Related papers: Proving relations between modular graph functions
We discuss a relation between two-loop bosonic worldline Green functions which are obtained by Schmidt and Schubert in two different parametrizations of a two-loop worldline. These Green functions are transformed into each other by some…
A short, elementary proof is given of the result: The number of components of a link arising from a medial graph M(G) by resolving vertices is equal to the nullity of the mod-2 Laplacian matrix of the graph G.
Arakelov-Green functions defined on metrized graphs have important role in relating arithmetical problems on algebraic curves into graph theoretical problems. In this paper, we clarify the combinatorial interpretation of certain…
Modular Graph Functions (MGFs) are SL(2,$\mathbb{Z}$)-invariant functions that emerge in the study of the low-energy expansion of the one-loop closed string amplitude. To find the string scattering amplitude, we must integrate MGFs over the…
Consider an algebraic identity between elliptic modular graphs where several vertices are at fixed locations (and hence unintegrated) while the others are integrated over the toroidal worldsheet. At any unintegrated vertex, we can glue an…
In this paper we extend the theory of bidimensionality to two families of graphs that do not exclude fixed minors: map graphs and power graphs. In both cases we prove a polynomial relation between the treewidth of a graph in the family and…
Any function can be constructed using a hierarchy of simpler functions through compositions. Such a hierarchy can be characterized by a binary rooted tree. Each node of this tree is associated with a function which takes as inputs two…
We generalize the methods used in the theory of correlation dynamics and establish a set of equations of motion for many-body correlation green's functions in the non-relativistic case. These non-linear and coupled equations of motion…
The gauge-gravity duality can be used to relate connected multi-point graviton functions to connected multi-point correlation functions of the stress tensor of a strongly coupled fluid. Here, we show how to construct the connected graviton…
The weak minor G of a graph G is the graph obtained from G by a sequence of edge-contraction operations on G. A weak-minor-closed family of upper embeddable graphs is a set G of upper embeddable graphs that for each graph G in G, every weak…
The present paper is the first one in the sequence of papers about a simple class of {\em framed $4$-graphs}; the goal of the present paper is to collect some well-known results on planarity and to reformulate them in the language of {\em…
We study energy functionals associated with quasi-linear Schr\"odinger operators on infinite graphs, and develop characterisations of (sub-)criticality via Green's functions, harmonic functions of minimal growth and capacities. We proof a…
We show that there is a system of 14 non-trivial finitary functions on the random graph with the following properties: Any non-trivial function on the random graph generates one of the functions of this system by means of composition with…
Using relationships between open and closed strings, we present a construction of tree-level scattering amplitudes for gravitons minimally coupled to matter in terms of gauge theory partial amplitudes. In particular, we present examples of…
We prove a neat factorization property of Feynman graphs in covariant perturbation theory. The contribution of the graph to the effective action is written as a product of a massless scalar momentum integral that only depends on the basic…
We define and study the link prediction problem in bipartite networks, specializing general link prediction algorithms to the bipartite case. In a graph, a link prediction function of two vertices denotes the similarity or proximity of the…
We study the category whose objects are graphs of fixed genus and whose morphisms are contractions. We show that the corresponding contravariant module categories are Noetherian and we study two families of modules over these categories.…
We extend the concept of the law of a finite graph to graphings, which are, in general, infinite graphs whose vertices are equipped with the structure of a probability space. By doing this, we obtain a vast array of new unimodular measures.…
Multiparticle systems on complicated metric graphs might have many applications in physics, biology and social life. But the corresponding science still does not exist. Here we start it with simplest examples where there is quadratic…
In this paper we give a method for constructing systematically all simple 2-connected graphs with n vertices from the set of simple 2-connected graphs with n-1 vertices, by means of two operations: subdivision of an edge and addition of a…