University of GuilanJournal of Mathematical Modeling2345-394X11120230301Improving Bitcoin price prediction power by time-scale decomposition and GMDH-type neural network: A comparison of different periods and features117580410.22124/jmm.2022.22638.2003ENMaryamSeifaddiniDepartment of Computer Science, University of Guilan, Rasht, IranAmirHabibdoustDepartment of Economics and Accounting, University of Guilan, Rasht, IranJournal Article20220708This paper aims to improve the predictability power of a machine learning method by proposing a two-stage prediction method. We use Group Modeling Data Handling (GMDH)-type neural network method to eliminate the user role in feature selection. To consider recent shocks in Bitcoin market, we consider three periods, before COVID-19, after COVID-19, and after Elon Musk's tweeter activity. Using time-scale analysis, we decomposed the data into different scales. We further investigate the forecasting accuracy across different frequencies. The findings show that in shorter period the first, second and third lag of daily prices and trade volume produce valuable information to predict Bitcoin price while the seven days lag can improve the prediction power over longer period. The results indicate a better performance of the wavelet base GMDH-neural network in comparison with the standard method. This reveals the importance of trade frequencies' impact on the forecasting power of models.https://jmm.guilan.ac.ir/article_5804_1b4fd175bdb70691b4001107a7c53602.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X11120230301Global stability and Hopf bifurcation of delayed fractional-order complex-valued BAM neural network with an arbitrary number of neurons1934589510.22124/jmm.2022.22299.1972ENElhamJavidmaneshDepartment of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, IranAlirezaZamani BahahbadiDepartment of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, IranJournal Article20220521In this paper, a general class of fractional-order complex-valued bidirectional associative memory neural network with time delay is considered. This neural network model contains an arbitrary number of neurons, i.e. one neuron in the X-layer and other neurons in the Y-layer. Hopf bifurcation analysis of this system will be discussed. Here, the number of neurons, i.e., $n$ can be chosen arbitrarily. We study Hopf bifurcation by taking the time delay as the bifurcation parameter. The critical value of the time delay for the occurrence of Hopf bifurcation is determined. Moreover, we find two kinds of appropriate Lyapunov functions that under some sufficient conditions, global stability of the system is obtained. Finally, numerical examples are also presented.https://jmm.guilan.ac.ir/article_5895_c668df7490ebb552209eda7229db752e.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X11120230301Applications of the proximal difference-of-convex algorithm with extrapolation in optimal correction3554589910.22124/jmm.2022.22498.1986ENSamiraShahsavariDepartment of Applied Mathematics, Faculty of Mathematical Sciences University of Guilan, Rasht, IranSaeedKetabchiDepartment of Applied Mathematics, Faculty of Mathematical Sciences University of Guilan, Rasht, IranJournal Article20220615This paper proposes a proximal difference-of-convex algorithm with extrapolation ($PDCA_e$) based on Dinkelbach's approach for the optimal correction of two types of piecewise linear systems, classical obstacle problems and equilibrium problems, and linear inequalities. Using Dinkelbach's theorem leads to getting the roots of two single-variable functions. Considering the non-convex and level-bounded properties of the obtained problems, we use a proximal difference-of-convex algorithm programming to solve them. The experimental results on several randomly generated test problems show that the $PDCA_e$-generalized Newton method outperforms other methods for both feasible and infeasible cases.https://jmm.guilan.ac.ir/article_5899_66338635390d14bd52c966e73943f022.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X11120230301Ranking the Pareto frontiers of multi-objective optimization problems by a new quasi-Gaussian evaluation measure5570610610.22124/jmm.2022.22547.1990ENHamid RezaYousefzadehDepartment of Mathematics, Payame Noor University (PNU), P.O. BOX 19395-4697, Tehran, Iran.ElhamZahiriDepartment of Mathematics, Payame Noor University (PNU), P.O. BOX 19395-4697, Tehran, Iran.AghilehHeydariDepartment of Mathematics, Payame Noor University (PNU), P.O. BOX 19395-4697, Tehran, Iran.Journal Article20220626The existence of different solution approaches that generate approximations to the optimal Pareto frontiers of a multi-objective optimization problem lead to different sets of non-dominated solutions. To evaluate the quality of these solution sets, one requires a comprehensive evaluation measure to consider the features of the solutions. Despite various valuation measures, the deficiency caused by the lack of such a comprehensive measure is visible. For this reason, in this paper, by considering some evaluation measures, first we evaluate the quality of the approximations to the optimal Pareto front resulting from the decomposition-based multi-objective evolutionary algorithm equipped with four decomposition approaches and investigate the related drawbacks. In the second step, we use the concept of Gaussian degree of closeness to combine the evaluation measures, and hence, we propose a new evaluation measure called the quasi-Gaussian integration measure. The numerical results obtained from applying the proposed measure to the standard test functions confirm the effectiveness of this measure in examining the quality of the non-dominated solution set in a more accurate manner. https://jmm.guilan.ac.ir/article_6106_eeb8ea8294502a77ca27c2f9d5a42ba2.