Epstein Secrets

he expected hitting time using combinatorial analysis (see Text SI for details). We now present the basic intuitive arguments of the main results. Markov chain on the one-dimensional grid For a single broad peak, due to symmetry we can interpret the evolutionary random walk as a Markov chain on the o

lam2, Martin A. Nowak2 1 IST Austria, KlostemeubLeg, Austria, 2 Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology, Department of Mathematics, Harvard University, Cambridge, Massachusetts, United States of America Abstract A fundamental question in biology is the following: what is the t

s another interesting problem. Materials and Methods Our results are based on a mathematical analysis of the underlying stochastic processes. For Markov chains on the one- dimensional grid, we describe recurrence relations for the expected hitting time and present lower and upper hounds on the expec

lam2, Martin A. Nowak2 11ST Austria, Klosterneuburg, AtIWIld, 2 Program for Evolutionary Dynamics, Department of Organismic and Evolutionary Biology. Department of Mathematics, Harvard University• Cambridge. Massachusetts. United States of America Abstract A fundamental question in biology is the following: what is the t

ase the problem can be reduced to computing absorption probabilities in Marken, chains, where each state represent the number of mutants. Hence the Markov chain Ls linear in the number of vertices of the graphs, and since absorption probabilities in Markov chains can be computed in polynomial time (by

n A. Nowak' 'IST Austria. Klosteineuburg. A 3400. Austria. and 'Program for Evolutionary Dynamics. Department of Organismic and Evolutionary Biology. Department of Mathematics. Harvard University. Cambridge. MA 02138. USA Submitted to Proceedings of the National Academy of Sciences of the United States of America There a