Amirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24491220200901Roadside acoustic sensors to support vulnerable pedestrians via their smartphones135143331210.22060/ajmc.2019.15479.1017ENMehdiGhateeDepartment of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran0000-0002-9558-8286MasoomehKhaliliDepartment of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, IranMehdiTeimouriFaculty of New Sciences and Technologies, University of Tehran, Tehran, IranMohammad MahdiBejaniDepartment of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, IranJournal Article20181218This paper proposes a smartphone-based warning system to evaluate the risk of a motor vehicle for vulnerable pedestrians (VP). The acoustic sensors are embedded in the roadside to receive vehicle sounds and they are classified into heavy vehicles, light vehicles with low speed, light vehicles with high speed, and no vehicle classes. For this aim, we extract new features by Mel-frequency Cepstrum Coefficients (MFCC) and Linear Predictive Coefficients (LPC) algorithms. We use different classification algorithms and show that MLP neural network achieves at least $96.77$% accuracy criterion. To install this system, directional microphones are embedded on the roadside and the risk is classified. Then, for every microphone, a danger area is defined and the warning alarms have been sent to every VPs’ smartphones covered in this danger area.https://ajmc.aut.ac.ir/article_3312_9418b8be2fef85561e0bb01705f4d053.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24491220200901Approximation algorithms for multi-multiway cut and multicut problems on directed graphs145152381010.22060/ajmc.2018.15109.1014ENRaminYarinezhadDepartment of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, IranSeyed NaserHashemiDepartment of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, IranJournal Article20181008In this paper, we study the directed multicut and directed multimultiway cut problems. The input to the directed multi-multiway cut problem is a weighted directed graph $G=(V,E)$ and $k$ sets $S_1, S_2,\cdots, S_k$ of vertices. The goal is to find a subset of edges of minimum total weight whose removal will disconnect all the connections between the vertices in each set $S_i$, for $1\leq i\leq k$. A special case of this problem is the directed multicut problem whose input consists of a weighted directed graph $G=(V,E)$ and a set of ordered pairs of vertices $(s_1,t_1),\cdots,(s_k,t_k)$. The goal is to find a subset of edges of minimum total weight whose removal will make for any $i, 1\leq i\leq k$, there is no directed path from si to ti . In this paper, we present two approximation algorithms for these problems. The so called region growing paradigm is modified and used for these two cut problems on directed graphs. using this paradigm, we give an approximation algorithm for each problem such that both algorithms have the approximation factor of $O(k)$ the same as the previous works done on these problems. However, the previous works need to solve $k$ linear programming, whereas our algorithms require only one linear programming. Therefore, our algorithms improve the running time of the previous algorithms.https://ajmc.aut.ac.ir/article_3810_69f25b4f5d961c6937f15882badbf69f.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24491220200901Heuristic artificial bee colony algorithm for solving the Homicidal Chauffeur differential game153163381910.22060/ajmc.2019.16949.1025ENZahraYazdaniyanDepartment of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran,
IranM.ShamsiDepartment of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran,
IranMaria Do RosarioDe PinhoDepartment of Electrical and Computer Engineering, SYSTEC, Faculdade de Engenharia, Universidade do Porto, 4200-465, Porto,
PortugalZ.ForoozandehDepartment of Electrical and Computer Engineering, SYSTEC, Faculdade de Engenharia, Universidade do Porto, 4200-465, Porto, PortugalJournal Article20190821In this paper, we consider the Homicidal Chauffeur (HC) problem as an interesting and practical differential game. At first, we introduce a bilevel optimal control problem (BOCP) and prove that a saddle point solution for this game exists if and only if this BOCP has an optimal solution in which the optimal value of the objective function is equal to $1$. Then, BOCP is discretized and converted to a nonlinear bilevel programming problem. Finally, an Artificial Bee Colony (ABC) algorithm is used for solving this problem, in which the lower-level problem will be considered as a constraint and solved by an NLP-solver. Finally, to demonstrate the effectiveness of the presented method, various cases of HC problem are solved and the simulation results are reported.https://ajmc.aut.ac.ir/article_3819_d7bf45bb8b6003cc03fb68a78cdb6ff7.