Convergence of eigenfunction expansions corresponding to nonlinear Sturm-Liouville operators

It is well known that the classical linear Sturm-Liouville eigenvalue problem is self-adjoint and possesses a family of eigenfunctions which form an orthonormal basis for the space L. A natural question is to ask if a similar result holds for nonlinear problems. In the present paper, we examine the basis property for eigenfunctions of nonlinear Sturm-Liouville equations subject to general linear, separated boundary conditions

The Brain Health Index: Towards a combined measure of neurovascular and neurodegenerative structural brain injury

Background: A structural magnetic resonance imaging measure of combined neurovascular and neurodegenerative burden may be useful as these features often coexist in older people, stroke and dementia. Aim: We aimed to develop a new automated approach for quantifying visible brain injury from small vessel disease and brain atrophy in a single measure, the brain health index. Materials and methods: We computed brain health index in N = 288 participants using voxel-based Gaussian mixture model cluster analysis of T1, T2, T2*, and FLAIR magnetic resonance imaging. We tested brain health index against a validated total small vessel disease visual score and white matter hyperintensity volumes in two patient groups (minor stroke, N = 157; lupus, N = 51) and against measures of brain atrophy in healthy participants (N = 80) using multiple regression. We evaluated associations with Addenbrooke’s Cognitive Exam Revised in patients and with reaction time in healthy participants. Results: The brain health index (standard beta = 0.20–0.59, P < 0.05) was significantly and more strongly associated with Addenbrooke’s Cognitive Exam Revised, including at one year follow-up, than white matter hyperintensity volume (standard beta = 0.04–0.08, P > 0.05) and small vessel disease score (standard beta = 0.02–0.27, P > 0.05) alone in both patient groups. Further, the brain health index (standard beta = 0.57–0.59, P < 0.05) was more strongly associated with reaction time than measures of brain atrophy alone (standard beta = 0.04–0.13, P > 0.05) in healthy participants. Conclusions: The brain health index is a new image analysis approach that may usefully capture combined visible brain damage in large-scale studies of ageing, neurovascular and neurodegenerative disease

Bottom trawl fishing footprints on the world’s continental shelves

Publication history: Accepted - 23 August 2018; Published online - 8 October 2018.Bottom trawlers land around 19 million tons of fish and invertebrates annually, almost one-quarter of wild marine landings. The extent of bottom trawling footprint (seabed area trawled at least once in a specified region and time period) is often contested but poorly described. We quantify footprints using high-resolution satellite vessel monitoring system (VMS) and logbook data on 24 continental shelves and slopes to 1,000-m depth over at least 2 years. Trawling footprint varied markedly among regions: from <10% of seabed area in Australian and New Zealand waters, the Aleutian Islands, East Bering Sea, South Chile, and Gulf of Alaska to >50% in some European seas. Overall, 14% of the 7.8 million-km2 study area was trawled, and 86% was not trawled. Trawling activity was aggregated; the most intensively trawled areas accounting for 90% of activity comprised 77% of footprint on average. Regional swept area ratio (SAR; ratio of total swept area trawled annually to total area of region, a metric of trawling intensity) and footprint area were related, providing an approach to estimate regional trawling footprints when highresolution spatial data are unavailable. If SAR was ≤0.1, as in 8 of 24 regions, therewas >95% probability that >90%of seabed was not trawled. If SAR was 7.9, equal to the highest SAR recorded, there was >95% probability that >70% of seabed was trawled. Footprints were smaller and SAR was ≤0.25 in regions where fishing rates consistently met international sustainability benchmarks for fish stocks, implying collateral environmental benefits from sustainable fishing.Funding for meetings of the study group and salary support for R.O.A. were provided by the following: David and Lucile Packard Foundation; the Walton Family Foundation; the Alaska Seafood Cooperative; American Seafoods Group US; Blumar Seafoods Denmark; Clearwater Seafoods Inc.; Espersen Group; Glacier Fish Company LLC US; Gortons Seafood; Independent Fisheries Limited N.Z.; Nippon Suisan (USA), Inc.; Pesca Chile S.A.; Pacific Andes International Holdings, Ltd.; San Arawa, S.A.; Sanford Ltd. N.Z.; Sealord Group Ltd. N.Z.; South African Trawling Association; Trident Seafoods; and the Food and Agriculture Organisation of the United Nations. Additional funding to individual authors was provided by European Union Project BENTHIS EU-FP7 312088 (to A.D.R., O.R.E., F.B., N.T.H., L.B.-M., R.C., H.O.F., H.G., J.G.H., P.J., S.K., M.L., G.G.-M., N.P., P.E.P., T.R., A.S., B.V., and M.J.K.); the Instituto Português do Mar e da Atmosfera, Portugal (C.S.); the International Council for the Exploration of the Sea Science Fund (R.O.A. and K.M.H.); the Commonwealth Scientific and Industrial Research Organisation (C.R.P. and T.M.); the National Oceanic and Atmospheric Administration (R.A.M.); New Zealand Ministry for Primary Industries Projects BEN2012/01 and DAE2010/ 04D (to S.J.B. and R.F.); the Institute for Marine and Antarctic Studies, University of Tasmania and the Department of Primary Industries, Parks, Water and Environment, Tasmania, Australia (J.M.S.); and UK Department of Environment, Food and Rural Affairs Project MF1225 (to S.J.)

