DS for Neuro

Contact me for the following programs. You can also browse the public repositories on GitHub and GitLab.

This Julia package aims at tractography by taking advantage of parallel and specific hardwares (e.g. GPU). Tractography aims at reconstructing white matter fiber bundles using diffusion-weighted MRI. It thus aim to study the structural connectivity of the brain.

Bifurcation analysis code in Julia programming language. It allows to perform numerical continuation and (automatic) bifurcation analysis in large dimensions on CPUs / GPUs. ODEs, DDEs, PDEs are also well within the scope of the package. The organisation bifurcationkit regroups many plugins, for example to follow homoclinic orbits. The main package has more than 400 stars.

📖 Documentation

📚 Citations of the package

Main repository for Synapse simulations in Julia. Published in eLife (2023).

Simulation of PDMPs in Julia with C-level performance. Based on this paper.

Old Codes

Julia wrapper for the LSODA ODE solver by Petzold & Hindmarsh. Automatically switches between stiff and non-stiff integration.

  • Neuron Code

Download ASIC model container Associated with a BioRxiv preprint.

  • PyTrilinos

Developed with Sandia Labs. See PyTrilinos for nonlinear/numerical continuation in Trilinos.

  • Neural Field Equations in PETSc

Simulation using petsc4py Parallel, fast solver for large-scale neural field equations and bifurcation analysis.

ddtV(x,t)=−V(x,t)+∫ΩJ(x,y)S(V(y,t))dy,y∈R2 \frac{d}{d t} V(x, t)=-V(x, t)+\int_{\Omega} J(x, y) S(V(y, t)) d y, y \in \mathbb{R}^2

  • Hopf Curves for DDE

Computes Hopf bifurcation curves for delay differential equations. See paper.

(λ+l)Ui(x)=∑j=1p∫ΩJij(x,y)e−λτ(x,y)Uj(y)dy,1≤i≤p,x,y∈Rd (\lambda+l) U_i(x)=\sum_{j=1}^p \int_{\Omega} J_{i j}(x, y) e^{-\lambda \tau(x, y)} U_j(y) d y, 1 \leq i \leq p, x, y \in \mathbb{R}^d
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