Analysis of Bounds on Hybrid Vector Clocks

Hybrid vector clocks (HVC) implement vector clocks (VC) in a space-efficient manner by exploiting the availability of loosely-synchronized physical clocks at each node. In this paper, we develop a model for determining the bounds on the size of HVC. Our model uses four parameters, epsilon: uncertainty window, delta: minimum message delay, alpha: communication frequency and n: number of nodes in the system. We derive the size of HVC in terms of a differential equation, and show that the size predicted by our model is almost identical to the results obtained by simulation. We also identify closed form solutions that provide tight lower and upper bounds for useful special cases. Our model and simulations show the HVC size is a sigmoid function with respect to increasing epsilon; it has a slow start but it grows exponentially after a phase transition. We present equations to identify the phase transition point and show that for many practical applications and deployment environments, the size of HVC remains only as a couple entries and substantially less than n. We also find that, in a model with random unicast message transmissions, increasing n actually helps for reducing HVC size

Acute Thrombotic Occlusion of Right Coronary and Left Circumflex Coronary Arteries in a Patient with Antiphospholipid Syndrome: Successful Stent Implantation

Antiphospholipid syndrome is a rare disorder. Acute myocardial infarction is uncommon among these patients. Here we report a case of a 44-year-old man with antiphospholipid syndrome admitted for acute inferior myocardial infarction. Performed coronary angiography revealed that both the right coronary and the left circumflex coronary arteries were occluded by thrombi. We successfully performed primary angioplasty and stent implantation for both of the occluded coronary arteries. In the literature, this is the first case with antiphospholipid syndrome in which primary coronary angioplasty with stent implantation was successfully performed for two coronary arteries with acute thrombotic occlusion