Category
Discrete mathematics
Related publications (1,000)
The connection of the acyclic disconnection and feedback arc sets - On an open problem of Figueroa et al.
We examine the connection of two graph parameters, the size of a minimum feedback arcs set and the acyclic disconnection. A feedback arc set of a directed graph is a subset of arcs such that after deletion the graph becomes acyclic. The acyclic disconnecti ...
Elsevier2024The Power of Two Matrices in Spectral Algorithms for Community Recovery
Spectral algorithms are some of the main tools in optimization and inference problems on graphs. Typically, the graph is encoded as a matrix and eigenvectors and eigenvalues of the matrix are then used to solve the given graph problem. Spectral algorithms ...
Ieee-Inst Electrical Electronics Engineers Inc2024Non-planarity of Markoff graphs mod p
We prove the non-planarity of a family of 3-regular graphs constructed from the solutions to the Markoff equation x2 + y2 + z2 = xyz modulo prime numbers greater than 7. The proof uses Euler characteristic and an enumeration of the short cycles in these gr ...
Berlin2024Data-Driven Reactive Power Optimization of Distribution Networks via Graph Attention Networks
Wenlong Liao, Qi Liu, Zhe Yang
Reactive power optimization of distribution networks is traditionally addressed by physical model based methods, which often lead to locally optimal solutions and require heavy online inference time consumption. To improve the quality of the solution and r ...
State Grid Electric Power Research Inst2024Towards an Understanding of Hydraulic Sensitivity: Graph Theory Contributions to Water Distribution Analysis
Water distribution systems (WDSs) are complex networks with numerous interconnected junctions and pipes. The robustness and reliability of these systems are critically dependent on their network structure, necessitating detailed analysis for proactive leak ...
Basel2024Network-based kinetic models: Emergence of a statistical description of the graph topology
In this paper, we propose a novel approach that employs kinetic equations to describe the collective dynamics emerging from graph-mediated pairwise interactions in multi-agent systems. We formally show that for large graphs and specific classes of interact ...
Cambridge2024BENIGN LANDSCAPES OF LOW-DIMENSIONAL RELAXATIONS FOR ORTHOGONAL SYNCHRONIZATION ON GENERAL GRAPHS
Orthogonal group synchronization is the problem of estimating n elements Z(1),& mldr;,Z(n) from the rxr orthogonal group given some relative measurements R-ij approximate to Z(i)Z(j)(-1). The least-squares formulation is nonconvex. To avoid its local minim ...
Siam Publications2024A Note on Lenses in Arrangements of Pairwise Intersecting Circles in the Plane
Let F be a family of n pairwise intersecting circles in the plane. We show that the number of lenses, that is convex digons, in the arrangement induced by F is at most 2n - 2. This bound is tight. Furthermore, if no two circles in F touch, then the geometr ...
Electronic Journal Of Combinatorics2024Exponential convergence to steady-states for trajectories of a damped dynamical system modeling adhesive strings
We study the global well-posedness and asymptotic behavior for a semilinear damped wave equation with Neumann boundary conditions, modeling a one-dimensional linearly elastic body interacting with a rigid substrate through an adhesive material. The key fea ...
World Scientific Publ Co Pte Ltd2024An interior penalty coupling strategy for isogeometric non-conformal Kirchhoff-Love shell patches
Annalisa Buffa, Pablo Antolin Sanchez, Giuliano Guarino
This work focuses on the coupling of trimmed shell patches using Isogeometric Analysis, based on higher continuity splines that seamlessly meet the C 1 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackag ...
Springer2024