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

我的第一个研究重点是社交网络中的谣言来源检测领域。在这方面，我的目标是解决一系列悬而未决的问题，以便提供与当前最先进的技术相比更现实的结果。特别是，提出的第一个未决问题是在谣言开始时间未知的情况下确定消息来源。第二个悬而未决的问题是设计一种有效的多源估计方法。第三，在现实世界中，信息的传播发生在多个社交网络上。因此，在互联网络中寻找谣言来源是一个悬而未决的问题。为了应对这些挑战，我的目标是开发网络中信息传播的准确数学模型。此外，我计划将这些模型整合到高效和可扩展的算法中，这是在大规模网络中快速识别罪魁祸首的一个重要实用方面。我的第二个研究目标集中在从这种扩散产生的时间痕迹估计信息传播的隐藏底层结构的理论和技术上。特别是，我对从钙离子浓度的双光子成像中获得的神经元信号的分析和解释感兴趣，以便开发出大脑拓扑推断的方法。我的第三个研究兴趣在于基于脉冲的传感和处理领域。特别是，我想了解神经元的编码机制，它将输入的刺激信号转换为一系列尖峰信号。这可以进一步阐明生物神经回路的行为，其分析可以提供大脑内信息处理的功能特征。这引发了一个问题，即是否有可能从编码的时间事件序列中重建原始信号。因此，我想要解决的公开问题是时间编码机制是否可逆，以及哪些条件保证从其尖峰序列表示中完美地重建原始信号。这些研究课题可能在各种现实世界的应用中感兴趣。数字网络上信息耗散的数学模型可以帮助识别通过社交媒体传播的信息的可靠性。开发准确推断大脑拓扑的方法可能会彻底改变对神经元疾病的医学诊断，启发新的机器学习算法，并彻底改变视觉识别等领域。此外，了解神经元对信息的编码和解码可以揭示神经电路如何执行计算，这是神经科学中最具挑战性的开放问题之一。最后，重要的是，我的研究兴趣与EPSRC的以下研究领域一致。首先，我的研究集中在社会和生物神经网络等随机系统中的概率建模和推理，因此与统计和应用概率领域相关。此外，通过非均匀采样理论和事件驱动数据处理算法的发展，我的研究也进入了数字信号处理领域。最后，我的研究属于复杂性科学的广泛主题，通过开发数学公式来模拟复杂行为，例如谣言在社交网络中的传播，以及动作电位在神经网络中的扩散。

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.