C4

 A continuum is a non-empty compact connected metric space. Given a continuum X let P(X) be the power set of X. We define the following set functions:
T:P(X) to P(X) given by, for each A in P(X), T(A) = X \ { x in X : there is a continuum W such that x is in Int(W) and W does not intersect A}
K:P(X) to P(X) given by, for each A in P(X), K(A) = Intersection{ W : W is a subcontinuum of X and A is in the interior of W}
S:P(X) to P(X) given by, for each A in P(X), S(A) = { x in T(A) : A intersects T(x)}
Some properties and relations between these functions are going to be presented.

Cox processes arise as a natural extension of inhomogeneous Poisson Processes, when the intensity function itself is taken to be stochastic. In multiple applications one is often concerned with characterizing the posterior distribution over the intensity process (given some observed data). Markov Chain Monte Carlo methods have historically been successful at such tasks. However, direct methods are doubly intractable, especially when the intensity process takes values in a space of continuous functions.

In this talk I'll be presenting a method to overcome this intractability that is based on the idea of "thinning" and that does not resort to approximations.

A solid object placed at a liquid-gas interface causes the formation of a meniscus around it. In the case of a vertical circular cylinder, the final state of the static meniscus is well understood, from both experimental and theoretical viewpoints. Experimental investigations suggest the presence of two different power laws in the growth of the meniscus. In this talk I will introduce a theoretical model for the dynamics and show that the early-time growth of the meniscus is self-similar, in agreement with one of the experimental predictions. I will also discuss the use of a numerical solution to investigate the validity of the second power law.

Pluripotency is a key feature of embryonic stem cells (ESCs), and is defined as the ability to give rise to all cell lineages in the adult body. Currently, there is a good understanding of the signals required to maintain ESCs in the pluripotent state and the transcription factors that comprise their gene regulatory network. However, little is known about how ESCs exit the pluripotent state and begin the process of differentiation. We aim to understand the molecular events associated with this process via an experiment-model cycle.