Affine and convex spaces: blending the analytic and geometric viewpoints

  title={Affine and convex spaces: blending the analytic and geometric viewpoints},
  author={PierGianLuca Porta Mana},
  journal={arXiv: Classical Physics},
This is a short introduction to affine and convex spaces, written especially for physics students. It summarizes different elementary presentations available in the mathematical literature, and blends analytic- and geometric-flavoured presentations. References are also provided, as well as a brief discussion of Grassmann spaces and an example showing the relevance and usefulness of affine spaces in Newtonian physics. 
Perfect Detection of Spikes in the Linear Sub-threshold Dynamics of Point Neurons
The present work offers an alternative geometric point of view on neuronal dynamics, and derives, implements, and benchmarks a method for perfect retrospective spike detection, which can be applied to neuron models with affine or linear subthreshold dynamics.
Dimensional analysis in relativity and in differential geometry
This note provides a short guide to dimensional analysis in Lorentzian and general relativity and in differential geometry. It tries to revive Dorgelo and Schouten’s notion of ‘intrinsic’ or