Contagion Source Detection in Epidemic and Infodemic Outbreaks: Mathematical Analysis and Network Algorithms

This monograph provides an overview of the mathematical theories and computational algorithm design for contagion source detection in large networks. By leveraging network centrality as a tool for statistical inference, we can accurately identify the source of contagions, trace their spread, and predict future trajectories. This approach provides fundamental insights into surveillance capability and asymptotic behavior of contagion spreading in networks. Mathematical theory and computational algorithms are vital to understanding contagion dynamics, improving surveillance capabilities, and developing effective strategies to prevent the spread of infectious diseases and misinformation.Comment: Suggested Citation: Chee Wei Tan and Pei-Duo Yu (2023), "Contagion Source Detection in Epidemic and Infodemic Outbreaks: Mathematical Analysis and Network Algorithms", Foundations and Trends in Networking: Vol. 13: No. 2-3, pp 107-251. http://dx.doi.org/10.1561/130000006

Rank-preserving geometric means of positive semi-definite matrices

The generalization of the geometric mean of positive scalars to positive definite matrices has attracted considerable attention since the seminal work of Ando. The paper generalizes this framework of matrix means by proposing the definition of a rank-preserving mean for two or an arbitrary number of positive semi-definite matrices of fixed rank. The proposed mean is shown to be geometric in that it satisfies all the expected properties of a rank-preserving geometric mean. The work is motivated by operations on low-rank approximations of positive definite matrices in high-dimensional spaces.Comment: To appear in Linear Algebra and its Application

Exploring the spectroscopic diversity of type Ia supernovae with DRACULA: a machine learning approach

The existence of multiple subclasses of type Ia supernovae (SNeIa) has been the subject of great debate in the last decade. One major challenge inevitably met when trying to infer the existence of one or more subclasses is the time consuming, and subjective, process of subclass definition. In this work, we show how machine learning tools facilitate identification of subtypes of SNeIa through the establishment of a hierarchical group structure in the continuous space of spectral diversity formed by these objects. Using Deep Learning, we were capable of performing such identification in a 4 dimensional feature space (+1 for time evolution), while the standard Principal Component Analysis barely achieves similar results using 15 principal components. This is evidence that the progenitor system and the explosion mechanism can be described by a small number of initial physical parameters. As a proof of concept, we show that our results are in close agreement with a previously suggested classification scheme and that our proposed method can grasp the main spectral features behind the definition of such subtypes. This allows the confirmation of the velocity of lines as a first order effect in the determination of SNIa subtypes, followed by 91bg-like events. Given the expected data deluge in the forthcoming years, our proposed approach is essential to allow a quick and statistically coherent identification of SNeIa subtypes (and outliers). All tools used in this work were made publicly available in the Python package Dimensionality Reduction And Clustering for Unsupervised Learning in Astronomy (DRACULA) and can be found within COINtoolbox (https://github.com/COINtoolbox/DRACULA).Comment: 16 pages, 12 figures, accepted for publication in MNRA