CRM: Centro De Giorgi
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Advanced asymptotics of PDEs, modeling and extreme statistics and their applications to data analysis in cell biology

15 September 2018 - 3 November 2018

Planned Activities

Outline of Program Structure:

The first workshop coincides with the beginning of the program, with the aim of establishing a common language between the participants in statistical physics and applied mathematics; highlighting major open problems related methods to the themes of the other workshops. The remaining five workshops are being developed to each focus on a subset of the wide range of models, numerical methods and modeling of cellular biological at a molecular level.

We have chosen to partition the workshop themes based on the level of physical detail of the underlying models in cell biology. In particular, the first, second and third workshops of the program will focus on asymptotic methods of PDE, stochastic processes and extreme statistics, numerical methods which are at the basis of modern methods used to analyze large data sets of molecular and cellular systems.

The fourth workshop is dedicated to numerical approaches and methods and biological applications in synaptic transmission and transduction.

The last two workshops of the program will focus on more microscopic spatial models, stochastic approaches and modeling used to extract features from data and polymer models and analysis used to reconstruct the nuclear organization.

Six workshops (one every week) of the program are:

1- Probabilistic methods in statistical physics for extreme statistics and rare events.

2- Advanced asymptotics in PDEs and applications.

3- Multiscale modeling and simulations to bridge molecular and cellular scales.

4- Nanoscale mathematical modeling of synaptic transmission, calcium dynamics, transduction and cell sensing.

5-Reverse mathematical methods for reconstructing single molecular dynamics in cell.

6- Multiscale analysis and reconstruction of chromatin and nuclear organization.

A list of key publications:

1- A. Lindsay and A. Bernoff M. Ward, First Passage Statistics for the Capture of a Brownian Particle by a Structured Spherical Target with Multiple Surface Traps, SIAM J. Multiscale Modeling and Simulation, Vol 15, No. 1, (2017), pp.~74--109.

2- A. J. Bray, S. N. Majumdar, G. Schehr, Persistence and first passage properties in non-equilibrium systems, Adv. Phys. 62, 225-361 (2013)

3- Jia Gou, Wei-Yin Chiang, Pik-Yin Lai, and Yue-Xian Li, M. Ward, A Theory of Synchrony by Coupling Through a Diffusive Chemical Signal , Physica D, Vol. 339 (2017), pp.~1--17)

4- D. Holcman, Z Schuss, The narrow escape problem, SIAM Review 56 (2), 213-257 (2014).

5-D. Holcman, Z Schuss, Stochastic Narrow Escape in Molecular and Cellular Biology, Springer 2015.

6- Lampo TJ, Kennard AS, Spakowitz AJ.Physical Modeling of Dynamic Coupling between Chromosomal Loci. Biophys J.;110(2):338-47 (2016).

7- R Metzler, J Klafter, The random walk's guide to anomalous diffusion: a fractional dynamics approach, Physics reports 339 (1), 1-77 (2000).

8- M Zheng, F Liu, Q Liu, K Burrage, MJ Simpson, Numerical solution of the time fractional reaction–diffusion equation with a moving boundary, Journal of Computational Physics 338, 493-510 (2017).

9- M. Sheinman, O. Bénichou, Y. Kafri, R. Voituriez, Classes of fast and specific search mechanisms for proteins on DNA, Rep. Prog. Phys. 75, 026601 (2012).

10- A. Rosa, C. Zimmer, Computational models of large-scale genome architecture, International Review of Cell and Molecular Biology 307, 275 (2014).

11- J. D. Halverson, J. Smrek, K. Kremer, A. Yu. Grosberg, From a melt of rings to chromosome territories: the role of topological constraints in genome folding, Rep. Prog. Phys. 77, 022601 (2014).

12- F. Serra, M. Di Stefano, Y. G. Spill, Y. Cuartero, M. Goodstadt, D. Baù, M. Marti-Renom, Restraint-based three-dimensional modeling of genomes and genomic domains, FEBS Letters 589, 2987 (2015).