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Diffusion in Networks: Source Localization, History Reconstruction and Real-Time Network Robustification

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Diffusion processes in networks can be used to model many real-world processes, such as the propagation of a rumor on social networks and cascading failures on power networks. Analysis of diffusion processes in networks can help us answer important questions

Diffusion processes in networks can be used to model many real-world processes, such as the propagation of a rumor on social networks and cascading failures on power networks. Analysis of diffusion processes in networks can help us answer important questions such as the role and the importance of each node in the network for spreading the diffusion and how to top or contain a cascading failure in the network. This dissertation consists of three parts.

In the first part, we study the problem of locating multiple diffusion sources in networks under the Susceptible-Infected-Recovered (SIR) model. Given a complete snapshot of the network, we developed a sample-path-based algorithm, named clustering and localization, and proved that for regular trees, the estimators produced by the proposed algorithm are within a constant distance from the real sources with a high probability. Then, we considered the case in which only a partial snapshot is observed and proposed a new algorithm, named Optimal-Jordan-Cover (OJC). The algorithm first extracts a subgraph using a candidate selection algorithm that selects source candidates based on the number of observed infected nodes in their neighborhoods. Then, in the extracted subgraph, OJC finds a set of nodes that "cover" all observed infected nodes with the minimum radius. The set of nodes is called the Jordan cover, and is regarded as the set of diffusion sources. We proved that OJC can locate all sources with probability one asymptotically with partial observations in the Erdos-Renyi (ER) random graph. Multiple experiments on different networks were done, which show our algorithms outperform others.

In the second part, we tackle the problem of reconstructing the diffusion history from partial observations. We formulated the diffusion history reconstruction problem as a maximum a posteriori (MAP) problem and proved the problem is NP hard. Then we proposed a step-by- step reconstruction algorithm, which can always produce a diffusion history that is consistent with the partial observations. Our experimental results based on synthetic and real networks show that the algorithm significantly outperforms some existing methods.

In the third part, we consider the problem of improving the robustness of an interdependent network by rewiring a small number of links during a cascading attack. We formulated the problem as a Markov decision process (MDP) problem. While the problem is NP-hard, we developed an effective and efficient algorithm, RealWire, to robustify the network and to mitigate the damage during the attack. Extensive experimental results show that our algorithm outperforms other algorithms on most of the robustness metrics.

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Date Created
2018

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Model Based Automatic and Robust Spike Sorting for Large Volumes of Multi-channel Extracellular Data

Description

Spike sorting is a critical step for single-unit-based analysis of neural activities extracellularly and simultaneously recorded using multi-channel electrodes. When dealing with recordings from very large numbers of neurons, existing methods, which are mostly semiautomatic in nature, become inadequate.

This dissertation

Spike sorting is a critical step for single-unit-based analysis of neural activities extracellularly and simultaneously recorded using multi-channel electrodes. When dealing with recordings from very large numbers of neurons, existing methods, which are mostly semiautomatic in nature, become inadequate.

This dissertation aims at automating the spike sorting process. A high performance, automatic and computationally efficient spike detection and clustering system, namely, the M-Sorter2 is presented. The M-Sorter2 employs the modified multiscale correlation of wavelet coefficients (MCWC) for neural spike detection. At the center of the proposed M-Sorter2 are two automatic spike clustering methods. They share a common hierarchical agglomerative modeling (HAM) model search procedure to strategically form a sequence of mixture models, and a new model selection criterion called difference of model evidence (DoME) to automatically determine the number of clusters. The M-Sorter2 employs two methods differing by how they perform clustering to infer model parameters: one uses robust variational Bayes (RVB) and the other uses robust Expectation-Maximization (REM) for Student’s 𝑡-mixture modeling. The M-Sorter2 is thus a significantly improved approach to sorting as an automatic procedure.

M-Sorter2 was evaluated and benchmarked with popular algorithms using simulated, artificial and real data with truth that are openly available to researchers. Simulated datasets with known statistical distributions were first used to illustrate how the clustering algorithms, namely REMHAM and RVBHAM, provide robust clustering results under commonly experienced performance degrading conditions, such as random initialization of parameters, high dimensionality of data, low signal-to-noise ratio (SNR), ambiguous clusters, and asymmetry in cluster sizes. For the artificial dataset from single-channel recordings, the proposed sorter outperformed Wave_Clus, Plexon’s Offline Sorter and Klusta in most of the comparison cases. For the real dataset from multi-channel electrodes, tetrodes and polytrodes, the proposed sorter outperformed all comparison algorithms in terms of false positive and false negative rates. The software package presented in this dissertation is available for open access.

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Date Created
2019