We show that in the Poisson continuum percolation model on the plane there is a sharp transition from a regime which admits unbounded vacant clusters to a regime which admits unbounded occupied clusters.

Let a_1, a_2, ..., a_n and b_1, b_2, ..., b_n be positive integers each of which is at most n bits long. Let S be the difference between the sum of square roots of a_i's and the sum of square roots of the b_j's.

Various in silico methods are employed to predict toxicity in pharmaceutical R&D. The methods can range from simple structural alerts all the way to detailed mechanistic modeling of biological systems.

Regular expressions are mostly known as pattern matching expressions in scripting languages (Perl, sed, awk, etc.). They are also theoretically studied for their strong relationship with Automata Theory.