50 citations · 330 across the 31 of their papers we have counts for
37 papers
Graph-theoretic design of lasing networks for physical vision
Paul Obernolte, Jakub Dranczewski, Yixiu Yin +10
Physical neural networks perform learning through the intrinsic nonlinear dynamics of matter. Optimising their design presents a considerable challenge: complex many-body physics c…
A unified framework for Simplicial Kuramoto models
Marco Nurisso, Alexis Arnaudon, Maxime Lucas +4
Simplicial Kuramoto models have emerged as a diverse and intriguing class of models describing oscillators on simplices rather than nodes. In this paper, we present a unified frame…
Interpretable statistical representations of neural population dynamics and geometry
Adam Gosztolai, Robert L. Peach, Alexis Arnaudon +2
The dynamics of neuron populations commonly evolve on low-dimensional manifolds. Thus, we need methods that learn the dynamical processes over neural manifolds to infer interpretab…
PyGenStability: Multiscale community detection with generalized Markov Stability
Alexis Arnaudon, Juni Schindler, Robert L. Peach +4
We present PyGenStability, a general-use Python software package that provides a suite of analysis and visualisation tools for unsupervised multiscale community detection in graphs…
Sensitivity and spectral control of network lasers
Dhruv Saxena, Alexis Arnaudon, Oscar Cipolato +7
Recently, random lasing in complex networks has shown efficient lasing over more than 50 localised modes, promoted by multiple scattering over the underlying graph. If controlled,…
Connecting Hodge and Sakaguchi-Kuramoto: a mathematical framework for coupled oscillators on simplicial complexes
Alexis Arnaudon, Robert L. Peach, Giovanni Petri +1
We formulate a general Kuramoto model on weighted simplicial complexes where phases oscillators are supported on simplices of any order . Crucially, we introduce linear and non-…
Moment evolution equations and moment matching for stochastic image EPDiff
Alexander Christgau, Alexis Arnaudon, Stefan Sommer
Models of stochastic image deformation allow study of time-continuous stochastic effects transforming images by deforming the image domain. Applications include longitudinal medica…
Unfolding the multiscale structure of networks with dynamical Ollivier-Ricci curvature
Adam Gosztolai, Alexis Arnaudon
Describing networks geometrically through low-dimensional latent metric spaces has helped design efficient learning algorithms, unveil network symmetries and study dynamical networ…
Relative, local and global dimension in complex networks
Robert L. Peach, Alexis Arnaudon, Mauricio Barahona
Dimension is a fundamental property of objects and the space in which they are embedded. Yet ideal notions of dimension, as in Euclidean spaces, do not always translate to physical…
A Unifying and Canonical Description of Measure-Preserving Diffusions
Alessandro Barp, So Takao, Michael Betancourt +2
A complete recipe of measure-preserving diffusions in Euclidean space was recently derived unifying several MCMC algorithms into a single framework. In this paper, we develop a geo…
Diffusion bridges for stochastic Hamiltonian systems and shape evolutions
Alexis Arnaudon, Frank van der Meulen, Moritz Schauer +1
Stochastically evolving geometric systems are studied in shape analysis and computational anatomy for modelling random evolutions of human organ shapes. The notion of geodesic path…
Semi-supervised classification on graphs using explicit diffusion dynamics
Robert L. Peach, Alexis Arnaudon, Mauricio Barahona
Classification tasks based on feature vectors can be significantly improved by including within deep learning a graph that summarises pairwise relationships between the samples. In…
Scale-dependent measure of network centrality from diffusion dynamics
Alexis Arnaudon, Robert L. Peach, Mauricio Barahona
Classic measures of graph centrality capture distinct aspects of node importance, from the local (e.g., degree) to the global (e.g., closeness). Here we exploit the connection betw…
Irreversible Langevin MCMC on Lie Groups
Alexis Arnaudon, Alessandro Barp, So Takao
It is well-known that irreversible MCMC algorithms converge faster to their stationary distributions than reversible ones. Using the special geometric structure of Lie groups $\mat…
Selective metamorphosis for growth modelling with applications to landmarks
Andreas Bock, Alexis Arnaudon, Colin Cotter
We present a framework for shape matching in computational anatomy allowing users control of the degree to which the matching is diffeomorphic. This control is given as a function…
Stochastic Image Deformation in Frequency Domain and Parameter Estimation using Moment Evolutions
Line Kühnel, Alexis Arnaudon, Tom Fletcher +1
Modelling deformation of anatomical objects observed in medical images can help describe disease progression patterns and variations in anatomy across populations. We apply a stoch…
Engineering solitons and breathers in a deformed ferromagnet: Effect of localised inhomogeneities
Manickam Saravanan, Alexis Arnaudon
We investigate the soliton dynamics of the electromagnetic wave propagating in an inhomogeneous or deformed ferromagnet. The dynamics of magnetization and the propagation of electr…
String Methods for Stochastic Image and Shape Matching
Alexis Arnaudon, Darryl Holm, Stefan Sommer
Matching of images and analysis of shape differences is traditionally pursued by energy minimization of paths of deformations acting to match the shape objects. In the Large Deform…
Networks of Coadjoint Orbits: from Geometric to Statistical Mechanics
Alexis Arnaudon, So Takao
A class of network models with symmetry group that evolve as a Lie-Poisson system is derived from the framework of geometric mechanics, which generalises the classical Heisenbe…
Structure preserving noise and dissipation in the Toda lattice
Alexis Arnaudon
In this paper, we use Flaschka's change of variables of the open Toda lattice and its interpretation in term of the group structure of the LU factorisation as a coadjoint motion on…
Contractions of group representations via geometric quantisation
Rauan Akylzhanov, Alexis Arnaudon
We propose a general framework to contract unitary dual of Lie groups via holomorphic quantization of their co-adjoint orbits. The sufficient condition for the contractability of a…
Differential geometry and stochastic dynamics with deep learning numerics
Line Kühnel, Alexis Arnaudon, Stefan Sommer
In this paper, we demonstrate how deterministic and stochastic dynamics on manifolds, as well as differential geometric constructions can be implemented concisely and efficiently u…
Stochastic metamorphosis with template uncertainties
Alexis Arnaudon, Darryl Holm, Stefan Sommer
In this paper, we investigate two stochastic perturbations of the metamorphosis equations of image analysis, in the geometrical context of the Euler-Poincaré theory. In the metamor…
Bridge Simulation and Metric Estimation on Landmark Manifolds
Stefan Sommer, Alexis Arnaudon, Line Kuhnel +1
We present an inference algorithm and connected Monte Carlo based estimation procedures for metric estimation from landmark configurations distributed according to the transition d…