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It is well known that after placing n balls independently and uniformly at random into n bins, the fullest bin holds Θ(log n/ log log n) balls with high probability. More recently, Azar et al. analyzed the following process: randomly choose d bins for each ball, and then place the balls, one by one, into the least full bin from its d choices . They show… (More)
We present a v ery simple, randomized approximation algorithm for determining the number of cliques in a random graph.
In their natural ecosystems, adult male and female Asian elephants, Elephas maximus, live separately. For several weeks prior to ovulation, female elephants release a substance in their urine which elicits a high frequency of non-habituating chemosensory responses, especially flehmen responses, from male elephants. These responses occur prior to, and are an… (More)
Flehmen-like responses (urine tests) are one of the characteristic behavioral reactions of male Asian elephants (Elephants maximus) to cow elephants in estrus. Components of the urine of estrous cow elephants were extracted with organic solvents and partially purified by chromatography and shown to evoke Flehmen-like responses when they were presented to… (More)
(MATH) We study approximation algorithms for the permanent of an <i>n</i> x <i>n</i> (0,1) matrix <i>A</i> based on the following simple idea: obtain a random matrix <i>B</i> by replacing each 1-entry of <i>A</i> independently by ± <i>e</i>, where <i>e</i> is a random basis element of a suitable algebra; then output |det(<i>B</i>)|<sup>2</sup>. This… (More)
BACKGROUND The dorsal extension of the tip of the trunk of Asian elephants (Elephas maximus), often referred to as "the finger," possesses remarkable mechanical dexterity and is used for a variety of special behaviors including grasping food and tactile and ultimately chemosensory recognition via the vomeronasal organ. The present study describes a unique… (More)
It is well known that after placing n balls independently and uniformly at random into n bins, the fullest bin holds @(log n/ log log n) balls with high probability. Recently, Azar et al. analyzed the following: randomly choose d bins for each ball, and then sequentially place each ball in the least full of its chosen bins . They show that the fullest… (More)