# Agenda

# Wednesday 20 November 2019

### Number-theoretic spin chains

#### Vojkan Jaksic, UCP-IEA and McGill

The number theoretic spin chains were introduced in 1993 by A. Knauf in an influential paper.

In this talk I will describe a research program that connects:

(1) Statistical mechanics of number theoretic spin chains.

(2) Large deviation principle

(3) Multi-fractal analysis of Bernoulli convolutions

(4) Theory of repeated quantum measurements.

### Mapping single molecule dynamics in living cells

#### Christian Vestergaard (Institut Pasteur)

Single molecule tracking in live cells is providing unprecedented insights into the nano- and micro-scale dynamics underlying cellular function. By accessing the full distribution of molecular properties, rather than simply their average values, the great advantage of single molecule measurements is their ability to identify static and dynamic heterogeneities as well as rare behaviors.

Thanks to photoactivatable dyes, millions of individual molecule trajectories can now be acquired using techniques such as PALM or uPAINT at the scale of entire cells and over time intervals lasting many hours. As SM experiments generate more and more data, the development of a principled and unifying statistical framework becomes ever more necessary. While the large amounts of data open up new research venues for understanding biological processes, the wealth of information also come with more variability and noise. Statistically robust tools are needed to handle the complex structure of the large datasets and to account for the various sources of experimental and systemic noise and variability.

I will here give an overview of the different sources of noise and variability in single molecule tracking data and how they affect recorded data. I will next present a global probabilistic framework for inferring spatially and temporally varying physical parameters from experimentally recorded biomolecule motion. I will in particular show how to account for the noise and variability of recordings. Finally, I will demonstrate links between inferred physical maps and the underlying biology.

The probabilistic inference framework is being developed as an open source Python library: TRamWAy.readthedocs.io