Geometric realization of opinion is considered as a simplex and the opinion space of a group of individuals is a simplicial complex whose topological features are monitored in the process of opinion formation. The agents are physically located on the nodes of the scale-free network. Social interactions include all concepts of social dynamics present in the mainstream models augmented by four ad...

We establish an expansion by Γ-convergence of the Fisher information relative to the reference measure e−βV dx, where V is a generic multiwell potential and β → ∞. The expansion reveals a hierarchy of multiple scales reflecting the metastable behavior of the underlying overdamped Langevin dynamics: distinct scales emerge and become relevant depending on whether one considers probability measure...

The Laplacian spectral recursion, satisfied by matroid complexes and shifted complexes, expresses the eigenvalues of the combinatorial Laplacian of a simplicial complex in terms of its deletion and contraction with respect to vertex e, and the relative simplicial pair of the deletion modulo the contraction. We generalize this recursion to relative simplicial pairs, which we interpret as convex ...

In this paper, we prove that the L combinatorial torsion of an amenable covering space can be approximated by the combinatorial torsions of a regular exhaustion. An ancillary theorem shows the L spectral density function of the combinatorial Laplacian on L-cochains on the covering space is approximated by the average spectral density functions of the combinatorial Laplacian on the cochains of t...

the k-th semi total point graph of a graph g, , ‎is a graph‎ obtained from g by adding k vertices corresponding to each edge and‎ connecting them to the endpoints of edge considered‎. ‎in this paper‎, a formula for laplacian polynomial of in terms of‎ characteristic and laplacian polynomials of g is computed‎, ‎where is a connected regular graph‎.the kirchhoff index of is also computed‎.

We make a spectral analysis of discrete Schrödinger operators on the half-line, subject to complex Robin-type boundary couplings and complex-valued potentials. First, optimal enclosures are obtained for summable Second, general smallness conditions potentials guaranteeing stability established. Third, identity which allows generate Hardy inequalities Dirichlet Laplacian half-line is proved.

The Laplacian spread of a graph is defined as the difference between the largest and second smallest eigenvalues of the Laplacian matrix of the graph. In this paper, bounds are obtained for the Laplacian spread of graphs. By the Laplacian spread, several upper bounds of the Nordhaus-Gaddum type of Laplacian eigenvalues are improved. Some operations on Laplacian spread are presented. Connected c...

In this article, we associate a Hermitian matrix to multidigraph G. We call it the complex Laplacian of G and denote by L​C(G). It is shown that generalization graph. But, unlike graph, may not always be singular. obtain necessary sufficient condition for For G, if L​C(G) singular, say L​C-singular. generalize some properties Fiedler vectors undirected graphs eigenvectors corresponding second s...