We study an area preserving map of the exterior of a smooth convex curve in the hyperbolic plane, defined by a natural geometrical construction and called the dual billiard map. We consider two problems: stability and the area spectrum. The dual billiard map is called stable if all its orbits are bounded. We show that both stable and unstable behaviours may occur. If the map at infinity has a h...

We prove that if R is a Hensel local ring with infinite residue field k, the natural map Hi(GLn(R),Z/p) → Hi(GLn(k), Z/p) is an isomorphism for i ≤ 3, p 6= char k. This implies rigidity for Hi(GLn), i ≤ 3, which in turn implies the Friedlander–Milnor conjecture in positive characteristic in degrees ≤ 3. A fundamental question in the homology of linear groups is that of rigidity: given a smooth ...

Given a point set S and a polygonal curve P in R, we study the problem of finding a polygonal curve through S, which has a minimum Fréchet distance to P . We present an efficient algorithm to solve the decision version of this problem in O(nk) time, where n and k represent the sizes of P and S, respectively. A curve minimizing the Fréchet distance can be computed in O(nk log(nk)) time. As a by-...

This study tests the hypothesis that the area postrema (AP) is necessary for endogenous ANG II to chronically maintain lumbar sympathetic nerve activity (LSNA) and heart rate (HR) in conscious sodium-deprived rats. The effect of the ANG II type 1-receptor antagonist, losartan, on LSNA and HR was determined in rats that were either AP lesioned (APX) or sham lesioned. The sham rats were divided i...

During high-frequency oscillatory ventilation (HFOV), the primary variable affecting lung volume is the mean airway pressure (MAP). To effectively maintain lung recruitment and optimal gas exchange without overstretching (or collapsing) the lung, MAP should be set between the lower and upper inflection points of the pressure-volume curve of the lung. At present, there is no efficacious means th...

BACKGROUND AND PURPOSE The choice of arterial input function (AIF) can have a profound effect on the blood flow maps generated on perfusion-weighted MR imaging (PWI). Automation of this process could substantially reduce operator dependency, increase consistency, and accelerate PWI analysis. We created an automated AIF identification program (auto-AIF) and validated its performance against conv...

This paper presents an evaluation of the map-matching scheme of an integrated GPS/INS system in urban areas. Data fusion using a Kalman filter and map matching are effective approaches to improve the performance of navigation system applications based on GPS/MEMS IMUs. The study considers the curve-to-curve matching algorithm after Kalman filtering to correct mismatch and eliminate redundancy. ...

We present Syndy, a technique for automatically synthesizing randomized map/fold computations that trade accuracy for performance. Given a specification of a fully accurate computation, Syndy automatically synthesizes approximate implementations of map and fold tasks, explores the approximate computation space that these approximations induce, and derives an accuracy versus performance tradeoff...

We construct a map injecting the set of infrastructure ideals in a real function field into the class group of the correspoding hyperelliptic curve. This map respects the ‘group-like’ structure of the infrastructure, as a consequence of this construction we show that calculating distances in the set of infrastructure ideals is equivalent to the DLP in the underlying hyperelliptic curve. We also...