Supplemental code and data for paper "Mechanics of exploration in Drosophila melanogaster" by Jane Loveless, Konstantinos Lagogiannis, and Barbara Webb.

All code was written by Jane Loveless. All data files were generated by the code included in this repo, with the exception of "./data/szigeti_modes/szigeti_modes.mat" which was originally generated by Balázs Szigeti and published in "Searching for motifs in the behaviour of larval Drosophila melanogaster and Caenorhabditis elegans reveals continuity between behavioural states" by Balázs Szigeti, Ajinkya Deogade, and Barbara Webb, Journal of the Royal Society Interface.

The provided code consists of a Python module, neuromech, along with several Python scripts which use this module to generate data, run analyses, and produce the plots shown in the main paper.

There are a few dependencies for this code to work : numpy (ideally compiled with support for LAPACK/BLAS), scipy (ideally compiled with support for LAPACK/BLAS), sympy, matplotlib (animation backend is required to reproduce supplemental video content), odespy (available at https://github.com/hplgit/odespy; this must be compiled with support for the ODEPACK solvers and FORTRAN compilation), powerlaw (available at https://pypi.python.org/pypi/powerlaw)

The neuromech module is split into a set of submodules, as follows :

symbol defines several useful mathematical symbols used in other submodules, e.g. t for time, V for membrane voltage/neuron activation

model defines generic model classes, mechanical models, and neural models. Also provides some helper functions for doing classical mechanics in a Hamiltonian framework.

analysis provides routines for analysing models, either directly or via data generated through simulation

util provides utility functions and wrappers, e.g. tools for pretty plotting; tools for numerical integration using odespy; tools for generating FORTRAN source code compatible with odespy from a system of symbolic differential equations using sympy

Typical workflow within a script will consist of defining symbolic mechanical and neural models before combining them and converting the composite system of symbolic dynamical equations into compilable FORTRAN source code for numerical investigation. Analysis is then either done on the symbolic models directly or the numerical models directly or on simulation outputs, or some combination thereof.

The included scripts are :

1_modal_analysis.py corresponds to figure 3 in paper. Symbolic analysis of the body's small-amplitude motion.

2_peristalsis.py corresponds to figure 4 in paper. Numerically integrate dissipative axial motion; bifurcation analysis; visualisation using modal coordinates

3_conservative_head.py corresponds to figure 5 and 6 in paper. Analysis of head's large-amplitude behaviour and transition to chaotic motion; uses Poincare section, LCE estimation, power spectrum, autocorrelation

4_conservative_body.py corresponds to figure 7 in paper. Analysis of full body's large-amplitude behaviour; uses LCE estimation, power spectrum, autocorrelation

5_exploration.py corresponds to figure 8 and 9 in paper. Generate trajectories for full model; LCE estimation. This script does not perform any plotting.

6_trajectory_analysis.py corresponds to figure 8 and 9 in paper. Analysis of trajectories generated by previous script; uses power spectrum, autocorrelation, correlation dimension, box-counting dimension, 2-segment analysis, run-length distribution, body bend distribution, mean-squared displacement, etc.

LCE_test_lorenz.py tests LCE estimation algorithm on Lorenz system

LCE_test_rossler.py tests LCE estimation algorithm on Rossler system