Utilizing genomic signatures from diagnostic tumor samples to forecast clinical behavior and response to therapy has long been a goal, and we are now poised to further refine how we can identify the relatively rare patients with aggressive neuroblastoma masquerading as patients with a more benign form of the disease. Clin Cancer Res; 21(8); 1782-5. ©2014 AACR. See related article by Oberthuer e...

In this paper we give a historical account of the development of Poisson approximation using Stein’s method and present some of the main results. We give two recent applications, one on maximal arithmetic progressions and the other on bootstrap percolation. We also discuss generalisations to compound Poisson approximation, Poisson process approximation and multivariate Poisson approximation, an...

We study the time until first occurrence, the first-passage time, of rare density fluctuations in diffusive systems. We approach the problem using a model consisting of many independent random walkers on a lattice. The existence of spatial correlations makes this problem analytically intractable. However, for a mean-field approximation in which the walkers can jump anywhere in the system, we ob...

Dynamics in nature often proceed in the form of rare transition events: The system under study spends very long periods of time at various metastable states; only very rarely it hops from one metastable state to another. Understanding the dynamics of such systems requires us to study the ensemble of transition paths between the different metastable states. Transition path theory is a general ma...