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2D hyperchaotic Styblinski-Tang map for image encryption and its hardware implementation
(Springer Link, 2024) Üstün, Deniz; Erkan, Uğur; Toktaş, Abdurrahim; Lai, Qiang; Yang, Liang
A novel 2D chaotic system is presented, which is inspired by Styblinski Tang (ST) function employed as optimization test function. It is a challenge function because of having many local optima. The performance of the chaotic system namely 2D Styblinski Tang (2D-ST) map is corroborated through an extensive comparison with the literature in terms of the sensitive chaos metrics as well as its randomness is verified over TestU0. The 2D-ST map manifests the best hyperchaotic behavior due to higher ergodicity and complexity characteristics. Moreover, the 2D-ST map is implemented to a microcontroller hardware, and it is seen that the results manifests that the proposed 2D-ST can be a potential practical candidate thanks to excellent hyperchaotic performance.
A novel genetic search scheme based on nature-inspired evolutionary algorithms for binary self-dual codes
(American Institute of Mathematical Sciences (AIMS), 2022) Korban, Adrian; Şahinkaya, Serap; Üstün, Deniz
In this paper, a genetic algorithm, one of the evolutionary algorithm optimization methods, is used for the first time for the problem of computing extremal binary self-dual codes. We present a comparison of the computational times between the genetic algorithm and a linear search for different size search spaces and show that the genetic algorithm is capable of computing binary self-dual codes significantly faster than the linear search. Moreover, by employing a known matrix construction together with the genetic algorithm, we are able to obtain new binary self-dual codes of lengths 68 and 72 in a significantly short time. In particular, we obtain 11 new binary self-dual codes of length 68 and 17 new binary self-dual codes of length 72.
A symbiotic organisms search algorithm-based design optimization of constrained multi-objective engineering design problems
(Emerald Insight, 2021) Üstün, Deniz; Carbas, Serdar; Toktaş, Abdurrahim
Purpose In line with computational technological advances, obtaining optimal solutions for engineering problems has become attractive research topics in various disciplines and real engineering systems having multiple objectives. Therefore, it is aimed to ensure that the multiple objectives are simultaneously optimized by considering them among the trade-offs. Furthermore, the practical means of solving those problems are principally concentrated on handling various complicated constraints. The purpose of this paper is to suggest an algorithm based on symbiotic organisms search (SOS), which mimics the symbiotic reciprocal influence scheme adopted by organisms to live on and breed within the ecosystem, for constrained multi-objective engineering design problems. Design/methodology/approach Though the general performance of SOS algorithm was previously well demonstrated for ordinary single objective optimization problems, its efficacy on multi-objective real engineering problems will be decisive about the performance. The SOS algorithm is, hence, implemented to obtain the optimal solutions of challengingly constrained multi-objective engineering design problems using the Pareto optimality concept. Findings Four well-known mixed constrained multi-objective engineering design problems and a real-world complex constrained multilayer dielectric filter design problem are tackled to demonstrate the precision and stability of the multi-objective SOS (MOSOS) algorithm. Also, the comparison of the obtained results with some other well-known metaheuristics illustrates the validity and robustness of the proposed algorithm. Originality/value The algorithmic performance of the MOSOS on the challengingly constrained multi-objective multidisciplinary engineering design problems with constraint-handling approach is successfully demonstrated with respect to the obtained outperforming final optimal designs.
Additive complementary dual codes from group characters
(Institute of Electrical and Electronics Engineers (IEEE), 2022) Dougherty, S. T.; Şahinkaya, Serap; Üstün, Deniz
Additive codes have become an increasingly important topic in algebraic coding theory due to their applications in quantum error-correction and quantum computing. Linear Complementary Dual (LCD) codes play an important role for improving the security of information against certain attacks. Motivated by these facts, we define additive complementary dual codes (ACD for short) over a finite abelian group in terms of an arbitrary duality on the ambient space and examine their properties. We show that the best minimum weight of ACD codes is always greater than or equal to the best minimum weight of LCD codes of the same size and that this inequality is often strict. We give some matrix constructions for quaternary ACD codes from a given quaternary ACD code and also from a given binary self-orthogonal code. Moreover, we construct an algorithm to determine if a given quaternary additive code is an ACD code with respect to all possible symmetric dualities. We also determine the largest minimum distance of quaternary ACD codes for lengths n <= 10. The obtained codes are either optimal or near optimal according to Bierbrauer et al+. (2009).
