I couldn’t resist taking this photo in the office of Edinburgh mathematician Nikola Popovic. The central image is the result of a conversation between Nikola and visiting speaker Vahid Shahrezaei about the reproduction of yeast. Yeast cells normally reproduce asexually by budding, but cells of opposite mating types (a and α) can also reproduce sexually. The bulge which forms when a cell responds to pheromones of the opposite type is called a shmoo – this is a reference to a cartoon character of that shape invented in 1948. It’s a brilliant word which has found its way into other areas of science too, including a type of reproducing material good in economics, a larva found in sea urchins, and high energy cosmic ray survey instrument.
Other parts of the board refer to Nikola’s work on gene regulatory networks, where he is trying to model processes which have both ‘fast’ and ‘slow’ components, and to see how these components interact with each other.
This board comes from the office of Peter Keller, a new postdoc working at the University of Edinburgh. He is currently thinking about multi-type branching processes in biology and wanted to draw some pictures on the board to help him figure out what was going on. In a branching process you have a population of individuals who each produce a random number of offspring, and you want to ask questions like “How big will the population be at a certain time in the future?”, or “What is the chance of the population ever becoming extinct?”. In a multi-type branching process, there are different types of individuals. For example, when bacteria reproduce, they may either replicate themselves, or they may produce a mutant form. Mutants can then only replicate into mutants. We can then ask what the proportion of mutants to normal individuals is likely to be after a certain amount of time.
I have no idea what the reference to martingales and larks is. Please leave a comment if you think you know!