Article
Quantum Science & Technology
Hari Krovi
Summary: We present generalized and improved quantum algorithms for inhomogeneous linear and nonlinear ordinary differential equations (ODE) over prior work. Our algorithm for linear ODEs can handle many non-diagonalizable matrices, including singular matrices, and is exponentially faster than previous bounds for certain diagonalizable matrices. We apply our linear ODE algorithm to nonlinear differential equations using Carleman linearization, resulting in an exponential improvement in error dependence and the ability to handle any sparse matrix with a negative log-norm, without the requirement of normality.
Article
Automation & Control Systems
Kai Wang, Wenyin Gong, Zuowen Liao, Ling Wang
Summary: This article proposes a hybrid niching-based differential evolution algorithm with two archives, HNDE/2A, for locating multiple roots of nonlinear equation systems within a limited computational budget. By combining the techniques of crowding and speciation, as well as utilizing a root archive and an inferior offspring archive, the algorithm achieves better results in terms of root ratio and success rate compared to other algorithms.
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS
(2022)
Article
Engineering, Electrical & Electronic
Xianchao Xiu, Yunhui Li
Summary: This article proposes a new nonlinear PM approach called joint sparse constrained kernel CCA and graph learning (JSKCCA-GL) which can fully exploit the global and local structure of process variables. The proposed method is extensively verified on the benchmark Tennessee Eastman process (TEP) and a practical cylinder-piston assembly (CPA) of marine diesel engines. The results show a significant improvement in fault detection rate (FDR) values for unknown-type faults in the TEP.
IEEE SENSORS JOURNAL
(2023)
Article
Computer Science, Information Systems
Rami Sihwail, Obadah Said Solaiman, Khairuddin Omar, Khairul Akram Zainol Ariffin, Mohammed Alswaitti, Ishak Hashim
Summary: A novel hybrid method NHHO is proposed for solving systems of nonlinear equations by combining Newton's method and Harris hawks optimization. Experimental results show that NHHO outperforms other optimization algorithms in terms of efficiency, fitness value, and convergence speed.
Article
Engineering, Chemical
Fahim Abdullah, Mohammed S. Alhajeri, Panagiotis D. Christofides
Summary: SINDy is a nonlinear modeling technique that shows superior performance in handling time-series data but requires careful consideration of noise. In this study, SINDy is combined with ensemble learning to identify multiple models for improving overall nonlinear model performance.
INDUSTRIAL & ENGINEERING CHEMISTRY RESEARCH
(2022)
Article
Mathematics
Jie Xu
Summary: We present an iterative method to prove the existence and uniqueness of complex-valued nonlinear elliptic PDEs with specific boundary conditions on precompact domains and smooth, compact Riemannian manifolds. The method also provides a solution for an integral version of these PDEs using parametrix methods.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Chemistry, Multidisciplinary
Jorge Perez-Aracil, Carlos Camacho-Gomez, Alejandro Mateo Hernandez-Diaz, Emiliano Pereira, Sancho Salcedo-Sanz
Summary: This paper introduces a novel procedure for optimal design of geometrically nonlinear submerged arches, combining a new arch shape parameterization with the Coral Reefs Optimization with Substrate Layers algorithm. Numerical experiments demonstrate the importance of considering the second-order behavior of the arch structure, and show that the algorithm leads to nearly-optimal solutions while ensuring stability and reducing bending moment values.
APPLIED SCIENCES-BASEL
(2021)
Article
Biotechnology & Applied Microbiology
Robert Piotrowski, Krzysztof Milewski, Bartosz Maciag
Summary: Wastewater treatment plays a crucial role in the modern world, as insufficient treatment can result in environmental pollution and pose risks to human health. However, designing an efficient and optimal control system for wastewater treatment plants is challenging due to the complexity of the processes involved.
