Related papers: Vertex electrical model: lagrangian and non-negati…
We propose a new approach to studying electrical networks interpreting the Ohm law as the operator which solves certain Local Yang-Baxter equation. Using this operator and the medial graph of the electrical network we define a vertex…
Pairwise network comparison is essential for various applications, including neuroscience, disease research, and dynamic network analysis. While existing literature primarily focuses on comparing entire network structures, we address a…
This paper deals with the state estimation of non-linear and non-Gaussian systems with an emphasis on the numerical solution to the Bayesian recursive relations. In particular, this paper builds upon the Lagrangian grid-based filter (GbF)…
Network theory and inverse modeling are two standard tools of applied physics, whose combination is needed when studying the dynamical organization of spatially distributed systems from indirect measurements. However, the associated…
A method for embedding graphs in Euclidean space is suggested. The method connects nodes to their geographically closest neighbors and economizes on the total physical length of links. The topological and geometrical properties of…
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
In the framework of on nonassociative geometry, we introduce a new effective model that extends the statistical treatment of complex networks with hidden geometry. The small-world property of the network is controlled by nonlocal curvature…
We present a comprehensive extension of the latent position network model known as the random dot product graph to accommodate multiple graphs -- both undirected and directed -- which share a common subset of nodes, and propose a method for…
Signed graphs have appeared in a broad variety of applications, ranging from social networks to biological networks, from distributed control and computation to power systems. In this paper, we investigate spectral properties of signed…
Spatially embedded networks are shaped by a combination of purely topological (space-independent) and space-dependent formation rules. While it is quite easy to artificially generate networks where the relative importance of these two…
Based on our previous graph covering method, we introduce weighted graph covering models and flexible graph covering models that are almost equivalent to the well-known Bratteli--Vershik models. These models play important roles in showing…
We present a novel spectral embedding of graphs that incorporates weights assigned to the nodes, quantifying their relative importance. This spectral embedding is based on the first eigenvectors of some properly normalized version of the…
In recent years, network embedding methods have garnered increasing attention because of their effectiveness in various information retrieval tasks. The goal is to learn low-dimensional representations of vertexes in an information network…
This paper addresses the mode collapse for generative adversarial networks (GANs). We view modes as a geometric structure of data distribution in a metric space. Under this geometric lens, we embed subsamples of the dataset from an…
In this paper, we provide a review on both fundamentals of social networks and latent space modeling. The former discusses important topics related to network description, including vertex characteristics and network structure; whereas the…
A comparative analysis of two different versions of the Legendre transformation is presented. We provide an almost complete although somewhat superficial review of the geometric background for analytical mechanics. Complete coordinate…
When analyzing weighted networks using spectral embedding, a judicious transformation of the edge weights may produce better results. To formalize this idea, we consider the asymptotic behavior of spectral embedding for different…
We present a systematic approach to embed $n$-dimensional vacuum general relativity in an $(n + 1)$-dimensional pseudo-Riemannian spacetime whose source is either a (non)zero cosmological constant or a scalar field minimally-coupled to…
Lagrangian and Hamiltonian neural networks (LNNs and HNNs, respectively) encode strong inductive biases that allow them to outperform other models of physical systems significantly. However, these models have, thus far, mostly been limited…
This article determines the spectral data, in the integrable systems sense, for all weakly conformally immersed Hamiltonian stationary Lagrangian in $\R^4$. This enables us to describe their moduli space and the locus of branch points of…