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

Lead Research Organisation: Imperial College London
Department Name: Electrical and Electronic Engineering


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.

Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/N509486/1 01/10/2016 30/09/2021
2029304 Studentship EP/N509486/1 01/10/2017 30/06/2021 Roxana Irina Alexandru
Description In the area of information processing over graphs, we introduced mathematical models of infection, which capture the realistic temporal dynamics of information propagation and have shown how we can use these analytical infection likelihoods in efficient single-source detection algorithms. In the area of information processing in the brain, we presented an efficient method for estimating the topology of neuronal networks. We have also studied the problem of time encoding and decoding, using the integrate-and-fire mechanism of neurons in the brain. In particular, we derived sufficient conditions which guarantee many classes of non-bandlimited signals can be perfectly retrieved from their spike train representations.
Exploitation Route Inferring the source responsible for spreading of data within a social network could help determine the individuals who set trends and who successfully spread rumours. Similarly, other important applications are the inference of the causes of cascading failures in large systems such as financial markets or sensor networks, the contaminant in a water distribution network, the leader of a spy or political network, or the origin of infectious disease.

Sampling inspired by the brain could lead to very simple and highly efficient devices, ranging from analog to digital converters, to neuromorphic computing or event-based vision sensors, which record only changes in the input intensity, leading to low power consumption and fewer storage requirements. Beyond that, the study of time encoding and decoding may bring us closer to understanding the neural language, which is one of the most important open problems in computational neuroscience.
Sectors Aerospace, Defence and Marine,Digital/Communication/Information Technologies (including Software),Electronics,Manufacturing, including Industrial Biotechology,Other