This paper establishes the proper notation and precise interpretation for Laplacian flows on
simplicial complexes. In particular, we have shown how to interpret these flows as time …

Application of the Ramsey graph theory to the analysis of physical systems is reported.
Physical interactions may be very generally classified as attractive and repulsive. This …

We show that arising out of noncommutative geometry is a natural family of edge Laplacians
on the edges of a graph. The family includes a canonical edge Laplacian associated to the …

We construct noncommutative “Riemannian manifold” structures on dual quasitriangular
Hopf algebras such as ℂ q [SU 2] with its standard bicovariant differential calculus, using the …

We propose a new formulation which realizes exact twisted supersymmetry for all the
supercharges on a lattice by twisted superspace formalism. We show explicit examples of …

Let V be a finite set. Let K be a simplicial complex with its vertices in V. In this paper, the
author discusses some differential calculus on V. He constructs some constrained homology …

We revisit the construction of quantum Riemannian geometries on graphs starting from a
hermitian metric compatible connection, which always exists. We use this method to find …

The purpose of this paper is to give a short and understandable exposition on differential
operators over modules and rings. The described methods allow for the use of algebra in …

We study the noncommutative Riemannian geometry of the alternating group A 4=(Z 2× Z
2)⋊ Z 3 using the recent formulation for finite groups. We find a unique 'Levi …

A major obstacle in the numerical simulation of general relativistic spacetimes is the fact that
coordinates have to be specified in order to obtain a well-defined numerical evolution. While …