University of KashanMathematics Interdisciplinary Research2538-36399220240601Upgrading Uncapacitated Multiple Allocation P-Hub Median Problem Using Benders Decomposition Algorithm13115011431810.22052/mir.2023.253217.1422ENAli HosseinzadehDepartment of Mathematics, Shahed University, Tehran, I. R. Iran0009-0003-6164-7908Ardeshir DolatiDepartment of Computer Sciences,
Shahed University,
Tehran, I. R. Iran0000-0001-9617-5187Journal Article20230710The Hub Location Problem (HLP) is a significant problem in combinatorial optimization consisting of two main components: location and network design. The HLP aims to develop an optimal strategy for various applications, such as product distribution, urban management, sensor network design, computer network, and communication network design. Additionally, the upgrading location problem arises when modifying specific components at a cost is possible. This paper focuses on upgrading the uncapacitated multiple allocation p-hub median problem (u-UMApHMP), where a pre-determined budget and bound of changes are given. The aim is to modify certain network parameters to identify the p-hub median that improves the objective function value concerning the modified parameters. We propose a non-linear mathematical formulation for u-UMApHMP to achieve this goal. Then, we employ the McCormick technique to linearize the model. Subsequently, we solve the linearized model using the CPLEX solver and the Benders decomposition method. Finally, we present experimental results to demonstrate the effectiveness of the proposed approach.https://mir.kashanu.ac.ir/article_114318_66853ce0d9c4a45eb20281756b9b8c06.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36399220240601Improving Probabilistic Bisimulation for MDPs Using Machine Learning15116911432210.22052/mir.2023.253367.1431ENMohammadsadegh MohagheghiDepartment of Computer Science,
Vali-e-Asr University of Rafsanjan,
Rafsanjan, I. R. Iran0000-0001-8059-3691Khayyam SalehiDepartment of Computer Science,
Shahrekord University,
Shahrekord, I. R. Iran0000-0002-3379-798XJournal Article20230806The utilization of model checking has been suggested as a formal verification technique for analyzing critical systems. However, the primary challenge in applying to complex systems is the state space explosion problem. To address this issue, bisimulation minimization has emerged as a prominent method for reducing the number of states in a system, aiming to overcome the difficulties associated with the state space explosion problem. For systems with stochastic behaviors, probabilistic bisimulation is employed to minimize a given model, obtaining its equivalent form with fewer states. In this paper, we propose a novel technique to partition the state space of a given probabilistic model to its bisimulation classes. This technique uses the PRISM program of a given model and constructs some small versions of the model to train a classifier. It then applies supervised machine learning techniques to approximately classify the related partition. The resulting partition is then used to accelerate the standard bisimulation technique, significantly reducing the running time of the method. The experimental results show that the approach can decrease significantly the running time compared to state-of-the-art tools.https://mir.kashanu.ac.ir/article_114322_d21590eb7919d74be95308a790bc5283.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36399220240601Critical Metrics Related to Quadratic Curvature Functionals over Generalized Symmetric Spaces of Dimension Four17118311432310.22052/mir.2023.253649.1440ENAmirhesam ZaeimDepartment of Mathematics,
Payame Noor University (PNU),
P.O. Box 19395-4697,Tehran, Iran0000-0001-9304-275XMehdi JafariDepartment of Mathematics,
Payame Noor University (PNU),
P.O. Box 19395-4697,Tehran, Iran0000-0002-7154-7527Seyed Mohammad MortazaviDepartment of Mathematics,
Payame Noor University (PNU),
P.O. Box 19395-4697,Tehran, Iran0000-0000-0000-0001Journal Article20230925Our examination of quadratic curvature functionals in Generalized Symmetric Spaces has resulted in the comprehensive classification of critical metric sets within diverse categories of these spaces.https://mir.kashanu.ac.ir/article_114323_b20b6a55be9d364514dd783ef4b0a4cb.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36399220240601On Minimum Algebraic Connectivity of Tricyclic Graphs18519711432710.22052/mir.2024.253568.1437ENHassan TaheriFaculty of Mathematical Science,
Department of Pure Mathematics,
University of Kashan,
Kashan 87317-51167, I. R. Iran0009-0008-6033-3532Gholam Hossein Fath-TabarFaculty of Mathematical Science,
