[School of Natural Sciences PhD Scholarships] Higher‑Order Tensor Compression for Spatio-Temporal Data

About the project

About the Project Dynamic multilayer networks—such as communication systems, financial transaction streams, and international relations—exhibit complex dependencies across dyads, relational layers, and time. These systems rarely follow simple temporal decay patterns or low dimensional relational structures, yet most existing statistical network models assume fixed decay parameters and rely on hand crafted covariates that struggle to capture the richness of temporal–relational interactions. This project proposes an integrated methodological framework to address these limitations by advancing tensor compression theory, developing flexible temporal decay models, and building empirical infrastructure for multilayer event analysis. The first component of the research develops a new class of higher order tensor compression methods tailored to network tensors indexed by sender, receiver, relation, and time. Recent advances in spatio temporal modelling demonstrate that random matrix theory can effectively separate meaningful structure from noise in high dimensional data. However, these techniques have not yet been extended to tensors with four or more modes, which are central to multilayer network analysis. This project will generalise these methods by establishing random matrix asymptotics for higher order structures and designing efficient algorithms for tensor unfolding, spectral decomposition, and noise separation. The resulting compressed signals will provide dynamically evolving, low rank representations of latent temporal–relational structure. The second component introduces statistical models capable of estimating heterogeneous temporal decay within relational event models (REMs) and temporal exponential random graph models (TERGMs). Instead of imposing fixed decay parameters, the proposed framework allows decay rates to vary across mechanisms, layers, and units, reflecting the empirical reality that different types of interactions decay at different speeds. Integrating compressed tensor signals as covariates further enables these models to capture latent dependencies that are inaccessible to conventional features. Together, these innovations aim to improve model fit, interpretability, and predictive performance in dynamic network settings. A third component of the project focuses on empirical infrastructure. To support methodological development and facilitate future research, the project will assemble a validated, openly accessible multilayer event database capturing contemporary patterns of conflict, competition, and cooperation. Using natural language processing pipelines with manual training and validation, the database will provide high quality temporal multilayer data for testing the proposed models and for broader use in the research community. The expected contributions include: (1) a general higher order tensor compression methodology with open source software; (2) enhanced REM and TERGM implementations incorporating heterogeneous decay and compressed covariates; (3) a validated multilayer event database; and (4) high impact publications across statistics, network science, and international relations. By combining theoretical innovation, statistical modelling, and empirical data infrastructure, this project will significantly expand the methodological toolkit for analysing complex spatio temporal systems and deepen our understanding of dynamic multilayer networks. This project is expected to start in September 2027. Before you apply: We strongly recommend that you contact the supervisors for this project before you apply. How to apply: To be considered for this project you must complete a formal application through our online application portal. If you already have an applicant account this link will directly open an application for PhD School of Natural Sciences Scholarships . If you don’t already have an applicant account, please follow the instructions here . When applying, please specify the full title and supervisor/s of the project, details of your previous study, and names and contact details of two referees. You must also upload a Supporting Statement describing your motivation to apply to the project, your CV and transcripts of awarded and in-progress university qualifications . Please note late or incomplete applications will not be considered. Equality, diversity and inclusion are fundamental to the success of The University of Manchester and central to all our activities. A diverse research community strengthens creativity, productivity and quality, while increasing the societal and economic impact of our work. We welcome applicants from all career paths, backgrounds and sections of the community, regardless of age, disability, ethnicity, gender, gender expression, sexual orientation or transgender status. We welcome applications from candidates returning to study after a career break or experience in other roles. Flexible study arrangements may be available, including part-time study at 50%, 60% or 80%, subject to the requirements of the project and funder. Eligibility : The standard academic entry requirement for this PhD is an upper second-class (2:1) honours degree (or international equivalent) in Statistics, Mathematics, or allied areas (with a substantial background in statistics) OR any upper-second class (2:1) honours degree and a Master’s degree at merit (or international equivalent) in Statistics, Mathematics, or allied areas (with a substantial background in statistics). Previous research experience in Statistics, Mathematics, or allied areas is desirable along with skill in R programming (substantiated by curriculum taken and/or projects), proficiency in oral & written communication in English. Also desirable is evidence of interest in research, experience in (statistical) modelling and analysis of spatio-temporal data. This project will remain open until filled. If your application is submitted by 1 st November 2026, you can expect a decision by 18 th December 2026. If your application is submitted by 15 th January 2027, you can expect a decision by 30 th March 2027. Self or externally funded students can also be considered for this project. FSESoNS

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