Additive skew G-codes over finite fields
(Springer Link, 2023) Dougherty, S. T.; Korban, Adrian; Şahinkaya, Serap; Üstün, Deniz
We define additive skew G-codes over finite fields and discuss several dualities attached to these codes. We examine the properties of self-dual skew G-codes and in particular we show that the dual, under any duality, of an additive skew G-code is also an additive skew G-code. Additionally, we propose a matrix construction for additive skew G-codes and use it to construct several examples of extremal self-dual additive skew G-codes over the finite field F4. Such codes have a strong connection to quantum error correcting codes.
Adjustment of the evaporation pan coefficient: Case study of Konya closed basin
(Springer Link, 2022) Cicibıyık, Alara; Şarlak, Nermin; Üstün, Deniz
Global warming is an accepted fact by everyone, even if climate change still seems to be a controversial issue. The increase in temperature caused by global warming increases the rate of evaporation from open water surfaces. Although it is necessary that the presence of water and removing the saturated vapour layer from the air with the wind to keep on evaporation, temperature is an essential factor. Evaporation is the most difficult component of the hydrological cycle to determine. Evaporation can be estimated by various methods. One of them is the evaporation pan even if the value measured cannot be expected to represent evaporation in large bodies of water. The pan is more easily affected by changes in temperature in the air. Another is the empirical evaporation estimation methods based on measured meteorological parameters. One of these methods is Penman. The Penman method is used as a reference method in studies related to evaporation since it gives the closest results to the measured data in different parts of the world. In this study, evaporation rate was estimated by the Penman method using data measured at five meteorological stations in the Konya Closed Basin. The aim of the study is to recalculate the pan coefficient, which is used as 0.7 in Turkey. The Artificial bee colony algorithm, one of the statistical optimization techniques, was used for this purpose. It was concluded that the measurements would close to Penman estimates if the pan coefficient was taken as 0.79 for the Konya Closed Basin.
An Application of the Virus Optimization Algorithm to the Problem of Finding Extremal Binary Self-Dual Codes
(American Institute of Mathematical Sciences, 2021) Korban, Adrian; Şahinkaya, Serap; Üstün, Deniz
In this paper, a virus optimization algorithm, which is one of the metaheuristic optimization technique, is employed for the first time to the problem of finding extremal binary self-dual codes. We present a number of generator matrices of the form [I36 | ?3(v)], where I36 is the 36 × 36 identity matrix, v is an element in the group matrix ring M3(F2)G and G is a finite group of order 12, which we then employ together with the the virus optimization algorithm and the genetic algorithm to search for extremal binary self-dual codes of length 72. We obtain that the virus optimization algorithm finds more extremal binary self-dual codes than the genetic algorithm. Moreover, by employing the above mentioned constructions together with the virus optimization algorithm, we are able to obtain 39 Type I and 19 Type II codes of length 72, with parameters in their weight enumerators that were not known in the literature before.
An image encryption scheme based on an optimal chaotic map derived by multi-objective optimization using ABC algorithm
(Springer Link, 2021) Toktaş, Abdurrahim; Üstün, Deniz; Erkan, Uğur
A novel optimal chaotic map (OCM) is proposed for image encryption scheme (IES). The OCM is constructed using a multi-objective optimization strategy through artificial bee colony (ABC) algorithm. An empirical model for the OCM with four unknown variables is first constituted, and then, these variables are optimally found out using ABC for minimizing the multi-objective function composed of the information entropy and Lyapunov exponent (LE) of the OCM. The OCM shows better chaotic attributes in the evaluation analyses using metrics such as bifurcation, 3D phase space, LE, permutation entropy (PE) and sample entropy (SE). The encrypting performance of the OCM is demonstrated on a straightforward IES and verified by various cryptanalyses that compared with many reported studies, as well. The main superiority of the OCM over the studies based on optimization is that it does not require any optimization in the encrypting operation; thus, OCM works standalone in the encryption. However, those reported studies use ciphertext images obtained through encrypting process in every cycle of optimization algorithm, resulting in long processing time. Therefore, the IES with OCS is faster than the others optimization-based IES. Furthermore, the proposed IES with the OCM manifests satisfactory outcomes for the compared results with the literature.
