Related papers: Generating function for web diagrams
We show that the essentially algebraic theory of generalized algebraic theories, regarded as a category with finite limits, has a universal exponentiable arrow in the sense that any exponentiable arrow in any category with finite limits is…
Networks are a powerful abstraction with applicability to a variety of scientific fields. Models explaining their morphology and growth processes permit a wide range of phenomena to be more systematically analysed and understood. At the…
We provide a novel approach to construct generative models for graphs. Instead of using the traditional probabilistic models or deep generative models, we propose to instead find an algorithm that generates the data. We achieve this using…
We propose a generating functional for nonrelativistic gauge invariant actions. In particular, we consider actions without the usual magnetic term. Like in the Born-Infeld theory, there is an upper bound to the electric field strength in…
Originally motivated by algebraic invariant theory, we present an algorithm to enumerate integer vectors modulo the action of a permutation group. This problem generalizes the generation of unlabeled graph up to an isomorphism. In this…
We show how to construct a tensor network representation of the path integral for reduced staggered fermions coupled to a non-abelian gauge field in two dimensions. The resulting formulation is both memory and computation efficient because…
A new modelling approach for the analysis of weighted networks with ordinal/polytomous dyadic values is introduced. Specifically, it is proposed to model the weighted network connectivity structure using a hierarchical multilayer…
Graph-based semantic representations are valuable in natural language processing, where it is often simple and effective to represent linguistic concepts as nodes, and relations as edges between them. Several attempts has been made to find…
We discuss topological theories, arising from the general $\mathcal{N}=2$ twisted gauge theories. We initiate a program of their study in the Gromov-Witten paradigm. We re-examine the low-energy effective abelian theory in the presence of…
Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…
We introduce a general framework for undirected graphical models. It generalizes Gaussian graphical models to a wide range of continuous, discrete, and combinations of different types of data. The models in the framework, called exponential…
We discuss a remarkable new approach initiated by Cachazo, Svrcek and Witten for calculating gauge theory amplitudes. The formalism amounts to an effective scalar perturbation theory which in many cases offers a much simpler alternative to…
Webs are weighted sets of Feynman diagrams which build up the logarithms of correlators of Wilson lines, and provide the ingredients for the computation of the soft anomalous dimension. We present a general analysis of multiple gluon…
We develop a technique to formulate quantum field theory on arbitrary network, based on different, randomly disposed sets of scattering's. We define R-matrix of the whole network as a product of R-matrices attached to each of scattering…
Webs are sets of Feynman diagrams which manifest soft gluon exponentiation in gauge theory scattering amplitudes: individual webs contribute to the logarithm of the amplitude and their ultraviolet renormalization encodes its infrared…
We consider a theory of fermions interacting with a (in general, non-Abelian) gauge field. The theory is assumed to be essentially inhomogeneous, which might be provided by non-trivial background fields interacting with both fermions and…
We make use of product integrals to provide an unambiguous mathematical representation of Wilson line and Wilson loop operators. Then, drawing upon various properties of product integrals, we discuss such properties of these operators as…
A new topological field theory is constructed, which is characterized by cubic interactions similar to those of non-abelian Chern-Simons field theories, but still retains the simplicity of the abelian case. The perturbative expansion of…
Maps are polygonal cellular networks on Riemann surfaces. This paper analyzes the construction of closed form general representations for the enumerative generating functions associated to maps of fixed but arbitrary genus. The method of…
A seminal technique of theoretical physics called Wick's theorem interprets the Gaussian matrix integral of the products of the trace of powers of Hermitian matrices as the number of labelled maps with a given degree sequence, sorted by…