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A computational supervised neural network procedure for the fractional SIQ mathematical model

European Physical Journal: Special Topics 2023年第5期232卷 535-546页

作者： Mukdasai, Kanit Sabir, Zulqurnain Raja, Muhammad Asif Zahoor Singkibud, Peerapongpat Sadat, R. Ali, Mohamed R. Department of Mathematics Faculty of Science Khon Kaen University Khon Kaen 40002 Thailand Department of Mathematics and Statistics Hazara University Mansehra Pakistan Future Technology Research Center National Yunlin University of Science and Technology 123 University Road Section 3 Yunlin Douliou 64002 Taiwan Department of Applied Mathematics and Statistics Faculty of Science and Liberal Arts Rajamangala University of Technology Isan Nakhon Ratchasima 30000 Thailand Department of Mathematics Faculty of Engineering Zagazig University Zagazig Egypt Faculty of Engineering and Technology Future University in Egypt New Cairo 11835 Egypt Basic Engineering Science Department Benha Faculty of Engineering Benha University Benha Egypt Department of Computer Science and Mathematics Lebanese American University Beirut Lebanon

The purpose of the current work is to provide the numerical solutions of the fractional mathematical system of the susceptible, infected and quarantine (SIQ) system based on the lockdown effects of the coronavirus disease. These investigations provide more accurateness by using the fractional SIQ system. The investigations based on the nonlinear, integer and mathematical form of the SIQ model together with the effects of lockdown are also presented in this work. The impact of the lockdown is classified into the susceptible/infection/quarantine categories, which is based on the system of differential models. The fractional study is provided to find the accurate as well as realistic solutions of the SIQ model using the artificial intelligence (AI) performances along with the scale conjugate gradient (SCG) design, i.e., AI-SCG. The fractional-order derivatives have been used to solve three different cases of the nonlinear SIQ differential model. The statics to perform the numerical results of the fractional SIQ dynamical system are 7% for validation, 82% for training and 11% for testing. To observe the exactness of the AI-SCG procedure, the comparison of the numerical attained performances of the results is presented with the reference Adam solutions. For the validation, authentication, aptitude, consistency and validity of the AI-SCG solver, the computing numerical results have been provided based on the error histograms, state transition measures, correlation/regression values and mean square error. © 2022, The Author(s), under exclusive licence to EDP sciences, Springer-Verlag GmbH Germany, part of Springer Nature.

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Optimal Resource Allocation for NOMA Wireless Networks

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computers, Materials & Continua 2023年第2期74卷 3249-3261页

作者： Fahad R.Albogamy M.A.Aiyashi Fazirul Hisyam Hashim Imran Khan Bong Jun Choi Turabah University College Computer Sciences ProgramTaif UniversityP.O.Box 11099Taif21944Saudi Arabia Department of Mathematics Jazan UniversityJazanP.O.Box 218Saudi Arabia Department of Computer and Communication Systems Engineering Faculty of EngineeringUniversiti Putra Malaysia(UPM)43400SerdangMalaysia Department of Electrical Engineering University of Engineering and Technology PeshawarP.O.Box 814Pakistan School of Computer Science and Engineering Soongsil UniversitySeoulKorea

The non-orthogonal multiple access(NOMA)method is a novel multiple access technique that aims to increase spectral efficiency(SE)and accommodate enormous user ***-user signals are superimposed and transmitted in the power domain at the transmitting end by actively implementing controllable interference information,and multi-user detection algorithms,such as successive interference cancellation(SIC),are performed at the receiving end to demodulate the necessary user *** its basic signal waveform,like LTE baseline,could be based on orthogonal frequency division multiple access(OFDMA)or discrete Fourier transform(DFT)-spread OFDM,NOMA superimposes numerous users in the power *** contrast to the orthogonal transmission method,the nonorthogonal method can achieve higher spectrum ***,it will increase the complexity of its *** power allocation techniques will have a direct impact on the system’s *** a result,in order to boost the system capacity,an efficient power allocation mechanism must be *** research developed an efficient technique based on conjugate gradient to solve the problem of downlink power *** major goal is to maximize the users’maximum weighted sum *** suggested algorithm’s most notable feature is that it converges to the global optimal *** compared to existing methods,simulation results reveal that the suggested technique has a better power allocation capability.

