finitely generated groups. In particular, we answer a question of Woess and prove a conjecture of Diestel and Leader by showing that certain homogeneous graphs are not quasi-isometric to a Cayley graph of a finitely generated group. This paper is the first in a sequence of papers proving results announced in [EFW0]. In particular, this paper contains many steps in the proofs of quasi-isometric rigidity of lattices in Sol and of the quasi-isometry classification of lamplighter groups. The proofs of those results are completed in [EFW1]. The method used here is based on the idea of "coarse differentiation" introduced in [EFW0].Comment: 44 pages; 4 figures; minor corrections addressing comments by the refere

A crisis of enforcement: the decriminalisation of death and injury at work

Fatalities and injuries caused through work are far more prevalent than the Health and Safety Executive (HSE) currently reports. For example, they fi nd that more than 80 per cent of officially recorded work-related fatalities are fi ltered out from the HSE’s headline figure and remain buried in other categories in the official data. The official data made available by HSE reporting methodology may thus only serve to mask the true quantity and quality of harm that takes place during work processes. After re-assessing the scale of the harms caused, Tombs and Whyte conclude that being a victim of a work-related fatality or injury is far more likely than experiencing conventionally defi ned and measured violence and homicide. While such siphoning seems an inevitable and inherent characteristic of legal and regulatory systems, this briefi ng suggests that it may be only through the acknowledgement of ‘safety crime’ by agencies such as the Home Office, the police, the courts and the Scottish Government that safety crimes can be recast as ‘real’ crime and thus dealt with more appropriately. The authors’ conclusion, that most safety crimes are either undetected or filtered out from offi cial channels of resolution, begs the question whether burdens have been displaced to employees and members of the public

Triennial Review of the Health and Safety Executive. Submission to the Department for Work and Pensions

In this response we have chosen not to address the guided questions specifically, but rather to respond to the general coverage of the document, not least that set out at Annex E, “Background to the Health and Safety Executive”, where it is stated that: HSE’s functions are undertaken in the pursuit of four headline aims that support delivery of its mission. These aims, set out in the HSE’s Business Plan for 2012-15, are to: Lead others to improve health and safety in the workplace; Provide an effective regulatory framework; Secure compliance with the law; and, Reduce the likelihood of low frequency, high-impact catastrophic incidents. (Department for Work & Pensions, 2013: Annex E, 14) Our response addresses many of the claims made in that Annex regarding enforcement and inspection. We welcome this review of the HSE since, as the evidence set out in this response demonstrates, it is clear that the regulator is increasingly unfit for purpose. It is presently unable to provide either minimal inspection coverage or a credible threat of enforcement, and is therefore in no position to secure compliance with the law

Coarse differentiation of quasi-isometries II: Rigidity for Sol and Lamplighter groups

In this paper, which is the continuation of [EFW2], we complete the proof of the quasi-isometric rigidity of Sol and the lamplighter groups. The results were announced in [EFW1].Comment: 47 pages, 3 figures. Minor revisions addressing comments by the refere

Alcohol-related mortality in deprived UK cities: worrying trends in young women challenge recent national downward trends

Background: Glasgow, the largest city in Scotland, has high levels of deprivation and a poor-health profile compared with other parts of Europe, which cannot be fully explained by the high levels of deprivation. The ‘excess’ premature mortality in Glasgow is now largely attributable to deaths from alcohol, drugs, suicide and violence. Methods: Alcohol-related mortality in Glasgow from 1980 to 2011 was examined relative to the equally deprived UK cities of Manchester and Liverpool with the aim of identifying differences across the cities, with respect to gender, age and birth cohort, that could help explain the ‘excess’ mortality in Glasgow. Results: In the 1980s, alcohol-related mortality in Glasgow was three times higher than in Manchester and Liverpool. Alcohol-related mortality increased in all three cities over the subsequent three decades, but a sharp rise in deaths in the early 1990s was unique to Glasgow. The increase in numbers of deaths in Glasgow was greater than in Manchester and Liverpool, but there was little difference in the pattern of alcohol-related deaths, by sex or birth cohort that could explain the excess mortality in Glasgow. The recent modest decrease in alcohol-related mortality was largely experienced by all birth cohorts, with the notable exception of the younger cohort (born between 1970 and 1979): women in this cohort across all three cities experienced disproportionate increases in alcohol-related mortality. Conclusions: It is imperative that this early warning sign in young women in the UK is acted on if deaths from alcohol are to reduce in the long term

Rheology of the gel formed in the California Mastitis Test

The California Mastitis Test has previously been adapted for use in an inline, cow-side sensor and relies on the fact that the viscosity of the gel formed during the test is proportional to the somatic cell concentration. In this paper, the use of capillary and rotational viscometry was compared in light of the expected rheology of the gel formed during the test. It was found that the gel is non-Newtonian, but the initial phase of viscosity increase was not due to shear dependence, but rather due to the gelation reaction. The maximum apparent viscosity of the gel was shear dependent while the time it took to reach the maximum was not truly shear dependent, but was rather dependent on the degree of mixing during gelation. This was confirmed by introducing a delay time prior to viscosity measurement, in both capillary and rotational viscometry. It was found that by mixing the reagent and infected milk, then delaying viscosity measurement for 30 s, shortened the time it took to reach maximum viscosity by more than 60 s. The maximum apparent viscosity, however, was unaffected. It was found that capillary viscometry worked well to correlate relative viscosity with somatic cell count, but that it was sensitive to the reagent concentration. It can therefore be deduced that the rheology of the gel is complicated not only by it being non-Newtonian, but also by the strong dependence on test conditions. These make designing a successful sensor much more challenging

Chemical and rheological aspects of gel formation in the California Mastitis Test

The rheological properties of the CMT gel were analysed. Data are presented to demonstrate that the gel is a non-homogenous, visco-elastic, non-Newtonian fluid with rheopectic, and rheodestructive behaviour. The fundamental chemistry of the CMT is reviewed and a modified theory of gel formation is presented. The implications of the rheological properties and modified theory of gel formation for an automatic sensor are discussed