An optimized surrogate model using differential evolution algorithm for computing parameters of antennas
(Wiley, 2022) Üstün, Deniz; Toktaş, Feyza; Toktaş, Abdurrahim
In this study, a method based on surrogate model (SM) for computational analysis of antenna parameters such as the resonant frequency (RF) and bandwidth (BW) is presented. Moreover, it is attempted to optimize the SM using evolutionary optimization algorithms in order to further improve the accuracy of the SM. In the conventional computational approaches, the weighting vectors of the SM have been analytically determined. We have optimally achieved the weighting vectors of the SM through differential evolution (DE) and particle swarm optimization (PSO) algorithms. The capabilities of the algorithms are hereby compared with each other. The methodology is applied to the analysis of rectangular microstrip antenna (RMA), including a number of 33 measured RMAs with different geometrical and electrical parameters. From the total number of RMAs, 27 and 6 RMAs are, respectively, used in the construction and the test of the SM. Furthermore, the SM is verified through a comparison with the literature in terms of total absolute errors (TAEs). The results show that the SM with DE computes the most accurate RF and BW with the TAEs of 0.0099 GHz and 0.131%, respectively. The accuracy of the SM is further raised by 78%, thanks to the optimization of SM with DE. Therefore, a novel computational analysis method based on SM is implemented to computation of an antenna parameter with higher accuracy, and SM is successfully optimized by DE. The proposed method is able to easily implement to the stringent engineering problems based on simulated or measured data for computer-aided design (CAD).
An S-Box construction from exponentiation in finite fields and its application in RGB color image encryption
(Springer, 2024) Klobusicky, J.; Dougherty, S. T.; Şahinkaya, Serap; Üstün, Deniz
In this study, the utilization of exponentiation in finite fields is investigated for the purpose of generating pseudo-random sequences which have a crucial role in cryptographic applications. More precisely, a novel method for generating pseudo-random sequences is proposed to construct an initial S-Box which is a key component in various encryption schemes. In addition to that, a shuffling algorithm that leverages the pseudo-random sequences is developed to enhance the effectiveness of the initial S-Box. The utilization of the proposed S-Box is applied to the RGB color images to showcase its performance and robustness in an image encryption scheme.
Approaching the Minimum Distance Problem by Algebraic Swarm-Based Optimizations
(Dergipark, 2021) Şahinkaya, Serap; Üstün, Deniz
In 1948, Claude Shannon, published ”A Mathematical Theory of Communication,” a seminal paper, which was about reliable data transmission over noisy channels [12]. Efficient and reliable data transmission, which can be done by some error-control techniques, are one of the main interests of coding theory. Error detecting and correcting capability are very important feature of a code and it is determined by the minimum distance of the code. Computing the minimum distance of a linear code C of large length is a difficult problem in coding theory. In [14], Vardy showed that this computation is an NP-hard type. The problem of finding minimum distance is getting harder when the size of the code grows. Therefore, some meta-heuristic algorithms have been used to approach the problem. In most of the existing literature, genetic algorithms are used for the considered problem. As far as our knowledge, among the algorithms in the literature that are based on swarm intelligence, only the ant colony algorithm (ACO) was used for the minimum-weight codeword problem [4,5]. It is well known that there is no heuristic algorithm which can perform good enough to solve optimization problems, please see [13] for details. . Therefore, it is natural to try the other swarm-based optimization techniques for the considered problem. In this paper, bat algorithm (BA) and firefly algorithm (FA) are applied to the minimum distance problem by integrating the algebraic operator to the handled algorithms. Most of the papers in the literature uses codewords as a search space for the minimum distance problem. Recently, generator matrices were considered as a search space, which turned out to be a better approach than using the codewords as a search space, please see [1] for details. In this work, we also consider generator matrices as a search space. In coding theory, the BCH codes or BoseOCoChaudhuriOCoHocquenghemcodes form a class of cyclic error-correcting codes that are constructed using polynomials over a finite field. Effectiveness of the presented algorithm is controlled by running the algorithm on BCH codes since they are the standard codes with known minimum distance values [3, 9]
Binary self-dual and LCD codes from generator matrices constructed from two group ring elements by a heuristic search scheme
(American Institute of Mathematical Sciences (AIMS), 2022) Dougherty, S. T.; Korban, Adrian; Şahinkaya, Serap; Üstün, Deniz
We present a generator matrix of the form [?(v1) | ?(v2)], where v1 ? RG and v2 ? RH, for finite groups G and H of order n for constructing self-dual codes and linear complementary dual codes over the finite Frobenius ring R. In general, many of the constructions to produce self-dual codes forces the code to be an ideal in a group ring which implies that the code has a rich automorphism group. Unlike the traditional cases, codes constructed from the generator matrix presented here are not ideals in a group ring, which enables us to find self-dual and linear complementary dual codes that are not found using more traditional techniques. In addition to that, by using this construction, we improve 10 of the previously known lower bounds on the largest minimum weights of binary linear complementary dual codes for some lengths and dimensions. We also obtain 82 new binary linear complementary dual codes, 50 of which are either optimal or near optimal of lengths 41 ? n ? 61 which are new to the literature.
