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

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

Prevention of awareness during general anesthesia

Awareness during general anesthesia with subsequent explicit recall is a serious and frequently preventable problem that is gaining attention from clinicians and patients alike. Cost-effective interventions that increase vigilance should be implemented to decrease the likelihood of this complication

Protocol for the Reconstructing Consciousness and Cognition (ReCCognition) Study

Important scientific and clinical questions persist about general anesthesia despite the ubiquitous clinical use of anesthetic drugs in humans since their discovery. For example, it is not known how the brain reconstitutes consciousness and cognition after the profound functional perturbation of the anesthetized state, nor has a specific pattern of functional recovery been characterized. To date, there has been a lack of detailed investigation into rates of recovery and the potential orderly return of attention, sensorimotor function, memory, reasoning and logic, abstract thinking, and processing speed. Moreover, whether such neurobehavioral functions display an invariant sequence of return across individuals is similarly unknown. To address these questions, we designed a study of healthy volunteers undergoing general anesthesia with electroencephalography and serial testing of cognitive functions (NCT01911195). The aims of this study are to characterize the temporal patterns of neurobehavioral recovery over the first several hours following termination of a deep inhaled isoflurane general anesthetic and to identify common patterns of cognitive function recovery. Additionally, we will conduct spectral analysis and reconstruct functional networks from electroencephalographic data to identify any neural correlates (e.g., connectivity patterns, graph-theoretical variables) of cognitive recovery after the perturbation of general anesthesia. To accomplish these objectives, we will enroll a total of 60 consenting adults aged 20–40 across the three participating sites. Half of the study subjects will receive general anesthesia slowly titrated to loss of consciousness (LOC) with an intravenous infusion of propofol and thereafter be maintained for 3 h with 1.3 age adjusted minimum alveolar concentration of isoflurane, while the other half of subjects serves as awake controls to gauge effects of repeated neurobehavioral testing, spontaneous fatigue and endogenous rest-activity patterns

Impact of Gender on the Myocardial Metabolic Response to Obesity

ObjectivesWe sought to determine the gender-specific effects of obesity on myocardial metabolism, work, and efficiency.BackgroundMyocardial metabolism abnormalities may contribute to the development of obesity-related heart failure. Increased myocardial oxygen consumption (MVO2) and fatty acid (FA) metabolism and decreased efficiency occur with obesity in women. It is unknown whether similar changes occur with obesity in men.MethodsWe quantified cardiac work, efficiency, myocardial blood flow (MBF), MVO2, glucose, and FA metabolism with echocardiography and positron emission tomography in nonobese and obese men and women (N = 86).ResultsThere were significant differences between the obese (n = 35) and nonobese (n = 51) subjects in age, body composition, plasma lipids, and insulin resistance in addition to differences between the men (n = 30) and women (n = 56) in body composition and plasma lipids. Female gender independently predicted increased cardiac work (p < 0.001). Female gender also related to lower efficiency (p < 0.05). Obesity and female gender independently predicted greater MBF (p < 0.01, p < 0.0005, respectively) and MVO2 (p < 0.0005, p < 0.0001). Myocardial glucose uptake was not different among the 4 subject groups, but obesity and gender interacted in predicting glucose uptake (p < 0.05). Lower myocardial glucose utilization was independently predicted by female gender (p < 0.05), and it independently predicted lower myocardial glucose utilization/plasma insulin (p < 0.05). Obesity and gender significantly interacted in the determination of glucose utilization/plasma insulin (p = 0.01). There were no differences in FA uptake among the 4 groups, and although increasing obesity correlated with greater myocardial FA utilization and oxidation; female gender (p < 0.005, p < 0.01) and plasma triglycerides (p < 0.05, p < 0.005) were their independent predictors.ConclusionsWomen's and men's myocardial metabolic responses to obesity are not exactly the same. Obesity and gender modulate MBF and MVO2, are related to myocardial substrate metabolism, and sometimes interact in its prediction. Gender modifies efficiency. Gender-related differences in myocardial metabolism may affect the development of/adaptation to obesity-related cardiac disease

Probing short-term face memory in developmental prosopagnosia

It has recently been proposed that the face recognition deficits seen in neurodevelopmental disorders may reflect impaired short-term face memory. For example, introducing a brief delay between the presentation of target and test faces seems to disproportionately impair matching or recognition performance on individuals with Autism Spectrum Disorders. The present study sought to determine whether deficits of short-term face memory contribute to impaired face recognition seen in Developmental Prosopagnosia. To determine whether developmental prosopagnosics exhibit impaired short-term face memory, the present study used a six-alternative-forced-choice match-to-sample procedure. Memory demand was manipulated by employing a short or long delay between the presentation of the target face, and the six test faces. Crucially, the perceptual demands were identical in both conditions, thereby allowing the independent contribution of short-term face memory to be assessed. Prosopagnostics showed clear evidence of a category-specific impairment for face-matching in both conditions; they were both slower and less accurate than matched controls. Crucially however, the prosopagnosics showed no evidence of disproportionate face recognition impairment in the long-interval condition. While individuals with developmental prosopagnosia may have problems with the perceptual encoding of faces, it appears that their representations are stable over short durations. These results suggest that the face recognition difficulties seen in developmental prosopagnosia and autism may be qualitatively different, attributable to deficits of perceptual encoding and perceptual maintenance, respectively