Retrospective, unblinded, nonrandomized comparisons between these 2 strategies have been inconclusive 13 and no randomized evaluation of these strategies has been conducted.14 We hypothesized that the combination of aspirin plus clopidogrel was 25% superior to dose-adjusted warfarin on prevention of new vascular Background and Purpose-Severe atherosclerosis in the aortic arch is associated with a high risk of recurrent vascular events, but the optimal antithrombotic strategy is unclear. Methods-This prospective randomized controlled, open-labeled trial, with blinded end point evaluation (PROBE design) tested superiority of aspirin 75 to 150 mg/d plus clopidogrel 75 mg/d (A+C) over warfarin therapy (international normalized ratio 2-3) in patients with ischemic stroke, transient ischemic attack, or peripheral embolism with plaque in the thoracic aorta >4 mm and no other identified embolic source. The primary end point included cerebral infarction, myocardial infarction, peripheral embolism, vascular death, or intracranial hemorrhage. Follow-up visits occurred at 1 month and then every 4 months post randomization. Results-The trial was stopped after 349 patients were randomized during a period of 8 years and 3 months. After a median follow-up of 3.4 years, the primary end point occurred in 7.6% (13/172) and 11.3% (20/177) of patients on A+C and on warfarin, respectively (log-rank, P=0.2). The adjusted hazard ratio was 0.76 (95% confidence interval, 0.36-1.61; P=0.5). Major hemorrhages including intracranial hemorrhages occurred in 4 and 6 patients in the A+C and warfarin groups, respectively. Vascular deaths occurred in 0 patients in A+C arm compared with 6 (3.4%) patients in the warfarin arm (log-rank, P=0.013). Time in therapeutic range (67% of the time for international normalized ratio 2-3) analysis by tertiles showed no significant differences across groups. Conclusions-Because of lack of power, this trial was inconclusive and results should be taken as hypothesis generating. Clinical Trial Registration-URL: http://www.clinicaltrials.gov. Unique identifier: NCT00235248.
Abstract-The population protocol model provides theoretical foundations for analyzing the properties emerging from simple and pairwise interactions among a very large number n of anonymous agents. The problem tackled in this paper is the following one: is there an efficient population protocol that exactly counts the difference κ between the number of agents that initially and independently set their state to A and the one that initially set it to B, assuming that each agent only uses a finite set of states ? We propose a solution which guarantees with any high probability that after O(log n) interactions any agent outputs the exact value of κ. Simulation results illustrate our theoretical analysis.
The computational model of population protocols is a formalism that allows the analysis of properties emerging from simple and pairwise interactions among a very large number of anonymous finite-state agents. Significant work has been done so far to determine which problems are solvable in this model and at which cost in terms of states used by the agents and time needed to converge. The problem tackled in this paper is the population proportion problem: each agent starts independently from each other in one of two states, say A or B, and the objective is for each agent to determine the proportion of agents that initially started in state A, assuming that each agent only uses a finite set of states, and does not know the number n of agents. We propose a solution which guarantees that in presence of a uniform probabilistic scheduler every agent outputs the population proportion with any precision ε ∈ (0, 1) with any high probability after having interacted O(log n) times. The number of states maintained by every agent is optimal and is equal to 2 3/(4ε) + 1. Finally, we show that our solution is optimal in time and space to solve the counting problem, a generalization of the proportion problem. Finally, simulation results illustrate our theoretical analysis.
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