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24491220200901A new hash function and its use in read mapping on genome165170382010.22060/ajmc.2019.15991.1020ENFarzanehSalariDepartment of Mathematics and computer science, Amirkabir University of Technology, Tehran, IranFatemehZare MirakabadDepartment of Mathematics and computer science, Amirkabir University of Technology, Tehran, IranMehdiSadeghiNational Institute of Genetic Engineering and Biotechnology, Tehran, IranJournal Article20190313Mapping reads onto genomes is an indispensable step in sequencing data analysis. A widely used method to speed up mapping is to index a genome by a hash table, in which genomic positions of $k$-mers are stored in the table. The hash table size increases exponentially with the $k$-mer length and thus the traditional hash function is not appropriate for a $k$-mer as long as a read. We present a hashing mechanism by two functions named $score1$ and $score2$ which can hash sequences with the length of reads. The size of hash table is directly proportional to the genome size, which is absolutely lower than that of hash table built by the conventional hash function. We evaluate our hashing system by developing a read mapper and running the mapper on $E. coli$ genome with some simulated data sets. The results show that the high percentage of simulated reads can be mapped to correct locations on the genome.https://ajmc.aut.ac.ir/article_3820_de7ce01f748ce6cb663e3e2cb327db6f.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24491220200901Counting closed billiard paths171177382110.22060/ajmc.2020.17320.1026ENZahedRahmatiDepartment of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, IranSinaFarahzadDepartment of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, IranAliRahmatiMalek-Ashtar University of Technology, Tehran, IranJournal Article20191104Given a pool table enclosing a set of axis-aligned rectangles, with a total of n edges, this paper studies $\it{closed~billiard~paths}$. A closed billiard path is formed by following the ball shooting from a starting point into some direction, such that it doesn’t touch any corner of a rectangle, doesn’t visit any point on the table twice, and stops exactly at the starting position. The $\it{signature}$ of a billiard path is the sequence of the labels of edges in the order that are touched by the path, while repeated edge reflections like $abab$ are replaced by $ab$. We prove that the length of a signature is at most $4.5n−9$, and we show that there exists an arrangement of rectangles where the length of the signature is $1.25n+2$. We also prove that the number of distinct signatures for fixed shooting direction ($45^{\circ}$) is at most $1.5n−6$.https://ajmc.aut.ac.ir/article_3821_9489e0477a249fc2d912a25b0c2814a4.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24491220200901A model transformation approach to perform refactoring on software architecture using refactoring patterns based on stakeholder requirements179216382210.22060/ajmc.2020.17541.1027ENMohammadTanhaeiDepartment of Engineering, Ilam University, Ilam, IranJournal Article20191215Software Architecture (SA) generally has a considerable influence on software quality attributes. Coordination of software architecture to the requirements of the stakeholders and avoiding common mistakes and faults in designing SA increases the chance of success of the project and satisfaction of the stakeholders. Making the wrong decisions at the architectural design phase usually proves very costly later on. Refactoring is a method which helps in detecting and avoiding complications, improving the internal characteristics of software, while keeping the external behavior intact. Various problems can undermine the architecture refactoring process. The existence of different requirements in different domains, the diversity of architecture description languages, and the difficulty of describing refactoring patterns lead to the difficulty of performing automatic and semi-automatic refactoring on the SA. In this study, we use model transformation as a way to overcome the above mentioned difficulties. In this regard, the first step is converting the SA to a pivot-model. Then, based on the refactoring patterns, the refactoring process is performed on the pivotmodel. And finally, the pivot-model is converted back to the original (source) model. In this paper, the requirements of the stakeholders are taken into account in the refactoring process by modeling them as refactoring goals. These goals show the importance of the quality attributes in the project and the process of refactoring. The applicability of the framework is demonstrated using a case study.https://ajmc.aut.ac.ir/article_3822_46e6f2074d7747b2d0708cec653d86e3.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24491220200901The regularity of binomial edge ideals of graphs217221392910.22060/ajmc.2020.16433.1024ENSaraSaeedi MadaniFaculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic),Tehran, IranDariushKianiFaculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic),Tehran, IranJournal Article20190528In this paper, we study the Castelnuovo-Mumford regularity and the graded Betti numbers of the binomial edge ideals of some classes of graphs. Our special attention is devoted to a conjecture which asserts that the number of maximal cliques of a graph provides an upper bound for the regularity of its binomial edge ideal.https://ajmc.aut.ac.ir/article_3929_619ad9ec206e7628fa7f63da7155254e.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24491220200901Lie group analysis for short pulse equation223227399710.22060/ajmc.2020.18416.1032ENMehdiNadjafikhahDepartment of Pure Mathematics, School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16846-13114,
