Related papers: Effective Resistance in Simplicial Complexes as Bi…
Finding the equivalent resistance of an infinite ladder circuit is a classical problem in physics. We expand this well-known challenge to new classes of network topologies, in which the unit cells are much more entangled together. The exact…
In this paper, we present two new matrices, namely the resistance Laplacian and resistance signless Laplacian matrix of a connected graph. We provide a generalized form of these matrices for different classes of graphs, including the…
The complex morphologies exhibited by spatially confined thin objects have long challenged human efforts to understand and manipulate them, from the representation of patterns in draped fabric in Renaissance art to current day efforts to…
We consider the phase-integral method applied to an arbitrary ordinary linear differential equation of the second-order and study how its symmetries affect the connection matrices associated with its general solution. We reduce the obtained…
Computing the effective resistance between nodes in finite discrete resistor grids is a classical problem in circuit analysis with applications in VLSI power delivery network analysis, graph theory, and network science. Recent advances,…
We investigate the effective resistance $R_n$ and conductance $C_n$ between the root and leaves of a binary tree of height $n$. In this electrical network, the resistance of each edge $e$ at distance $d$ from the root is defined by…
In graph signal processing, data samples are associated to vertices on a graph, while edge weights represent similarities between those samples. We propose a convex optimization problem to learn sparse well connected graphs from data. We…
A subcomplex $\mathcal{X}$ of a cell complex $\mathcal{C}$ is called \emph{rigid} with respect to another cell complex $\mathcal{C}'$ if every injective simplicial map $\lambda:\mathcal{X} \rightarrow \mathcal{C}'$ has a unique extension to…
Simplicial surfaces describe the incidence relations between vertices, edges and faces of triangulated 2-dimensional manifolds in a purely combinatorial way. By considering only the incidences of edges and faces, simplicial surfaces are…
The theory of Force-Free Electrodynamics (FFE) provides a robust framework for modeling the magnetospheres of compact objects, where the electromagnetic field's energy density dominates the surrounding plasma. Central to this theory is the…
This paper introduces a scalable algorithmic framework (HyperEF) for spectral coarsening (decomposition) of large-scale hypergraphs by exploiting hyperedge effective resistances. Motivated by the latest theoretical framework for…
Cascading failures are one of the main reasons for blackouts in power transmission grids. The topology of a power grid, together with its operative state determine, for the most part, the robustness of the power grid against cascading…
Persistent homology is a popular data analysis technique that is used to capture the changing topology of a filtration associated with some simplicial complex $K$. These topological changes are summarized in persistence diagrams. We propose…
We report an approach to obtain effective pair potentials which describe the structure of two-dimensional systems of active Brownian particles. The pair potential is found by an inverse method, which matches the radial distribution function…
This work explores the definiteness of the weighted graph Laplacian matrix with negative edge weights. The definiteness of the weighted Laplacian is studied in terms of certain matrices that are related via congruent and similarity…
In this article we establish two fundamental results for the sublevel set persistent homology for stationary processes indexed by the positive integers. The first is a strong law of large numbers for the persistence diagram (treated as a…
This expository manuscript presents generalized expressions for the low-frequency voltage gain and terminal impedances of each of the three fundamental bipolar-amplifier topologies (i.e., common emitter, common base, and common collector).…
Graph condensation (GC) has gained significant attention for its ability to synthesize smaller yet informative graphs. However, existing studies often overlook the robustness of GC in scenarios where the original graph is corrupted. In such…
We consider the problem of two-point resistance in a resistor network previously studied by one of us [F. Y. Wu, J. Phys. A {\bf 37}, 6653 (2004)]. By formulating the problem differently, we obtain a new expression for the two-point…
We introduce a persistence-type invariant for finite weighted graphs based on combinatorial multivector dynamics. For each threshold parameter, a relation matrix determines a graph multivector field, whose induced directed dynamics admits a…