关键词： Non-orthogonalmultiple access wireless networks power domain 5G networks

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A Comparative Study of Sensitivity Computations in ESDIRK-Based Optimal Control Problems

arXiv

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arXiv 2024年

作者： Andersen, Anders Hilmar Damm Jørgensen, John Bagterp The Department of Applied Mathematics and Computer Science Technical University of Denmark Kgs. LyngbyDK-2800 Denmark

In this paper, we compare the impact of iterated and direct approaches to sensitivity computation in fixed-step explicit singly diagonally-implicit Runge–Kutta (ESDIRK) methods when applied to optimal control problems (OCPs). We use the principle of internal numerical differentiation (IND) strictly for the iterated approach, i.e., reusing the iteration matrix factorizations, the number of Newton-type iterations, and Newton iterates, to compute the sensitivities. The direct method computes the sensitivities without using the Newton schemes. We compare the impact of the iterated and direct sensitivity computations in OCPs for the quadruple tank system. We benchmark the iterated and direct approaches with a base case. This base case is an OCP that applies an ESDIRK method that refactorizes the iteration matrix in every Newton iteration and uses a direct approach for sensitivity computations. In these OCPs, we vary the number of integration steps between control intervals and we evaluate the performance based on the number of SQP and QPs iterations, KKT violations, and the total number of function evaluations, Jacobian updates, and iteration matrix factorizations. The results indicate that the iterated approach outperforms the direct approach but yields similar performance to the base case. Copyright © 2024, The Authors. All rights reserved.

关键词： Iterative methods

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Solutions of stationary McKean-Vlasov equation on a high-dimensional sphere and other Riemannian manifolds

arXiv

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arXiv 2024年

作者： Shalova, Anna Schlichting, André Department of Mathematics and Computer Science Eindhoven University of Technology Netherlands Institute of Applied Analysis Ulm University Germany

We study stationary solutions of McKean-Vlasov equation on a high-dimensional sphere and other compact Riemannian manifolds. We extend the equivalence of the energetic problem formulation to the manifold setting and characterize critical points of the corresponding free energy functional. On a sphere, we employ the properties of spherical convolution to study the bifurcation branches around the uniform state. We also give a sufficient condition for an existence of a discontinuous transition point in terms of the interaction kernel and compare it to the Euclidean setting. We illustrate our results on a range of system, including the particle system arising from the transformer models and the Onsager model of liquid crystals. Copyright © 2024, The Authors. All rights reserved.

关键词： Spheres

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Optimal price signal generation for demand-side energy management

arXiv

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arXiv 2024年

作者： Tohidi, Seyed Shahabaldin Madsen, Henrik Calì, Davide Ritschel, Tobias K.S. Department of Applied Mathematics and Computer Science Technical University of Denmark Kgs. LyngbyDK-2800 Denmark

Renewable Energy Sources play a key role in smart energy systems. To achieve 100% renewable energy, utilizing the flexibility potential on the demand side becomes the cost-efficient option to balance the grid. However, it is not trivial to exploit these available capacities and flexibility options profitably. The amount of available flexibility is a complex and time-varying function of the price signal and weather forecasts. In this work, we use a Flexibility Function to represent the relationship between the price signal and the demand and investigate optimization problems for the price signal computation. Consequently, this study considers the higher and lower levels in the hierarchy from the markets to appliances, households, and districts. This paper investigates optimal price generation via the Flexibility Function and studies its employment in controller design for demand-side management, its capability to provide ancillary services for balancing throughout the Smart Energy Operating System, and its effect on the physical level performance. Sequential and simultaneous approaches for computing the price signal, along with various cost functions are analyzed and compared. Simulation results demonstrate the generated price/penalty signal and its employment in a model predictive controller. © 2024, CC BY-NC-ND.

关键词： Demand response

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Numerical optimal control for distributed delay differential equations: A simultaneous approach based on linearization of the delayed variables

arXiv

引用

arXiv 2024年

作者： Ritschel, Tobias K.S. Department of Applied Mathematics and Computer Science Technical University of Denmark Kgs. LyngbyDK-2800 Denmark

Time delays are ubiquitous in industrial processes, and they must be accounted for when designing control algorithms because they have a significant effect on the process dynamics. Therefore, in this work, we propose a simultaneous approach for numerical optimal control of delay differential equations with distributed time delays. Specifically, we linearize the delayed variables around the current time, and we discretize the resulting implicit differential equations using Euler’s implicit method. Furthermore, we transcribe the infinite-dimensional optimal control problem into a finite-dimensional nonlinear program, which we solve using Matlab’s fmincon. Finally, we demonstrate the efficacy of the approach using a numerical example involving a molten salt nuclear fission reactor. Copyright © 2024, The Authors. All rights reserved.

关键词： MATLAB

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Sum-of-norms regularized Nonnegative Matrix Factorization

arXiv

引用

arXiv 2024年

作者： Ang, Andersen Hamed, Waqas Bin De Sterck, Hans School of Electronics and Computer Science University of Southampton United Kingdom Department of Applied Mathematics University of Waterloo Canada