BIOCHEMICAL ENGINEERING JOURNAL
(2023)
Article
Mathematics, Applied
Alok Shukla, Prakash Vedula
Summary: A hybrid classical-quantum approach based on Walsh-Hadamard basis functions for solving nonlinear ordinary differential equations is proposed. The computation of the Walsh-Hadamard transform of arbitrary vectors is central to this approach, which is achieved using quantum Hadamard gates and various operations. The proposed hybrid approach shows a significantly lower computational complexity for the Walsh-Hadamard transform compared to the Fast Walsh-Hadamard transform, and it also provides satisfactory results for solving nonlinear differential equations.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Mathematics, Interdisciplinary Applications
Faical Hamidi, Houssem Jerbi, Hadeel Alharbi, Victor Leiva, Dumitru Popescu, Wajdi Rajhi
Summary: In this article, a metaheuristic-based solution is provided for stability analysis of nonlinear systems. The optimal level set in the state space of these systems is identified by combining two optimization phases. The first phase is an external optimization to search for a definite positive Lyapunov function, and the second phase is an internal optimization to ensure an accurate estimate of the attraction region. The proposed approach is validated through numerical experiments and has potential real-world applications.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Applied
Janak Raj Sharma, Sunil Kumar
Summary: We propose a composite Newton-Jarratt iterative method that is more efficient in approximating the solutions of systems of nonlinear equations. The novelty of the method lies in increasing the convergence order by two in each step at the cost of only one additional function evaluation. Theoretical results regarding convergence and computational efficiency are verified through numerical problems, showing that the novel method outperforms existing methods, especially for solving large systems of equations.
COMPUTATIONAL & APPLIED MATHEMATICS
(2022)
Article
Automation & Control Systems
Xia Jiang, Xianlin Zeng, Jian Sun, Jie Chen
Summary: This study proposes a distributed impulsive algorithm for solving large-scale nonlinear optimization problems, which combines continuous-time and discrete-time updates. By utilizing stability theory of impulsive dynamical systems, the algorithm is proven to converge to an optimal solution with linear convergence rate for agents' states. Numerical simulations also demonstrate the performance advantages of the proposed impulsive method compared to conventional continuous-time algorithms.
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
(2021)
Article
Computer Science, Artificial Intelligence
Huimin Guan, Yang Liu, Kit Ian Kou, Jinde Cao, Leszek Rutkowski
Summary: In this paper, a distributed optimization method is proposed to solve nonlinear equations with constraints. The multiple constrained nonlinear equations are transformed into an optimization problem and solved in a distributed manner. To deal with the nonconvexity issue, a multi-agent system based on an augmented Lagrangian function is introduced and proven to converge to a locally optimal solution. Moreover, a collaborative neurodynamic optimization method is adopted to obtain a globally optimal solution. The effectiveness of the proposed method is illustrated through three numerical examples.
Article
Engineering, Chemical
Vikas Kumar, Kanak Kalita, S. Madhu, Uvaraja Ragavendran, Xiao-Zhi Gao
Summary: A novel hybrid genetic programming-gray wolf optimizer approach is proposed in this paper for the process optimization of biodiesel production. The results show that the proposed approach is simple, accurate, and robust.
Article
Computer Science, Theory & Methods
Xianzhi Zhang, Yipeng Zhou, Di Wu, Miao Hu, Xi Zheng, Min Chen, Song Guo
Summary: This paper presents a white-box approach to optimize video caching at the edge, using a mathematical model called HRS model to accurately capture the evolution of video popularity. An online HRS-based video caching algorithm is designed and experiments demonstrate its superiority in terms of cache hit rate over existing algorithms.
IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS
(2022)
Article
Engineering, Industrial
Rajan Mondal, Subhajit Das, Subhash Chandra Das, Ali Akbar Shaikh, Asoke Kumar Bhunia
Summary: This paper investigates a partially backlogged inventory model with interval uncertainty, considering the availability of advance payment and discounts. The objective function is transformed into interval-valued and solved using c-r optimization technique and three variants of QPSO. The feasibility of the proposed model is demonstrated through numerical examples.
INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE-OPERATIONS & LOGISTICS
(2023)
Article
Engineering, Industrial
Subhajit Das, Md Sadikur Rahman, Ali Akbar Shaikh, Asoke Kumar Bhunia, Ali Ahmadian
Summary: The goal of this work is two-fold: (i) to theoretically develop optimality conditions for a variational problem with interval uncertainty, and (ii) to apply the established results in a production inventory model with interval uncertainty. The necessary and sufficient optimality conditions for the interval-valued variational problem (IVVP) are proposed using interval order relations. A production inventory model is formulated considering interval-valued time-dependent production and demand rates. The optimal policy of the proposed model is studied using the established optimality conditions.
INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE-OPERATIONS & LOGISTICS
(2023)
Article
Mathematics, Applied
Subhajit Das, Md Sadikur Rahman, Ali Akbar Shaikh, Asoke Kumar Bhunia, Ioannis Konstantaras
Summary: This work explores the Laplace and inverse transforms of interval valued functions and emphasizes on their properties under interval flexibility. The formal definition of interval Laplace transform is proposed, along with derived properties and the existence conditions. The study also discusses crucial results related to switching points of the interval Laplace transform and provides numerical examples. Finally, the definition of inverse transform for interval valued functions is introduced, and its application is demonstrated in a production inventory model under interval uncertainty.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Engineering, Mechanical
Subhashis Das, Madhurima Mukherjee, Argha Mondal, Kshitish Ch. Mistri, Sanat Kumar Mahato, M. A. Aziz-Alaoui
Summary: This article demonstrates an analytical approach to show the emerging traveling pulses for the local evolution of a set of diffusively coupled dynamical equations representing neuronal impulses. The derived dynamics governing the traveling pulses solution is described in a space-time reference frame with a two-dimensional excitable Hindmarsh-Rose (H-R) type oscillator. The conditions that allow us to describe explicitly the nature of propagating traveling pulses are deduced. The obtained results reveal the possibility of collective behavior for information processing in excitable systems.
NONLINEAR DYNAMICS
(2023)
Article
Computer Science, Artificial Intelligence
Md Sadikur Rahman, Amalesh Kumar Manna, Ali Akbar Shaikh, Ioannis Konstantaras, Asoke Kumar Bhunia
Summary: The concepts of generalized Hukuhara difference and interval differential equation have significant applications in various research fields, including optimization, information theory, and inventory control. This paper focuses on the application of Hukuhara difference and interval differential equation in inventory management, proposing an inventory model for imperfect production process under warranty-dependent demand and carbon tax regulatory mechanism. By utilizing the interval arithmetic, the generalized Hukuhara difference, and the existence and uniqueness theorem of interval differential equation, the corresponding average profit function is obtained. A center-radius optimization technique is introduced to maximize the average profit, and numerical examples are solved using different variants of quantum-behaved particle swarm optimization algorithms.
Article
Computer Science, Artificial Intelligence
Goutam Mandal, Nirmal Kumar, Avijit Duary, Ali Akbar Shaikh, Asoke Kumar Bhunia
Summary: The key to avoiding local optima in solving optimization problems using metaheuristic algorithms is to enhance exploration and exploitation. This can be achieved through processes like enhancing search agents and hybridization. This study introduces a novel hybrid algorithm based on the strategies of group league and knock-out system using the quantum particle swarm optimization (QPSO) metaheuristic algorithm.
Article
Biology
Prasenjit Mahato, Sanat Kumar Mahato, Subhashis Das
Summary: We propose and study a susceptible-exposed-infected-recovered (XY ZW) epidemic model with saturated treatment function. The effect of delayed treatment on disease transmission is examined by considering a saturated treatment function in the epidemic system. The existence and uniqueness of the positive solution as well as stochastic boundedness, permanence, and extinction of the model are investigated. Numerical simulations are performed to illustrate the results, and the sensitivity analysis of the basic reproduction number is conducted.
JOURNAL OF BIOLOGICAL SYSTEMS
(2023)
Article
Engineering, Mechanical
Subhashis Das, Sanat Kumar Mahato, Argha Mondal, Eva Kaslik
Summary: This article introduces a three-dimensional fractional-order slow-fast prey-predator model to explore the impact of pest-control strategy on integrated pest management. The dynamics of the prey-predator system and its qualitative properties are analyzed using a fractional-order model. The stability and the occurrence of Hopf bifurcations in the model are found to be influenced by the fractional-order exponent.
