Payame Noor University (PNU)Control and Optimization in Applied Mathematics2383-31308120230601Solving a Class of Nonlinear Optimal Control Problems Using Haar Wavelets and Hybrid GA117957110.30473/coam.2023.65549.1214ENSaeedNezhadhoseinDepartment of Mathematics, Payame Noor University (PNU), P.O. BOX 19395-4697, Tehran, Iran.RezaGhanbariFaculty of Mathematical Sciences, Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.0000-0003-3876-7584KhatereGhorbani-MoghadamMosaheb Institute of Mathematics, Kharazmi University, Tehran, Iran.0000-0003-0109-6406Journal Article20220920In this paper, we solve a class of nonlinear optimal control problems using a hybrid genetic algorithm (HGA) and a direct method based on the Haar wavelets where the performance index is Bolza-form and the dynamic system is linear. First, we change the problem by using HWs to a static optimization problem in which the decision variables are the unknown coefficients of the state and control variables in the Haar series. Next, we apply HGA with a local search for higher power of GA in investigating the search space for solving optimization problems. Finally, we give some examples to illustrate the high accuracy of the proposed method.https://mathco.journals.pnu.ac.ir/article_9571_16d7b99096ad8cba1d4f3e288abfc2c5.pdfPayame Noor University (PNU)Control and Optimization in Applied Mathematics2383-31308120230601A Proximal Method of Stochastic Gradient for Convex Optimization1932977610.30473/coam.2023.64060.1205ENZeinabSaeidianDepartment of Mathematics, University of Kashan, Kashan, Iran.0000-0002-6279-7217MaryamMahmoudoghliK.N. Toosi University of Technology, Tehran, Iran.Journal Article20220523The Proximal Stochastic Average Gradient (Prox-SAG+) is a primary method used for solving optimization problems that contain the sum of two convex functions. This kind of problem usually arises in machine learning, which utilizes a large amount of data to create component functions from a dataset. A proximal operation is applied to obtain the optimal value due to its appropriate properties. The Prox-SAG+ algorithm is faster than some other methods and has a simpler algorithm than previous ones. Moreover, using this specific operator can help to reassure that the achieved result is optimal. Additionally, it has been proven that the proposed method has an approximately geometric rate of convergence. Implementing the proposed operator makes the method more practical than other algorithms found in the literature. Numerical analysis also confirms the efficiency of the proposed scheme.https://mathco.journals.pnu.ac.ir/article_9776_0897b20087851592b6ed7be668554e56.pdfPayame Noor University (PNU)Control and Optimization in Applied Mathematics2383-31308120230601Effective Data Reduction for Time-Aware Recommender Systems3353978410.30473/coam.2023.66162.1221ENHadisAhmadian YazdiDepartment of Computer Engineering, Neyshabur Branch, Islamic Azad University, Neyshabur, Iran0000-0001-7435-9903Seyed JavadSeyyed Mahdavi ChabokDepartment of Electrical Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran0000-0003-1856-4579MaryamKheirAbadiDepartment of Computer Engineering, Neyshabur Branch, Islamic Azad University, Neyshabur, Iran0000-0001-8980-4299Journal Article20221121In recent decades, the amount and variety of data have grown rapidly. As a result, data storage, compression, and analysis have become critical subjects in data mining and machine learning. It is essential to achieve accurate compression without losing important data in the process. Therefore, this work proposes an effective data compression method for recommender systems based on the attention mechanism. The proposed method performs data compression on two levels: features and records. It is time-aware and based on time windows, taking into account users' activity and preventing the loss of important data. The resulting technique can be efficiently utilized for deep networks, where the amount of data is a significant challenge. Experimental results demonstrate that this technique not only reduces the amount of data and processing time but also achieves acceptable accuracy.https://mathco.journals.pnu.ac.ir/article_9784_ab05fc375d5c6cf3902a99d01874cad6.pdfPayame