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Superspreading events represent a critical aspect of infectious disease transmission, where a small number of individuals are responsible for a large number of secondary infections. These events are particularly evident in respiratory infections such as COVID-19, SARS, and measles.

In our latest research, we have developed a branching model based on mobility networks. This model provides insights into the spatial and temporal aspects of disease spread. A key finding is that superspreading contributes significantly to the rapid spatial expansion of disease in the initial stages of an outbreak.

Additionally, we have integrated Graphical Neural Networks to estimate the dispersion rate, shedding light on the heterogeneous nature of disease transmission.

This groundbreaking work is a collaborative effort with Chester Tan from the Center for Artificial Intelligence and Data Science (CAIDAS) at Julius-Maximilians-Universität Würzburg. Together, we aim to deepen the understanding of disease dynamics and contribute to more effective outbreak management strategies.

Networks and community structures permeate every facet of our lives, from biological, ecological, communication, information, financial, and even social networks. These systems have underlying architectures that can be quantified, even when they become exponentially larger and more complex. We have devised measurements for shareholder investment networks through the mapping of common interests between these individuals.

Within the financial world, network science can be applied to examine the relationships between shareholders and the subsequent impact on their investing behaviour in different business sectors. Each individual company within this system is denoted as a node. This allows for the ability to model associations between individuals. The work ‘How the network properties of shareholders vary with investor type and country’ is published in PLOS ONE. This work is inspired by my past working experience with DealGlobe Ltd, a platform/FA for cross-border M&A.

Ruiqi Li at Beijing University of Chemical Technology and I are investigating the venture capital markets in China. Our research is about the relationships between network effects and specialisation in the investment stage and industry.

We have applied the gravity model to study human movement patterns when using shared bicycles in Beijing and Shanghai. Our work ‘Gravity model in dockless bike-sharing systems within cities‘ is published in PRE. We have collaborating on the VC networks in China, in the work ‘Syndication network associates with specialisation and performance of venture capital firms’ we published with Journal of Physics: Complexity, we innovatively adapted Moran’s I measurements in conjunction with network metrics. Specifically, we substituted the conventional distance measurement in Moran’s I with the path length between nodes in the network.

This approach allows for the understanding of ‘spatial’ relationships and interconnectedness within the VC landscape. By integrating these measurements, we aim to provide deeper insights into the dynamics of venture capital networks in China. We are also working with Wanru Jing, the director from elink-vc in Shanghai, China

Mengqiu Cao at the University of Westminster and I have studied the spatial distribution of Covid-19 impacts. The work titled ‘Development of a composite regional vulnerability index and its relationship with the impacts of the COVID-19 pandemic‘ is about to appear on Computational Urban Science.

We introduce a ‘rewiring based on random walk on directed graph’ model (RRWD) on shareholder investment networks, to augment traditional random walk models. The team applied their model to a directed graph, wherein the edges in a network have direction, and then projected it onto an unordered, undirected graph.

A conventional random walk on a graph is traditionally applied to portray the approach utilised by individuals to seek new connections within a network.

The issue with this standard approach is that it omits the true nature of dynamic systems - ignoring the various combinations of interactions and possibilities between the relationship of Nodes A, B and C. ‘It is a more realistic picture of the real world: not everyone connects to everyone,’

The article is now in the arXiv.

Random walk theory reinforces the sporadic nature of information and relationships flowing through these networks. Rewiring edges through random walk models to imitate real-life situations as dynamic entities allows for a greater understanding of the complex systems in which we operate.

Attempting to comprehend the shared behaviour of a complex system is something that cannot be viewed as separate from the system to which it belongs. For instance, an individual cannot be viewed separately from the society in which they reside; we are inextricable from our environment. The same methodology applies to understanding dynamic systems, as they are very rarely static in nature. As such, dynamic systems can be defined as the temporal evolution of networks.

