The ITU Department of Mathematics Engineering has had a remarkable year in 2024, marked by significant academic achievements and groundbreaking research. Faculty members and students have been recognized for their contributions to advancing mathematical knowledge, publishing in prestigious journals, and participating in impactful interdisciplinary projects. These accomplishments highlight the department’s dedication to excellence in both research and education. By fostering a collaborative and innovative academic environment, ITU Mathematics Engineering continues to expand the boundaries of theoretical and applied mathematics. As the year progresses, the department looks forward to building on this momentum, driving forward innovation, and addressing complex challenges across diverse fields.
Contrast and content-preserving HDMR-based color-to-gray conversion
The article entitled 'Contrast and Content Preserving HDMR-Based Color-to-Gray Conversion', authored by ITU Department of Mathematics Engineering faculty member Assoc. Prof. Dr. Burcu Tunga, her PhD student Ayça Ceylan, and Dr. Evrim Korkmaz Özay, who graduated from ITU Informatics Institute, was published in Computers & Graphics.
In this study, we present an innovative image decolorization algorithm based on High Dimensional Model Representation (HDMR), designed to convert color images to grayscale while preserving key attributes, including color contrast, sharpness, and luminance. Our approach involves decomposing the image into HDMR components, categorizing them as either colored or colorless, and then reconstructing the image by merging these components with optimized weight coefficients. This optimization process provides exceptional flexibility, enabling the generation of grayscale images customized to various contrast thresholds. Through extensive visual and quantitative comparisons with state-of-the-art methods, we demonstrated that our algorithm not only outperforms existing techniques but also stands out as the only approach, to the best of our knowledge, capable of achieving this level of adaptability and performance.
To access the full article, https://doi.org/10.1016/j.cag.2024.104110
Machine Learning-Based Tomographic Imaging for Non-Destructive Detection of Internal Tree Defects
The article titled "Machine Learning-Based Tomographic Image Reconstruction Technique to Detect Hollows in Wood", based on the studies conducted by Assoc. Prof. Dr. Burcu Tunga, a faculty member of the Department of Mathematics Engineering; Ecem Nur Yıldızcan, a Mathematics Engineering master's student; and Prof. Dr. Ali Gelir, a faculty member of the Department of Physics Engineering, has been published in Wood Science and Technology.
Non-destructive detection of internal defects in wood is crucial for forest management and the preservation of trees. This study presents a novel machine learning-based approach for creating tomographic images of tree defects using stress wave propagation data. The proposed two-stage algorithm begins with ray segmentation, accurately modeling stress wave propagation. Subsequently, advanced classification algorithms like K-Nearest Neighbors (KNN) and Gaussian Process Classifier (GPC) are employed to map and visualize defects.
Results demonstrate that this approach effectively addresses challenges in segmentation and classification, achieving over 90% success in accuracy, precision, F1 score, and Dice coefficient across multiple datasets. Comparisons with existing methods highlight significant improvements, ranging from 7% to 22% in key metrics. Synthetic and real-world tree data validated the method's robustness, with visualization revealing intricate defect patterns.
This method is particularly innovative in its use of parameter-free ray segmentation and machine learning integration, setting a benchmark for non-destructive wood analysis. Its adaptability and reliability make it a valuable tool for assessing tree health and ensuring the sustainability of forest ecosystems. Future research could focus on refining thresholding strategies and incorporating additional features to enhance defect detection accuracy further.
To access the full article, https://doi.org/10.1007/s00226-024-01580-z
DeepEMPR: Coffee Leaf Disease Detection with Deep Learning
and Enhanced Multivariance Product Representation
The article entitled “DeepEMPR: coffee leaf disease detection with deep learning and enhanced multivariance product representation” is based on the studies conducted by Department of Mathematics Engineering members Assoc. Prof. Dr. Burcu Tunga and Res. Asst. Ahmet Topal was published in PeerJ Computer Science.
