Mathematics Interdisciplinary Research
https://mir.kashanu.ac.ir/
Mathematics Interdisciplinary Researchendaily1Sat, 01 Jun 2024 00:00:00 +0330Sat, 01 Jun 2024 00:00:00 +0330Upgrading Uncapacitated Multiple Allocation P-Hub Median Problem Using Benders Decomposition Algorithm
https://mir.kashanu.ac.ir/article_114318.html
&lrm;The Hub Location Problem (HLP) is a significant problem in combinatorial optimization consisting of two main components&lrm;: &lrm;location and network design&lrm;. &lrm;The HLP aims to develop an optimal strategy for various applications&lrm;, &lrm;such as product distribution&lrm;, &lrm;urban management&lrm;, &lrm;sensor network design&lrm;, &lrm;computer network&lrm;, &lrm;and communication network design&lrm;. &lrm;Additionally&lrm;, &lrm;the upgrading location problem arises when modifying specific components at a cost is possible&lrm;. &lrm;This paper focuses on upgrading the uncapacitated multiple allocation p-hub median problem (u-UMApHMP)&lrm;, &lrm;where a pre-determined budget and bound of changes are given&lrm;. &lrm;The aim is to modify certain network parameters to identify the p-hub median that improves the objective function value concerning the modified parameters&lrm;. &lrm;We propose a non-linear mathematical formulation for u-UMApHMP to achieve this goal&lrm;. &lrm;Then&lrm;, &lrm;we employ the McCormick technique to linearize the model&lrm;. &lrm;Subsequently&lrm;, &lrm;we solve the linearized model using the CPLEX solver and the Benders decomposition method&lrm;. &lrm;Finally&lrm;, &lrm;we present experimental results to demonstrate the effectiveness of the proposed approach&lrm;.Improving Probabilistic Bisimulation for MDPs Using Machine Learning
https://mir.kashanu.ac.ir/article_114322.html
&lrm;The utilization of model checking has been suggested as a formal verification technique for analyzing critical systems&lrm;. &lrm;However&lrm;, &lrm;the primary challenge in applying to complex systems is the state space explosion problem&lrm;. &lrm;To address this issue&lrm;, &lrm;bisimulation minimization has emerged as a prominent method for reducing the number of states in a system&lrm;, &lrm;aiming to overcome the difficulties associated with the state space explosion problem&lrm;. &lrm;For systems with stochastic behaviors&lrm;, &lrm;probabilistic bisimulation is employed to minimize a given model&lrm;, &lrm;obtaining its equivalent form with fewer states&lrm;. &lrm;In this paper&lrm;, &lrm;we propose a novel technique to partition the state space of a given probabilistic model to its bisimulation classes&lrm;. &lrm;This technique uses the PRISM program of a given model and constructs some small versions of the model to train a classifier&lrm;. &lrm;It then applies supervised machine learning techniques to approximately classify the related partition&lrm;. &lrm;The resulting partition is then used to accelerate the standard bisimulation technique&lrm;, &lrm;significantly reducing the running time of the method&lrm;. &lrm;The experimental results show that the approach can decrease significantly the running time compared to state-of-the-art tools&lrm;.Critical Metrics Related to Quadratic Curvature Functionals over Generalized Symmetric Spaces of Dimension Four
https://mir.kashanu.ac.ir/article_114323.html
&lrm;Our 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&lrm;.On Minimum Algebraic Connectivity of Tricyclic Graphs
https://mir.kashanu.ac.ir/article_114327.html
&lrm;Consider a simple&lrm;, &lrm;undirected graph $ G=(V,E)$&lrm;, &lrm;where $A$ represents the adjacency matrix and $Q$ represents the Laplacian matrix of $G$&lrm;. &lrm;The second smallest eigenvalue of Laplacian matrix of $G$ is called the algebraic connectivity of $G$&lrm;. &lrm;In this article&lrm;, &lrm;we present a Python program for studying the Laplacian eigenvalues of a graph&lrm;. &lrm;Then&lrm;, &lrm;we determine the unique graph of minimum algebraic connectivity in the set of all tricyclic graphs&lrm;.Fractional Dynamics of Infectious Disease Transmission with Optimal Control
https://mir.kashanu.ac.ir/article_114340.html
This article investigates and studies the dynamics of infectious disease transmission using a fractional mathematical model based on Caputo fractional derivatives&lrm;. &lrm;Consequently&lrm;, &lrm;the population studied has been divided into four categories&lrm;: &lrm;susceptible&lrm;, &lrm;exposed&lrm;, &lrm;infected&lrm;, &lrm;and recovered. The basic reproduction rate&lrm;, &lrm;existence&lrm;, &lrm;and uniqueness of disease-free as well as infected steady-state&lrm; equilibrium points of the mathematical model have been investigated in this study&lrm;. &lrm;The local and global stability of both equilibrium points has&lrm; been investigated and proven by Lyapunov functions&lrm;. &lrm;Vaccination and drug therapy are two controllers that may be used to control the spread of diseases in society&lrm;, &lrm;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&lrm;. &lrm;The&lrm; numerical simulation of the fractional optimal control problem indicates that vaccination of the susceptible subjects in the community reduces&lrm;&lrm;horizontal transmission while applying drug control to the infected subjects reduces vertical transmission&lrm;. &lrm;Furthermore&lrm;, &lrm;the simultaneous use of&lrm; both controllers is much more effective and leads to a rapid increase in the cured population and it prevents the disease from spreading and&lrm; turning into an epidemic in the community&lrm;.Solving Graph Coloring Problem Using Graph Adjacency Matrix Algorithm
https://mir.kashanu.ac.ir/article_114365.html
&lrm;Graph coloring is the assignment of one color to each vertex of a graph so that two adjacent vertices are not of the same color&lrm;. &lrm;The graph coloring problem (GCP) is a matter of combinatorial optimization&lrm;, &lrm;and the goal of GCP is determining the chromatic number $\chi(G)$&lrm;. &lrm;Since GCP is an NP-hard problem&lrm;, &lrm;then in this paper&lrm;, &lrm;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&lrm;. &lrm;To prove the correctness of the proposed algorithm&lrm;, &lrm;we implement it in MATLAB software&lrm;, &lrm;and for analysis in terms of solution and execution time&lrm;, &lrm;we compare our algorithm with some of the best existing algorithms that are already implemented in MATLAB software&lrm;, &lrm;and we present the results in tables of various graphs&lrm;. &lrm;Several available algorithms used the largest degree selection strategy&lrm;, &lrm;while our proposed algorithm uses the graph adjacency matrix to select the vertex that has the smallest degree for coloring&lrm;. &lrm;We provide some examples to compare the performance of our algorithm to other available methods&lrm;. &lrm;We make use of the Dolan-Mor\'e performance profiles to assess the performance of the numerical algorithms&lrm;, &lrm;and demonstrate the efficiency of our proposed approach in comparison with some existing methods&lrm;.