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The goal of cancer genome sequencing projects is to determine the genetic alterations that cause common cancers. Many malignancies arise during the clonal expansion of a benign tumor which motivates the study of recurrent selective sweeps in an exponentially growing population. To better understand this process, Beerenwinkel et al. [PLoS Comput. Biol. 3 (2007) 2239--2246] consider a Wright--Fisher model in which cells from an exponentially growing population accumulate advantageous mutations. Simulations show a traveling wave in which the time of the first $k$-fold mutant, $T_k$, is approximately linear in $k$ and heuristics are used to obtain formulas for $ET_k$. Here, we consider the analogous problem for the Moran model and prove that as the mutation rate $muto0$, $T_ksim c_klog(1/mu)$, where the $c_k$ can be computed explicitly. In addition, we derive a limiting result on a log scale for the size of $X_k(t)={}$the number of cells with $k$ mutations at time $t$.
Freshwater Unionid bivalves have recently faced ecological upheaval through pollution, barriers to dispersal, human harvesting, and changes in fish-host prevalence. Currently, over 70% of species are threatened, endangered or extinct. To characterize
In this paper we prove that a class of non self-adjoint second order differential operators acting in cylinders $Omegatimesmathbb Rsubseteqmathbb R^{d+1}$ have only real discrete spectrum located to the right of the right most point of the essential
We define a mapping of the QCD Balitsky-Kovchegov equation in the diffusive approximation with noise and a generalized coupling allowing a common treatment of the fixed and running QCD couplings. It corresponds to the extension of the stochastic Fish
We describe the dynamic response of a two-dimensional hexagonal packing of uncompressed stainless steel spheres excited by localized impulsive loadings. After the initial impact strikes the system, a characteristic wave structure emerges and continuo
The most attractive application of fluid-based thermoacoustic (TA) energy conversion involves traveling wave devices due to their low onset temperature ratios and high growth rates. Recently, theoretical and numerical studies have shown that thermoac