Fractional derivatives have been around for centuries [22, 26] but recently they have found new applications in physics [2, 6, 7, 9, 15, 18, 19, 29], hydrology [1, 4, 5, 10, 14, 28], and finance [24, 25, 27]. Analytical solutions of ordinary fractional differential equations [22, 23] and partial fractional differential equations [8, 16] are now available in some special cases. But the solution ...

We construct an ancient solution to planar curve shortening. The is at all times compact and embedded. For t ≪ 0 t\ll 0</...

BACKGROUND Diastolic fractional flow reserve (dFFR) has been shown to be highly sensitive for detection of inducible myocardial ischemia. However, its reliance on measurement of left-ventricular pressure for zero-flow pressure correction, as well as manual extraction of the diastolic interval, has been its major limitation. Given previous reports of minimal zero-flow pressure at end-diastole, w...

We revisit the pairwise kidney exchange problem established by Roth Sonmez and Unver [23]. Our goal, explained in terms of graph theory, is to find a maximum fractional matching on an undirected graph, that Lorenz-dominates any other fractional matching. The Lorenz-dominant fractional matching, which can be implemented as a lottery of integral matchings, is in some sense the fairest allocation ...

BACKGROUND The instantaneous wave-free ratio (iFR) is a novel method to assess the ischemic potential of coronary artery stenoses. Clinical trial data have shown that iFR has acceptable diagnostic agreement with fractional flow reserve (FFR), the reference standard for the functional assessment of coronary stenoses. This study compares iFR measurements with FFR measurements in a real world, sin...

In a postasphyxia neonatal lamb model, the responses of the cerebral circulation to hypoxic hypoxia and changes in systemic arterial blood pressure were examined. Ventilated newborn lambs (n = 14) were subjected to a gradual asphyxial insult, resuscitated, and returned to control ventilator settings. During the time 2-5 hours after asphyxia, the responses of cerebral blood flow (CBF), cerebral ...

We define a parameterization for an n-holed tori based on the hyperbolic polygon. We model the domain using a manifold with 2n+ 2 charts, and linear fractional transformations for transition functions. We embed the manifold using standard spline techniques to produce a surface. CR Categories: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling, Curve, Surface, Solid, and Objec...