Projects | Hanlin Sun

Applications of network theory

Wed, 01 Jan 2025 00:00:00 +0000

I apply network science tools to problems in statistical physics and quantum systems, and study novel percolation processes with non-local rules.

Statistical physics of networks

Using network-based measures and topological data analysis, I characterised phase transitions in the Ising model, revealing distinct network-science Ising states of matter. I also developed non-parametric learning approaches for critical behavior in Ising partition functions using PCA entropy and intrinsic dimension.

Quantum networks

I studied entanglement transmission in quantum networks, uncovering the importance of nonshortest paths — a finding that challenges conventional shortest-path-based analyses of quantum communication.

Non-local percolation

I investigated shortest-path percolation, a novel process where edges are removed in a spatially and temporally correlated fashion, and revealed markedly different critical behaviour on Erdős–Rényi and scale-free networks.

Unveiling the importance of nonshortest paths in quantum networks — Science Advances
Network science: Ising states of matter — Physical Review E
Non-parametric learning critical behavior in Ising partition functions: PCA entropy and intrinsic dimension — SciPost Physics Core
Shortest-path percolation on scale-free networks — Physical Review E

Higher-order network modelling

Sun, 01 Jan 2023 00:00:00 +0000

Higher-order networks — including hypergraphs, simplicial complexes, and networks with triadic interactions — encode the group interactions present in real-world complex systems. While percolation has been well studied on pairwise networks, little was known about how higher-order interactions affect critical phenomena. My work addresses this from several complementary angles.

Percolation on higher-order structures

On pseudofractal simplicial and cell complexes, I showed that percolation displays two distinct critical thresholds and an unusual critical exponent, in contrast to standard percolation on dyadic networks.

I introduced multiplex hypergraphs as a general framework to study percolation on higher-order structures, characterising how hyperedge organisation such as hyperedge correlation affects critical behaviour.

Networks with triadic interactions

I proposed a novel higher-order network model called networks with triadic interactions and developed a percolation theory on these structures, showing that triadic regulation can turn percolation into a fully dynamical process displaying periodic oscillations and chaos. I further extended this framework to spatial networks, random hypergraphs, and multilayer networks, and explored its implications for neuronal dynamics.

The dynamic nature of percolation on networks with triadic interactions — Nature Communications
Topology shapes dynamics of higher-order networks — Nature Physics
Triadic percolation induces dynamical topological patterns in higher-order networks — PNAS Nexus
Triadic percolation on multilayer networks — Physical Review E (Editors’ Suggestion)
Higher-order triadic percolation on random hypergraphs — Physical Review E
Spatio-temporal activity patterns induced by triadic interactions in an in silico neural medium — Journal of Physics: Complexity
Higher-order percolation processes on multiplex hypergraphs — Physical Review E
Renormalization group theory of percolation on pseudofractal simplicial and cell complexes — Physical Review E

Epidemic spreading modelling

Fri, 01 Jan 2021 00:00:00 +0000

I have developed several models for epidemic spreading that highlight how realistic mechanisms reshape classical epidemic wisdom.

Higher-order epidemic spreading

I proposed a hypergraph model for epidemic spreading that jointly captures the heterogeneity of infectious environments and individual participation. I showed that heterogeneous exposure and minimal infective dose induce a universal nonlinear infection kernel, leading to discontinuous transitions, super-exponential spread, and hysteresis.

Digital contact tracing

I analysed digital contact tracing and demonstrated a highly nonlinear relationship between app adoption and the epidemic threshold, providing one of the first theoretical assessments of app-based mitigation strategies.

Time-dependent branching processes

I studied the effect of time-dependent infectivity induced by containment measures in a stochastic branching-process framework, showing how temporal modulation and stochasticity jointly control critical exponents and offering an explanation for power-law growth regimes observed during COVID-19.

Universal Nonlinear Infection Kernel from Heterogeneous Exposure on Higher-Order Networks — Physical Review Letters
Message-passing approach to epidemic tracing and mitigation with apps — Physical Review Research
Critical time-dependent branching process modelling epidemic spreading with containment measures — Journal of Physics A

Inference and optimal control of network dynamics

Fri, 01 Jan 2021 00:00:00 +0000

Building on the dynamic message-passing (DMP) approach, I develop computationally efficient algorithms to predict and control spreading processes on complex networks.

Interacting spreading processes

I developed a DMP-based algorithm to predict the dynamics of multiple interacting (collaborative or competitive) spreading processes on sparse networks. The framework captures how coupled contagions reshape each other’s dynamics beyond what standard independent models can describe.

Optimal control under budget constraints

I further proposed an optimisation framework for the control of interacting spreading processes via resource allocation under realistic budget constraints and finite time horizons. The resulting algorithms can both enhance desirable diffusion (e.g., information or awareness campaigns) and suppress harmful spread (e.g., coupled epidemic strains), outperforming standard topology-based strategies for epidemic control.

Competition, Collaboration, and Optimization in Multiple Interacting Spreading Processes — Physical Review X

Projects | Hanlin Sun

Applications of network theory

Statistical physics of networks

Quantum networks

Non-local percolation

Related publications

Higher-order network modelling

Percolation on higher-order structures

Networks with triadic interactions

Related publications

Epidemic spreading modelling

Higher-order epidemic spreading

Digital contact tracing

Time-dependent branching processes

Related publications

Inference and optimal control of network dynamics

Interacting spreading processes

Optimal control under budget constraints

Related publications