Events of the ERC MsMath 2017

Workshops and programs

Working Group

  • January 10th – Spectral theory for random Poincaré maps (M. Baudel).
  • January 30th- Fitting non-bonded parameters from and for condensed phase simulations (F. Hedin).

    •  The quality of atomistic simulations depends decisively on the accuracy of the underlying energy function (force field). Of particular importance for condensed-phase properties are nonbonded interactions, including the electrostatic and Lennard-Jones
      terms. Permanent atomic multipoles (MTPs) are an extension to common point-charge (PC) representations in atomistic simulations. MTPs are commonly determined from and fitted to an ab initio Electrostatic Potential (ESP), and Lennard-Jones (LJ) parameters are obtained from comparison of experimental and computed observables using molecular dynamics (MD) simulations. For this a set of thermodynamic observables such as density, heat of vaporization, and hydration free energy is chosen, to which the parametrization is fitted.
      A toolkit for optimizing non-bonded interactions for atomistic force fields of different qualities will be presented. It supports fitting of standard PC-based force fields and more physically motivated multipolar (MTP) force fields. Validation was done with a set of 20 molecules ranging from N-methyl-acetamide and benzene to halogenated benzenes, phenols, anilines, and pyridines. ( )
    • Investigating the stability of solvated Hæmoglobin Tetramers using Molecular Dynamics (Florent Hedin ).
      Hæmoglobin is a metalloprotein (containing iron), in charge of oxygen transport in red blood cells of animals. It transports oxygen from the lungs to the rest of the body where it releases the oxygen for cell use. Human hæmoglobin is a tetrameric protein consisting of two α and two β subunits.
      Each subunit contains a heme group at the center to which molecular oxygen or other ligands bind: the ligand-bound (oxy) state is identified as R-state or 2DN2, and the ligand-free (deoxy) state as T state or 2DN3. The distance between the two terminal Histidines of the β chains is characteristic of each state: this distance fluctuates between 10 – 15 Å for the compact oxy 2DN3 state, and 30 – 35 Å for the more extended deoxy 2DN2 state. Although the deoxy state should be thermodynamically stable and remain in an extended state (as it is the case experimentally), several previous MD studies 1 found that the tetramers adopt a compact structure, similar to the oxy one (i.e. a T ↔ R transition was found).
      The stability of the tetramer in water boxes of increasing size is investigated, over several hundreds of nanoseconds, using the CHARMM ForceField and the GROMACS software. A coarse-grained definition of the water density is used for analyzing instantaneous fluctuations of th density at the protein-solvent interface.
  • February 9th – On the coarse-graining of Hamiltonian dynamics (V. Ehrlacher)
  • February 27th

    • Letif Mones, de Cambridge et Warwick, Gaussian process regression in potential of mean force calculations.
    • Stefan Chmiela (Institute of Software Engineering and Theoretical Computer Science, Berlin)
      • Résumé : Using conservation of energy – a fundamental property of closed classical and quantum mechanical systems – we develop an efficient gradient-domain machine learning (GDML) approach to construct accurate molecular force fields using a restricted number of samples from ab initio molecular dynamics (AIMD) trajectories. The GDML implementation is able to reproduce global potential-energy surfaces of intermediate-size molecules with an accuracy of 0.3 kcal/mol for energies and 1 kcal/mol/A for atomic forces using only 1000 conformational geometries for training. We demonstrate this accuracy for AIMD trajectories of molecules, including benzene, toluene, naphthalene, ethanol, uracil, and aspirin. The challenge of constructing conservative force fields is accomplished in our work by learning in a Hilbert space of vector-valued functions that obey the law of energy conservation. The GDML approach enables quantitative molecular dynamics simulations for molecules at a fraction of cost of explicit AIMD calculations, thereby allowing the construction of efficient force fields with the accuracy and transferability of high-level ab initio methods.
  • March 14th – About “Grandes déviations à l’équilibre pour des systèmes invariants par translation”  (J. Reygner).
  • April 5th – About “Coarse-graining limits in Fokker-Planck equations: a variational approach inspired by large deviations ”  (U. Sharma)
  • May 11, 02:00 pm, at CERMICS (room F102). Laura Joana Silva Lopes will present : Méthodes pour obtenir le chemin réactif préférentiel en dynamique moléculaire.
  • May 19th, 11:00 am, at CERMICS (B211 seminar room). Frédéric Lavancier (Laboratoire Jean Leray, Nantes), will present : processus ponctuels determinantaux
  • May 23th, 10;00 am, at CERMICS (B211 seminar room). Erwan Scornet (CMAP) will present: Walk on random forests.

    Abstract: The recent and ongoing digital world expansion now allows anyone to have access to a tremendous amount of information. However collecting data is not an end in itself and thus techniques must be designed to gain in-depth knowledge from these large data bases. This has led to a growing interest for statistics, as a tool to find patterns in complex data structures, and particularly for turnkey algorithms which do not require specific skills from the user.

    Such algorithms are quite often designed based on a hunch without any theoretical guarantee. Indeed, the overlay of several simple steps (as in random forests or neural networks) makes the analysis more arduous. Nonetheless, the theory is vital to give assurance on how algorithms operate thus preventing their outputs to be misunderstood. Among the most basic statistical properties is the consistency which states that predictions are asymptotically accurate when the number of observations increases. In this talk, I will present a first result on Breiman’s forests consistency and show how it sheds some lights on its good performance in a sparse regression setting.

  • October 5th, 10;00 am, at CERMICS (B211 seminar room). Grégoire Ferré (CERMICS) will present: On the discretization of Feynman-Kac semi-groups

    Abstract : In this presentation, I will present a framework for the numerical analysis in the discretization time step of Feynman-Kac semigroups. I will first explain why these semigroups naturally appear in several fields, in particular large deviation theory and Diffusion Monte Carlo (DMC). Then, I will present elements of analysis of the error on the invariant measure that is done when discretizing a stochastic differential equation. Finally, I will show how we extended these results to the case of Feynman-Kac semi-groups, and why this analysis is interesting in general to discretize non probability-conserving processes, reviewing some theoretical and practical open problems suggested by this work.. This analysis is supported by relevant numerical applications.

  • November 9th, 10am at CERMICS . Laurent Michel (Université de Nice).
  • November 23rd, 10am at CERMICS. N. Nuksen.
  • December 14th, 10am, A. Schlichting.