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In this paper we study the complexity of sets that reduce to sparse sets (and tally sets), and the complexity of the simplest sparse sets to which such sets reduce. We show even with respect to very flexible reductions that NP cannot have sparse hard sets unless P = NP; an immediate consequence of our results is: If any NP-complete set conjunctively reduces to a sparse set, then P = NP. We also show...
Between 1978 and 1993, prosthetic valve replacement was performed in 62 patients with active infective endocarditis of the native valves. Vegetation attached to the diseased valves was disclosed by two-dimensional echocardiography in most of the patients, except three who had calcified organic valvular regions. Operative procedures were determined only by echocardiographic findings without cardiac...
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