Graduate Student Seminar

Speaker 1: Abhishek Guin

Title

Buffon's needle problem

Abstract

One of the earliest problems in geometrical probability, Buffon's needle problem is deceptively simple: Find the probability that a needle of length l will land on a line, given a floor with equally spaced parallel lines at distance d apart. We present an ingenious proof of the problem followed by a discussion on how it gives rise to an experiment to estimate π and a famous hoax behind it.

Speaker 2: Mingkai Yu

Title

The random time change representation of stochastic chemical systems

Abstract

In many cases, ordinary differential equation (ODE) models are a good approximation for chemical reaction systems. In the study of intracellular systems where some reactant species are present only in very small numbers, the discrete and stochastic nature of the chemical reactions cannot be captured by ODE models. A better description is given by a Markov process model in continuous time with the non-negative integer lattice as state space. We use the random time change representation that exploits the idea of an internal clock to formulate a stochastic simulation algorithm that handles computations corresponding to individual reaction paths. This algorithm also allows for more efficient sensitivity analysis.