Backbone Decomposition of Multitype Superprocesses

Brownian bugs and superprocesses

Advection-diffusion-reaction (adr) models link physical oceanography and biological oceanography. These models, which describe biology using continuous concentration fields, usually neglect individual-scale fluctuations. I describe a stochastic individual-based model, called the Brownian bug process, which illustrates some of the surprising issues associated with the neglect of fluctuations by ...

Interacting Superprocesses and Conditional Independence

Non-linear superprocesses

Non-linear martingale problems in the McKean-Vlasov sense for superprocesses are studied. The stochastic calculus on historical trees is used in order to show that there is a unique solution of the non-linear martingale problems under Lipschitz conditions on the coe cients. Mathematics Subject Classi cation (1991): 60G57, 60K35, 60J80.

Geometric aspects of Fleming-Viot and superprocesses

The main purpose of this paper is to show that the intrinsic metric of the Fleming-Viot process is given by anàngular distance' on the space of probability measures. It turns out that it is closely related to the branching structure of a continuous superprocess, which itself induces the Kakutani-Hellinger distance. The corresponding ge-ometries are studied in some detail. In particular, represe...

Process-based network decomposition reveals backbone motif structure.

A central challenge in systems biology today is to understand the network of interactions among biomolecules and, especially, the organizing principles underlying such networks. Recent analysis of known networks has identified small motifs that occur ubiquitously, suggesting that larger networks might be constructed in the manner of electronic circuits by assembling groups of these smaller modu...