Located at the heart of the main national research and higher education cluster, member of the Université Paris Saclay, a major actor in the French Investments for the Future Programme (Idex, LabEx, IRT, Equipex) and partner of the main establishments present on the plateau, the centre is particularly active in three major areas: data and knowledge; safety, security and reliability; modelling, simulation and optimisation (with priority given to energy).   

The 450 researchers and engineers from Inria and its partners who work in the research centre's 32 teams, the 60 research support staff members, the high-level equipment at their disposal (image walls, high-performance computing clusters, sensor networks), and the privileged relationships with prestigious industrial partners, all make Inria Saclay Île-de-France a key research centre in the local landscape and one that is oriented towards Europe and the world.

Within the framework of a partnership (you can choose between)

• not applicable,

a package

• SpinDoctor-Toolbox for diffusion MRI simulations in Matlab and Julia

  https://github.com/SpinDoctorMRI

For a better knowledge of the proposed research subject :

http://www.cmap.polytechnique.fr/~jingrebeccali/papers/Paper_SpinDoctor.pdf

https://github.com/SpinDoctorMRI.

Collaboration :

Superviser Jing-Rebecca Li (email: jingrebecca.li@inria.fr, web: http://www.cmap.polytechnique.fr/~jingrebeccali)

Responsibilities :

Algorithm development, code implementation.

We plan to further develop SpinDoctor in several directions:

1. Investigate domain decomposition: the particularity of the diffusion MRI problem makes it especially meaningful to divide the computational domain according to the biological distinction between cell parts. Specifically, for whole neuron simulations, we plan to divide the neuron computational geometry into a soma section, and dendrite branch sections.  With domain decomposition, it becomes natural to consider parallel computing in the subdomains and communication between them. 
2. Investigate space and time discretization/adaptivity that are different in each subdomain.
3. Pre-compute and store Laplace eigenfunctions information so users can directly compute the diffusion MRI signals without performing PDE solves;
4. Perform timing experiments of benchmark examples;
5. Improve the Julia version of SpinDoctor

The intern and the supervisor decide together on a subset of the above directions to work on during the internship.   If the intern makes good progress during the internship, we expect to submit the results for publication as a scientific article.

This project requires the knowledge of basic partial differential equations (diffusion equation properties), numerical analysis (ODE solvers, numerical stiffness), and finite elements (constructing finite element matrices).  It is necessary that the student can write good code in “Matlab” (correct and fast to run, i.e., using matrix/vector operations rather than loops, etc…).  Knowledge of Julia is a plus.

• Subsidized meals
• Partial reimbursement of public transport costs
• Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
• Possibility of teleworking (after 6 months of employment) and flexible organization of working hours
• Professional equipment available (videoconferencing, loan of computer equipment, etc.)
• Social, cultural and sports events and activities
• Access to vocational training
• Social security coverage

Remuneration : gratification