We examined the effects of interactions within dynamic systems by observing three-node dynamics (A – B – C) through the use of a transition matrix. They demonstrated that such ‘higher-order’ interactions are necessary in comprehending the evolution of networks, as displayed in an application to an Email Network with an EU institution, which highlighted that if three nodes were linked in an earlier temporal snapshot, they possess a smaller chance of being disconnected in the subsequent snapshot.  

This logic reinforces the interconnectivity of nodes over time. By adopting a holistic, time-based model, we can capture the network characteristics using three-node dynamics.

The team’s work reinforces the fact that observing the development of small graphs over brief temporal segments can disclose vital information and can allow for network evolution extrapolation in the future. The breakdown of a larger period into smaller segments yields the ability to make comparisons of temporal snapshots and reduces the analytical and computational time required.  

This work is published in the Scientific Reports 'Higher-order temporal network effects through triplet evolution'. I worked closely with Bingsheng Chen for this project.

The higher-order interactions can be identified through our frame in the temporal data sets.

The day-to-day temperature difference is different but as important as the temperature itself. In a broader sense, it is a first-order derivation. Its nice scaling properties are universal. After collapsing, they do not depend on geometric positions, highlighting the universal underline mechanism, which can be explored furthermore.

Our study ‘Emergence of universal scaling in extreme weather events’ is in the preprints [arXiv:2209.02292]. Prof. Jingfang Fan, Prof. Lucarini Valerio, Prof. Kim Christensen, Prof. Henrik Jeldtoft Jensen, and Dr Jun Meng are working together on this project. We are now investigating the synchronisation of extreme events.

The synchrony phenomenon is widely observed in various systems, like nervous (e.g. the firing of the neurons), biological (e.g. synchronous flashing fireflies), social (e.g.the, the perception of social bonding) and etc. systems. A coupled oscillator system, a typical real non-equilibrium system, is an ideal and abstract model of interacting elements to model synchronisation. The Kuramoto model is one of the most profound and classical toy models of coupled phase oscillators. Although this model can successfully produce various synchrony phenomena, its phase transition analysis is limited to mean-field approximation, which is characterised by the order parameter. However, it is hard to define a single variable to represent the order for a real system where the Hamiltonian function is unknown, heterogeneity exists, and the states of each interacting component are available. To better understand the real-world synchronisation phenomenon without a well-defined order parameter, we apply the Eigen Microstate Method to revisit the globally coupled Kuramoto model, of which the calculation of mean-field approximation is valid. Therefore, after exploring the finite-size scaling near the onset of the phase transition, we can compare the scaling exponents of both methods.

I am also looking at the Kuramoto model on the networks with different coupling strengths between communities. This new setting will introduce the fruitful phase transition phenomenon: the explosive phase transition, asynchronisation with different communities.

The emergence of synchronisation through coupling dynamics creates orders. However, as an isolated system, how can the entropy, which describes the possible configurations, decrease?

The answer can be found in the information perspective, which implies that through interaction, mutual information or interdependency is created.

We generalise the global cascade condition of Watts Threshold Model to incorporate arbitrary seed size. For random network ensembles in the thermodynamic limit, the critical point of discontinuous transition is analytically characterised and the phase diagram plotted, distinguishing three regions of parameters where networks are "fragile", "quasi-robust" or "robust" against threshold cascades respectively. For single finite network including relevant empirical networks, a similar condition for threshold cascades to grow explosively from arbitrary seed size is established and the critical threshold criterion found numerically. Results from Monte Carlo simulations corroborate our theoretical predictions.  

One of my long-time interests is the study of causation. Currently, I have not done anything serious. I am always wondering what gives rise to the emergence of the directions of the systems, i.e., most of their evolution is irreversible.

The three main fields concern causal inference. The first one is from the physics community, which deals with the quantum physics and geometry of gravity. The noticing work is the causal set (another approach to studying quantum gravity). The node is the event in the context of the graph theory.

The second study stream is from statistics, which makes inferences for medical and social contexts. The Bayes network(Bayesian network) is widely used. Social network inference treats individuals as nodes.

The third is more from math/philosophy, studying the common principles which may apply to both streams mentioned before.