NONLINEAR DYNAMICS
(2023)
Article
Automation & Control Systems
Subhajit Das, Hachen Ali, Ali Akbar Shaikh, Asoke Kumar Bhunia
Summary: Considering the impact of emission on the environment, reduction of emission during the production process has become increasingly important for manufacturing companies. In order to survive in the competitive market, manufacturing companies must offer various facilities to consumers. This study presents an imperfect manufacturing inventory model that takes into account the linear increase in customer demand with emission reduction levels and the nonlinear decrease with item price. The goal is to maximize the average profit by solving optimal control problems and using the Hamiltonian maximum principle.
OPTIMAL CONTROL APPLICATIONS & METHODS
(2023)
Article
Biology
Prasenjit Mahato, Sanat Kumar Mahato, Subhashis Das, Partha Karmakar
Summary: In this article, the dynamical properties of the susceptible-vaccinated-infected-susceptible (SVIS) epidemic system with saturated incidence rate and vaccination strategies are studied. The existence and uniqueness of the stochastic system are examined by constructing a suitable Lyapunov function. A critical value R-s* is established with respect to the basic reproduction number R* of the deterministic system. Under the condition of R-s* > 1, a unique ergodic stationary distribution is investigated, representing the long-term persistence of the disease. The main focus of the study is the analysis of the probability density function of the stochastic system around the quasi-endemic equilibrium. The existence of the ergodic stationary distribution and density function under R-s* > 1 can explain all the dynamical behavior of the disease persistence. The condition for disease extinction is derived, and numerical results and sensitivities of the biological parameters are discussed to support the theoretical study. Results and conclusions are highlighted.
THEORY IN BIOSCIENCES
(2023)
Article
Engineering, Multidisciplinary
Subhashis Das, Sanat Kumar Mahato, Prasenjit Mahato
Summary: In this paper, a mathematical model for COVID-19 is developed, dividing the population into six classes. The concept of shield immunity is utilized to get back to normal, considering the interaction between recovered and susceptible/infected individuals. The model's stability and optimal control are analyzed, and simulations are conducted with real data to predict different scenarios.
JOURNAL OF APPLIED NONLINEAR DYNAMICS
(2023)
Article
Green & Sustainable Science & Technology
M. Mukherjee, D. Pal, S. K. Mahato
Summary: Based on the Lotka-Volterra model and biological parameters, this paper investigates the harvesting system of prey-predator species using intuitionistic fuzzy numbers. The existence and local stability of equilibrium points are analyzed, and the condition for global stability is derived using suitable Lyapunov function. The study also explores the economic aspects and optimal harvesting policies, and analyses the existence of limit cycles in the fuzzy prey-predator model through numerical simulations.
JOURNAL OF ENVIRONMENTAL ACCOUNTING AND MANAGEMENT
(2023)
Article
Engineering, Multidisciplinary
Md Sadikur Rahman, Subhash Chandra Das, Md. Al-Amin Khan, Ali Akbar Shaikh, Asoke Kumar Bhunia
Summary: This paper discusses the importance of advance payment and the lifetime of an item in the business sector and proposes a non-deterministic inventory model to address these issues. The models consider variable holding cost, variable demand, and advertisement frequency under an advance payment policy. The interval optimization problems related to both models are solved using interval mathematics and interval order relations. Two examples are used to validate the models and sensitivity analyses are performed to study the impact of parameter deviations on optimality. The paper concludes by providing potential management insights and future research directions.
INTERNATIONAL JOURNAL OF MODELLING AND SIMULATION
(2023)
Article
Mathematics, Applied
Subhashis Das, Prasenjit Mahato, Sanat Kumar Mahato
Summary: A non-linear mathematical model is proposed in this paper to study the dynamics of disease transmission via pests. The crisp model is converted to a fuzzy model and a graded mean integration technique is used for defuzzification. The model is compared with a stochastic model and the existence, uniqueness, and boundedness of the solution are discussed. Equilibrium points, local stability, global stability analysis, and Hopf bifurcations are investigated. Numerical experiments with MATLAB are conducted, and the sensitivities of the control parameters are analyzed graphically.
DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS
(2023)
