A Note on Lenses in Arrangements of Pairwise Intersecting Circles in the Plane

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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 ...

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 ...

This thesis presents a comprehensive theory of information-theoretic measures for characterizing the complexity and higher-order dependence structures of graphs. We introduce multivariate complexity and dependence measures for graphs within the framework o ...

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 ...

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 ...

We study the hitting probabilities of the solution to a system of d stochastic heat equations with additive noise subject to Dirichlet boundary conditions. We show that for any bounded Borel set with positive (d-6)\documentclass[12pt]{minimal} \usepackage{ ...

In this article, we propose a dynamical system to avoid obstacles which are star shaped and simultaneously converge to a goal. The convergence is almost-global in a domain and the stationary points are identified explicitly. Our approach is based on the id ...

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 ...

Strong gravitational lenses provide unique laboratories for cosmological and astrophysical investigations, but they must first be discovered - a task that can be met with significant contamination by other astrophysical objects and asterisms. Here we revie ...

Decision-making permeates every aspect of human and societal development, from individuals' daily choices to the complex decisions made by communities and institutions. Central to effective decision-making is the discipline of optimization, which seeks th ...

Glass has been the material of choice for making optical elements, in large part due to its intrinsic properties: a temperature-dependent viscosity, which enables shaping the material into a broad variety of functional and artistic glassware. Silica glass ...

Image information about the state of a building after an earthquake, which can be collected without endangering the post-earthquake reconnaissance activities, can be used to reduce uncertainties in response predictions for future seismic events. This paper ...

Due to its high parallelism, belief propagation (BP)decoding is amenable to high-throughput applications and thusrepresents a promising solution for the ultra-high peak datarate required by future communication systems. To bridge theperformance gap compare ...

Modern integrated circuits are tiny yet incredibly complex technological artifacts, composed of millions and billions of individual structures working in unison. Managing their complexity and facilitating their design drove part of the co-evolution of mode ...

Graph machine learning offers a powerful framework with natural applications in scientific fields such as chemistry, biology and material sciences. By representing data as a graph, we encode the prior knowledge that the data is composed of a set of entiti ...

When can a unimodular random planar graph be drawn in the Euclidean or the hyperbolic plane in a way that the distribution of the random drawing is isometry-invariant? This question was answered for one-ended unimodular graphs in Benjamini and Timar, using ...

Resting-state fMRI has proven to entail subject-specific signatures that can serve as a fingerprint to identify individuals. Conventional methods are based on building a connectivity matrix based on correlation between the average time course of pairs of b ...

This work presents a graph neural network (GNN) framework for solving the maximum independent set (MIS) problem, inspired by dynamic programming (DP). Specifically, given a graph, we propose a DP-like recursive algorithm based on GNNs that firstly construc ...

In the ITER Tokamak, four Electron Cyclotron Heating Upper Launchers (ECHUL) are needed to control plasma instabilities at the rational surfaces, most importantly the q = 3/2 and q = 2/1 neoclassical tearing modes (NTMs). Each ECHUL is equipped with a set ...

In this article, we consider decentralized optimization problems where agents have individual cost functions to minimize subject to subspace constraints that require the minimizers across the network to lie in low-dimensional subspaces. This constrained fo ...

A Note on Lenses in Arrangements of Pairwise Intersecting Circles in the Plane

Chattez avec Graph Search

Non-planarity of Markoff graphs mod p

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Brain Fingerprinting Using Fmri Spectral Signatures On High-Resolution Cortical Graphs

Maximum Independent Set: Self-Training through Dynamic Programming

Present design of the Steering Mirror Assembly (SMA) for ITER ECHUL

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