Related papers: Electrical networks and data analysis in phylogene…

Our work is motivated by and illustrated with application of association networks in computational biology, specifically in the context of gene/protein regulatory networks. Association networks represent systems of interacting elements,…

While deep learning is successful in a number of applications, it is not yet well understood theoretically. A satisfactory theoretical characterization of deep learning however, is beginning to emerge. It covers the following questions: 1)…

We study the question of reconstructing a weighted, directed network up to isomorphism from its motifs. In order to tackle this question we first relax the usual (strong) notion of graph isomorphism to obtain a relaxation that we call weak…

The study of neuronal morphology is important not only for its potential relationship with neuronal dynamics, but also as a means to classify diverse types of cells and compare than among species, organs, and conditions. In the present…

Much of social network analysis is - implicitly or explicitly - predicated on the assumption that individuals tend to be more similar to their friends than to strangers. Thus, an observed social network provides a noisy signal about the…

Comparing two population means of network data is of paramount importance in a wide range of scientific applications. Many existing network inference solutions focus on global testing of entire networks, without comparing individual network…

We study the properties of a leave-node-out jackknife procedure for network data. Under the sparse graphon model, we prove an Efron-Stein-type inequality, showing that the network jackknife leads to conservative estimates of the variance…

Distribution grids constitute complex networks of lines often times reconfigured to minimize losses, balance loads, alleviate faults, or for maintenance purposes. Topology monitoring becomes a critical task for optimal grid scheduling.…

In this article, we revisit and expand our prior work on graph similarity. As with our earlier work, we focus on a view of similarity which does not require node correspondence between graphs under comparison. Our work is suited to the…

We study complex networks under random matrix theory (RMT) framework. Using nearest-neighbor and next-nearest-neighbor spacing distributions we analyze the eigenvalues of adjacency matrix of various model networks, namely, random,…

In this paper, we quantify voltage and current phasor-based measurement requirements for the unique estimation of the electric grid topology and admittance parameters. Our approach is underpinned by the concept of a rigidity matrix that has…

Deep neural network architectures often consist of repetitive structural elements. We introduce an approach that reveals these patterns and can be broadly applied to the study of deep learning. Similarly to how a power strip helps untangle…

Graph neural networks (GNN) rely on graph operations that include neural network training for various graph related tasks. Recently, several attempts have been made to apply the GNNs to functional magnetic resonance image (fMRI) data.…

This paper presents a set of validation metrics for transmission network parameters that is applicable in both creation of synthetic power system test cases and validation of existing models. Using actual data from two real-world power…

Foundation models (FMs) currently dominate news headlines. They employ advanced deep learning architectures to extract structural information autonomously from vast datasets through self-supervision. The resulting rich representations of…

Phylogenetic networks are rooted, labelled directed acyclic graphs which are commonly used to represent reticulate evolution. There is a close relationship between phylogenetic networks and multi-labelled trees (MUL-trees). Indeed, any…

Networks are paradigms for describing complex biological, social and technological systems. Here I argue that networks provide a coherent framework to construct coarse-grained models for many different physical systems. To elucidate these…

The electromagnetic analog of an elastic spring-mass network is constructed. These electromagnetic circuits offer the promise of manipulating electromagnetic fields in new ways, and linear electrical circuits correspond to a subclass of…

An antithetical concept, adaptive symmetry, to conservative symmetry in physics is proposed to understand the deep neural networks (DNNs). It characterizes the invariance of variance, where a biotic system explores different pathways of…

We present for the first time a complex network approach to the study of the electrical properties of single protein devices. In particular, we consider an electronic nanobiosensor based on a G-protein coupled receptor. By adopting a coarse…