Next Mark Kac seminar

Friday April 6
Utrecht, Janskerkhof 3, room 019

Speaker: Gioia Carinci (Delft)
Title  : Particle systems and free boundary problems

Speaker: Margriet Oomen (Leiden)
Title  : Spatial populations with seed-bank: Duality and dichotomy of clustering versus coexistence

Speaker: Clara Stegehuis (Eindhoven)
Title  : Optimal graphlet structures

Abstract Gioia Carinci
There are several systems of interest in  physics and biology which are
related to free boundary problems in PDE’s. In particular I will refer
to Brunet-Derrida models for biological selection mechanisms and to the
Fourier law for particles systems in domains changing in time due to the
action of reservoirs fixing the current (and not the densities as in the
traditional setting). In both cases the hydrodynamic (or continuum)
limit is described by parabolic equations with free boundaries. In this
talk I will give a short survey on the methods used to study such
particle systems and the free boundary problems for the corresponding

Abstract Margriet Oomen
We consider a system of interacting Wright-Fisher diffusions with seed-
bank. Individuals are of two types, live in colonies and are subject to
resampling and migration as long as they are active. Each colony has a
seed-bank into which individuals can retreat to become dormant,
suspending their resampling and migration until they become active
again. As geographic space we consider Z^d. Our goal is to identify the
change in behaviour induced by the seed-bank. In particular we want to
establish the dichotomy between clustering, a mono-type equilibrium, and
coexistence, a multi-type equilibrium. To analyze the dichotomy we first
show that the seed-bank model has a dual. This dual allows us to
establish the dichotomy via a random walk argument. It turns out that
the seed-bank affects the dichotomy if the seed-bank is large and the
wake up times of individuals have a fat tailed distribution. Joint work
with Andreas Greven and Frank den Hollander.

Abstract Clara Stegehuis
Subgraphs contain crucial information about network structure and
function. For inhomogeneous random graphs with infinite-variance power-
law degrees, we count the number of times a small connected graph occurs
as an induced subgraph (graphlet counting). We introduce an optimization
problem to identify the dominant structure of any given subgraph. The
unique optimizer describes the degrees of the vertices that together
span the most likely subgraph. We find that every subgraph occurs
typically between vertices with specific degree ranges. In this way, we
can count and characterize all subgraphs.

The Mark Kac seminar is an activity of the STAR stochastics cluster. See
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