Plant diseases threaten agricultural sustainability by reducing crop yields. Rapid and accurate disease identification is crucial for effective management. Recent advancements in artificial intelligence (AI) have facilitated the development of automated systems for disease detection. This study focuses on enhancing the classification of diseases and estimating their severity in coffee leaf images. To do so, we propose a novel approach as the preprocessing step for the classification in which enhanced multivariance product representation (EMPR) is used to decompose the considered image into components, a new image is constructed using some of those components, and the contrast of the new image is enhanced by applying high-dimensional model representation (HDMR) to highlight the diseased parts of the leaves. Popular convolutional neural network (CNN) architectures, including AlexNet, VGG16, and ResNet50, are evaluated. Results show that VGG16 achieves the highest classification accuracy of approximately 96%, while all models perform well in predicting disease severity levels, with accuracies exceeding 85%. Notably, the ResNet50 model achieves accuracy levels surpassing 90%. This research contributes to the advancement of automated crop health management systems.
To access the full article, https://peerj.com/articles/cs-2406/
A Novel Image Denoising Model Using Caputo-Type Fractional Operators
for Enhanced Noise Reduction
The article entitled “A novel image denoising technique with Caputo type space-time fractional operators” is based on the studies conducted by Lecturer Evren Tanriover, Prof. Dr. Ahmet Kiris, Assoc. Prof. Dr. Burcu Tunga in collaboration with Prof. Dr. M. Alper Tunga was published in Nonlinear Dynamics.
This study presents the Full Fractional Total Variation (TVFF) model for image denoising, innovatively integrating Caputo and Riesz-Caputo fractional derivatives with variable length-scale parameters. Unlike conventional models, TVFF accounts for nonlocal pixel relationships, improving noise removal and edge preservation. Stability, convergence analyses, and performance under varied noise types demonstrate TVFF's superiority over existing methods, including ROF and TVF, in metrics like SNR, SSIM, and ERR.
Image denoising is critical for enhancing the usability and accuracy of digital images. Existing techniques often fail to balance noise reduction with texture preservation. To address this, we propose the Full Fractional Total Variation (TVFF) model, combining Caputo time-fractional and Riesz-Caputo space-fractional derivatives. These fractional operators, alongside variable length-scale parameters, emphasize the influence of nearby pixels and introduce a memory effect that iteratively improves results.
The TVFF model surpasses its predecessors, such as the ROF and TVF models, by mitigating issues like excessive smoothing and loss of texture detail. Numerical experiments validate its efficiency under Gaussian, Poisson, Speckle, and Salt & Pepper noise, outperforming traditional filters in Signal-to-Noise Ratio (SNR), Structural Similarity Index Measure (SSIM), and Edge Retention Ratio (ERR). Additionally, the method adapts seamlessly across diverse datasets, including synthetic and blind images, proving its versatility.
This work not only enhances image quality but also sets a foundation for advanced denoising methodologies leveraging fractional-order equations. Future research will explore optimization strategies and real-time applications.
To access the full article, https://doi.org/10.1007/s11071-024-10087-y
Stability of periodic waves for the defocusing fractional cubic nonlinear Schrödinger equation
The study “Stability of periodic waves for the defocusing fractional cubic nonlinear Schrödinger equation” conducted by ITU Department of Mathematics member Prof. Dr. Gülçin M. Muslu, in collaboration with Assoc. Prof. Dr. Handan Borluk and Assoc. Prof. Dr. Fábio Natali, was published in “Communications in Nonlinear Science and Numerical Simulation”.
In this paper, we determine the spectral instability of periodic odd waves for the defocusing fractional cubic nonlinear Schrödinger equation. Our approach is based on periodic perturbations that have the same period as the standing wave solution, and we construct real periodic waves by minimizing a suitable constrained problem. The odd solution generates three negative simple eigenvalues for the associated linearized operator, and we obtain all this spectral information by using tools related to the oscillation theorem for fractional Hill operators. Newton’s iteration method is presented to generate the odd periodic standing wave solutions and numerical results have been used to apply the spectral stability theory via Krein signature.