Codes from the Skew Ring ... - ...
(American Mathematical Society, 2023) Dougherty, S. T.; Şahinkaya, Serap; Üstün, Deniz
In this work, we study codes generated by elements in the skew group matrix ring M k ( R ) ? ? G M_k(R)\rtimes _{\varphi }G , where R R is a finite commutative Frobenius ring, G G is an arbitrary finite group, and ? \varphi is a group homomorphism from G G to A u t ( M k ( R ) ) Aut(M_k(R)) . We then determine all possible group homomorphisms ? : G ? A u t ( M 2 ( F 2 ) ) , \varphi : G \rightarrow Aut(M_2(\mathbb {F}_2)), for the cases where G G is a cyclic group and a dihedral group. Finally, by using skew generator matrices we provide examples of binary self-dual codes and also binary linear optimal codes.
Combustion characteristics of trimethyl borate, diesel, and trimethyl borate-diesel blend droplets
(Elsevier, 2022) Yontar, Ahmet Alper; Özgüner, Ayşe Gizem; Adıgüzel, Mehmet Ali; Üstün, Deniz
In this study, droplet tests were carried out for pure and blended forms of diesel fuel, which is the traditional fuel, and trimethyl borate fuel, which is new generation fuels. In this context, the evolution of fuel droplet diameter, flame structure, and flame temperature over time was observed using a high-speed camera and a thermal camera simultaneously. Measurements were made for the addition of 20%, 40%, 60%, and 80% trimethyl borate fuel to diesel fuel in fuel blends. The curves of the time-dependent change of the dimensionless square of the droplet diameter (D/D0)2 of the fuel droplets considered in the study, in general, have been determined to comply with the D2-law. Also, as the amount of diesel rose, there were high changes in droplet distortion and high deviations from the hemispherical geometry, and also elongation in the dominant shape droplet shape changed times. While the highest flame temperature was monitored by the thermal camera in the flame formed by the trimethyl borate droplet, as the amount of diesel fuel in the mixture increased, the maximum flame temperature decreased, but the burning time of the droplet was prolonged. On the other hand, the shortest ignition delay was measured for trimethyl borate, while the longest ignition delay time was detected for diesel fuel droplet. In general, it has been observed that the addition of trimethyl borate reduces the ignition delay, shortens the extinction time, and increases the temperature during combustion compared to diesel.
Construction of DNA Codes From Composite Matrices and a Bio-Inspired Optimization Algorithm
(IEEE-INST Electrical Electronics Engineers Inc., 2023) Korban, Adrian; Şahinkaya, Serap; Üstün, Deniz; Dougherty, S. T.
Indexed keywords SciVal Topics Metrics Funding details Abstract In this work, we present a new construction method for reversible codes. We employ composite matrices derived from group rings and show how to construct these matrices so that they are also reversible. Also in this work, we give an algorithm for calculating conflict free DNA codes that satisfy the Hamming distance, the reverse, the reverse-complement, the GC-content constraints with each DNA codeword being free from reverse complement sub-strings. By employing our construction method for reversible codes and our algorithm, we construct a number of DNA codes that satisfy the above constraints. Many of the codes we obtain have better parameters than some known DNA codes and many have parameters that are new to the literature.
