Related papers: Scaled Relative Graph of Normal Matrices
The Random Geometric Graph (RGG) is a random graph model for network data with an underlying spatial representation. Geometry endows RGGs with a rich dependence structure and often leads to desirable properties of real-world networks such…
The concept of universality has shaped our understanding of many-body physics, but is mostly limited to homogenous systems. Here, we present a study of universality on a non-homogeneous graph, the long-range diluted graph (LRDG). Its…
Graphs, and sequences of growing graphs, can be used to specify the architecture of mathematical models in many fields including machine learning and computational science. Here we define structured graph "lineages" (ordered by level…
Graphs are widely adopted tools for encoding information. Generally, they are applied to disparate research fields where data needs to be represented in terms of local and spatial connections. In this context, a structure for ditigal image…
Similarity search is a fundamental building block for information retrieval on a variety of datasets. The notion of a neighbor is often based on binary considerations, such as the k nearest neighbors. However, considering that data is often…
The scaled graph has been introduced recently as a nonlinear extension of the classical Nyquist plot for linear time-invariant systems. In this paper, we introduce a modified definition for the scaled graph, termed the signed scaled graph…
Representing a graph as a vector is a challenging task; ideally, the representation should be easily computable and conducive to efficient comparisons among graphs, tailored to the particular data and analytical task at hand. Unfortunately,…
The operator-theoretic renormalization group (RG) methods are powerful analytic tools to explore spectral properties of field-theoretical models such as quantum electrodynamics (QED) with non-relativistic matter. In this paper these methods…
This paper proposes a frequency-wise approach for stability analysis of multi-input, multi-output (MIMO) Linear Time-Invariant (LTI) feedback systems through Scaled Relative Graphs (SRGs). Unlike traditional methods, such as the Generalized…
A straight line triangle representation (SLTR) of a planar graph is a straight line drawing such that all the faces including the outer face have triangular shape. Such a drawing can be viewed as a tiling of a triangle using triangles with…
This thesis focuses on theoretical and algorithmic tools for determining the numbers of induced subgraphs in strongly regular graphs, SRGs, and on further applications of such numbers. We consider in more detail a restricted class of these…
The renormalization group (RG) is a powerful theoretical framework developed to consistently transform the description of configurations of systems with many degrees of freedom, along with the associated model parameters and coupling…
We present a spectral analysis for matrix scaling and operator scaling. We prove that if the input matrix or operator has a spectral gap, then a natural gradient flow has linear convergence. This implies that a simple gradient descent…
The hyperbolic random graph model (HRG) has proven useful in the analysis of scale-free networks, which are ubiquitous in many fields, from social network analysis to biology. However, working with this model is algorithmically and…
Scaled Relative Graphs (SRGs) provide an intuitive graphical frequency-domain method for the analysis of Nonlinear (NL) systems, generalizing the Nyquist diagram. In this paper, we develop a method for computing $L_2$-gain bounds for Lur'e…
Graph neural networks (GNNs) are a popular class of parametric model for learning over graph-structured data. Recent work has argued that GNNs primarily use the graph for feature smoothing, and have shown competitive results on benchmark…
A generalization of the random geometric graph (RGG) model is proposed by considering a set of points uniformly and independently distributed on a rectangle of unit area instead of on a unit square [0,1]^2. The topological properties of the…
Matrix Graph Grammars (MGG) is a novel approach to the study of graph dynamics ([15]). In the present contribution we look at MGG as a formal grammar and as a model of computation, which is a necessary step in the more ambitious program of…
We investigate the quantum networks that their nodes are considered as quantum harmonic oscillators. The entanglement of the ground state can be used to quantify the amount of information one part of a network shares with the other part of…
Symbolic regression (SR) is a powerful technique for discovering the analytical mathematical expression from data, finding various applications in natural sciences due to its good interpretability of results. However, existing methods face…