https://hdl.handle.net/20.500.12809/238 2026-07-03T05:23:44Z 2026-07-03T05:23:44Z Balcı, Mehmet Ali Çetin, Erbil Çalıbaşı-Kocal, Gizem Akgüller, Ömer https://hdl.handle.net/20.500.12809/11230 2026-06-25T12:29:53Z 2026-01-01T00:00:00Z

Pocket-Surface Discrete Differential Geometry as a Leakage-Robust Feature Class for Protein–Ligand Binding Affinity Prediction Balcı, Mehmet Ali; Çetin, Erbil; Çalıbaşı-Kocal, Gizem; Akgüller, Ömer Protein-ligand binding affinity prediction underpins structure-based drug discovery, yet random partitions of public benchmarks overestimate generalisation due to protein-family and ligand leakage, and the marginal value of explicit pocket-geometry descriptors over atom-level graph neural networks remains unclear. We computed a 59-dimensional discrete differential geometry descriptor on the ligand-aware solvent-excluded surface of 3285 PDBBind v2020 complexes, combining curvature distributions, the leading sixteen Laplace-Beltrami eigenvalues and a ten-point heat-kernel signature, and evaluated it in gradient-boosted tree pipelines across progressively stricter split regimes and two leak-proof external benchmarks, together with four mechanistically distinct injection strategies in a SchNet-style graph neural network. The descriptor lifted Pearson correlations by 0.111 on cluster-disjoint testing, 0.258 on LP-PDBBind DataSAIL S2 and 0.365 on CASF-2016, while in isolation reaching 0.456 to 0.594 on external benchmarks, on a par with X-Score and AutoDock Vina (version 1.2). TreeSHAP attribution localised the dominant signal to the heat-kernel signature. The four graph neural network injection strategies produced no statistically significant lift, indicating that distance-based message passing on atomic coordinates already captures much of the geometric content. Pocket-surface discrete differential geometry, therefore, offers an interpretable, leakage-robust and lightweight feature class for early-stage virtual screening, and motivates hybrid mesh-to-atom architectures.

2026-01-01T00:00:00Z Kandemir, Mustafa Burç https://hdl.handle.net/20.500.12809/10928 2023-08-29T10:34:41Z 2023-01-01T00:00:00Z

Basic theory of s-posets Kandemir, Mustafa Burç In this paper, we have established the notions of soft order relations and studied its basic structural properties. We give the concepts of soft maximum, soft minimum, soft maximal, soft minimal, soft infimum and soft supremum in any s-poset. Then, the concept of soft order preserving mapping is defined and given some basic results. Moreover, it has been shown that the topology derived from a soft partial order relation is a soft topology which will substitute as a soft version of Alexandroff topology in classical theory. With all that, we obtained the category SPOSET of s-posets, and constructed a functor which is called ostracizer functor between the categories SPOSET and POSET .

2023-01-01T00:00:00Z Koşunalp, Hatice Yalman Gülsu, Mustafa https://hdl.handle.net/20.500.12809/10859 2023-08-08T07:55:45Z 2023-01-01T00:00:00Z

Towards solving linear fractional differential equations with Hermite operational matrix Koşunalp, Hatice Yalman; Gülsu, Mustafa This paper presents the derivation of a new operational matrix of Caputo fractional derivatives through Hermite polynomials with Tau method to solve a set of fractional differential equations (FDEs). The proposed algorithm is intended to solve linear type of FDEs with the pre-defined conditions into a matrix form for redefining the complete problem as a system of a algebraic equations.The proposed strategy is then applied to solve the simplified FDEs in linear form. To assess the performance of the proposed method, exact and approximate solutions for a number of illustrative examples are obtained which prove the effectiveness of the idea.

2023-01-01T00:00:00Z Koç, Dilara Altan https://hdl.handle.net/20.500.12809/10846 2024-04-04T08:27:06Z 2023-01-01T00:00:00Z

A Numerical Scheme for Time-Fractional Fourth-Order Reaction-Diffusion Model Koç, Dilara Altan In fractional calculus, the fractional differential equation is physically and theoretically important. In this article an efficient numerical process has been developed. Numerical solutions of the time fractional fourth order reaction diffusion equation in the sense of Caputo derivative is obtained by using the implicit method, which is a finite difference method and is developed by increasing the number of iterations. The advantage of the implicit difference scheme is unconditionally stable. The stability analysis and convergency have been proven. A numerical example has been presented, and the validity of the method is supported by tables and graphics.

2023-01-01T00:00:00Z