1) Research and implementation of novel algebraic algorithms for computer vision. The research focused on modeling SfM problems with rolling shutter cameras. Classifying and identifying minimal problems for basic rolling-shutter camera models was an important part of this work. Ready-to-run solver and classifier code was developed. This work resulted in the publication
Marvin Anas Hahn, Kathlén Kohn, Orlando Marigliano, and Tomas Pajdla. Order-One Rolling Shutter Cameras. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) (2025), 27007–27016
which was designated as “Highlight” by the CVPR community. Its methodology received positive feedback from conference attendees.
2) Research and manuscript revision for Gaussian statistical models with maximum likelihood degree one. A new description of these models in terms of partial differential equations was developed. As a consequence, important obstacles to achieving a full classification of such models were identified. Notably, a complete classification would entail resolving a long-standing open problem in rational algebraic geometry. This work led to the publication
Carlos Améndola, Lukas Gustafsson, Kathlén Kohn, Orlando Marigliano and Anna Seigal. Differential equations for Gaussian statistical models with rational maximum likelihood estimator. SIAM Journal on Applied Algebra and Geometry 8 (2024), 465–492.
3) Exploration of new research directions in statistical modeling, focusing on algebraic approaches to compositional data. This line of inquiry was not developed further, but this work enhanced the research group’s understanding of the structural limitations of compositional models.
4) Training, communication and dissemination activities, research visit, conference travel. The researcher attended a MSCA-focused workshop at University of Genoa and participated in four European conferences in statistics, applied algebra, and computer vision, delivering two conference talks. A research visit was made at TU Munich to explore new research directions.
5) Development of research ideas on Gaussian non-exponential families. Formulation of a research plan involving these ideas, to be implemented later in the researcher’s career.
6) Revision of a manuscript on the classification of discrete statistical models with maximum likelihood degree one, resulting in the publication
Arthur Bik and Orlando Marigliano. Classifying one-dimensional discrete models with maximum likelihood degree one. Advances in Applied Mathematics 170 (2025), 102928.
This publication inspired subsequent work by C. Améndola, V. D. Nguyen, J. Oldekop (ArXiv: 2507.18686).
7) Training, communication and dissemination activities, conference travel. The researcher and supervisor held an algebraic statistics seminar at University of Genoa. The researcher attended a career development workshop and scientific conference on algebraic statistics in Munich.
8) Research on statistical modeling and the development of new methods for the analysis of categorical data. The theory of Markov combinations for these data was developed, providing several ways to combine modeling hypotheses and evidence from multiple sources. The research manuscript
Orlando Marigliano and Eva Riccomagno. Markov combinations of discrete statistical models. ArXiv:2509.18983 2025
was drafted and submitted to leading statistics journals. A comprehensive treatment of discrete Markov combinations and their sampling, algorithmic, and theoretical aspects was achieved.
