Energy-Motivated Equivariant Pretraining for 3D Molecular Graphs

Statistically Motivated 3D Faces Reconstruction

Facial surgeons require a vast amount of knowledge about the human face, in order to decide how to reconstruct an injured or traumatized part. Does this knowledge consist only of explicit notions about face anatomy, or is there also an implicit knowledge of the normal appearance of a face? And if the answer to the latter question is affirmative, is there a way for a computer to automatically le...

Perceptually Motivated Constraints on 3D Visualizations

Energy of Graphs, Matroids and Fibonacci Numbers

The energy E(G) of a graph G is the sum of the absolute values of the eigenvalues of G. In this article we consider the problem whether generalized Fibonacci constants $varphi_n$ $(ngeq 2)$ can be the energy of graphs. We show that $varphi_n$ cannot be the energy of graphs. Also we prove that all natural powers of $varphi_{2n}$ cannot be the energy of a matroid.

On net-Laplacian Energy of Signed Graphs

A signed graph is a graph where the edges are assigned either positive ornegative signs. Net degree of a signed graph is the dierence between the number ofpositive and negative edges incident with a vertex. It is said to be net-regular if all itsvertices have the same net-degree. Laplacian energy of a signed graph is defined asε(L(Σ)) =|γ_1-(2m)/n|+...+|γ_n-(2m)/n| where γ_1,...,γ_n are the ei...

Average Degree-Eccentricity Energy of Graphs

The concept of average degree-eccentricity matrix ADE(G) of a connected graph $G$ is introduced. Some coefficients of the characteristic polynomial of ADE(G) are obtained, as well as a bound for the eigenvalues of ADE(G). We also introduce the average degree-eccentricity graph energy and establish bounds for it.