Department of Pure Mathematics,
University of Kashan,
Kashan 87317-51167, I. R. IranJournal Article20230925Consider a simple, undirected graph $ G=(V,E)$, where $A$ represents the adjacency matrix and $Q$ represents the Laplacian matrix of $G$. The second smallest eigenvalue of Laplacian matrix of $G$ is called the algebraic connectivity of $G$. In this article, we present a Python program for studying the Laplacian eigenvalues of a graph. Then, we determine the unique graph of minimum algebraic connectivity in the set of all tricyclic graphs.https://mir.kashanu.ac.ir/article_114327_65963fe40f3d819f233406d3954b9d84.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36399220240601Fractional Dynamics of Infectious Disease Transmission with Optimal Control19921311434010.22052/mir.2023.253000.1410ENReza AkbariDepartment of Mathematics,
Payame Noor University, (PNU),
Tehran, I. R. Iran0000-0002-2972-4091Leader NavaeiDepartment of Statistics,
Payame Noor University, (PNU),
Tehran, I. R. Iran0000-0002-0047-6530Journal Article20230526This article investigates and studies the dynamics of infectious disease transmission using a fractional mathematical model based on Caputo fractional derivatives. Consequently, the population studied has been divided into four categories: susceptible, exposed, infected, and recovered. The basic reproduction rate, existence, and uniqueness of disease-free as well as infected steady-state equilibrium points of the mathematical model have been investigated in this study. The local and global stability of both equilibrium points has been investigated and proven by Lyapunov functions. Vaccination and drug therapy are two controllers that may be used to control the spread of diseases in society, and the conditions for the optimal use of these two controllers have been prescribed by the principle of Pontryagin's maximum. The stated theoretical results have been investigated using numerical simulation. The numerical simulation of the fractional optimal control problem indicates that vaccination of the susceptible subjects in the community reduces<br />horizontal transmission while applying drug control to the infected subjects reduces vertical transmission. Furthermore, the simultaneous use of both controllers is much more effective and leads to a rapid increase in the cured population and it prevents the disease from spreading and turning into an epidemic in the community.https://mir.kashanu.ac.ir/article_114340_99804a7b55fab8f539c30917d36b763b.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36399220240601Solving Graph Coloring Problem Using Graph Adjacency Matrix Algorithm21523611436510.22052/mir.2023.253223.1428ENHanife MousaviDepartment of Applied Mathematics, Faculty of Mathematical Sciences,
Ferdowsi University of Mashhad,
P.O. Box 1159, Mashhad 91775, I. R. Iran0000-0001-8960-588XMostafa TavakoliDepartment of Applied Mathematics, Faculty of Mathematical Sciences,
Ferdowsi University of Mashhad,
P.O. Box 1159, Mashhad 91775, I. R. Iran0000-0002-3315-1759Khatere Ghorbani-MoghadamMosaheb Institute of Mathematics,
Kharazmi University, Tehran, I. R. IranJournal Article20230725Graph coloring is the assignment of one color to each vertex of a graph so that two adjacent vertices are not of the same color. The graph coloring problem (GCP) is a matter of combinatorial optimization, and the goal of GCP is determining the chromatic number $\chi(G)$. Since GCP is an NP-hard problem, then in this paper, we propose a new approximated algorithm for finding the coloring number (it is an approximation of chromatic number) by using a graph adjacency matrix to colorize or separate a graph. To prove the correctness of the proposed algorithm, we implement it in MATLAB software, and for analysis in terms of solution and execution time, we compare our algorithm with some of the best existing algorithms that are already implemented in MATLAB software, and we present the results in tables of various graphs. Several available algorithms used the largest degree selection strategy, while our proposed algorithm uses the graph adjacency matrix to select the vertex that has the smallest degree for coloring. We provide some examples to compare the performance of our algorithm to other available methods. We make use of the Dolan-Mor\'e performance profiles to assess the performance of the numerical algorithms, and demonstrate the efficiency of our proposed approach in comparison with some existing methods.https://mir.kashanu.ac.ir/article_114365_c868980d403a0fffefea025c5535ae23.pdf