To access the full article, https://doi.org/10.1016/j.cnsns.2024.107953
On solitary-wave solutions of Rosenau-type equations
The study “On solitary-wave solutions of Rosenau-type equations” conducted by ITU Department of Mathematics member Prof. Dr. Gülçin M. Muslu, in collaboration with Prof. Dr. Angel Durán, was published in “Communications in Nonlinear Science and Numerical Simulation”.
The present paper is concerned with the existence of solitary wave solutions of Rosenau-type equations. By using two standard theories, Normal Form Theory, and Concentration-Compactness Theory, some results of the existence of solitary waves of three different forms are derived. The results depend on some conditions on the speed of the waves with respect to the parameters of the equations. They are discussed for several families of Rosenau equations present in the literature. The analysis is illustrated with a numerical study of the generation of approximate solitary-wave profiles from a numerical procedure based on Petviashvili iteration.
To access the full article, https://doi.org/10.1016/j.cnsns.2024.108130
Controlling Symmetry Breaking in Optical Solitons via Fourth-Order Diffraction
The study titled “Suppression of symmetry breaking bifurcation of solitons by fourth-order diffraction in a parity-time symmetric potential” was published in “Chaos, Solitons & Fractals” by ITU Department of Mathematics Engineering members Res. Asst. Melis Turgut, and Prof. Dr. İlkay Bakırtaş.
The researchers investigated the dynamics of solitons in cubic-quintic nonlinear media under Wadati-type parity-time symmetric potentials through detailed numerical simulations and stability analyses. Their findings reveal that symmetry breaking, a process where symmetric solitons evolve into asymmetric states, can be entirely suppressed by fine-tuning the strength of fourth-order diffraction (FOD). This suppression was accompanied by a remarkable transformation in soliton shapes—from double-humped structures to single-humped profiles—as the FOD became more dominant. Furthermore, the study demonstrated that higher FOD strengths significantly improved both solitons’ linear and nonlinear stability, enhancing their robustness during propagation.
These findings enhance our understanding of soliton dynamics and their potential applications in advanced optical systems. The demonstrated control over diffraction and stability dynamics highlights possibilities for improving precision-guided wave devices and soliton-based technologies in optical fibers and photonic crystals. This work contributes to a deeper understanding of soliton behavior and may inspire future advancements in optical communication and nonlinear wave management.
To access the full article, https://doi.org/10.1016/j.chaos.2024.115260
A discretization-free deep neural network-based approach
for advection-dispersion-reaction mechanisms
The study titled “A discretization-free deep neural network-based approach for advection-dispersion-reaction mechanisms” was published in “Physica Scripta” by Prof. Dr. Murat Sarı, in collaboration with Res. Assis. Dr. Hande Uslu Tuna and Assist. Prof. Dr. Tahir Coşgun.
This study explores the application of artificial intelligence, particularly deep neural networks and physics-informed neural networks (PINNs), to predict behaviors in nonlinear dispersive processes governed by partial differential equations. By incorporating initial and boundary conditions into the loss function, the method achieves accurate kink and anti-kink solutions with minimal loss (around 0.01%), outperforming traditional discretization approaches.
Partial differential equations (PDEs) are foundational in modeling dynamic phenomena such as fluid dynamics and heat conduction, offering critical insights into real-world systems across science and engineering. Among these, the advection-dispersion-reaction (ADR) equation stands out for its ability to describe complex natural processes involving advective, dispersive, and reactive interactions. These equations are particularly valuable for modeling systems exhibiting solitary wave propagation, with kink and anti-kink solutions playing a central role in dispersive models like the sine-Gordon equation, generalized Korteweg–de Vries (gKdV) equation, and nonlinear Klein–Gordon equations.
Traditional numerical techniques, including the finite element method (FEM), finite volume method (FVM), and finite difference method (FDM), have been widely applied to solve PDEs. However, these methods face challenges in handling the nonlinear and dispersive components of equations like ADR, often leading to high computational costs and numerical inaccuracies, especially for advection-dominated scenarios. Analytical approaches, while effective for specific cases, are limited in their scope and fail to address the complexity of real-world problems.
