Developing mathematical models to understand and influence complex phenomena in social and biological networks

My first research focus lies in the area of rumour source detection in social networks. In this context, I aim to address a range of open issues, in order to provide more realistic results compared to the current state-of-the-art. In particular, the first open issue proposed is the identification of sources in the context of unknown rumour start time. The second open issue is the design of an efficient multi-source estimation method. Third, the spreading of information occurs over multiple social networks in the real world. Therefore, there is an open issue of finding the rumour origin in interconnected networks. In order to address these challenges, I aim to develop accurate mathematical models of information propagation in a network. Moreover, I plan to incorporate these models into efficient and scalable algorithms, which represents an important practical aspect for fast culprit identification in large-scale networks.
My second research objective focuses on the theory and techniques that estimate the hidden underlying structure of information propagation, from the temporal traces that this diffusion generates. In particular, I am interested in the analysis and interpretation of neuronal signals obtained from two-photon imaging of calcium ion concentration, in order to develop methods for brain topology inference.
My third research interest lies in the area of spike-based sensing and processing. In particular, I would like to understand the encoding mechanism of a neuron, which transforms input stimulus signals into a sequence of spikes. This could shed further light on the behaviour of a biological neural circuit, and its analysis could provide functional characterization of information processing within the brain. This motivates the question of whether it is possible to reconstruct original signals, from their encoded sequence of time events. Therefore, the open issue I would like to address is whether the time encoding mechanism is invertible, and which conditions guarantee perfect reconstruction of the original signal from its spike train representation.

These research topics could be of interest in various real-world applications. Mathematical models of information dissipation over digital networks could help identify the reliability of information that propagates through social media. Developing methods that accurately infer the brain topology could revolutionize medical diagnosis of neuronal disease, inspire new machine learning algorithms, and revolutionize areas such as visual identification. Furthermore, understanding the neuronal encoding and decoding of information could shed light on how neural circuits perform computations, which is one of the most challenging open problems in neuroscience.

Finally yet importantly, my research interest aligns with the following EPSRC research areas. First, my research focuses on probabilistic modelling and inference in stochastic systems such as social and biological neuronal networks, hence being relevant in the area of Statistics and applied probability. Furthermore, through the development of theory in the area of non-uniform sampling and algorithms for processing event-driven data, my research is included in the area of Digital Signal Processing. Lastly, my research falls under the broad theme of Complexity science, through the development of mathematical formulae that model complex behaviours, such as spreading of rumours in a social network, and the diffusion of action potentials in a neuronal network.