Maximally degenerate laplacians

The Multiple Point Principle: Realized Vacuum in Nature is Maximally Degenerate

We put forward the multiple point principle as a fine-tuning mechanism that can explain why the parameters of the standard model have the values observed experimentally. The principle states that the parameter values realized in Nature coincide with the surface (e.g. the point) in the action parameter space that lies in the boundary that separates the maximum number of regulator-induced phases ...

4 Connections to Laplacians

Laplacians of Covering Complexes

The Laplace operator on a simplicial complex encodes information about the adjacencies between simplices. A relationship between simplicial complexes does not always translate to a relationship between their Laplacians. In this paper we look at the case of covering complexes. A covering of a simplicial complex is built from many copies of simplices of the original complex, maintaining the adjac...

Laplacians for flow networks

We define a class of Laplacians for multicommodity, undirected flow networks, and bound their smallest nonzero eigenvalues with a generalization of the sparsest cut.

Laplacians on Shifted Multicomplexes

The Laplacian of an undirected graph is a square matrix, whose eigenvalues yield important information. We can regard graphs as one-dimensional simplicial complexes, and as whether there is a generalisation of the Laplacian operator to simplicial complexes. It turns out that there is, and that is useful for calculating real Betti numbers [8]. Duval and Reiner [5] have studied Laplacians of a sp...