Recent advancements in artificial intelligence (AI) have introduced innovative tools for modeling complex physical systems. Physics-informed neural networks (PINNs), which embed physical laws into the training process of deep neural networks (DNNs), have emerged as a powerful alternative to traditional methods. PINNs demonstrate remarkable accuracy in predicting physical behaviors while maintaining computational efficiency. By incorporating initial and boundary conditions as constraints in the loss function, they effectively handle nonlinearities and dispersive terms.
This study explores the potential of PINNs in solving the ADR equation, a third-order nonlinear dispersive PDE, aiming to capture its unique characteristics with high precision. The results highlight the ability of PINNs to outperform traditional methods, offering computational efficiency, scalability, and significantly reduced error margins.
To access the full article, https://doi.org/10.1088/1402-4896/ad5258
Improving Predictive Efficacy for Drug Resistance in Novel HIV-1 Protease Inhibitors through Transfer Learning Mechanisms
The study titled “Improving Predictive Efficacy for Drug Resistance in Novel HIV-1 Protease Inhibitors through Transfer Learning Mechanisms” was published in “Journal of Chemical Information and Modeling” conducted by Prof. Dr. Murat Sarı, a faculty member of the ITU Department of Mathematics Engineering, in collaboration with Assist. Prof. Dr. Hüseyin Tunç, Assist. Prof. Dr. Enes Seyfullah Kotil, Assoc. Prof. Özge Şenşoy, Prof. Dr. Serdar Durdağı, Sümeyye Yılmaz, Büşra Nur Darendeli Kiraz.
The human immunodeficiency virus (HIV) poses a global challenge due to rapid mutation and drug resistance. This study introduces a drug-isolate-fold change (DIF) model framework to predict drug resistance scores using protein and inhibitor representations. By employing transfer learning with graph neural networks, the model achieves high accuracy (0.802), AUROC (0.874), and r (0.727) on external data, outperforming traditional isolate-fold change models.
Human immunodeficiency virus (HIV) remains a significant global health challenge due to its rapid mutation and resistance to antiretroviral drugs. Protease inhibitors (PIs) play a vital role in HIV treatment, requiring multiple mutations to develop resistance, making them a key focus for predicting drug resistance mechanisms. Traditional genotypic and phenotypic tests for detecting resistance are time-consuming and costly, leading to the development of mathematical and machine learning (ML) models for more efficient predictions. However, existing models often rely on predefined mutation and inhibitor rules, limiting their generalizability.
This study introduces the drug-isolate-fold change (DIF) approach to predict HIV-1 protease drug resistance scores using molecular and protein sequence representations. Utilizing ML and deep learning (DL) models, such as gradient-boosting machines and graph neural networks (GNNs), the DIF framework explores innovative computational experiments, including leave-one-out (LOO) mutation strategies and learned representations. By incorporating transfer learning through Chemprop, inhibitors are represented using learned features, improving molecular learning accuracy.
Performance metrics were evaluated using internal and external data sets, including 343 unique molecules and over 2000 genotype–phenotype associations curated from the ChEMBL database. Results demonstrate the superiority of learned features over traditional fingerprint representations. The DIF approach achieved accurate predictions for FDA-approved and novel inhibitors against clinically relevant multidrug-resistant variants. This study highlights the potential of transfer learning and novel protein-inhibitor representations in advancing predictive modeling for HIV drug resistance.
To access the full article, https://doi.org/10.1021/acs.jcim.4c01037
Various optimized artificial neural network simulations of advection-diffusion processes
The study titled “Various optimized artificial neural network simulations of advection-diffusion processes” was published in “Physica Scripta” by ITU Department of Mathematics member Prof. Dr. Murat Sarı, in collaboration with Assoc. Prof. Seda Gülen, Pelin Celenk.
This study explores an artificial neural network (ANN)-based approach using feed-forward neural networks (FFNN) to solve advection-diffusion equations. By employing gradient descent (GD), particle swarm optimization (PSO), and artificial bee colony (ABC), the study compares gradient and gradient-free techniques. Results demonstrate that PSO achieves superior accuracy, aligning well with numerical methods and physics-informed neural networks (PINNs) in the literature.
