Singular systems of linear forms and non-escape of mass in the space of lattices

Singular systems of linear forms were introduced by Khintchine in the 1920s, and it was shown by Dani in the 1980s that they are in one-to-one correspondence with certain divergent orbits of oneparameter diagonal groups on the space of lattices. We give a (conjecturally sharp) upper bound on the Hausdor dimension of the set of singular systems of linear forms (equivalently the set of lattices with divergent trajectories) as well as the dimension of the set of lattices with trajectories `escaping on average' (a notion weaker than divergence). This extends work by Cheung, as well as by Chevallier and Cheung. Our method di ers considerably from that of Cheung and Chevallier, and is based on the technique of integral inequalities developed by Eskin, Margulis and Mozes

Singular systems of linear forms and non-escape of mass in the space of lattices

Singular systems of linear forms were introduced by Khintchine in the 1920s, and it was shown by Dani in the 1980s that they are in one-to-one correspondence with certain divergent orbits of oneparameter diagonal groups on the space of lattices. We give a (conjecturally sharp) upper bound on the Hausdor dimension of the set of singular systems of linear forms (equivalently the set of lattices with divergent trajectories) as well as the dimension of the set of lattices with trajectories `escaping on average' (a notion weaker than divergence). This extends work by Cheung, as well as by Chevallier and Cheung. Our method di ers considerably from that of Cheung and Chevallier, and is based on the technique of integral inequalities developed by Eskin, Margulis and Mozes

Heating due to momentum transfer in low-energy positronium-antiproton scattering

Discovery that the elastic scattering cross sections in the antiproton-positronium system are very large close to threshold, particularly for excited positronium states.The implications for experiments aiming to use the positronium-antiproton system for antihydrogen formation are explored

Associations of the lipidome with ageing, cognitive decline and exercise behaviours

One of the most recognisable features of ageing is a decline in brain health and cognitive dysfunction, which is associated with perturbations to regular lipid homeostasis. Although ageing is the largest risk factor for several neurodegenerative diseases such as dementia, a loss in cognitive function is commonly observed in adults over the age of 65. Despite the prevalence of normal age-related cognitive decline, there is a lack of effective methods to improve the health of the ageing brain. In light of this, exercise has shown promise for positively influencing neurocognitive health and associated lipid profiles. This review summarises age-related changes in several lipid classes that are found in the brain, including fatty acyls, glycerolipids, phospholipids, sphingolipids and sterols, and explores the consequences of age-associated pathological cognitive decline on these lipid classes. Evidence of the positive effects of exercise on the affected lipid profiles are also discussed to highlight the potential for exercise to be used therapeutically to mitigate age-related changes to lipid metabolism and prevent cognitive decline in later life

Associations of the lipidome with ageing, cognitive decline and exercise behaviours

One of the most recognisable features of ageing is a decline in brain health and cognitive dysfunction, which is associated with perturbations to regular lipid homeostasis. Although ageing is the largest risk factor for several neurodegenerative diseases such as dementia, a loss in cognitive function is commonly observed in adults over the age of 65. Despite the prevalence of normal age-related cognitive decline, there is a lack of effective methods to improve the health of the ageing brain. In light of this, exercise has shown promise for positively influencing neurocognitive health and associated lipid profiles. This review summarises age-related changes in several lipid classes that are found in the brain, including fatty acyls, glycerolipids, phospholipids, sphingolipids and sterols, and explores the consequences of age-associated pathological cognitive decline on these lipid classes. Evidence of the positive effects of exercise on the affected lipid profiles are also discussed to highlight the potential for exercise to be used therapeutically to mitigate age-related changes to lipid metabolism and prevent cognitive decline in later life