Highlighted Articles Published by ITU's Department of Mathematics Engineering in 2025
The ITU Department of Mathematics Engineering has experienced a remarkable second half of 2025, defined by significant academic achievements and groundbreaking research. Faculty members and students have been recognized for their pivotal contributions to advancing mathematical knowledge, securing publications in prestigious journals, and engaging in high-impact interdisciplinary projects. These accomplishments underscore the department’s unwavering dedication to excellence in both research and education. By fostering a collaborative and innovative academic environment, ITU Mathematics Engineering continues to push the boundaries of theoretical and applied mathematics. Looking ahead, the department is eager to build on this momentum, driving further innovation and addressing complex challenges across diverse fields.
Modeling Opinion Polarization: Can We Control Public Discourse?
The article titled “Modeling Opinion Polarization: Can We Control Public Discourse?”, authored by ITU Department of Mathematics Engineering faculty members Assoc. Prof. Dr. Ali Demirci, Assoc. Prof. Dr. Ayşe Peker-Dobie, and Dr. Sevgi Harman, was published in Frontiers in Physics.
In this novel study, the researchers propose an epidemiologically inspired model to analyze the evolution of public opinion and the dynamics of polarization. Unlike traditional approaches, this framework classifies the population into five distinct groups: Susceptible, Exposed, Positive, Negative, and Mixed-Emotion communicators. This model uniquely incorporates a time-dependent control function to simulate engagement surges driven by external events. By focusing on short intervention windows, this research demonstrates how targeted strategies can effectively steer public discourse. A derived basic reproduction number serves as a critical threshold, determining whether opposing groups persist or fade away. Ultimately, this study offers powerful theoretical tools for evaluating how platform algorithms and governmental interventions can be leveraged to mitigate or amplify polarization in digital environments.
To access the full article, https://doi.org/10.3389/fphy.2025.1626026.
Machine Learning Tree Trimming for Faster Markov Reward Game Solutions
The article titled “Machine Learning Tree Trimming for Faster Markov Reward Game Solutions”, authored by Prof. Dr. Burhaneddin İzgi from the ITU Department of Mathematics Engineering, Dr. Murat Özkaya from the Canakkale Onsekiz Mart University (a Ph.D. student of Prof. Dr. İzgi), Assoc. Prof. Dr. Nazım Kemal Üre from the ITU Department of Artificial Intelligence and Data Engineering, and Professor Matjaz Perc from the University of Maribor, was published in Journal of Computational Science.
In this research, the authors address the high computational burden of existing iterative algorithms for solving Markov Reward Games (MRGs). To overcome these challenges, this paper introduces a novel neural network architecture designed to solve MRGs with large state-action sets by effectively trimming the decision tree. This framework utilizes a holistic matrix norm-based solution method to generate training datasets, employing a unique vectorization process to adapt payoff and transition matrices. By treating the problem as a classification task, the model identifies optimal paths by distinguishing between rewarding and non-rewarding branches. The results reveal that this system efficiently predicts optimal strategies, achieving F1-scores exceeding 0.97. Ultimately, this study proposes a powerful architecture for solving MRGs in real-time, significantly enhancing their practicality for complex, real-world applications.
To access the full article, https://doi.org/10.1016/j.jocs.2025.102726.
The Copositive Range
The article titled “The Copositive Range”, authored by ITU Department of Mathematics Engineering member Dr. Nurhan Çolakoğlu, in collaboration with Dr. Seong Jun Park and Dr. Michael Tsatsomeros from the Washington State University, was published in Electronic Journal of Linear Algebra.
This study aims to advance the theory, detection, and categorization of copositive matrices by introducing a novel concept: the “Copositive Range”. Motivated by the classical numerical range, this research defines the copositive range for a matrix as the set . While copositivity, first introduced by Motzkin in 1952, plays a crucial role in reformulating nonconvex mixed quadratic programs and solving Linear Complementarity Problems (LCP), effective characterization remains a challenge. This paper addresses that gap by extending the numerical range concept specifically to non-negative vectors. Ultimately, this work provides a unified framework that bridges theoretical matrix analysis with practical applications in differential equations and theoretical economics.
To access the full article, https://doi.org/10.13001/ela.2025.9741.
