Bartlomiej Waclaw

TL;DR: A model for tumour evolution is described that shows how short-range dispersal and cell turnover can account for rapid cell mixing inside the tumour, and shows that even a small selective advantage of a single cell within a large tumour allows the descendants of that cell to replace the precursor mass in a clinically relevant time frame.

TL;DR: It is shown that the stationary probability of finding a particle performing maximal entropy random walk localizes in the largest nearly spherical region of the lattice which is free of defects.

TL;DR: It is predicted that the radius of an incompressible, strictly two-dimensional colony cannot grow linearly in time, unless it develops branches, and mechanical interactions can also account for the nonequilibrium transition between circular and branching colonies.

TL;DR: It is shown that the eigenvalue density of a product X=X1X2...XM of M independent NxN Gaussian random matrices in the limit N-->infinity is rotationally symmetric in the complex plane and it is conjecture that this distribution also holds for any matrices whose elements are independent centered random variables with a finite variance or even more generally for matrices which fulfill Pastur-Lindeberg's condition.

TL;DR: It is shown that a nonuniform drug distribution has the potential to accelerate the emergence of resistance when the mutational pathway involves a long sequence of mutants with increasing resistance, but if the pathway is short or crosses a fitness valley, the evolution of resistance may actually be slowed down by drug gradients.