Graduate School of Applied Mathematics

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Recent Submissions

Increasing and other subsequence problems for random interval sequences Arslan, İlker; Işlak, Ümit (2026-05-01) Various relations for comparison of intervals of real numbers are introduced, and the expected length of the corresponding longest increasing subsequence is analyzed. When intervals are randomly generated by taking the min...
A PINN-enhanced SUPG-stabilized hybrid finite element framework with shock-capturing for computing steady convection-dominated flows Cengizci, Süleyman; Uğur, Ömür; Natesan, Srinivasan (2026-05-01) This study introduces a novel hybrid machine learning (ML) framework for solving steady-state, advection-dominated convection–diffusion–reaction (CDR)-type partial differential equations (PDEs). The approach enhances stabi...
Efficient and secure Montgomery curves over TMVP-friendly primes for next-generation ECC Orhon Kılıç, Neriman Gamze; Yayla, Oğuz; Cenk, Murat; Department of Cryptography (2026-3-25) As elliptic curve cryptography enters an era of hybrid post-quantum deployment and long-term data protection, there is growing demand for curves that combine security margins well beyond current standards with efficient, c...
Black-Box System Identification with Deep Recurrent Networks and Classical Models Avan, Beyza; Türk, Önder; Gökgöz Küçüksakallı, Nurgül; Department of Scientific Computing (2026-2-20) Deep learning has demonstrated significant, well-established success across a range of application domains; however, its use in nonlinear system identification remains an active area of research. This thesis provides a rig...
Nested Copula Reserving for Claims in General Insurance Koçer, Günay Burak; Kestel, Sevtap Ayşe; Department of Financial Mathematics (2026-2-10) Regulatory frameworks such as Solvency II and IFRS 17 require credible identification of reserve uncertainty and tail risk, which encourages models that move beyond deterministic Chain-Ladder approaches. This study propose...
COLLUSION-RESISTANT TLS ATTESTATION PROTOCOLS: A VERIFIABLE, MODULAR FRAMEWORK FOR DECENTRALIZED APPLICATIONS Şen, Uğur; Yayla, Oğuz; Osmanoğlu, Murat; Department of Cryptography (2026-2-10) A significant portion of today’s accessible data is stored on centralized servers and is typically accessed through the Transport Layer Security (TLS) protocol, which provides confidentiality and integration guarantees. Ho...
PIR Schemes from nD-Cyclic and nD-Constacyclic Codes and Their Monomial Equivalence Grassl, Markus; Yılmaz, Burcu Ecem; Özbudak, Ferruh; Özkaya, Buket (2026-02-01)
On PIR schemes from nD-cyclic codes and the Schur product of some algebraic codes Karakaş, Burcu Ecem; Özkaya, Buket; Özbudak, Ferruh; Department of Cryptography (2026-1-22) Private Information Retrieval (PIR) schemes aim to retrieve data from a database without revealing any details which data has been retrieved. A PIR scheme for coded storage systems with colluding servers gives a better PIR...
FACDO: Feature-Aware Conditional Diffusion Oversampler for Robust Minority Oversampling in Imbalanced Credit Risk and Fraud Classification YAMAN, ONUR; Uğur, Ömür; Department of Scientific Computing (2026-1-22) Datasets used in credit risk modelling and fraud detection are typically highly imbalanced, where defaults or fraudulent transactions constitute only a small fraction of all observations. Accurately identifying these minor...
CRYPTOGRAPHICALLY SECURE RANDOM NUMBER GENERATION BASED ON A CHAOTIC SYSTEM: A NOVEL ENTROPY LAMP SYSTEM Güneyi, Hakan Önder; Demirköz, Melahat Bilge; Yayla, Oğuz; Department of Cryptography (2026-1-21) Chaotic systems are sensitive to initial conditions and enhance security by introducing unpredictability. This study aims to develop a cryptographically secure random number generator using captured pixels from an entropy ...
ANALYSIS OF ISOGENY-BASED CRYPTOSYSTEMS RENAN, FARZIN; Özkaya, Buket; Kutas, Péter; Department of Cryptography (2026-1-16) This thesis advances isogeny-based, quantum-resistant cryptographic constructions by designing and analyzing novel signature schemes with advanced functionalities, together with a verifiable delay function that extends cap...
An introduction to block cipher cryptanalysis Şencan, Hüseyin; Özkaya, Buket; Department of Cryptography (2026-1) Ensuring the security of encryption algorithms is a fundamental requirement before employing them to protect sensitive information. The most reliable way to evaluate the strength of a cipher is through cryptanalysis, which...
Strong Order Runge-Kutta Method for Stochastic Optimal Control Problems of the Merton Jump Diffusion Model YILMAZ, FİKRİYE NURAY; Aydın, Elif; Temoçin, Büşra Zeynep; ALTINTAN, DERYA (2026-01-01) This paper studies stochastic Runge-Kutta (SRK) approximation for solving stochastic optimal control problems where the state process is governed by Merton's jump-diffusion model. We propose a practical numerical scheme ba...
Analysis of clustering and degree index in random graphs and complex networks Işlak, Ümit; YEŞİLOĞLU, BARIŞ (2026-01-01) The purpose of this paper is to analyze the degree index and the clustering index in dense random graphs. The degree index in our setup is a certain measure of degree irregularity whose basic properties are well studied in...
Blockchain-Based Carbon Footprint Management Pekel, Umut; Yayla, Oğuz (2026-01-01) This paper introduces a novel approach to managing carbon footprints using blockchain technology to integrate these footprints intrinsically into the attributes of products, akin to their price. In contrast to conventional...
HESITANT FUZZY LINGUISTIC MATRIX GAME AND ITS APPLICATION IN MCDM PROBLEM Jana, Jishu; Roy, Sankar Kumar; Weber, Gerhard Wilhelm (2026-01-01) . This study focuses on how to establish a connection between game theory and decision making under an uncertain environment. To tackle this uncertainty, an expansion of the hesitant fuzzy set and linguistic term set, i.e....
Random Data and Its Cryptographic Applications Yavuzyiğit, Ayşe Eda; Yayla, Oğuz (2026-01-01) Random sequence construction represents fundamental components of modern cryptographic systems. The quantitative assessment of randomness relies upon rigorous statistical testing methodologies, establishing statistical ran...
DYNAMIC PROPORTION PORTFOLIO INSURANCE FOR MANAGING GAP RISK Saydam, Su; Temoçin, Büşra Zeynep; Department of Financial Mathematics (2025-12-30) This thesis applies the dynamic proportion portfolio insurance strategy to manage gap risk—the probability that the portfolio value falls below the guaranteed floor between discrete rebalancing dates. The CPPI multiplier i...
Multi-criteria group decision-making method using Spherical Fuzzy Z-Numbers for smart technology revolution in municipal waste management Ashraf, Shahzaib; Naeem, Muhammad; Jana, Chiranjibe; Akram, Maria; Weber, Gerhard Wilhelm (2025-12-01) Due to the new phenomenon of globalization and the fast growing cities, there is drastic pressure on the conventional methods of waste management hence the need for innovative management wastage that is proactive to the th...
A Machine Learning Integrated Portfolio Rebalance Framework with Risk Aversion Adjustment Temoçin, Büşra Zeynep (2025-12-01)

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