Bifurcation Structure and Stability of Solitary Waves in Nonlinear Optical Systems
The article titled “Bifurcation Structure and Stability of Solitary Waves in the Cubic–Quintic Nonlinear Schrödinger Equation with Self-Steepening”, authored by ITU Department of Mathematics Engineering faculty members Res. Assist. Eril Güray Çelik and Prof. Dr. Nalan Antar, was published in European Physical Journal Plus.
This study presents a comprehensive analysis of the bifurcation structure and stability of solitary waves governed by the cubic-quintic nonlinear Schrödinger equation with self-steepening in a symmetric double-well potential. The research specifically investigates how higher-order effects, specifically self-steepening and quintic nonlinearity, influence localized states in nonlinear optical systems.
The investigation examines two primary regimes. In the focusing-defocusing regime, the interplay between cubic focusing and quintic defocusing generates a complex bifurcation landscape, including supercritical pitchfork, double-pitchfork, and saddle-node bifurcations. This analysis reveals that increasing the self-steepening parameter compresses unstable regions and reduces multistability, effectively eliminating upper solution branches. In contrast, the fully focusing regime exhibits a more robust structure characterized by a single supercritical pitchfork bifurcation that remains qualitatively unchanged under parameter variations.
A notable methodological innovation of this work is the first application of the pseudospectral renormalization (PSR) method to construct bifurcation diagrams in cubic-quintic systems. By combining PSR for solution computation with Fourier collocation for stability analysis, this study provides critical theoretical insights into how higher-order nonlinearities dictate symmetry breaking and stability in externally confined nonlinear environments.
To access the full article, https://doi.org/10.1140/epjp/s13360-025-07053-x.
Optimizing Treatment of Brain Cancer Through Mathematics
The study titled "An accurate and effective computational method to solve brain tumor problems: a Jacobian-free Newton Krylov method with an innovative preconditioning strategy II", authored by ITU Department of Mathematics Engineering faculty members Res. Assist. Ece Hazal Korkmaz, Prof. Dr Samet Yücel Kadıoğlu and Prof. Dr. Ersin Özuğurlu, was published in Computational and Applied Mathematics.
Glioblastoma multiforme (GBM) is one of the most aggressive brain cancers, and even combined surgery, radiotherapy, and temozolomide chemotherapy often fail to halt its progression. In this study, Korkmaz, Kadıoğlu, and Özuğurlu investigate how mathematical modeling and high-performance computation can contribute to more effective treatment strategies.
They construct a reaction–diffusion model that captures the proliferation and invasive spread of GBM cells, then incorporate detailed representations of radiotherapy and chemotherapy to examine how different treatment schedules reshape tumor evolution. Rather than producing a single simulation, the objective is to identify dosing patterns and timing strategies capable of measurably extending survival.
The primary obstacle is computational: realistic tumor geometries and months-long treatment windows generate large, nonlinear systems. To overcome this, the authors use a Jacobian-free Newton–Krylov method supported by a physics-based preconditioner that targets the stiffest components of the model. This approach significantly reduces iteration counts and computation time, enabling high-resolution simulations that would otherwise be infeasible.
The resulting model reproduces clinically consistent behavior, such as untreated tumors reaching lethal size within roughly a year, and shows that hyperfractionated radiotherapy—delivering two smaller fractions per day—can outperform conventional single-fraction protocols. By enabling rapid evaluation of alternative treatment regimens, this work provides a computational framework that may support future patient-specific optimization of GBM therapy.
To access the full article, https://doi.org/10.1007/s40314-025-03406-5.
Processing and Analysis of Quadratic Spectrum Approximation for Three Bounded Operators via Generalized ν-Convergence
The article titled "Processing and Analysis of Quadratic Spectrum Approximation for Three Bounded Operators via Generalized ν-Convergence", authored by ITU Department of Mathematics Engineering member Prof. Dr. Muhammed Kurulay, in collaboration with S. Kamouche, H. Guebbai and M. Ghiat (Universite 8 Mai 1945 Guelma, University of Blida), was published in Lobachevskii Journal of Mathematics.
