Hip strength: Ankle proprioceptive threshold ratio predicts falls and injury in diabetic neuropathy

Introduction : We determined lower limb neuromuscular capacities associated with falls and fall‐related injuries in older people with declining peripheral nerve function. Methods : Thirty‐two subjects (67.4 ± 13.4 years; 19 with type 2 diabetes), representing a spectrum of peripheral neurologic function, were evaluated with frontal plane proprioceptive thresholds at the ankle, frontal plane motor function at the ankle and hip, and prospective follow‐up for 1 year. Results : Falls and fall‐related injuries were reported by 20 (62.5%) and 14 (43.8%) subjects, respectively. The ratio of hip adductor rate of torque development to ankle proprioceptive threshold (Hip STR /Ank PRO ) predicted falls (pseudo‐R 2  = .726) and injury (pseudo‐R 2  = .382). No other variable maintained significance in the presence of Hip STR /Ank PRO . Conclusions : Fall and injury risk in the population studied is related inversely to Hip STR /Ank PRO . Increasing rapidly available hip strength in patients with neuropathic ankle sensory impairment may decrease risk of falls and related injuries. Muscle Nerve 50 : 437–442, 2014Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/108329/1/mus24134.pd

Tools, Objects, and Chimeras: Connes on the Role of Hyperreals in Mathematics

We examine some of Connes' criticisms of Robinson's infinitesimals starting in 1995. Connes sought to exploit the Solovay model S as ammunition against non-standard analysis, but the model tends to boomerang, undercutting Connes' own earlier work in functional analysis. Connes described the hyperreals as both a "virtual theory" and a "chimera", yet acknowledged that his argument relies on the transfer principle. We analyze Connes' "dart-throwing" thought experiment, but reach an opposite conclusion. In S, all definable sets of reals are Lebesgue measurable, suggesting that Connes views a theory as being "virtual" if it is not definable in a suitable model of ZFC. If so, Connes' claim that a theory of the hyperreals is "virtual" is refuted by the existence of a definable model of the hyperreal field due to Kanovei and Shelah. Free ultrafilters aren't definable, yet Connes exploited such ultrafilters both in his own earlier work on the classification of factors in the 1970s and 80s, and in his Noncommutative Geometry, raising the question whether the latter may not be vulnerable to Connes' criticism of virtuality. We analyze the philosophical underpinnings of Connes' argument based on Goedel's incompleteness theorem, and detect an apparent circularity in Connes' logic. We document the reliance on non-constructive foundational material, and specifically on the Dixmier trace (featured on the front cover of Connes' magnum opus) and the Hahn-Banach theorem, in Connes' own framework. We also note an inaccuracy in Machover's critique of infinitesimal-based pedagogy.Comment: 52 pages, 1 figur