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X11120230301A new approximation method for convection-diffusion equation by the fundamental solutions7181611510.22124/jmm.2022.22266.1968ENSiamakBaneiDepartment of Mathematics, University of Kurdistan, Sanandaj, IranKamalShanazariDepartment of Mathematics, University of Kurdistan, Sanandaj, IranJournal Article20220520This paper develops a new numerical method of fundamental solutions for the non-homogeneeous convection-diffusion equations with time-dependent heat sources. A summation of the fundamental solutions of the diffusion operator is considered with time-dependent coefficients for the solution of the underlying problem. By the $\theta$-weight discretiztion for the time derivative and selecting the source points and the field points at each time level, the solutions of all time levels are obtained. In addition, the stability of this approach is analyzed by considering $\theta=1$ in numerical results. This method is truly meshless and it is not necessary to discretize any part of the domain or boundary.<br />As a result, this method is easily applicable to higher dimensional problems with irregular domains. In this work, we consider a non-homogeneous convection-diffusion equation (NCDE) in 2D with a regular domain and present some numerical results to show the effectiveness of the proposed method.https://jmm.guilan.ac.ir/article_6115_3995c4c1906608c7463f2ebf5f8c1ab9.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X11120230301Multilinear discriminant analysis using tensor-tensor products83101611710.22124/jmm.2023.22841.2026ENFranckDufrenoisLISIC,50 rue F. Buisson, ULCO Calais, FranceAlaaEl IchiLaboratoire de Mathématiques, Informatique et Applications, Securite de l'Information LABMIA-SI, University Mohamed V, Rabat Morocco; University Littoral Cote d'Oplae, FranceKhalideJbilouLMPA, 50 rue F. Buisson, ULCO Calais, France; Mohammed VI Polytechnic University, Green City, MoroccoJournal Article20220826Multilinear Discriminant Analysis (MDA) is a powerful dimension reduction method specifically formulated to deal with tensor data. Precisely, the goal of MDA is to find mode-specific projections that optimally separate tensor data from different classes. However, to solve this task, standard MDA methods use alternating optimization heuristics involving the computation of a succession of tensor-matrix products. Such approaches are most of the time difficult to solve and not natural, highligthing the difficulty to formulate this problem in fully tensor form. In this paper, we propose to solve multilinear discriminant analysis (MDA) by using the concept of transform domain (TD) recently proposed in [15]. We show here that moving MDA to this specific transform domain make its resolution easier and more natural. More precisely, each frontal face of the transformed tensor is processed independently to build a separate optimization sub-problems easier to solve. Next, the obtained solutions are converted into projective tensors by inverse transform. By considering a large number of experiments, we show the effectiveness of our approach with respect to existing MDA methods.https://jmm.guilan.ac.ir/article_6117_3b0e6647f4a92249762e577460d9eb26.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X11120230301Numerical solution of an influenza model with vaccination and antiviral treatment by the Newton-Chebyshev polynomial method103116612510.22124/jmm.2022.21989.1933ENBahmanBabayar-RazlighiDepartment of Mathematics, Qom University of Technology, P.O.Box 1519-37195, Qom, IranJournal Article20220319We consider a mathematical model of an influenza disease with vaccination and antiviral treatment. This model is expressed by a system of nonlinear ordinary differential equations. We linearize this system by the Newton's method and obtain a sequence of linear systems. The linear systems can be solved by the Chebyshev polynomial solutions, which is a convergence method for numerical solution of linear systems. We solve the problem on a union of many partial intervals. In each partial interval, we first obtain a crude approximation for starting the Newton's method, then solve the problem on current interval by using the lag intervals. An illustration of procedures, we give an algorithm for the initial guess and apply this algorithm for obtaining the total algorithm of the method. We investigate the convergence conditions of the Newton's method for the presented model. In the numerical examples section, we provide some numerical examples to illustrate of the accuracy of the method, and see that the main criterion of the convergence is true for such problems.https://jmm.guilan.ac.ir/article_6125_c783d9416fb86f63c4348674c31449f0.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X11120230301Second order spline method for fractional Bagley-Torvik equation with variable coefficients and Robin boundary conditions117132612610.22124/jmm.2022.23040.2047ENJoe Christin MarySDepartment of Mathematics, Bharathidasan University,
Tiruchirappalli - 620 024, Tamilnadu, IndiaAyyaduraiTamilselvanDepartment of Mathematics, Bharathidasan University,