Noor University (PNU)Control and Optimization in Applied Mathematics2383-31308120230601Optimal Edges in Morphological Snakes5567951810.30473/coam.2022.61960.1185ENRasoolHatamian JoghaliDepartment of Mathematics, Payame Noor University (PNU), P.O. BOX 19395-4697, Tehran, Iran.Journal Article20211203In 2010, Alvarez et al. proposed an algorithm for morphological snakes that could detect objects whose edges consist of convex sets and polygonal edges. However, the algorithm may not detect the boundary well if the edges of an object contain a convex set or if there are several separated objects in an image. In this paper, we present two optimal sub-algorithms that are modifications to the Alvarez et al. algorithm. Our algorithms provide optimal edge detection for images and we present examples to demonstrate their effectiveness.https://mathco.journals.pnu.ac.ir/article_9518_7d3142760f40294e98d31d3836a65d97.pdfPayame Noor University (PNU)Control and Optimization in Applied Mathematics2383-31308120230601Mathematical Modeling Considering Agricultural and Non-Agricultural Habitats for Biological Losses on Roads6981948310.30473/coam.2023.63543.1198ENMohammad HosseinRahmani DoustDepartment of mathematics, Faculty of Basic Sciences, University of Neyshabur, Neyshabur, Iran.0000-0001-6603-5503Mohammad NasserModoodiDepartment of Horticulture Science and Engineering, Torbat-e Jam University, Torbat-e Jam, Iran.0000-0003-0223-4778ArashMowdoudiDepartment of Informatics, Universita della Svizzera Italiana, Lugano, Switzerland.0000-0003-4028-5541Journal Article20220407Mathematical modeling has been a significant tool in biological sciences for several decades. Modern agricultural practices have had numerous effects on different aspects of ecosystems, particularly on animal populations. This research focuses on road collisions involving wildlife and emphasizes the effects of agricultural and non-agricultural surrounding lands. Using non-parametric Mann-Whitney U and Spearman's Rank tests, as well as SPSS software, the study found that the highest number of wildlife deaths, especially for mammals, birds, and reptiles, occurred in areas surrounded by natural regions (non-agricultural lands). Furthermore, the study found that the number of casualties was highest in the middle month of spring and those morning observations resulted in more collisions than evening ones. The correlation coefficients confirmed a significant relationship between the frequency of accidents and the type of surrounding landscape. Additionally, the researchers proposed a logistic mathematical model to investigate the relationship between animal losses and vehicle collisions. After identifying the equilibrium points, the study analyzed the solution behavior around these points.https://mathco.journals.pnu.ac.ir/article_9483_1efeb0e5aa9b791afff4eab9b5b1923f.pdfPayame Noor University (PNU)Control and Optimization in Applied Mathematics2383-31308120230601The Smallest Number of Colors Needed for a Coloring of the Square of the Cartesian Product of Certain Graphs8393923910.30473/coam.2022.54855.1194ENSajadSohrabi HesanDepartment of Applied Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, Iran.FreydoonRahbarniaDepartment of Applied Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, Iran.MostafaTavakolliDepartment of Applied Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, Iran.0000-0002-3315-1759Journal Article20220205Given any graph G, its square graph G^2 has the same vertex set as G, with two vertices adjacent in G^2 whenever they are at distance 1 or 2 in G. The Cartesian product of graphs G and H is denoted by G□ H. One of the most studied NP-hard problems is the graph coloring problem. A method such as Genetic Algorithm (GA) is highly preferred to solve the Graph Coloring problem by researchers for many years. In this paper, we use the graph product approach to this problem. In fact, we prove that X((D(m',n')□D(m,n))^2)<= 10 for m,n => 3, where D(m, n) is the graph obtained by joining a vertex of the cycle C_m to a vertex of degree one of the paths P_n and X(G) is the chromatic number of the graph $G$.https://mathco.journals.pnu.ac.ir/article_9239_ede0c8486ecb075276aa3067e789b2b0.pdf