This study presents an artificial neural network (ANN)-based approach for solving advection-diffusion equations, utilizing feed-forward neural networks (FFNN) combined with optimization techniques. While traditional numerical methods like finite element and finite difference techniques are effective for these equations, they can be computationally intensive and memory-demanding. In contrast, the proposed ANN method offers a flexible and efficient alternative by minimizing errors through trial functions embedded in the differential equations.
The study employs three optimization techniques—gradient descent (GD), particle swarm optimization (PSO), and artificial bee colony (ABC)—to solve linear and nonlinear advection-diffusion equations. Each method is evaluated for accuracy and computational efficiency, with PSO demonstrating superior accuracy across test cases. The results are benchmarked against numerical methods and physics-informed neural networks (PINNs), showing promising alignment with existing solutions and improvements in computational efficiency.
Applications of the ANN method are illustrated using various parameter values, including Peclet numbers, to highlight the technique's adaptability. The findings reveal that ANN approaches, particularly PSO-optimized ones, can capture the behavior of complex advection-diffusion processes without numerical instabilities. This study concludes that ANN methods not only provide accurate solutions but also offer significant advantages in reducing computational cost and memory usage, establishing their potential for broader applications in solving partial differential equations.
To access the full article, https://doi.org/10.1088/1402-4896/ad8190
Researchers from the Department of Mathematics Engineering investigated the propagation of dispersive shock waves in two differential equation models
The study titled “Evolution of Nonlinear Periodic Waves in the Focusing and Defocusing Cylindrical Modified Korteweg-de Vries Equations” was published in International Journal of Theoretical Physics by ITU Mathematics Engineering faculty members Dr. Neşe Özdemir, Assoc. Prof. Dr. Ali Demirci and Prof. Dr. Semra Ahmetolan.
This study investigates the evolution of dispersive shock wave (DSW) solutions within the focusing and defocusing cylindrical modified Korteweg-de Vries (cmKdV(f)) and (cmKdV(d)) equations under Riemann-type initial conditions. Using Whitham modulation theory, we derive and numerically solve the Whitham systems, enabling a comparison between these asymptotic solutions and direct numerical simulations of the cmKdV equations. The results provide a detailed classification of wave structures in both focusing and defocusing cases of the cmKdV equations. This research offers new insights into the behavior and classification of nonlinear periodic waves in the cmKdV equations.
To access the full article, https://doi.org/10.1007/s10773-024-05841-2
Long-time behavior of solutions to the general class of coupled nonlocal
nonlinear wave equations
The study titled “Long-time behavior of solutions to the general class of coupled nonlocal nonlinear wave equations” was published in “Zeitschrift für angewandte Mathematik und Physik” by ITU Department of Mathematics member Res. Assis. Dr. Şenay Pasinlioğlu.
Coupled nonlocal nonlinear wave equations describe the dynamics of wave systems with multiple interacting components in a wide range of physical applications. In this study, solitary wave solutions to the coupled nonlocal nonlinear wave equations with a general class of kernel functions are generated numerically using the Petviashvili iteration method, and the long-time behavior of the obtained solutions is investigated.
Coupled nonlocal nonlinear wave equations are widely applied to model complex wave phenomena involving multiple interacting components in fields such as optics, plasma physics, and fluid mechanics. Numerical studies of solitary wave solutions provide valuable insights into the dynamics of these complex systems. In this study, solitary wave solutions and their time evolution were investigated numerically. Since such solutions for general kernels are not analytically known, the solitary wave profile was first constructed using Petviashvili’s method. Next, a numerical method combining a Fourier pseudo-spectral method for spatial discretization and a fourth-order Runge–Kutta scheme for temporal discretization was proposed to study the time evolution of these solutions. The efficiency of the proposed methods was validated through extensive experiments with different kernels. Additionally, the stability of the obtained solitary wave solutions was examined under small perturbations. The accuracy of the method was tested for specific parameters, and the validity of the method was supported by figures. The results confirm that the proposed numerical method converges fourth-order in time and exponentially in space, which means that the proposed numerical scheme converges considerably well with the solution.
