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From: Nowak, Martin Sent: Wednesday, October 15, 2014 4:05 PM To: Jeffrey Epstein Subject: Fwd: 70 year old problem solved :) tibor announces solution of luria delbrueck Begin forwarded message: From: Tibor=Antal <Tibor.Antal@ed.ac.uk <mailto:Tibor.Antal@ed.ac.uk> =gt; Subject: 70=year old problem solved :) Date: Octob=r 15, 2014 11:46:27 AM EDT To: "=Nowak, Martin" <martin=nowak@harvard.edu <mailto:martin_nowak@harvard.edu», Ivana Bozic <ibozic@math.harvard.edu <mailto:ibozic@math.h=rvard.edu», Ben Allen <benjcallen@gmail.com> Dear Martin, Ivana, Ben, we just put online this paper on the number of mutants in an exponenti=lly growing population. Cell death is included and mutations can be advantageous, neutral or d=leterious. http://arxiv.org/abs/1410=3307v1 <http://arxiv.orgiabs/1410.3307v1> I'm very happy about this. This is the problem set up by Luria and Delbruck and generalized to ou= setup by Martin, Yoh and Francisca. We completed those results. Also, Kessler and Levine gave an approximate method and solve the larg= population small mutation limit. Our solution is for general parameters, but recover their results as l=mits, in a much simpler and rigorous way. That's all, these results now can be used in future models. All the best, Tibor Tibor ANTAL =el: +44 1316-517-672 School of Mathematics, Edinburgh University http://www.maths.ed.ac.ukhant=1<http://www.maths.ed.ac.ukhantal> JCMB5403 The University of Edinburgh is a charitable body, registered in Scotland, with registration number SC005336. EFTA_R1_01303371 EFTA02339895 2 EFTA_R1_01303372 EFTA02339896