When applying nonnegative matrix factorization (NMF), generally the rank parameter is unknown. Such rank in NMF, called the nonnegative rank, is usually estimated heuristically since computing the exact value of it is NP-hard. In this work, we propose an approximation method to estimate such rank while solving NMF on-the-fly. We use sum-of-norm (SON), a group-lasso structure that encourages pairwise similarity, to reduce the rank of a factor matrix where the rank is overestimated at the beginning. On various datasets, SON-NMF is able to reveal the correct nonnegative rank of the data without any prior knowledge nor tuning. SON-NMF is a nonconvx nonsmmoth non-separable non-proximable problem, solving it is nontrivial. First, as rank estimation in NMF is NP-hard, the proposed approach does not enjoy a lower computational complexity. Using a graph-theoretic argument, we prove that the complexity of the SON-NMF is almost irreducible. Second, the per-iteration cost of any algorithm solving SON-NMF is possibly high, which motivated us to propose a first-order BCD algorithm to approximately solve SON-NMF with a low per-iteration cost, in which we do so by the proximal average operator. Lastly, we propose a simple greedy method for post-processing. SON-NMF exhibits favourable features for applications. Beside the ability to automatically estimate the rank from data, SON-NMF can deal with rank-deficient data matrix, can detect weak component with small energy. Furthermore, on the application of hyperspectral imaging, SON-NMF handle the issue of spectral variability naturally. © 2024, CC BY.

关键词： Matrix algebra

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Numerical Discretization Methods for Linear Quadratic Control Problems with Time Delays

arXiv

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arXiv 2024年

作者： Zhang, Zhanhao Hørsholt, Steen Jørgensen, John Bagterp Department of Applied Mathematics and Computer Science Technical University of Denmark Kgs. LyngbyDK-2800 Denmark

This paper presents the numerical discretization methods of the continuous-time linear-quadratic optimal control problems (LQ-OCPs) with time delays. We describe the weight matrices of the LQ-OCPs as differential equations systems, allowing us to derive the discrete equivalent of the continuous-time LQ-OCPs. Three numerical methods are introduced for solving proposed differential equations systems: 1) the ordinary differential equation (ODE) method, 2) the matrix exponential method, and 3) the step-doubling method. We implement a continuous-time model predictive control (CT-MPC) on a simulated cement mill system, and the objective function of the CT-MPC is discretized using the proposed LQ discretization scheme. The closed-loop results indicate that the CT-MPC successfully stabilizes and controls the simulated cement mill system, ensuring the viability and effectiveness of LQ discretization. © 2024, CC BY.

关键词： Model predictive control

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Meal Image Recognition and Healthy Meal Combination Recommendation System Integrated with Generative Artificial Intelligence 6

Meal Image Recognition and Healthy Meal Combination Recommen...

引用

6th IEEE Eurasia Conference on Biomedical Engineering, Healthcare and Sustainability, ECBIOS 2024

作者： Chang, Chin-Chih Wei, Chi-Hung Hsiao, Sean Yang, Chyuan-Huei Thomas Chung Hua University Department of Computer Science and Information Engineering Hsinchu Taiwan Chung Hua University Ph.D. Program in Engineering Science Hsinchu Taiwan Chung Hua University Program in Applied Foreign Language and Smart Commerce Hsinchu Taiwan School of Information Engineering Shandong Vocational and Technical University of International Studies Shandong China

ISBN: (纸本)9798350396133

People increasingly prioritize a balanced diet to enhance well-being, yet making informed dietary choices remains challenging amidst the abundance of options. To address this, we developed a meal image recognition and healthy meal combination recommender system, integrating generative artificial intelligence (AI). Convolutional neural networks were used for precise meal image recognition to identify diverse food items. The generative AI-augmented recommendation engine offers personalized meal suggestions aligned with nutritional goals and dietary preferences, utilizing a nutrition knowledge base to ensure overall well-being. The system's feasibility was validated, illustrating its excellence in meal recognition accuracy, recommendation diversity, and user engagement. By integrating generative AI, the system shows its potential to enhance dietary recommendations and public health. © 2024 IEEE.

关键词： Generative adversarial networks

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LOOPS, INVERSE LIMITS AND NON-DETERMINISM

arXiv

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arXiv 2025年

作者： Brattka, Vasco Faculty of Computer Science Universität der Bundeswehr München Germany Department of Mathematics and Applied Mathematics University of Cape Town South Africa

We introduce an operator on problems in Weihrauch complexity, which we call the inverse limit, and which corresponds to an infinite compositional product. This operation arises naturally whenever one implements algorithms that produce a sequence of results in an infinite loop, using some fixed subroutine. We prove that the corresponding operator is monotone with respect to (strong) Weihrauch reducibility but that it is not a closure operator. One of our findings is that weak Kőnig’s lemma is closed under inverse limits, which implies that the class of non-deterministically computable problems is also closed under this operation. Consequently, this class allows for a high degree of flexibility in programming. As our main technical tools, we present an injective version of the recursion theorem and an infinitary version of the so-called independent choice theorem. We also show that, in general, the inverse limit operator is more powerful than the composition of the diamond operator followed by the parallelization operator. However, in many practical scenarios, these compositions yield a result, which coincides with the application of the inverse limit operator. Finally, we discuss the special situation of loops for single-valued problems and for problems on Turing *** Codes 03D78 (Primary) 03D30 (Secondary) © 2025, CC BY.

关键词： Subroutines

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