We consider dynamics driven by interaction energies on graphs. introduce graph analogues of the continuum nonlocal-interaction equation and interpret them as gradient flows with respect to a Wasserstein distance. The particular distance we arises from analogue Benamou-Brenier formulation where continuity uses an upwind interpolation define density along edges. While this approach has both theor...

Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symm...

Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symm...