The effectiveness of Spatio-temporal Graph Neural Networks (STGNNs) in time-series applications is often limited by their dependence on fixed, hand-crafted input graph structures. Motivated by insights from the Topological Data Analysis (TDA) paradigm, of which real-world data exhibits multi-scale patterns, we construct several graphs using Persistent Homology Filtration -- a mathematical framework describing the multiscale structural properties of data points. Then, we use the constructed graphs as an input to create an ensemble of Graph Neural Networks. The ensemble aggregates the signals from the individual learners via an attention-based routing mechanism, thus systematically encoding the inherent multiscale structures of data. Four different real-world experiments on seismic activity prediction and traffic forecasting (PEMS-BAY, METR-LA) demonstrate that our approach consistently outperforms single-graph baselines while providing interpretable insights.

Survival analysis is a valuable tool for estimating the time until specific events, such as death or cancer recurrence, based on baseline observations. This is particularly useful in healthcare to prognostically predict clinically important events based on patient data. However, existing approaches often have limitations; some focus only on ranking patients by survivability, neglecting to estimate the actual event time, while others treat the problem as a classification task, ignoring the inherent time-ordered structure of the events. Furthermore, the effective utilization of censored samples - training data points where the exact event time is unknown - is essential for improving the predictive accuracy of the model. In this paper, we introduce CenTime, a novel approach to survival analysis that directly estimates the time to event. Our method features an innovative event-conditional censoring mechanism that performs robustly even when uncensored data is scarce. We demonstrate that our approach forms a consistent estimator for the event model parameters, even in the absence of uncensored data. Furthermore, CenTime is easily integrated with deep learning models with no restrictions on batch size or the number of uncensored samples. We compare our approach with standard survival analysis methods, including the Cox proportional-hazard model and DeepHit. Our results indicate that CenTime offers state-of-the-art performance in predicting time-to-death while maintaining comparable ranking performance. Our implementation is publicly available at https://github.com/ahmedhshahin/CenTime.

We introduce the concept of community trees that summarizes topological structures within a network. A community tree is a tree structure representing clique communities from the clique percolation method (CPM). The community tree also generates a persistent diagram. Community trees and persistent diagrams reveal topological structures of the underlying networks and can be used as visualization tools. We study the stability of community trees and derive a quantity called the total star number (TSN) that presents an upper bound on the change of community trees. Our findings provide a topological interpretation for the stability of communities generated by the CPM.

We propose a new Bayesian tracking and parameter learning algorithm for non-linear non-Gaussian multiple target tracking (MTT) models. We design a Markov chain Monte Carlo (MCMC) algorithm to sample from the posterior distribution of the target states, birth and death times, and association of observations to targets, which constitutes the solution to the tracking problem, as well as the model parameters. In the numerical section, we present performance comparisons with several competing techniques and demonstrate significant performance improvements in all cases.