Related papers: Scaled Relative Graph Analysis of Lur'e Systems an…
Reset systems can overcome fundamental limitations of linear time-invariant control. The recently introduced notion of scaled (relative) graphs provides a promising framework for developing graphical analysis and design tools for reset…
We introduce a novel approach to feedback stability analysis for linear time-invariant (LTI) systems, overcoming the limitations of the sectoriality assumption in the small phase theorem. While phase analysis for single-input single-output…
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…
Continued fractions are classical representations of complex objects (for example, real numbers) as sums and inverses of simpler objects (for example, integers). The analogy in linear circuit theory is a chain of series/parallel one-ports:…
The linear algorithm of the Wiener filter and constrained realizations (CRs) of Gaussian random fields is extended here to perform non-linear CRs. The procedure consists of: (1) Using low resolution data to constrain a high resolution…
Given two nonlinear systems which only violate incremental passivity when their incremental gains are sufficiently small, we give a condition for their negative feedback interconnection to have finite incremental gain, which generalizes the…
The linear algorithm of the the full non-linear large scale structure of Gaussian random fields is extended here to to perform non-linear CRs. The procedure consists of: (1) Using linear CR of low resolution data to construct a high…
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,…
A generalization of the Renormalization Group, which describes order-parameter fluctuations in finite systems, is developed in the specific context of percolation. This ``Stochastic Renormalization Group'' (SRG) expresses statistical…
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…
Graph Neural Networks (GNNs) and Graph Transformers (GTs) are now a fundamental paradigm for graph learning, combining the representation-learning capabilities of deep models with the sample efficiency induced by their inductive biases.…
Davis-Yin splitting (DYS) has found a wide range of applications in optimization, but its linear rates of convergence have not been studied extensively. The scaled relative graph (SRG) simplifies the convergence analysis of operator…
Graph Representation Learning (GRL) has experienced significant progress as a means to extract structural information in a meaningful way for subsequent learning tasks. Current approaches including shallow embeddings and Graph Neural…
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…
Subgraph-based graph representation learning (SGRL) has been recently proposed to deal with some fundamental challenges encountered by canonical graph neural networks (GNNs), and has demonstrated advantages in many important data science…
This work addresses a modification of the random geometric graph (RGG) model by considering a set of points uniformly and independently distributed on the surface of a $(d-1)$-sphere with radius $r$ in a $d-$dimensional Euclidean space,…
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…
Graph Neural Networks (GNNs) and their message passing framework that leverages both structural and feature information, have become a standard method for solving graph-based machine learning problems. However, these approaches still…
Conventional reinforcement learning (RL) algorithms exhibit broad generality in their theoretical formulation and high performance on several challenging domains when combined with powerful function approximation. However, developing RL…
Stochastic variance reduced gradient (SVRG) is a popular variance reduction technique for accelerating stochastic gradient descent (SGD). We provide a first analysis of the method for solving a class of linear inverse problems in the lens…