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

Related publications (30)

The 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 Inc2024

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

Lukas Fritz Felix Vogl

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 ...

Elsevier2024

Non-planarity of Markoff graphs mod p

Matthew De Courcy-Ireland

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 ...

European Mathematical Soc-Ems2024

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

Rom Pinchasi

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 Combinatorics2024

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

Nicolas Boumal

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 Publications2024

Towards an Understanding of Hydraulic Sensitivity: Graph Theory Contributions to Water Distribution Analysis

Jérôme Chenal

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 ...

MDPI2024

Graph generative deep learning models with an application to circuit topologies

Igor Krawczuk

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 ...

EPFL2024

Stochastic pairwise preference convergence in Bayesian agents

Max-Olivier Hongler

Beliefs inform the behaviour of forward-thinking agents in complex environments. Recently, sequential Bayesian inference has emerged as a mechanism to study belief formation among agents adapting to dynamical conditions. However, we lack critical theory to ...

2024

Social Opinion Formation and Decision Making Under Communication Trends

Ali H. Sayed, Virginia Bordignon, Mert Kayaalp

This work studies the learning process over social networks under partial and random information sharing. In traditional social learning models, agents exchange full belief information with each other while trying to infer the true state of nature. We stud ...

Ieee-Inst Electrical Electronics Engineers Inc2024

Acceleration of graph pattern mining and applications to financial crime

Jovan Blanusa

Various forms of real-world data, such as social, financial, and biological networks, can be represented using graphs. An efficient method of analysing this type of data is to extract subgraph patterns, such as cliques, cycles, and motifs, from graphs. For ...

EPFL2023

Discovering Influencers in Opinion Formation Over Social Graphs

Ali H. Sayed, Mert Kayaalp, Valentina Shumovskaia, Mert Cemri

The adaptive social learning paradigm helps model how networked agents are able to form opinions on a state of nature and track its drifts in a changing environment. In this framework, the agents repeatedly update their beliefs based on private observation ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2023

Equivariant Neural Architectures for Representing and Generating Graphs

Clément Arthur Yvon Vignac

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 ...

EPFL2023

A full characterization of invariant embeddability of unimodular planar graphs

Laszlo Marton Toth

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 ...

WILEY2023

Maximum Independent Set: Self-Training through Dynamic Programming

Volkan Cevher, Grigorios Chrysos, Efstratios Panteleimon Skoulakis

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 ...

2023

Novel Ordering-based Approaches for Causal Structure Learning in the Presence of Unobserved Variables

We propose ordering-based approaches for learning the maximal ancestral graph (MAG) of a structural equation model (SEM) up to its Markov equivalence class (MEC) in the presence of unobserved variables. Existing ordering-based methods in the literature rec ...

Association for the Advancement of Artificial Intelligence (AAAI)2023

Frequent asymmetric migrations suppress natural selection in spatially structured populations

Anne-Florence Raphaëlle Bitbol, Alia Abbara

Natural microbial populations often have complex spatial structures. This can impact their evolution, in particular the ability of mutants to take over. While mutant fixation probabilities are known to be unaffected by sufficiently symmetric structures, ev ...

Oxford Univ Press2023

Beyond Spectral Gap: The Role of the Topology in Decentralized Learning

Thijs Vogels, Hadrien Hendrikx, Martin Jaggi

In data-parallel optimization of machine learning models, workers collaborate to improve their estimates of the model: more accurate gradients allow them to use larger learning rates and optimize faster. In the decentralized setting, in which workers commu ...

Microtome Publishing2023

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

Dimitri Nestor Alice Van De Ville, Hamid Behjat, Maria Giulia Preti, Stefano Moia, Carlo Ferritto

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 ...

IEEE2023

Privatized graph federated learning

Ali H. Sayed, Stefan Vlaski, Elsa Rizk

Federated learning is a semi-distributed algorithm, where a server communicates with multiple dispersed clients to learn a global model. The federated architecture is not robust and is sensitive to communication and computational overloads due to its one-m ...

SPRINGER2023

Results on Sparse Integer Programming and Geometric Independent Sets

Jana Tabea Cslovjecsek

An integer linear program is a problem of the form max{c^T x : Ax=b, x >= 0, x integer}, where A is in Z^(n x m), b in Z^m, and c in Z^n. Solving an integer linear program is NP-hard in general, but there are several assumptions for which it becomes fixed ...

EPFL2023