Design Optimization of Multi-objective Structural Engineering Problems Via Artificial Bee Colony Algorithm
(Springer Link, 2021) Carbas, Serdar; Üstün, Deniz; Toktaş, Abdurrahim
The construction sector constitutes a significant portion of global gross national expenditures with huge financial budget requirements and provides employment for more than one hundred million people. Besides, considering that people spend more than 80% of their time indoors today, it is necessary to make optimal structure designs. This requirement stems from the inadequacy of existing structures in the face of today's changing conditions. Indeed, realistic design optimization of the structures can be done not only by taking into account a single objective but also considering a number of structural criteria. It means that there is inherent multi-purpose in most structural design optimization problems. Thus, it is very difficult engineering task to solve these kinds of problems, as it is necessary to optimize multiple purposes simultaneously to obtain optimal designs. With the help of the improvisation in optimization techniques used for multi-objective structural engineering design, algorithms are provided to achieve the optimal designs by creating a strong synergy between the structural requirements and constraints mentioned in the design specifications. The recent addition to this trend is so-called Artificial Bee Colony (ABC) algorithm which simulates the nectar searching ability of the bees in nature for nutrition. In this chapter, an optimal design algorithm via ABC is proposed in order to obtain the optimum design of multi-objective structural engineering design problems. The applications in design examples have shown the robustness, effectiveness, and reliability of ABC in attaining the design optimization of multi-objective constrained structural engineering design problems.
Design optimization of multilayer microwave filter using differential evolution algorithm
(Institute of Electrical and Electronics Engineers (IEEE), 2022) Toktaş, Abdurrahim; Üstün, Deniz
Three types of multilayer microwave filter (MMF) which are low-pass (LP), high-pass (HP) and band-pass (BP) are designed through a frequency-dependent material using Pareto-based multi-objective differential evolution (DE) (MODE) algorithm. To this end, a dual-objective electromagnetic (EM) model taking into account oblique incident wave angle with transverse electric (TE) or transverse magnetic (TM) polarization is constructed, which is based on total reflection (TR) for the passing and stopping bands. The global optimal designs (GODs) are selected from the Pareto optimal designs (PODs) by considering the trade-off among the objective values. The frequency and angular behavior of the MMFs are comparatively studied. The designed MMF are near ideal characteristic thanks to MODE having effective and powerful multi-objective strategy.
Designing of the Artificial Neural Network Model Trained by Using the Different Learning Algorithms to Classify the Electrocardiographic Signals
(European Journal of Science and Technology, 2022) Çelik, İbrahim; Üstün, Deniz; Akdağlı, Ali
An artificial neural network model trained by using various learning algorithms is designed to classify the electrocardiographic signals in this study. The model of artificial neural network is constructed on the structure consisting of a multilayered perceptron based on the feed forward back propagation. A data pool is built by using a dataset consists of 66 electrocardiographic data’s taken from the MIT BIH arrhythmia database to perform the training and testing processes of artificial neural network model. The training process of artificial neural network model is performed with 46 electrocardiographic data and then the accuracy of the model is tested via 20 electrocardiographic data. The artificial neural network is trained by 3 different learning algorithms to achieve a robust model. The performance of the learning algorithms used for training the model of the artificial neural network is evaluated according to percentage error. It illustrates that the artificial neural network model trained by Levenberg–Marquardt learning algorithm obtains the better classification result than other learning algorithms. The proposed artificial neural network model can be successfully used to classify the electrocardiographic signals.
Developing a secure image encryption technique using a novel S-box constructed through real-coded genetic algorithm’s crossover and mutation operators
(Pergamon, 2024) Üstün, Deniz; Şahinkaya, Serap; Atlı, Nurdan
The objective of this study is to craft a novel S-Box tailored to stringent security standards, achieved through iterative application of crossover and mutation operators inherent to real-coded genetic algorithms, ensuring robust image encryption. The designed S-Box is rigorously evaluated across multiple criteria, demonstrating its superiority over comparable S-Box designs found in existing literature. Furthermore, a secure image encryption method based on the designed S-Boxes devised and also including a 2D hyperchaotic Styblinski–Tang map. Thorough security assessments, encompassing statistical analysis and resilience testing against diverse attacks and noise, it is validated the encryption technique’s efficiency and applicability across varied scenarios.
Dihedral codes with 1-dimensional hulls and 1-dimensional linear complementary pairs of dihedral codes
(Springer Link, 2023) Dougherty, S. T.; Şahinkaya, Serap; Üstün, Deniz
In this paper, we study dihedral codes with 1-dimensional hulls and we determine precisely when dihedral codes over fnite felds with 1-dimensional hulls exist. Moreover, we show that these codes come canonically in pairs. We also introduce 1-dimensional linear complementary pairs of dihedral codes and examine the properties of this class of codes. As an application, we obtain 1-dimensional linear complementary pair of dihedral codes, which are either optimal or near optimal.

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