Related papers: Renormalization of Interacting Random Graph Models
We propose a wide class of preferential attachment models of random graphs, generalizing previous approaches. Graphs described by these models obey the power-law degree distribution, with the exponent that can be controlled in the models.…
Parametric causal modelling techniques rarely provide functionality for counterfactual estimation, often at the expense of modelling complexity. Since causal estimations depend on the family of functions used to model the data, simplistic…
Random intersection graphs containing an underlying community structure are a popular choice for modelling real-world networks. Given the group memberships, the classical random intersection graph is obtained by connecting individuals when…
A renormalization group flow of Hamiltonians for two-dimensional classical partition functions is constructed using tensor networks. Similar to tensor network renormalization ([G. Evenbly and G. Vidal, Phys. Rev. Lett. 115, 180405 (2015)],…
The `random intersection graph with communities' models networks with communities, assuming an underlying bipartite structure of groups and individuals. Each group has its own internal structure described by a (small) graph, while groups…
We introduce a new family of tensorial field theories by coupling different fields in a non-trivial way, with a view towards the investigation of the coupling between matter and gravity in the quantum regime. As a first step, we consider…
This paper is a direct continuation of an earlier work, where we studied Erd\"os-R\'enyi random graphs perturbed by an interaction Hamiltonian favouring the formation of short cycles. Here, we generalize these results. We keep the same…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…
We introduce a mapping between graphs and pure quantum bipartite states and show that the associated entanglement entropy conveys non-trivial information about the structure of the graph. Our primary goal is to investigate the family of…
We introduce the Graph Mixture Density Networks, a new family of machine learning models that can fit multimodal output distributions conditioned on graphs of arbitrary topology. By combining ideas from mixture models and graph…
A set of independence statements may define the independence structure of interest in a family of joint probability distributions. This structure is often captured by a graph that consists of nodes representing the random variables and of…
Graphs are a natural representation for systems based on relations between connected entities. Combinatorial optimization problems, which arise when considering an objective function related to a process of interest on discrete structures,…
Social learning algorithms provide models for the formation of opinions over social networks resulting from local reasoning and peer-to-peer exchanges. Interactions occur over an underlying graph topology, which describes the flow of…
The exponential family of random graphs represents an important and challenging class of network models. Despite their flexibility, conventionally used exponential random graphs have one shortcoming. They cannot directly model weighted…
Different network models have been suggested for the topology underlying complex interactions in natural systems. These models are aimed at replicating specific statistical features encountered in real-world networks. However, it is rarely…
Normalizing flows are powerful non-parametric statistical models that function as a hybrid between density estimators and generative models. Current learning algorithms for normalizing flows assume that data points are sampled…
We study countable graphs that -- up to isomorphism and with probability one -- arise from a random process, in a similar fashion as the Rado graph. Unlike in the classical case, we do not require that probabilities assigned to pairs of…
We introduce a statistical mechanics formalism for the study of constrained graph evolution as a Markovian stochastic process, in analogy with that available for spin systems, deriving its basic properties and highlighting the role of the…
Networks constitute efficient tools for assessing universal features of complex systems. In physical contexts, classical as well as quantum, networks are used to describe a wide range of phenomena, such as phase transitions, intricate…
We have developed a nonperturbative functional renormalization group approach for random field models and related disordered systems for which, due to the existence of many metastable states, conventional perturbation theory often fails.…