Recent work by Marcus, Spielman and Srivastava proves the existence of bipartite Ramanujan (multi) graphs of all degrees and all sizes. However, that paper did not provide a polynomial time algorithm ...

It replaces the graph convolution with a FIR filter (i.e. the use of a polynomial of the shift operator) by an ratio of polynomials. This architecture offers a good trade-off between number of ...

This pioneering book presents a study of the interrelationships among operator calculus, graph theory, and quantum probability in a unified manner, with significant emphasis on symbolic computations ...

We prove a characterization of all polynomial-time computable queries on the class of interval graphs by sentences of fixed-point logic with counting. More precisely, it is shown that on the class of ...

The graph polynomial of a Feynman diagram is defined in terms of the spanning trees and forests of the underlying graph. The associated Feynman integral can be expressed as a Mellin transform of a ...

The graph polynomial of a Feynman diagram is defined in terms of the spanning trees and forests of the underlying graph.

The graph polynomial of a Feynman diagram is defined in terms of the spanning trees and forests of the underlying graph. The associated Feynman integral can be expressed as a Mellin transform of a ...