During puberty, mouse mammary epithelial ducts invade the stromal mammary fat pad in a wave of branching morphogenesis to form a complex ductal tree. Using pharmacologic and genetic approaches, we find that mammary gland branching morphogenesis requires transient matrix metalloproteinase (MMP) activity for invasion and branch point selection. MMP-2, but not MMP-9, facilitates terminal end bud i...

We consider catalytic branching populations. They consist of a catalyst population evolving according to a critical binary branching process in continuous time with a constant branching rate and a reactant population with a branching rate proportional to the number of catalyst individuals alive. The reactant forms a process in random medium. We describe asymptotically the genealogy of catalytic...

BACKGROUND Variant anatomy of renal arteries is important in renal transplant, vascular reconstruction, and uroradiological procedures. The variations show ethnic and population differences. Data from Africans are scarce and altogether absent for Kenyans. OBJECTIVE To describe patterns of origin, trajectories and branching of renal arteries in a Kenyan population. STUDY DESIGN AND SETTING D...

We consider catalytic branching populations. They consist of a catalyst population evolving according to a critical binary branching process in continuous time with a constant branching rate and a reactant population with a branching rate proportional to the number of catalyst individuals alive. The reactant forms a process in random medium. We describe asymptotically the genealogy of catalytic...

Aims: Evolutionary branching is a process of evolutionary diversification induced by frequency-dependent ecological interaction. Here we show how to predict the occurrence of evolutionary branching in bivariate traits when populations are evolving directionally. Methods: Following adaptive dynamics theory, we assume low mutation rates and small mutational step sizes. On this basis, we generaliz...

This paper describes Olive, the first distributed block storage system to provide consistent pointin-time branching. Point-in-time branching allows users to recursively and quickly snapshot or clone the storage state. It has a wide range of applications including testing new deployments or upgrades without disrupting a running system, quickly provisioning large homogeneous systems, and preservi...

We define a doubly infinite, monotone labeling of Bienaymé–Galton– Watson (BGW) genealogies. The genealogy of the current generation backwards in time is uniquely determined by the coalescent point process (Ai ; i ≥ 1), where Ai is the coalescence time between individuals i and i + 1. There is a Markov process of point measures (Bi; i ≥ 1) keeping track of more ancestral relationships, such tha...

A general multi-type branching process where new individuals immigrate according to some point process is considered. An intrinsic submartingale is defined and a convergence result for processes counted with random characteristics is obtained. Some examples are given. GENERAL BRANCHING PROCESS; MULTI-TYPE; IMMIGRATION AMS 1991 SUBJECT CLASSIFICATION: PRIMARY 60180