The purpose of this paper is to demonstrate the efficacy of the generalized quadratic spectrum approximation in addressing the issue of spectral pollution that arises in the approximation of unbounded operator spectra. To achieve this, the authors investigate key analytical properties of the generalized quadratic resolvent function, such as holomorphicity and Fréchet differentiability, which are essential for developing the numerical framework. Furthermore, they extend the concept of ν-convergence, originally introduced for the classical spectrum, to establish property U convergence, a novel approach that effectively mitigates spectral pollution. This extension provides a more robust framework for addressing spectral contamination. To illustrate the practical applicability of the method, the authors focus on the quadratic pencil of Schrödinger's operator. By combining the finite differences method with the generalized quadratic spectral approximation, they estimate the eigenvalues of the selected operator. Extensive numerical experiments have been conducted to validate the efficiency and accuracy of the approach. The results confirm the effectiveness of the method in resolving spectral pollution and demonstrate its capability to deliver precise eigenvalue approximations. These findings highlight the potential of this technique for broader applications in spectral analysis.
To access the full article, https://doi.org/10.1134/S1995080225605806.
Effects of Surface Roughness on Generalised Rayleigh Waves in Elastic Waveguides
The article titled "Effects of Surface Roughness on Generalised Rayleigh Waves in Elastic Waveguides", authored by ITU Department of Mathematics Engineering members Tuğçe Sezer, Prof. Dr. Semra Ahmetolan, Assoc. Prof. Dr. Ayşe Peker-Dobie, and Assoc. Prof. Dr. Ali Demirci, was published in Wave Motion.
This work examines the propagation of Rayleigh surface waves in an elastic half-space covered by a layer with spatially varying surface corrugation. The mathematical model is established within the framework of two-dimensional linear elasticity, considering general roughness profiles for both the upper free surface and the interface of the layer. A perturbation method is employed to derive analytical expressions for the displacement fields, and dispersion relations are obtained by enforcing the relevant boundary and continuity conditions. The influence of surface corrugation parameters on phase velocity and wave propagation is examined numerically for periodic roughness profiles using selected real material models. The results demonstrate that both the amplitude and geometric characteristics of the surface irregularities have a pronounced impact on the dispersion behaviour of Rayleigh waves. These findings provide new insights into wave propagation in layered elastic media with irregular boundaries and may inform future applications in wave-based sensing, nondestructive evaluation, and acoustic material design.
To access the full article, https://doi.org/10.1016/j.wavemoti.2025.103658.
Mathematical Modeling on the Strategies of Imperfect Vaccination, Quarantine, and Natural Immunity
The study titled “Mathematical Modeling on the Strategies of Imperfect Vaccination, Quarantine, and Natural Immunity in a Future Epidemic”, derived from the master’s thesis of Seda Çelik under the supervision of ITU Department of Mathematics Engineering member Assoc. Prof. Dr. Saadet S. Özer, was published in Mathematical Methods in the Applied Sciences.
A mathematical analysis is being conducted to determine the extent to which contact measures such as masks and social distancing should be balanced with vaccine efficacy, vaccination rates, natural immunity, and quarantine in order to mitigate a future pandemic. A method is being formulated to answer the question of what should be implemented, when, and how.
Understanding epidemic dynamics is vital for global health security. A recent study, authored by Seda Çelik and Saadet S. Özer, investigates the complexities of pandemic management. Originating from a master's thesis and published in the Q1 journal Mathematical Methods in the Applied Sciences (Volume 48, Issue 11), this research offers a mathematical approach to optimizing control strategies for future outbreaks. The core challenge addressed is how to balance non-pharmaceutical interventions such as masks and social distancing with medical countermeasures like imperfect vaccination and quarantine. The researchers aimed to formulate a method to answer "what should be implemented, when, and how" to mitigate pandemics effectively, considering variables like natural immunity. The authors developed a system of nonlinear ordinary differential equations to model the population, categorizing individuals into nonvaccinated, vaccinated, exposed, quarantined, infected, and recovered groups. The study goes beyond the standard basic reproduction number calculating specific reproduction numbers for vaccination and quarantine to assess control efficacy. Through rigorous analysis, the study proves that the disease-free equilibrium is locally asymptotically stable if . Furthermore, global asymptotic stability is achieved under specific conditions where for a positive real . These theoretical results were validated through sensitivity analysis and numerical simulations. The findings provide a scientific basis for policymakers to balance lockdown policies, contact rates, and vaccine efficiency. By simulating strategies from the onset of an outbreak, including periods without vaccines, the study outlines how natural immunity and quarantine rates can be leveraged to control future pandemics.
To access the full article, https://doi.org/10.1002/mma.10980.