Tulczyjew's triples and lagrangian submanifolds in classical field theories

In this paper the notion of Tulczyjew's triples in classical mechanics is extended to classical field theories, using the so-called multisymplectic formalism, and a convenient notion of lagrangian submanifold in multisymplectic geometry. Accordingly, the dynamical equations are interpreted as the local equations defining these lagrangian submanifolds.Comment: 29 page

Discrete variational integrators and optimal control theory

A geometric derivation of numerical integrators for optimal control problems is proposed. It is based in the classical technique of generating functions adapted to the special features of optimal control problems.Comment: 17 page

Geometric numerical integration of nonholonomic systems and optimal control problems

A geometric derivation of numerical integrators for nonholonomic systems and optimal control problems is obtained. It is based in the classical technique of generating functions adapted to the special features of nonholonomic systems and optimal control problems.Comment: 6 pages, 1 figure. Submitted to IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, Sevilla 200

Reducing geographic inequalities in access times for acute treatment of myocardial infarction in a large country: the example of Russia.

Background: Russia has the largest area of any country in the world and has one of the highest cardiovascular mortality rates. Over the past decade, the number of facilities able to perform percutaneous coronary interventions (PCIs) has increased substantially. We quantify the extent to which the constraints of geography make equitable access to this effective technology difficult to achieve. Methods: Hospitals performing PCIs in 2010 and 2015 were identified and combined with data on the population of districts throughout the country. A network analysis tool was used to calculate road-travel times to the nearest PCI facility for those aged 40+ years. Results: The number of PCI facilities increased from 144 to 260 between 2010 and 2015. Overall, the median travel time to the closest PCI facility was 48 minutes in 2015, down from 73 minutes in 2010. Two-thirds of the urban population were within 60 minutes' travel time to a PCI facility in 2015, but only one-fifth of the rural population. Creating 67 new PCI facilities in currently underserved urban districts would increase the population share within 60 minutes' travel to 62% of the population, benefiting an additional 5.7 million people currently lacking adequate access. Conclusions: There have been considerable but uneven improvements in timely access to PCI facilities in Russia between 2010 and 2015. Russia has not achieved the level of access seen in other large countries with dispersed populations, such as Australian and Canada. However, creating a relatively small number of further PCI facilities could improve access substantially, thereby reducing inequality

Adiposity in middle and old age and risk of death from dementia: 40-year follow-up of 19,000 men in the Whitehall study.

AIMS AND OBJECTIVES: to examine the hypothesis that obesity is protective for dementia, we compared the associations of death from dementia with body weight and body mass index (BMI) in both middle and old age. DESIGN: height and weight were measured in a prospective study of 19,019 middle-aged men in the Whitehall study in 1967-70 and in 6,158 surviving participants at resurvey in 1997. Cox regression was used to examine the associations of death from dementia over a 40-year period with weight or BMI measured by health professionals in middle and old age adjusting for age, smoking habits, employment grade and marital status. SETTING: central government employees in London, UK. MAIN OUTCOMES MEASURE: death due to dementia in 320 participants. RESULTS: body weight measured in middle age was weakly inversely associated with death from dementia (hazard ratio 0.98 [95%CI: 0.97-0.99] per kg), but neither height nor BMI were related to risk of dementia. In contrast, body weight in old age was more strongly inversely related to deaths from dementia (0.96; [0.95-0.98] per kg) as was BMI (0.92 [0.86-0.97] per kg/m2). Weight loss over the 30 years between baseline and resurvey was associated with a higher risk of death from dementia, with an adjusted HR per kg/30 years of 1.04 [95%CI: 1.02-1.08] and the association with loss of BMI was even stronger (adjusted HR of 1.10 [1.03-1.19]) per kg/m2 decrease. CONCLUSIONS: the stronger inverse associations of deaths from dementia with BMI in old age, compared with middle age, together with strong positive associations of loss of BMI or body weight between middle and old age casts doubt on previous suggestions that obesity protects against death from dementia