Increasing frailty is associated with higher prevalence and reduced recognition of delirium in older hospitalised inpatients: results of a multi-centre study

Purpose: Delirium is a neuropsychiatric disorder delineated by an acute change in cognition, attention, and consciousness. It is common, particularly in older adults, but poorly recognised. Frailty is the accumulation of deficits conferring an increased risk of adverse outcomes. We set out to determine how severity of frailty, as measured using the CFS, affected delirium rates, and recognition in hospitalised older people in the United Kingdom. Methods: Adults over 65 years were included in an observational multi-centre audit across UK hospitals, two prospective rounds, and one retrospective note review. Clinical Frailty Scale (CFS), delirium status, and 30-day outcomes were recorded. Results: The overall prevalence of delirium was 16.3% (483). Patients with delirium were more frail than patients without delirium (median CFS 6 vs 4). The risk of delirium was greater with increasing frailty [OR 2.9 (1.8–4.6) in CFS 4 vs 1–3; OR 12.4 (6.2–24.5) in CFS 8 vs 1–3]. Higher CFS was associated with reduced recognition of delirium (OR of 0.7 (0.3–1.9) in CFS 4 compared to 0.2 (0.1–0.7) in CFS 8). These risks were both independent of age and dementia. Conclusion: We have demonstrated an incremental increase in risk of delirium with increasing frailty. This has important clinical implications, suggesting that frailty may provide a more nuanced measure of vulnerability to delirium and poor outcomes. However, the most frail patients are least likely to have their delirium diagnosed and there is a significant lack of research into the underlying pathophysiology of both of these common geriatric syndromes

On Summability of Spectral Expansions Corresponding to the Sturm-Liouville Operator

We study the completeness property and the basis property of the root function system of the Sturm-Liouville operator defined on the segment [0, 1]. All possible types of two-point boundary conditions are considered

Macroeconomic policy in an output-expenditure model

This paper proposes an alternative framework for examining the international macroeconomic impact of domestic monetary and fiscal policies and focuses on the distinction between national spending and national production and the reactive behavior of foreign investors to changing external account balances. It demonstrates that under a floating exchange rate regime, monetary and fiscal policies can affect aggregate expenditure and output quite differently, with important implications for the behavior of the exchange rate, the current account balance, and national income in the short run, as well as the economy's price level in the long run. In particular, this paper predicts that expansionary monetary and fiscal policies tend to depreciate the currency and only temporarily raise gross domestic product and the current account surplus, although permanently raise the domestic price level. This is a revised version of a paper presented at the Forty-Ninth International Atlantic Economic Conference, March 14–21, 2000, Munich, Germany