Higher-order networks have so far been considered primarily in the context of studying structure complex systems, i.e., higher-order or multi-way relations connecting constituent entities. More recently, a number studies dynamical processes that explicitly account for such dependencies, e.g., epidemic spreading opinion formation. In this chapter, we focus on closely related, but distinct third ...

In this paper we will present a theory for simplicial diffeomorphims, that is, diffeomorphims that preserve the incidence relations of a simplicial complex. Simplicial diffeomorphisms can be regarded as curvilinear barycentric coordinates. Using the combination of piecewise linear functions on complexes with simplicial diffeomorphisms, we also propose a new representation of curves and surfaces...

In this work, we define cooperative games on simplicial complexes, generalizing the study of probabilistic values Weber (1988) and quasi-probabilistic Bilbao et al. (2001). Applications to Multi-Touch Attribution interpretability Machine-Learning prediction models motivate these new developments (Lundberg Lee, 2017; Ribeiro al., 2016; Strumbelj Kononenko, 2013; Shrikumar Datta Bach 2015). We de...