A&P Seminar - Steve Pressé

The Analytical and Physical Seminar Series presents: Steve Pressé

Arizona State University

Host: Dima Makarov

Title: Inherited or produced?

Location: WEL 2.122

Refreshments served at 3:15pm

For the first problem, we ask a simple question: can we determine what fraction of proteins inside a cell are inherited from the mother cell versus being produced? 

As it turns out this simple problem is mathematically pathological. To determine what fraction of any specific protein type inside a cell is inherited, we need to consider the entire division-history of the cell. Put differently, this problem is non-Markovian and escapes simple mathematical formulation of a key quantity called the likelihood that serves as the stepping stone of any inference procedure to answer the question we just posed. To perform inference on such a problem, we show how we can extend rigorous likelihood-based inference to problems for which likelihoods cannot be written down using simulation-based inference within a Bayesian paradigm. More broadly, our framework proposes a scheme for direct model learning for systems where large-scale simulations are feasible and likelihoods are otherwise difficult or impossible to formulate.

As time allows, for the second problem we ask another question: how can we track particles, typically labeled molecules, if they move so fast we cannot even localize them frame to frame? To address this problem, we will be looking at how to track molecules in the extreme limit that only a few photons are collected in each frame and propose a new tracking paradigm that circumvents the need to localize molecules in each frame or link their positions frame to frame. To achieve this, we will be using the optics and detector physics to write down systematic likelihoods and determine (technically sample from the posterior) which trajectories are consistent with the smattering of photons in each frame across the entire frame stack as observed.