Tiruchirappalli - 620 024, Tamilnadu, IndiaJournal Article20221010A fractional Bagley-Torvik equation of variable coefficients with Robin boundary conditions is considered in this paper. We prove the existence of the solution which is demonstrated by converting the boundary value problem into a Volterra integral equation of the second kind and also prove the uniqueness of the solution by using the minimum principle. We propose a numerical method that combines the second order spline approximation for the Caputo derivative and the central difference scheme for the second order derivative term. Meanwhile, the Robin boundary conditions is approximated by three-point endpoint formula. It is to be proved that this method is of second order convergent. Numerical examples are provided to demonstrate the accuracy and efficiency of the method.https://jmm.guilan.ac.ir/article_6126_547b7620438b0ea28a7de272cd09f1be.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X11120230301An LN-stable method to solve the fractional partial integro-differential equations133156612810.22124/jmm.2023.22727.2013ENFahimehZiyaeeDepartment of Mathematics, Shahed University, Tehran, IranAbolfazlTariDepartment of Mathematics, Shahed University, Tehran, IranJournal Article20220730In this paper, a class of Volterra fractional partial integro-differential equations (VFPIDEs) with initial conditions is investigated. Here, the well-known method of lines (MOLs) is developed to solve the VFPIDEs. To this end, the VFPIDE is converted into a system of first-order ordinary differential equations (ODEs) in time variable with initial conditions. Then the resulting ODE system is solved by an LN-stable method, such as Radau IIA or Lobatto IIIC. It is proved that the proposed method is LN-stable. Also, the convergence of the proposed method is proved. Finally, some numerical examples are given to illustrate the efficiency and accuracy of the proposed method.https://jmm.guilan.ac.ir/article_6128_81cc0b3754c4903f5690e07f77557126.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X11120230301A $p$-Laplacian model for uneven illumination enhancement of document images157169615810.22124/jmm.2022.20993.1834ENFatim ZahraAit BellaCadi Ayyad University, LAMAI FST Marrakech, MoroccoMoadHakimCadi Ayyad University, LAMAI FST Marrakech, MoroccoIdrissEl MourabitCadi Ayyad University, EST Essaouira, MoroccoSaidRaghayCadi Ayyad University, LAMAI FST Marrakech, MoroccoJournal Article20211101The exponential growth of low-cost digital imagery is latterly observed. Images acquired under uneven lighting are prone to experience poor visibility, which may severely limit the performance of most computational photography and automatic visual recognition applications. Different from current optimization techniques, we design a novel partial differential equation-based model to rectify the variable illumination artifacts. In this study, a large number of document samples capturing uneven illumination and low contrast conditions are tested to compare the effectiveness of the proposed local and nonlocal approaches.https://jmm.guilan.ac.ir/article_6158_f9588bb59c8caf069dfcc34c9e5fc85e.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X11120230301An asymptotic computational method for the nonlinear weakly singular integral models in option pricing171185618310.22124/jmm.2023.23444.2096ENSalamnYazdaniFaculty of Mathematics, K. N. Toosi University of Technology, Tehran, IranMahmoudHadizadeh YazdiFaculty of Mathematics, K. N. Toosi University of Technology, Tehran, IranVahidFakoorDepartment of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, IranJournal Article20221216The integral representation of the optimal exercise boundary problem for generating the continuous-time early exercise boundary for the American put option is a well-known topic in the mathematical finance community. The main focus of this paper is to provide an efficient asymptotically computational method to improve the accuracy of American put options and their optimal exercise boundary. Initially, we reformulate the nonlinear singular integral model of the early exercise premium problem given in [Kim et al., A simple iterative method for the valuation of American options, Quant. Finance. 13 (2013) 885--895] to an equivalent form which is more tractable from a numerical point of view. We then obtain the existence and uniqueness results with verifiable conditions on the functions and parameters in the resulting operator equation. The asymptotic behavior for the early exercise boundary is also analyzed which is mostly compatible with some realistic financial models.https://jmm.guilan.ac.ir/article_6183_00daceed0dbc31178809c32ae537652a.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X11120230301Application of Green's function and Sinc approximation in the numerical solution of the fractional differential equations187205619310.22124/jmm.2022.22809.2022ENZahraBalaliDepartment of Mathematics, South Tehran Branch, Islamic Azad University,Tehran, IranNargesTaheriDepartment of Mathematics, South Tehran Branch, Islamic Azad University,Tehran, IranJalilRashidiniaSchool of Mathematics, Iran University of Science and Technology, Narmak,Tehran 168613114, IranJournal Article20220827The primary purpose of this paper is the construction of the Green's function and Sinc approximation for a class of Caputo fractional boundary value problems (CFBVPs). By using the inverse derivative of the fractional order, we can derive the equivalent fractional order Volterra integral equations from CFBVPs, which is considered Green's function. It is approximated by the Sinc-Collocation method. A convergence analysis of the presented method is given. Our approach is applied to five examples. We derive that our approach converges to the exact solution rapidly with the order of exponential accuracy.https://jmm.guilan.ac.ir/article_6193_549a715bcbdddfebe857a742d9a3fc55.pdf