To access the full article, https://doi.org/10.1007/s00033-024-02342-4
Nonlinear SH waves in an elastic layered half-space with a more realistic material inhomogeneity model
The study titled “SH Waves in a weakly inhomogeneous half-space with a nonlinear thin layer coating” was published in Zeitschrift Für Angewandte Mathematik Und Physik (ZAMP) by ITU Mathematics Engineering faculty members Prof. Dr. Semra Ahmetolan, Assoc. Prof. Dr. Ali Demirci, Assoc. Prof. Dr. Ayse Peker-Dobie, and Dr. Neşe Özdemir.
In this study, the self-modulation of Love waves propagating in a nonlinear half-space covered by a nonlinear layer was investigated. It was assumed that the constituent material of the layer is nonlinear, homogeneous, isotropic, compressible, and hyperelastic, whereas for the half-space, it is nonlinear, heterogeneous, compressible and a different hyperelastic material. By employing the nonlinear thin layer approximation, the problem of wave propagation in a layered half-space is reduced to the one for a nonlinear heterogeneous half-space with a modified nonlinear homogeneous boundary condition on the top surface. This new problem is analyzed by a relevant perturbation method, and a nonlinear Schrödinger (NLS) equation defining the self-modulation of waves asymptotically is obtained. The dispersion relation is derived for different heterogeneous properties of the half-space and the thin layer. Then the results of the thin layer approximation are compared with the ones for the finite layer. The solitary solutions of the derived NLS equation are obtained for selected real material models. It has been discussed how these solutions are influenced by the heterogeneity of the semi-infinite space.
To access the full article, https://doi.org/10.1007/s00033-024-02213-y
Alternative Solution Methods to Shapley Iteration for the Solution of
Stochastic Matrix Games
The research titled " Matrix norm based hybrid Shapley and iterative methods for the solution of stochastic matrix games", conducted by Assoc. Prof. Dr. Burhaneddin İzgi, faculty member of the Department of Mathematics Engineering and Assoc. Prof. Dr. Nazım Kemal Üre, a faculty member of the Department of Artificial Intelligence and Data Engineering, was published in Applied Mathematics and Computation. In this novel research, Murat Özkaya (Ph.D. student of Izgi) and Prof.Dr. Matjaz are also coauthors of the paper.
In this paper, they present four alternative solution methods to Shapley iteration for the solution of stochastic matrix games. They first combine the extended matrix norm method for stochastic matrix games with Shapley iteration and then state and prove the weak and strong hybrid versions of Shapley iterations. Then, they present the semi-extended matrix norm and iterative semi-extended matrix norm methods, which are analytic-solution-free methods, for finding the approximate solution of stochastic matrix games without determining the strategy sets. They illustrate comparisons between the Shapley iteration, weak and strong hybrid Shapley iterations, semi-extended matrix norm method, and iterative semi-extended matrix norm method with several examples. The results reveal that the strong and weak hybrid Shapley iterations improve the Shapley iteration and decrease the number of iterations, and the strong hybrid Shapley iteration outperforms all the other proposed methods. Finally, they compare these methods and present their performance analyses for large-scale stochastic matrix games as well.
To access the full article, https://doi.org/10.1016/j.amc.2024.128638
A Work on Stabilization of Self-Steepening Optical Solitons in a
Periodic PT-Symmetric Potential
The study titled “Stabilization of Self-Steepening Optical Solitons in a Periodic PT-Symmetric Potential” was published in Chaos, Solitons & Fractals by ITU Mathematics Engineering faculty members Prof. Dr. Nalan Antar and Res.Assis. Eril Güray Çelik.
In this study, they have made significant progress in controlling self-steepening solitons governed by the modified nonlinear Schrödinger (MNLS) equation. These solitons are crucial for fiber optic communication, but they undergo both a position shift and an amplitude increase during their propagation. This inherent instability hinders their effectiveness in practical applications. The study demonstrates that incorporating a periodic PT-symmetric potential into the MNLS equation significantly improves soliton behavior. This approach effectively suppresses both the position shift and amplitude increase, leading to more stable soliton propagation. This breakthrough paves the way for enhanced performance in fiber optic communication systems, relying on these robust solitons for clearer and more reliable data transmission.
