Damoon Soudbakhsh | Searcharxiv

arXiv2025

Longitudinal Omics Data Analysis: A Review on Models, Algorithms, and Tools

Longitudinal omics data (LOD) analysis is essential for understanding the dynamics of biological processes and disease progression over time. This review explores various statistical and computational approaches for analyzing such data, emphasizing their applications and limitations. The main characteristics of longitudinal data, such as imbalancedness, high-dimensionality, and non-Gaussianity are discussed for modeling and hypothesis testing. We discuss the properties of linear mixed models (LMM) and generalized linear mixed models (GLMM) as foundation stones in LOD analyses and highlight their extensions to handle the obstacles in the frequentist and Bayesian frameworks. We differentiate in dynamic data analysis between time-course and longitudinal analyses, covering functional data analysis (FDA) and replication constraints. We explore classification techniques, single-cell as exemplary omics longitudinal studies, survival modeling, and multivariate methods for clinical/biomarker-based applications. Emerging topics, including data integration, clustering, and network-based modeling, are also discussed. We categorized the state-of-the-art approaches applicable to omics data, highlighting how they address the data features. This review serves as a guideline for researchers seeking robust strategies to analyze longitudinal omics data effectively, which is usually complex.

stat.ME↗

arXiv2023

Probabilistic motion planning for non-Euclidean and multi-vehicle problems

Trajectory planning tasks for non-holonomic or collaborative systems are naturally modeled by state spaces with non-Euclidean metrics. However, existing proofs of convergence for sample-based motion planners only consider the setting of Euclidean state spaces. We resolve this issue by formulating a flexible framework and set of assumptions for which the widely-used PRM*, RRT, and RRT* algorithms remain asymptotically optimal in the non-Euclidean setting. The framework is compatible with collaborative trajectory planning: given a fleet of robotic systems that individually satisfy our assumptions, we show that the corresponding collaborative system again satisfies the assumptions and therefore has guaranteed convergence for the trajectory-finding methods. Our joint state space construction builds in a coupling parameter $1\leq p\leq \infty$, which interpolates between a preference for minimizing total energy at one extreme and a preference for minimizing the travel time at the opposite extreme. We illustrate our theory with trajectory planning for simple coupled systems, fleets of Reeds-Shepp vehicles, and a highly non-Euclidean fractal space.

cs.RO↗