The simplicity of planar networks

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Goal: Structural brain graphs are conventionally limited to defining nodes as gray matter regions from an atlas, with edges reflecting the density of axonal projections between pairs of nodes. Here we explicitly model the entire set of voxels within a brai ...

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 ...

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 ...

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 ...

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 ...

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 ...

Over the course of history, the relationship between cities and their waters has shown different gradients of interweaving, marked by cycles of bonding and distancing. Following a period of complete neglect of urban watercourses, the versatile, multifacete ...

Anthropogenic modification of natural landscapes to urban environments impacts land-atmosphere interactions in the boundary layer. Ample research has demonstrated the effect of such landscape transitions on development of the urban heat island (UHI), but c ...

Zoning reform is a crucial tool for cities to adapt to contemporary challenges. However, its implementation remains challenging. Property owners, with a vested interest in the value of their neighborhoods, are sensitive to local developments and the potent ...

As large, data-driven artificial intelligence models become ubiquitous, guaranteeing high data quality is imperative for constructing models. Crowdsourcing, community sensing, and data filtering have long been the standard approaches to guaranteeing or imp ...

The aim of my thesis is to provide urban architects and planners with working theoretical elements territorial project of the living. The living and the socio-ecological transition are key concepts in the nature and people paradigm, which asserts a human-n ...

Uncertainty of spillover effects – including property devaluation - from proposed land-use change elicits opposition to local development. This hinders cities’ ability to implement land-use policy aimed at housing affordability and environmental sustainabi ...

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 ...

Urban proximity planning is foreseen as a solution to foster a “sustainable” city, including economic viability, environmental soundness and social inclusivity. This paper focuses on the inclusivity aspects by questioning the adoption of urban proximities: ...

Upcoming wide-field surveys will discover thousands of new strongly lensed quasars which will be monitored with unprecedented cadence by the Legacy Survey of Space and Time (LSST). Many of these quasars will undergo caustic-crossing events over the 10-yr L ...

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 ...

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 ...

The simplicity of planar networks

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Voxel-Wise Brain Graphs From Diffusion MRI: Intrinsic Eigenspace Dimensionality and Application to Functional MRI

Non-planarity of Markoff graphs mod p

The Power of Two Matrices in Spectral Algorithms for Community Recovery

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

The connection of the acyclic disconnection and feedback arc sets - On an open problem of Figueroa et al

BENIGN LANDSCAPES OF LOW-DIMENSIONAL RELAXATIONS FOR ORTHOGONAL SYNCHRONIZATION ON GENERAL GRAPHS

Network-based kinetic models: Emergence of a statistical description of the graph topology

Graph generative deep learning models with an application to circuit topologies

Quartiers rhodaniens en transition

Urban boundary-layer flows in complex terrain: Dynamic interactions during a hot and dry summer season in Phoenix, Arizona

Spatial Modeling for Building Design Evaluation: from Visual Landscape Quality Assessment to Devaluation Risk Estimation

Extensions of Peer Prediction Incentive Mechanisms

Vers un projet territorial du vivant L'outil des réseaux écologiques comme projet urbanistique de revitalisation du paysage agricole

Using automated design appraisal to model building-specific devaluation risk due to land-use change

High-Throughput and Flexible Belief Propagation List Decoder for Polar Codes

Planning urban proximities: An empirical analysis of how residential preferences conflict with the urban morphologies and residential practices

Resolving the vicinity of supermassive black holes with gravitational microlensing

Equivariant Neural Architectures for Representing and Generating Graphs

A full characterization of invariant embeddability of unimodular planar graphs

Maximum Independent Set: Self-Training through Dynamic Programming