To access the full article, https://doi.org/10.1016/j.chaos.2024.115125
A Study Focusing on Singularly Perturbative Behaviour of Nonlinear
Advection–Diffusion-Reaction Processes
The study titled “Singularly perturbative behaviour of nonlinear advection–diffusion-reaction processes” conducted by ITU Department of Mathematics Engineering member Prof. Dr. Murat Sarı, , in collaboration with Assist. Prof.Dr. Tahir Coşgun was published in “The European Physical Journal Plus”.
The purpose of this paper is to use a wavelet technique to generate accurate responses for models characterized by the singularly perturbed generalized Burgers-Huxley equation (SPGBHE) while taking multi-resolution features into account. The SPGBHE’s behaviours have been captured correctly depending on the dominance of advection and diffusion processes. It should be noted that the required response was attained through integration and by marching on time. Haar wavelet method results are compared with corresponding results in the literature and are found in agreement in determining the numerical behaviour of singularly perturbed advection–diffusion processes. The most outstanding aspects of this research are to utilize the multi-resolution properties of wavelets by applying them to a singularly perturbed nonlinear partial differential equation and that no linearization is needed for this purpose.
To access the full article, https://doi.org/10.1140/epjp/s13360-024-04894-w
Mathematical Modelling of Antibiotic Interaction on Evolution of Antibiotic Resistance: An Analytical Approach
The study titled “Mathematical modelling of antibiotic interaction on evolution of antibiotic resistance: an analytical approach” conducted by ITU Department of Mathematics Engineering member Prof. Dr. Murat Sarı, in collaboration with Assist. Prof. Dr. Enes Seyfullah Kotil, Res. Assis. Ramin Nashebi was published in “PeerJ”.
The emergence and spread of antibiotic-resistant pathogens have led to the exploration of antibiotic combinations to enhance clinical effectiveness and counter resistance development. Synergistic and antagonistic interactions between antibiotics can intensify or diminish the combined therapy’s impact and evolve as bacteria transition from wildtype to mutant (resistant) strains. Experimental studies have shown that the antagonistically interacting antibiotics against wildtype bacteria slow down the evolution of resistance. Interestingly, other studies have shown that antibiotics that interact antagonistically against mutants accelerate resistance. However, it is unclear if the beneficial effect of antagonism in the wildtype bacteria is more critical than the detrimental effect of antagonism in the mutants. This study aims to illuminate the importance of antibiotic interactions against wildtype bacteria and mutants on the deacceleration of antimicrobial resistance.
To address this, a mathematical model that explores the population dynamics of wildtype and mutant bacteria under the influence of interacting antibiotics is developed and analyzed. The model investigates the relationship between synergistic and antagonistic antibiotic interactions with respect to the growth rate of mutant bacteria acquiring resistance.
To access the full article, https://doi.org/10.7717/peerj.16917
3D Plate Dynamics in the Framework of Space-Fractional Generalized Thermoelasticity – Theory and Validation.
The study titled “3D Plate Dynamics in the Framework of Space-Fractional Generalized Thermoelasticity – Theory and Validation” is published in American Institute of Aeronautics and Astronautics (AIAA) and authered by Assoc. Prof Dr. Soner Aydınlık, Prof. Ahmet Kiris and Prof. Dr. Wojciech Sumelka. The first author (SA) has been supported by The Scientific and Research Council of Turkey (TÜBİTAK) to conduct this research under TÜBİTAK-2219-International Postdoctoral Research Fellowship Program for Turkish Citizens. The support is gratefully acknowledged.
This study aims to examine the dynamics of 3D plates under uniform and non-uniform temperature distributions within the framework of the Fractional Generalized Thermoelasticity approach. The following crucial outcomes reflect the completeness of the proposed model:
• The variations of natural frequencies and mode shapes versus temperature are compared with the experimental results of the NASA report. It is observed that these are both fundamental for identifying the fractional material properties and the thermal and elastic ones.
