On the mean width of log-concave functions

In this work we present a new, natural, definition for the mean width of log-concave functions. We show that the new definition coincide with a previous one by B. Klartag and V. Milman, and deduce some properties of the mean width, including an Urysohn type inequality. Finally, we prove a functional version of the finite volume ratio estimate and the low-M* estimate.Comment: 15 page

Trajectories of depressive symptoms after hip fracture

BACKGROUND: Hip fracture is often complicated by depressive symptoms in older adults. We sought to characterize trajectories of depressive symptoms arising after hip fracture and examine their relationship with functional outcomes and walking ability. We also investigated clinical and psychosocial predictors of these trajectories. METHOD: We enrolled 482 inpatients, aged ≥60 years, who were admitted for hip fracture repair at eight St Louis, MO area hospitals between 2008 and 2012. Participants with current depression diagnosis and/or notable cognitive impairment were excluded. Depressive symptoms and functional recovery were assessed with the Montgomery–Asberg Depression Rating Scale and Functional Recovery Score, respectively, for 52 weeks after fracture. Health, cognitive, and psychosocial variables were gathered at baseline. We modeled depressive symptoms using group-based trajectory analysis and subsequently identified correlates of trajectory group membership. RESULTS: Three trajectories emerged according to the course of depressive symptoms, which we termed ‘resilient’, ‘distressed’, and ‘depressed’. The depressed trajectory (10% of participants) experienced a persistently high level of depressive symptoms and a slower time to recover mobility than the other trajectory groups. Stressful life events prior to the fracture, current smoking, higher anxiety, less social support, antidepressant use, past depression, and type of implant predicted membership of the depressed trajectory. CONCLUSIONS: Depressive symptoms arising after hip fracture are associated with poorer functional status. Clinical and psychosocial variables predicted membership of the depression trajectory. Early identification and intervention of patients in a depressive trajectory may improve functional outcomes after hip fracture

Almost Euclidean sections of the N-dimensional cross-polytope using O(N) random bits

It is well known that R^N has subspaces of dimension proportional to N on which the \ell_1 norm is equivalent to the \ell_2 norm; however, no explicit constructions are known. Extending earlier work by Artstein--Avidan and Milman, we prove that such a subspace can be generated using O(N) random bits.Comment: 16 pages; minor changes in the introduction to make it more accessible to both Math and CS reader

Obstructive sleep apnea as an independent predictor of postoperative delirium and pain: Protocol for an observational study of a surgical cohort [version 2; referees: 2 approved]

Introduction: Postoperative delirium and pain are common complications in adults, and are difficult both to prevent and treat. Obstructive sleep apnea (OSA) is prevalent in surgical patients, and has been suggested to be a risk factor for postoperative delirium and pain. OSA also might impact pain perception, and alter pain medication requirements. This protocol describes an observational study, with the primary aim of testing whether OSA is an independent predictor of postoperative complications, focusing on (i) postoperative incident delirium and (ii) acute postoperative pain severity. We secondarily hypothesize that compliance with prescribed treatment for OSA (typically continuous positive airway pressure or CPAP) might decrease the risk of delirium and the severity of pain. Methods and analysis: We will include data from patients who have been enrolled into three prospective studies: ENGAGES, PODCAST, and SATISFY-SOS. All participants underwent general anesthesia for a non-neurosurgical inpatient operation, and had a postoperative hospital stay of at least one day at Barnes Jewish Hospital in St. Louis, Missouri, from February 2013 to May 2018.  Patients included in this study have been assessed for postoperative delirium and pain severity as part of the parent studies. In the current study, determination of delirium diagnosis will be based on the Confusion Assessment Method, and the Visual Analogue Pain Scale will be used for pain severity. Data on OSA diagnosis, OSA risk and compliance with treatment will be obtained from the preoperative assessment record. Other variables that are candidate risk factors for delirium and pain will also be extracted from this record. We will use logistic regression to test whether OSA independently predicts postoperative delirium and linear regression to assess OSAs relationship to acute pain severity. We will conduct secondary analyses with subgroups to explore whether these relationships are modified by compliance with OSA treatment.</ns4:p

General anesthesia does not have persistent effects on attention in rodents

Background: Studies in animals have shown that general anesthesia can cause persistent spatial memory impairment, but the influence of anesthetics on other cognitive functions is unclear. This study tested whether exposure to general anesthesia without surgery caused a persistent deficit in attention in rodents.Methods: To evaluate whether anesthesia has persistent effects on attention, rats were randomized to three groups. Group A was exposed for 2 h to isoflurane anesthesia, and tested the following seven days for attentional deficits. Group B was used as a control and received room air before attentional testing. Since there is some evidence that a subanesthetic dose of ketamine can improve cognition and reduce disorders of attention after surgery, rats in group C were exposed to isoflurane anesthesia in combination with a ketamine injection before cognitive assessment. Attention was measured in rats using the 5-Choice Serial Reaction Time Task, for which animals were trained to respond with a nose poke on a touchscreen to a brief, unpredictable visual stimulus in one of five possible grid locations to receive a food reward. Attention was analyzed as % accuracy, % omission, and premature responses.Results: Evaluating acute attention by comparing baseline values with data from the day after intervention did not reveal any differences in attentional measurements. No significant differences were seen in % accuracy, % omission, and premature responses for the three groups tested for 7 consecutive days.Conclusion: These data in healthy rodents suggest that general anesthesia without surgery has no persistent effect on attention and the addition of ketamine does not alter the outcome