Related papers: Consensus on simplicial complexes, or: The nonline…
The processing of signals supported on non-Euclidean domains has attracted large interest recently. Thus far, such non-Euclidean domains have been abstracted primarily as graphs with signals supported on the nodes, though the processing of…
A normalizing flow models a complex probability density as an invertible transformation of a simple base density. Flows based on either coupling or autoregressive transforms both offer exact density evaluation and sampling, but rely on the…
In many social networks it is a useful assumption that, regarding a given quality, an underlying hierarchy of the connected individuals exists, and that the outcome of interactions is to some extent determined by the relative positions in…
We use the topology of simplicial complexes to model political structures following [1]. Simplicial complexes are a natural tool to encode interactions in the structures since a simplex can be used to represent a subset of compatible…
Networks are a widely used and efficient paradigm to model real-world systems where basic units interact pairwise. Many body interactions are often at play, and cannot be modelled by resorting to binary exchanges. In this work, we consider…
Networked dynamical systems are common throughout science in engineering; e.g., biological networks, reaction networks, power systems, and the like. For many such systems, nonlinearity drives populations of identical (or near-identical)…
Higher-order structures, consisting of more than two individuals, provide a new perspective to reveal the missed non-trivial characteristics under pairwise networks. Prior works have researched various higher-order networks, but research…
We study the realizability of simplicial complexes with a given pair of integer sequences, representing the node degree distribution and the facet size distribution, respectively. While the $s$-uniform variant of the problem is…
Lagrangian coherent structures (LCSs) are material surfaces that shape finite-time tracer patterns in flows with arbitrary time dependence. Depending on their deformation properties, elliptic and hyperbolic LCSs have been identified from…
The approach to decomposition of multidimensional network systems on monoflow multilayer network systems (MLNS) is proposed, which significantly simplifies the analysis of intersystem interactions in multipurpose and multifunctional…
Algorithms based on normalizing flows are emerging as promising machine learning approaches to sampling complicated probability distributions in a way that can be made asymptotically exact. In the context of lattice field theory,…
Recently, neural network architectures have been developed to accommodate when the data has the structure of a graph or, more generally, a hypergraph. While useful, graph structures can be potentially limiting. Hypergraph structures in…
Consensus networks are usually understood as arithmetic mean driven dynamical averaging systems. In applications, however, network dynamics often describe inherently non-arithmetic and non-linear consensus processes. In this paper, we…
We present Onsager formalism applied to random networks with arbitrary degree distribution. Using the well-known methods of non-equilibrium thermodynamics we identify thermodynamic forces and their conjugated flows induced in networks as a…
We propose a new approach to the theory of normal forms for Hamiltonian systems near a non-resonant elliptic singular point. We consider the space of all Hamiltonian functions with such an equilibrium position at the origin and construct a…
We present a simple model of network dynamics that can be solved analytically for uniform networks. We obtain the dynamics of response of the system to perturbations. The analytical solution is an excellent approximation for random…
In this paper, we study non-Newtonian fluids in a class of unbounded domains with noncompact boundaries. With respect to the resulting mathematical problems, we establish the global existence of solutions with arbitrary large flux under…
Most methods proposed to uncover communities in complex networks rely on their structural properties. Here we introduce the stability of a network partition, a measure of its quality defined in terms of the statistical properties of a…
In this chapter, we derive and analyse models for consensus dynamics on hypergraphs. As we discuss, unless there are nonlinear node interaction functions, it is always possible to rewrite the system in terms of a new network of effective…
We find explicit solutions of the Laplacian coflow of $G_2-$structures on seven-dimensional almost-abelian Lie groups. Moreover, we construct new examples of solitons for the Laplacian coflow which are not eigenforms of the Laplacian and we…