Related papers: Vertex electrical model: lagrangian and non-negati…

Learning efficient graph representation is the key to favorably addressing downstream tasks on graphs, such as node or graph property prediction. Given the non-Euclidean structural property of graphs, preserving the original graph data's…

In the last 15 years, statistical physics has been a very successful framework to model complex networks. On the theoretical side, this approach has brought novel insights into a variety of physical phenomena, such as self-organisation,…

We deal with Lagrangian systems that are invariant under the action of a symmetry group. The mechanical connection is a principal connection that is associated to Lagrangians which have a kinetic energy function that is defined by a…

Latent space models are powerful statistical tools for modeling and understanding network data. While the importance of accounting for uncertainty in network analysis has been well recognized, the current literature predominantly focuses on…

Here, we develop a gauge-independent Green function approach to characterize the Chern invariants of generic non-Hermitian systems. It is shown that analogous to the Hermitian case, the Chern number can be expressed as an integral of the…

While physics conveys knowledge of nature built from an interplay between observations and theory, it has been considered less importantly in deep neural networks. Especially, there are few works leveraging physics behaviors when the…

We develop a model-independent approach to lagrangian perturbation theory for the large scale structure of the universe. We focus on the displacement field for dark matter particles, and derive its most general structure without assuming a…

We introduce a non-backtracking Laplace operator for graphs and we investigate its spectral properties. With the use of both theoretical and computational techniques, we show that the spectrum of this operator captures several structural…

It is known that electrical networks with resistors are related to the Laplace operator and random walk on weighted graphs. In this paper we consider more general electrical networks with coils, capacitors, and resistors. We give two…

Learning workable representations of dynamical systems is becoming an increasingly important problem in a number of application areas. By leveraging recent work connecting deep neural networks to systems of differential equations, we…

We first write down a very general description of nonlinear classical electrodynamics, making use of generalized constitutive equations and constitutive tensors. Our approach includes non-Lagrangian as well as Lagrangian theories, allows…

In this article we give an in depth overview of the recent advances in the field of equilibrium networks. After outlining this topic, we provide a novel way of defining equilibrium graph (network) ensembles. We illustrate this concept on…

We develop a variational method for constructing positive entropy invariant measures of Lagrangian systems without assuming transversal intersections of stable and unstable manifolds, and without restrictions to the size of non-integrable…

We propose a generalisation of Gibbs' statistical mechanics into the domain of non-negligible phase space correlations. Derived are the probability distribution and entropy as a generalised ensemble average, replacing…

Inferring topological characteristics of complex networks from observed data is critical to understand the dynamical behavior of networked systems, ranging from the Internet and the World Wide Web to biological networks and social networks.…

This paper focuses on the comparison of networks on the basis of statistical inference. For that purpose, we rely on smooth graphon models as a nonparametric modeling strategy that is able to capture complex structural patterns. The graphon…

In this paper, we study a notion of what we call vertex Leibniz algebra. This notion naturally extends that of vertex algebra without vacuum, which was previously introduced by Huang and Lepowsky. We show that every vertex algebra without…

There is a growing attention given to utilizing Lagrangian and Hamiltonian mechanics with network training in order to incorporate physics into the network. Most commonly, conservative systems are modeled, in which there are no frictional…

A noncommutative algebra corresponding to the classical catenoid is introduced together with a differential calculus of derivations. We prove that there exists a unique metric and torsion-free connection that is compatible with the complex…

Learning accurate dynamics models is necessary for optimal, compliant control of robotic systems. Current approaches to white-box modeling using analytic parameterizations, or black-box modeling using neural networks, can suffer from high…