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Yayın On extensions, Lie-Poisson systems, and dissipation(Heldermann Verlag, 2022-07-06) Esen, Oğul; Özcan, Gökhan; Sütlü, SerkanLie-Poisson systems on the dual spaces of unified products are studied. Having been equipped with a twisted 2-cocycle term, the extending structure framework allows not only to study the dynamics on 2-cocycle extensions, but also to (de)couple mutually interacting Lie-Poisson systems. On the other hand, symmetric brackets; such as the double bracket, the Cartan-Killing bracket, the Casimir dissipation bracket, and the Hamilton dissipation bracket are worked out in detail. Accordingly, the collective motion of two mutually interacting irreversible dynamics, as well as the mutually interacting metriplectic flows, are obtained. The theoretical results are illustrated in three examples. As an infinite-dimensional physical model, decompositions of the BBGKY hierarchy are presented. As for the finite-dimensional examples, the coupling of two Heisenberg algebras, and the coupling of two copies of 3D dynamics are studied.Yayın Discrete dynamical systems over double cross-product Lie groupoids(World Scientific, 2021-03) Esen, Oğul; Sütlü, SerkanDiscrete Euler-Lagrange equations are studied over double cross product Lie groupoids. As such, a geometric framework for the local analysis of a discrete dynamical system is established. The arguments are elucidated on the local discrete dynamics of a gauge groupoid. The discrete Elroy's beanie is studied as a physical example.Yayın Retinal disease diagnosis in OCT scans using a foundational model(Springer Science and Business Media Deutschland GmbH, 2025) Nazlı, Muhammet Serdar; Turkan, Yasemin; Tek, Faik Boray; Toslak, Devrim; Bulut, Mehmet; Arpacı, Fatih; Öcal, Mevlüt CelalThis study examines the feasibility and performance of using single OCT slices from the OCTA-500 dataset to classify DR (Diabetic Retinopathy) and AMD (Age-Related Macular Degeneration) with a pre-trained transformer-based model (RETFound). The experiments revealed the effective adaptation capability of the pretrained model to the retinal disease classification problem. We further explored the impact of using different slices from the OCT volume, assessing the sensitivity of the results to the choice of a single slice (e.g., “middle slice”) and whether analyzing both horizontal and vertical cross-sectional slices could improve outcomes. However, deep neural networks are complex systems that do not indicate directly whether they have learned and generalized the disease appearance as human experts do. The original dataset lacked disease localization annotations. Therefore, we collected new disease classification and localization annotations from independent experts for a subset of OCTA-500 images. We compared RETFound’s explainability-based localization outputs with these newly collected annotations and found that the region attributions aligned well with the expert annotations. Additionally, we assessed the agreement and variability between experts and RETFound in classifying disease conditions. The Kappa values, ranging from 0.35 to 0.69, indicated moderate agreement among experts and between the experts and the model. The transformer-based RETFound model using single or multiple OCT slices, is an efficient approach to diagnosing AMD and DR.
