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Öğe Orthogonal Embedding-Based Artificial Neural Network Solutions to Ordinary Differential Equations(Afyon Kocatepe Üniversitesi, 2025) Uçar, Tolga RecepProviding numerical solutions to differential equations in cases where analytical solutions are not available is of great importance. Recently, obtaining more accurate numerical solutions with artificial neural network-based machine learning methods are seen as promising developments for numerical solutions of differential equations. In this paper, a low-cost, orthogonal embedding-based network with fast training by simple gradient descent algorithm is proposed to obtain numerical solutions of differential equations. This architecture is essentially a two-layer neural network that takes orthogonal polynomials as input. The efficiency and accuracy of the method used in this paper are demonstrated in various problems and comparisons are made with other methods. It is observed that the proposed method stands out especially when compared with high-cost solutions. - Analitik çözümlerin mevcut olmadığı durumlarda diferansiyel denklemler için nümerik çözümler elde etmek büyük önem taşımaktadır. Son zamanlarda, yapay sinir ağı tabanlı makine öğrenmesi yöntemleriyle daha tutarlı nümerik çözümlerin elde edilmesi diferansiyel denklemlerin nümerik çözümleri için ümit verici gelişmeler olarak görülmektedir. Bu makalede, diferansiyel denklemlerin nümerik çözümlerini elde etmek için basit gradyan düşüm algoritması ile hızlı eğime sahip düşük maliyetli bir ortogonal gömme tabanlı ağ önerilmektedir. Bu mimari, temelde, ortogonal polinomları girdi olarak alan iki katmanlı bir sinir ağıdır. Bu makalede kullanılan yöntemin verimliliği ve tutarlılığı, çeşitli problemlerde gösterilmiş ve diğer yöntemlerle karşılaştırmalar yapılmıştır. Kullanılan yöntemin, özellikle yüksek maliyetli çözümlerle karşılaştırıldığında öne çıktığı görülmüştür.Öğe AlzFormer: Video-based space-time attention model for early diagnosis of Alzheimer’s disease(Elsevier, 2025) Akan, Taymaz; Alp, Sait; Ledbetter, Christina Raye; Bhuiyan, Mohammad Alfrad NobelEarly and accurate Alzheimer’s disease (AD) diagnosis is critical for effective intervention, but it is still challenging due to neurodegeneration’s slow and complex progression. Recent studies in brain imaging analysis have highlighted the crucial roles of deep learning techniques in computer-assisted interventions for diagnosing brain diseases. In this study, we propose AlzFormer, a novel deep learning framework based on a space–time attention mechanism, for multiclass classification of AD, MCI, and CN individuals using structural MRI scans. Unlike conventional deep learning models, we used spatiotemporal self-attention to model inter-slice continuity by treating T1-weighted MRI volumes as sequential inputs, where slices correspond to video frames. Our model was fine-tuned and evaluated using 1.5 T MRI scans from the ADNI dataset. To ensure the anatomical consistency of all the MRI data, All MRI volumes were pre-processed with skull stripping and spatial normalization to MNI space. AlzFormer achieved an overall accuracy of 94 % on the test set, with balanced class-wise F1-scores (AD: 0.94, MCI: 0.99, CN: 0.98) and a macro-average AUC of 0.98. We also utilized attention map analysis to identify clinically significant patterns, particularly emphasizing subcortical structures and medial temporal regions implicated in AD. These findings demonstrate the potential of transformer-based architectures for robust and interpretable classification of brain disorders using structural MRIÖğe MRI-based alzheimer's disease classification using vision transformer and time-series transformer: a step-by-step guide(Elsevier B.V., 2025) Alp, Sait; Akan, Sara; Akan, TaymazThis study introduces a reproducible pipeline for classifying Alzheimer's Disease from structural brain MRI utilizing a joint transformer architecture that integrates Vision Transformer and Time-Series Transformer models. The proposed framework uses pre-trained ViT for feature extraction from 2D slices of MRI volumes, followed by sequential modeling with a transformer-based classifier to capture inter-slice dependencies. The method is evaluated on the ADNI dataset, involving both binary (AD vs. NC) and multiclass (AD, MCI, NC) classification tasks across axial, sagittal, and coronal planes.Öğe Barrow holographic dark energy models in Lyra and general relativity theories(Journal of New Results in Science, 2024) Aktaş, Arzu; Aygün, SezginThis study investigates the Barrow holographic dark energy (BHDE) matter distribution in the Bianchi I universe model in Lyra and General Relativity Theories. To this end, it obtains exact solutions by Hubble parameter, conservation equation, and BHDE energy density equation and supports them with graphics. The results show that the solutions are in harmony with the functioning of the universe and the nature of dark energy. It finally discusses the need for further research.
