arXiv subjects

James Noonan

Publications and source records attributed to James Noonan.

3 recordsLinked to original sources

arXiv2021

Dynamics of Majority Rule on Hypergraphs

A broad range of dynamical systems involve multi-body interactions, or group interactions, which may not be encoded in traditional graphical structures. In this work, we focus on a canonical example from opinion dynamics, the Majority Rule, and investigate the possibility to represent and analyse the system by means of hypergraphs. We explore the formation of consensus and restrict our attention to interaction groups of size $3$, in order to simplify our analysis from a combinatorial perspective. We propose different types of hypergraph models, incorporating modular structure or degree heterogeneity, and recast the dynamics in terms of Fokker-Planck equations, which allows us to predict the transient dynamics toward consensus. Numerical simulations show a very good agreement between the stochastic dynamics and theoretical predictions for large population sizes.

physics.soc-ph↗

arXiv2020

Interpretable Neuron Structuring with Graph Spectral Regularization

While neural networks are powerful approximators used to classify or embed data into lower dimensional spaces, they are often regarded as black boxes with uninterpretable features. Here we propose Graph Spectral Regularization for making hidden layers more interpretable without significantly impacting performance on the primary task. Taking inspiration from spatial organization and localization of neuron activations in biological networks, we use a graph Laplacian penalty to structure the activations within a layer. This penalty encourages activations to be smooth either on a predetermined graph or on a feature-space graph learned from the data via co-activations of a hidden layer of the neural network. We show numerous uses for this additional structure including cluster indication and visualization in biological and image data sets.

cs.LG↗

arXiv2018

On electromagnetic surface waves supported by an isotropic chiral material

Electromagnetic surface waves supported by an isotropic chiral material were investigated via the associated canonical boundary-value problem. Specifically, two scenarios were considered: surface waves guided by the planar interface of an isotropic chiral material and (a) an isotropic dielectric material and (b) a uniaxial dielectric (or plasmonic) material. Both plasmonic and non-plasmonic achiral partnering materials were investigated. In scenario (a) surface waves akin to surface-plasmon-polariton (SPP) waves were excited, while in scenario (b) surface waves akin to Dyakonov waves and akin to SPP waves were excited. For numerical studies, an isotropic chiral material capable of simultaneously supporting attenuation and amplification of plane waves, depending upon circular polarization state, was used. The amplitude of the SPP-like waves could be either amplified or attenuated, depending upon the relative permittivity of the isotropic dielectric partnering material for scenario (a), or depending upon the direction of propagation relative to the optic axis of the uniaxial dielectric partnering material for scenario (b).

physics.optics↗