IranJournal Article20200512In this paper, the classical Lie symmetry analysis and the generalized form of Lie symmetry method are performed for a general short pulse equation. The point, contact and local symmetries for this equation are given. In this paper, we generalize the results of H. Liu and J. Li [2], and add some further facts, such as an optimal system of Lie symmetry subalgebras and two local symmetries.https://ajmc.aut.ac.ir/article_3997_61935ef445eef5d128b2cf7df8033c1f.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24491220200901On the gradient Finsler Yamabe solitons229233399810.22060/ajmc.2020.18420.1034ENMohamadYar AhmadiDepartment of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, IranJournal Article20200513Here, it is proved that the potential functions of Finsler Yamabe solitons have at most quadratic growth in distance function. Also it is obtained a finite topological type property on complete gradient Finsler Yamabe solitons under suitable scalar curvature assumptions.https://ajmc.aut.ac.ir/article_3998_b1b16f83391a831c34da00226ab0aba8.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24491220200901Homotopy perturbation transform method for time-fractional Newell-Whitehead Segel equation containing Caputo-Prabhakar fractional derivative235250399910.22060/ajmc.2020.18012.1028ENMohammadhosseinDerakhshanFaculty of Mathematics, K. N. Toosi University of Technology, P. O. Box: 16765-3381, Tehran, IranAzimAminataeiFaculty of Mathematics, K. N. Toosi University of Technology, P. O. Box: 16765-3381, Tehran, IranJournal Article20200227The main aim of the current article is to find the solution for Newell Whitehead-Segel equations with constant coefficients containing Caputo-Prabhakar fractional derivative using the homotopy perturbation transform method. The convergence analysis of the obtained solution for the proposed fractional order model is presented. Four examples are presented to illustrate the efficiency and applicability and accurateness of the proposed numerical techniquehttps://ajmc.aut.ac.ir/article_3999_4955dedeffddde11820cf2ce1a74c6ba.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24491220200901New directions in general fuzzy automata: a dynamic-logical view251262402610.22060/ajmc.2020.18629.1040ENKhadijehAbolpourDept. of Math., Shiraz Branch, Islamic Azad University, Shiraz, IranMohammad MehdiZahediDept. of Math., Graduate University of Advanced Technology, Kerman, IranDept. of Math., Behbahan Khatam Alanbia University of Technology, Behbahan, IranMarziehShamsizadehDept. of Math., Graduate University of Advanced Technology, Kerman, IranDept. of Math., Behbahan Khatam Alanbia University of Technology, Behbahan, IranJournal Article20200624In the current study, by a general fuzzy automaton we aim at showing a set of propositions related to a given automaton showing that the truth-values are depended on thestates, inputs and membership values of active states at time t. This new approach enables us to consider automata from a different point of view which is more close to logical treatment and helps us make estimations about the behavior of automaton particularly in a nondeterministic mode. The logic consists of propositions on the given GFA and its dynamic nature is stated by means of the so-called transition functor. This logic enables us to derive a certain relation on the set of states labeled by inputs. In fact, it is shown that if our set of propositions is large enough, this recovering of the transition relation is possible. Through a synthesis in the theory of systems, this study contributes to construct a general fuzzy automaton which realizes a dynamic process at least partially known to the user, which has been fully achieved in Theorem 3.6. Also, we study the theory of general fuzzy automata by using the concepts of operators. Such operators help us in the algebraic study of general fuzzy automata theory and provide a platform to use fuzzy topological therein. Further, a Galois connection is obtained between the state-transition relation on states and thetransition operators on propositions. To illustrate the proposed approach, the subject matter is more elaborated in detail through examples.https://ajmc.aut.ac.ir/article_4026_e4987ba8281ce1725cd4a51bd420d7f2.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24491220200901A linear-time algorithm to compute total $[1,2]$-domination number of block graphs263270402910.22060/ajmc.2020.18444.1035ENPouyehSharifaniInstitute for Research in Fundamental Sciences (IPM), Tehran, IranDepartment of Computer Science, Yazd University, Yazd, IranMohammadrezaHooshmandaslDepartment of Computer Science, University of Mohaghegh Ardabili, Ardabil, IranDepartment of Computer Science, Yazd University, Yazd, IranSaeidAlikhaniDepartment of Mathematics, Yazd University, Yazd, IranJournal Article20200519Let $G=(V, E)$ be a simple graph without isolated vertices. A set $D\subseteq V$ is a total $[1,2]$-dominating set if for every vertex $v\in V , 1\leq |N(v)\cap D|\leq 2$. The total $[1,2]$-domination problem is to determine the total $[1,2]$-domination number $\gamma_{t[1,2]}(G)$, which is the minimum cardinality of a total $[1,2]$-dominating set for a graph $G$. In this paper, we present a linear-time algorithm to compute $\gamma_{t[1,2]}(G)$, for a block graph $G$.https://ajmc.aut.ac.ir/article_4029_db3fbe3f0db6f6079698d2381e798970.pdf