arXiv subjects

Eugene Tan

Publications and source records attributed to Eugene Tan.

4 recordsLinked to original sources

arXiv2026

Dynamics, Complexity and Time Series Analysis

The aim of this text is to provide a linguistically accessible, but comprehensive introduction into a variety of topics in dynamical systems and its applications. Whilst preliminary knowledge of dynamical systems is useful, it is not essential and readers are only assumed to have familiarity with foundational undergraduate mathematics topics of calculus, linear algebra and rudimentary statistics. A variety of extended topics on recent publications and research activities in the field have been included in the last four chapters, which the interested reader may use as an introduction into further reading. A collection of exercises and questions both theoretical and computational are also included in this text.

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arXiv2025

Do triangles matter? Replicating hypergraph disease dynamics with lower-order interactions

Disease spreading models such as the ubiquitous SIS compartmental model and its numerous variants are widely used to understand and predict the behaviour of a given epidemic or information diffusion process. A common approach to imbue more realism to the spreading process is to constrain simulations to a network structure, where connected nodes update their disease state based on pairwise interactions along the edges of their local neighbourhood. Simplicial contagion models (SCM) extend this to hypergraphs such that groups of three nodes are able to interact and propagate the disease along higher-order hyperedges (triangles). Though more flexible, it is not clear the extent to which the inclusion of these higher-order interactions result in dynamics that are characteristically different to those attained from simpler pairwise interactions. Here, we propose an agent-based model that unifies the classical SIS/SIR compartmental model and SCM, and extends it to allow for interactions along hyperedges of arbitrary order. Using this model, we demonstrate how the steady-state dynamics of pairwise interactions can be made to replicate those of simulations that include higher-order topologies by linearly scaling disease parameters based on a proposed measure of network activity. By allowing disease parameters to dynamically vary over time, lower-order pairwise interactions can be made to closely replicate both the transient and steady-state dynamics of higher-order simulations. We demonstrate that this relationship is robust to misspecification in the assumed higher-order interaction model, and applies to non-clique complex hypergraphs with non-trivial heterogeneous topology. For the latter case, it is found that heterogeneities in hypergraph topology result in weakened approximations of higher-order dynamics by pairwise interactions.

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arXiv2023

Selecting embedding delays: An overview of embedding techniques and a new method using persistent homology

Delay embedding methods are a staple tool in the field of time series analysis and prediction. However, the selection of embedding parameters can have a big impact on the resulting analysis. This has led to the creation of a large number of methods to optimise the selection of parameters such as embedding lag. This paper aims to provide a comprehensive overview of the fundamentals of embedding theory for readers who are new to the subject. We outline a collection of existing methods for selecting embedding lag in both uniform and non-uniform delay embedding cases. Highlighting the poor dynamical explainability of existing methods of selecting non-uniform lags, we provide an alternative method of selecting embedding lags that includes a mixture of both dynamical and topological arguments. The proposed method, {\em Significant Times on Persistent Strands} (SToPS), uses persistent homology to construct a characteristic time spectrum that quantifies the relative dynamical significance of each time lag. We test our method on periodic, chaotic and fast-slow time series and find that our method performs similar to existing automated non-uniform embedding methods. Additionally, $n$-step predictors trained on embeddings constructed with SToPS was found to outperform other embedding methods when predicting fast-slow time series.

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arXiv2022

Backpropagation on Dynamical Networks

Dynamical networks are versatile models that can describe a variety of behaviours such as synchronisation and feedback. However, applying these models in real world contexts is difficult as prior information pertaining to the connectivity structure or local dynamics is often unknown and must be inferred from time series observations of network states. Additionally, the influence of coupling interactions between nodes further complicates the isolation of local node dynamics. Given the architectural similarities between dynamical networks and recurrent neural networks (RNN), we propose a network inference method based on the backpropagation through time (BPTT) algorithm commonly used to train recurrent neural networks. This method aims to simultaneously infer both the connectivity structure and local node dynamics purely from observation of node states. An approximation of local node dynamics is first constructed using a neural network. This is alternated with an adapted BPTT algorithm to regress corresponding network weights by minimising prediction errors of the dynamical network based on the previously constructed local models until convergence is achieved. This method was found to be succesful in identifying the connectivity structure for coupled networks of Lorenz, Chua and FitzHugh-Nagumo oscillators. Freerun prediction performance with the resulting local models and weights was found to be comparable to the true system with noisy initial conditions. The method is also extended to non-conventional network couplings such as asymmetric negative coupling.

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