The Global Networked Value Circle: A new model for best-in-class manufacturing

As companies face deflation, slowing production and declining prices, they will need to assess their entire value chain as they look for ways to keep costs low and improve efficiencies while continuing to innovate. To help address this challenge, this report reflects fresh research undertaken by Capgemini in collaboration with the University of Edinburgh into the ?Best-in-Class Global Manufacturing Value Chain?

Branching Brownian Motion with catalytic branching at the origin

We consider a branching Brownian motion in which binary fission takes place only when particles are at the origin at a rate \beta > 0 on the local time scale. We obtain results regarding the asymptotic behaviour of the number of particles above \lambda t at time t, for \lambda > 0. As a corollary, we establish the almost sure asymptotic speed of the rightmost particle. We also prove a Strong Law of Large Numbers for this catalytic branching Brownian motion.Comment: 25 page

A strong law of large numbers for branching processes: almost sure spine events

We demonstrate a novel strong law of large numbers for branching processes, with a simple proof via measure-theoretic manipulations and spine theory. Roughly speaking, any sequence of events that eventually occurs almost surely for the spine entails the almost sure convergence of a certain sum over particles in the population.Comment: 6 page