Related papers: Generating function for web diagrams

We introduce a class of association schemes that generalizes the Hamming scheme. We derive generating functions for their eigenvalues, and use these to obtain a version of MacWilliams theorem.

The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…

Topological metrics of graphs provide a natural way to describe the prominent features of various types of networks. Graph metrics describe the structure and interplay of graph edges and have found applications in many scientific fields. In…

We study a generating function for the sum over fatgraphs with specified valences of vertices and faces, inversely weighted by the order of their symmetry group. A compact expression is found for general (i.e. non necessarily connected)…

Ensembles of networks arise in many scientific fields, but there are few statistical tools for inferring their generative processes, particularly in the presence of both dyadic dependence and cross-graph heterogeneity. To fill in this gap,…

We characterize the computational power of neural networks that follow the graph neural network (GNN) architecture, not restricted to aggregate-combine GNNs or other particular types. We establish an exact correspondence between the…

A new approach to deal with the scattering amplitudes in Glauber theory is proposed. It relies on the use of generating function, that has been explicitly found. The method is applied to the analytical calculation of the nucleus-nucleus…

In wireless communications, transforming network into graphs and processing them using deep learning models, such as Graph Neural Networks (GNNs), is one of the mainstream network optimization approaches. While effective, the generative AI…

We present a general method for approximately contracting tensor networks with an arbitrary connectivity. This enables us to release the computational power of tensor networks to wide use in inference and learning problems defined on…

In this paper, we hope to bring closer graph theory and consensus algorithms. Firstly, we give a brief introduction to graph theory by listing a concise definition. Then we analyze and visualize some commonly used graphs. Secondly, we…

We use the theory of normal variance-mean mixtures to derive a data augmentation scheme for models that include gamma functions. Our methodology applies to many situations in statistics and machine learning, including Multinomial-Dirichlet…

We use our extension of the symbolic method in enumerative combinatorics (we extend finite sums defining coefficients in generating functions to infinite series) to generalize P\'olya's theorem. This theorem determines limits of…

Power law distribution seems to be an important characteristic of web graphs. Several existing web graph models generate power law graphs by adding new vertices and non-uniform edge connectivities to existing graphs. Researchers have…

Mechanistic models can provide an intuitive and interpretable explanation of network growth by specifying a set of generative rules. These rules can be defined by domain knowledge about real-world mechanisms governing network growth or may…

We present a formalism to explicitly construct non-Abelian gauge theories on noncommutative spaces (induced via a star product with aconstant Poisson tensor) from a consistency relation. This results in an expansion of the gauge parameter,…

Graphical models are commonly used to represent conditional dependence relationships between variables. There are multiple methods available for exploring them from high-dimensional data, but almost all of them rely on the assumption that…

We find the exponential generating function for permutations with all valleys even and all peaks odd, and use it to determine the asymptotics for its coefficients, answering a question posed by Liviu Nicolaescu. The generating function can…

When one tries to take into account the non-trivial vacuum structure of Quantum Field Theory, the standard functional-integral tools such as generating functionals or transitional amplitudes, are often quite inadequate for such purposes.…

In this paper combinatorial aspects of normal ordering arbitrary words in the creation and annihilation operators of the q-deformed boson are discussed. In particular, it is shown how by introducing appropriate q-weights for the associated…

The generating functions for the Wilson loops in the symmetric and antisymmetric representations of the gauge group $U(N)$ are expressed in terms of the connected correlators of multiply-wound Wilson loops, using ingredients from the…