• The nonlocal approach using fractional calculus gives more consistent results with the experimental one than the classical local theory.
• In the model, the effects connected with thermoelastic damping result in the quadratic eigenvalue problem where complex frequencies and modes are obtained.
• The complex frequency spectrum and mode shapes of the 3D plate with free ends under two different temperature distributions are considered for different values of the fractional continua order and the length scale parameter.
• The fractional solution closest to the experimental results and the classical modes are compared for the first four frequencies. Moreover, the absolute differences between them are also presented with contour plots.
• For the uniform temperature distribution, a mode shifting is observed between the modes corresponding to the 4th and 5th frequencies, while this is not kept for the non-uniform temperature distribution.
• For the non-uniform temperature distribution, mode shape analysis is performed, assuming that elasticity modulus, thermal expansion, and specific heat parameters are functions of temperature.
• The frequencies close to the experimental values are obtained at smaller values of fractional order while temperature increases for the fixed length scale parameter.
• It is observed that the peak point of the out-of-plane displacement is shifted toward the warm zone under the non-uniform temperature distribution. This investigation shows a good agreement with the experimental observations.
These novelties indicate that combining fractional mechanics and Generalized thermoelasticity can establish a more accurate model for complex materials under thermal loading.
To access the full article, https://doi.org/10.2514/1.J063310
Matrix Norm Methods for Zero-Sum Fuzzy Matrix Games with Payoffs of Triangular Fuzzy Numbers
The research titled "Matrix norm methods for zero-sum fuzzy matrix games with payoffs of triangular fuzzy numbers", was conducted by Assoc. Prof. Dr. Burhaneddin İzgi, faculty member of the Department of Mathematics Engineering, was published in Applied Mathematics and Computation. In this novel research about the fuzzy matrix games, Murat Özkaya (Ph.D. student of Izgi) and Professor Hale Gonce Köçken from Yıldız Technical University are also coauthors of the paper.
In this paper, they mainly consider the solution of two-person zero-sum fuzzy matrix games with payoffs of triangular fuzzy numbers. Contrary to the literature, they focus on developing the methods to solve the game directly based on only the norms of the payoff matrix holistically, without solving a linear programming problem or handling sub-games created by taking the components of fuzzy numbers separately. For this purpose, they first present fuzzy versions of 1-norm and µ-norm with the help of a ranking function and develop the fuzzy matrix norm method to obtain an approximate solution of the zero-sum fuzzy matrix game. In addition to this approach, they provide the fuzzy extended matrix norm method as an enhanced version of the method, which involves the use of newly defined fuzzy matrix norms. Thus, they managed to avoid the complexity of the optimization process of the linear programming problem via the proposed matrix norm-based methods. Lastly, they illustrate the implementation of the methods by considering several benchmark examples and a 3 × 3 fuzzy matrix game.
To access the full article, https://doi.org/10.1016/j.amc.2024.128874
Innovative deep learning approach for cross-crop plant disease detection: A generalized method for identifying unhealthy leaves
The article entitled ‘Innovative deep learning approach for cross-crop plant disease detection: A generalized method for identifying unhealthy leaves', authored by ITU Department of Mathematics Engineering faculty member of Prof. Dr. Muhammed Kurulay, in collaboration with Assist. Prof. Dr. Imane Bouacida, Prof. Dr. Brahim Farou, Doç. Dr. Lynda Djakhdjakha , Prof. Dr. Hamid Seridi, was published in Information Processing in Agriculture.
In this paper, we address this issue by proposing a novel deep learning-based system capable of recognizing diseased and healthy leaves across different crops, even if the system was not trained on them. The key idea is to focus on recognizing the diseased small leaf regions rather than the overall appearance of the diseased leaf, along with determining the disease’s prevalence rate on the entire leaf. For efficient classification and to leverage the excellence of the Inception model in disease recognition, we employ a small Inception model architecture, which is suitable for processing small regions without compromising performance.