Related papers: Scaled relative graphs for system analysis
With the prevalence of social media, the connectedness between people has been greatly enhanced. Real-world relations between users on social media are often not limited to expressing positive ties such as friendship, trust, and agreement,…
This paper consists of a few results, discovered and proved during the 2012-2013 research group at Eastern Oregon University. Inertia tables are a visual representation of the possible inertias of a given graph. The inertia of a graph…
We derive exact scaling relations for two-dimensional relativistic hydrodynamic turbulence in the inertial range of scales. We consider both the energy cascade towards large scales and the enstrophy cascade towards small scales. We…
Scene graph generation (SGG) is built on top of detected objects to predict object pairwise visual relations for describing the image content abstraction. Existing works have revealed that if the links between objects are given as prior…
We demonstrate that graph-based models are fully capable of representing higher-order interactions, and have a long history of being used for precisely this purpose. This stands in contrast to a common claim in the recent literature on…
We use random matrix theory to study the spectrum of random geometric graphs, a fundamental model of spatial networks. Considering ensembles of random geometric graphs we look at short range correlations in the level spacings of the…
It is a key to construct a similarity graph in graph-oriented subspace learning and clustering. In a similarity graph, each vertex denotes a data point and the edge weight represents the similarity between two points. There are two popular…
Relative representations are an established approach to zero-shot model stitching, consisting of a non-trainable transformation of the latent space of a deep neural network. Based on insights of topological and geometric nature, we propose…
Kernel and linear regression have been recently explored in the prediction of graph signals as the output, given arbitrary input signals that are agnostic to the graph. In many real-world problems, the graph expands over time as new nodes…
Token graphs, or symmetric powers of graphs, see \cite{alavi2002survey} and \cite{Fabila-Monroy2012}, are defined on the $k$-combinations of the vertex set of some graph $L$, where edges exist between two such combinations, if their…
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…
We propose a new approach to text semantic analysis and general corpus analysis using, as termed in this article, a "bi-gram graph" representation of a corpus. The different attributes derived from graph theory are measured and analyzed as…
Symplectic gauge theories coupled to matter fields lead to symmetry enhancement phenomena that have potential applications in such diverse contexts as composite Higgs, top partial compositeness, strongly interacting dark matter, and…
A novel class of graphs, here named quasiperiodic, are constructed via application of the Horizontal Visibility algorithm to the time series generated along the quasiperiodic route to chaos. We show how the hierarchy of mode-locked regions…
Many dynamic networks coming from real-world contexts are link streams, i.e. a finite collection of triplets $(u,v,t)$ where $u$ and $v$ are two nodes having a link between them at time $t$. A very large number of studies on these objects…
Current graph neural networks (GNNs) lack generalizability with respect to scales (graph sizes, graph diameters, edge weights, etc..) when solving many graph analysis problems. Taking the perspective of synthesizing graph theory programs,…
Statistical pattern classification methods based on data-random graphs were introduced recently. In this approach, a random directed graph is constructed from the data using the relative positions of the data points from various classes.…
Directed graphs are widely used in modelling of nonsymmetric relations in various sciences and engineering disciplines. We discuss invariants of strongly connected directed graphs - minimal number of vertices or edges necessary to remove to…
The monitoring of large dynamic networks is a major chal- lenge for a wide range of application. The complexity stems from properties of the underlying graphs, in which slight local changes can lead to sizable variations of global prop-…
We introduce structured random matrix ensembles, constructed to model many-body quantum systems with local interactions. These ensembles are employed to study equilibration of isolated many-body quantum systems, showing that rather complex…