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

开发数学模型来理解和影响社会和生物网络中的复杂现象

• 批准号: 2029304
• 金额: --
• 依托单位: Imperial College London
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2017
• 资助国家: 英国
• 起止时间: 2017 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2029304
• 关键词: Developing; mathematical; models; understand; influence

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.

本文的第一个研究方向是社交网络中的谣言源检测。在这种情况下，我的目标是解决一系列开放的问题，以提供更现实的结果相比，目前的国家的最先进的。特别是，第一个开放的问题提出的是在未知的谣言开始时间的背景下，来源的识别。第二个开放的问题是一个有效的多源估计方法的设计。第三，信息的传播发生在真实的世界中的多个社交网络上。因此，在互联网络中找到谣言的起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精确数学模型。此外，我计划将这些模型纳入高效和可扩展的算法，这是一个重要的实用方面，快速罪犯识别在大规模network.My第二个研究目标的理论和技术，估计隐藏的底层结构的信息传播，从这种扩散产生的时间痕迹。特别是，我感兴趣的是从钙离子浓度的双光子成像获得的神经元信号的分析和解释，以开发脑拓扑推断的方法。我的第三个研究兴趣在于基于尖峰的感知和处理领域。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化为一系列尖峰信号。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。这激发了一个问题，即是否有可能从它们的编码时间事件序列中重建原始信号。因此，我想解决的开放性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完美重建原始信号。这些研究课题可能在各种现实世界的应用中感兴趣。数字网络上信息传播的数学模型可以帮助确定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结构的方法可以彻底改变神经元疾病的医学诊断，激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回路如何执行计算，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，我的研究兴趣与以下EPSRC研究领域保持一致。首先，我的研究重点是随机系统（如社会和生物神经网络）中的概率建模和推理，因此与统计学和应用概率领域相关。此外，通过在非均匀采样和处理事件驱动数据的算法领域的理论发展，我的研究被包括在数字信号处理领域。最后，我的研究福尔斯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，例如社交网络中的谣言传播，以及神经网络中动作电位的扩散。

项目成果

Reconstructing Classes of Non-Bandlimited Signals From Time Encoded Information

从时间编码信息重建非带限信号类

• DOI: 10.1109/tsp.2019.2961301
• 发表时间: 2020
• 期刊: IEEE Transactions on Signal Processing
• 影响因子: 5.4
• 作者: Alexandru R

Rumour Source Detection in Social Networks using Partial Observations

• DOI: 10.1109/globalsip.2018.8646695
• 发表时间: 2018-11
• 期刊: 2018 IEEE Global Conference on Signal and Information Processing (GlobalSIP)
• 作者: Roxana Alexandru;P. Dragotti

Time-based Sampling and Reconstruction of Non-bandlimited Signals

非带限信号的基于时间的采样和重构

• DOI: 10.1109/icassp.2019.8682626
• 发表时间: 2019
• 作者: Alexandru R

Estimating the Topology of Neural Networks from Distributed Observations

根据分布式观测估计神经网络的拓扑

• DOI: 10.23919/eusipco.2018.8553016
• 发表时间: 2018
• 作者: Alexandru R