Related papers: Noncommutative Network Models
Notes in a musical piece are building blocks employed in non-random ways to create melodies. It is the "interaction" among a limited amount of notes that allows constructing the variety of musical compositions that have been written in…
This work deals with the construction of networks of topological defects in models described by a single complex scalar field. We take advantage of the deformation procedure recently used to describe kinklike defects in order to build…
Replicated network data are increasingly available in many research fields. In connectomic applications, inter-connections among brain regions are collected for each patient under study, motivating statistical models which can flexibly…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
Networks are fundamental models for data used in practically every application domain. In most instances, several implicit or explicit choices about the network definition impact the translation of underlying data to a network…
This paper presents an approach to model melodies (and music pieces in general) as networks. Notes of a melody can be seen as nodes of a network that are connected whenever these are played in sequence. This creates a directed graph. By…
Many existing statistical and machine learning tools for social network analysis focus on a single level of analysis. Methods designed for clustering optimize a global partition of the graph, whereas projection based approaches (e.g. the…
We develop a new ensemble of modular random graphs in which degree-degree correlations can be different in each module and the inter-module connections are defined by the joint degree-degree distribution of nodes for each pair of modules.…
Network representations of systems from various scientific and societal domains are neither completely random nor fully regular, but instead appear to contain recurring structural building blocks. These features tend to be shared by…
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…
Network embedding, which aims to learn low-dimensional representations of nodes, has been used for various graph related tasks including visualization, link prediction and node classification. Most existing embedding methods rely solely on…
In order to maintain consistent quality of service, computer network engineers face the task of monitoring the traffic fluctuations on the individual links making up the network. However, due to resource constraints and limited access, it…
Network backbones provide useful sparse representations of weighted networks by keeping only their most important links, permitting a range of computational speedups and simplifying network visualizations. A key limitation of existing…
Higher-order networks are widely used to describe complex systems in which interactions can involve more than two entities at once. In this paper, we focus on inclusion within higher-order networks, referring to situations where specific…
Complex models, such as neural networks (NNs), are comprised of many interrelated components. In order to represent these models, eliciting and characterising the relations between components is essential. Perhaps because of this, diagrams,…
Neural networks based on metric recognition methods have a strictly determined architecture. Number of neurons, connections, as well as weights and thresholds values are calculated analytically, based on the initial conditions of tasks:…
We introduce a class of neural networks derived from probabilistic models in the form of Bayesian networks. By imposing additional assumptions about the nature of the probabilistic models represented in the networks, we derive neural…
In this paper, we introduce a conceptual framework that model human social networks as an undirected dot-product graph of independent individuals. Their relationships are only determined by a cost-benefit analysis, i.e. by maximizing an…
Graph independence (also known as $\epsilon$-independence or $\lambda$-independence) is a mixture of classical independence and free independence corresponding to graph products or groups and operator algebras. Using conjugation by certain…
Most real-world networks are weighted graphs with the weight of the edges reflecting the relative importance of the connections. In this work, we study non degree dependent correlations between edge weights, generalizing thus the…