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27th International Conference on Knowledge Based and Intelligent Information and engineering Sytems, KES 2023

作者： Kolodziejczyk, Joanna Tarasenko, Yuliia Sulikowski, Piotr Research Team on Intelligent Decision Support Systems Department of Artificial Intelligence Methods and Applied Mathematics Faculty of Computer Science and Information Technology West Pomeranian University of Technology in Szczecin ul. Zolnierska 49 Szczecin71-210 Poland National Institute of Telecommunications ul. Szachowa 1 Warsaw04-894 Poland Department of Information Systems Engineering Faculty of Computer Science and Information Technology West Pomeranian University of Technology in Szczecin ul. Zolnierska 49 Szczecin71-210 Poland

Particle Swarm Optimization (PSO) is a robust stochastic optimization algorithm for solving complex and constrained optimization problems. This paper aims to systematically investigate the influence of diverse random number distributions on the learning parameters of PSO and evaluate the algorithm's sensitivity based on these parameters. To this end, several exhaustive numerical experiments were conducted on several test functions, including asymmetric Sphere, Easom, and Csendes. Initially, appropriate random distributions were identified for the learning parameters and proceeded to compare these distributions using all potential combinations. The sensitivity of PSO to these parameters was evaluated using the mean best score, the relative proximity of the best particle to the theoretical optimum, and the average objective function evaluations. The most significant contribution of this research lies in the insights derived from the experimental data. The discovery was that highly skewed and long-tailed distributions such as Chi, Chi-square, Lomax, and Exponential often underperform. On the other hand, distributions that are bounded proportionally to the problem domain consistently surpass the performance of the standard uniform distribution. These findings significantly enhance the understanding of PSO algorithms and provide valuable guidelines for their practical deployment. © 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://***/licenses/by-nc-nd/4.0)

关键词： Particle Swarm Optimization random number distribution stochastic optimization

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Physics-Informed Neural Network for Solving Buckley-Leverett Equation of Plane Radial Flow

Physics-Informed Neural Network for Solving Buckley-Leverett...

引用

Data-driven Optimization of Complex Systems (DOCS), International Conference on

作者： Jianpeng Zang Yizhuo Song Junting Bai Kai Zhang Jian Wang Sergey V. Ablameyko School of Petroleum Engineering China University of Petroleum (East China) Qingdao China Engineering and Computer Science New York University Shanghai Shanghai China College of Science China University of Petroleum (East China) Qingdao China School of Petroleum Engineering China University of Petroleum (East China) Civil Engineering School Qingdao University of Technology Qingdao China Faculty of Applied Mathematics and Computer Science Belarusian State University Minsk Belarus

ISBN: (数字)9798350377842

ISBN: (纸本)9798350377859

The Buckley-Leverett (BL) equation of plane radial flow describes the flow state of two phases of oil and water in an ideal planar porous medium. It is a nonlinear hyperbolic conservation partial differential equation (PDE) with a jump value, making it difficult to solve numerically. This paper presents a physics-informed neural network (PINN) with entropy constraints to solve the BL equation of plane radial flow. Specifically, the Oleinik entropy condition is used to limit the change of the relationship between water content and saturation in accordance with the physical law, which does not change the structure of the target PDE to be fitted by the model. Benefit from the interpretability of PINN and its fit in solving PDE problems, the model can be trained in an unsupervised way, thus eliminating the effort of obtaining sample labels. The experimental results show that the root mean square error fluctuates between the interval [0.03436,0.16054], indicating a good fitting effect. Especially the jump value, which refers to the position of the leading edge of water saturation, can be clearly output by the model.

关键词： Partial differential equations Oils Neural networks Fitting Water conservation Mathematical models Entropy Surface fitting Root mean square Optimization

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Application of a Fourier-Type Series Approach based on Triangles of Constant Width to Letterforms

arXiv

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arXiv 2024年

作者： Wasem, Micha Yerly, Florence School of Engineering and Architecture HES-SO University of Applied Sciences and Arts Western Switzerland Pérolles 80 Fribourg1700 Switzerland Faculty of Mathematics and Computer Science UniDistance Suisse Schinerstrasse 18 Brig3900 Switzerland

In this work, we present a novel approach to type design by using Fourier-type series to generate letterforms. We construct a Fourier-type series for functions in L2(S1, C) based on triangles of constant width instead of circles to model the curves and shapes that define individual characters. In order to compute the coefficients of the series, we construct an isomorphism R: L2(S1, C) → L2(S1, C) and study its application to letterforms, thus presenting an alternative to the common use of Bézier curves. The proposed method demonstrates potential for creative experimentation in modern type design. Copyright © 2024, The Authors. All rights reserved.

关键词： Fourier series

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Multiple-criteria Heuristic Rating Estimation

arXiv

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arXiv 2022年

作者： Kędzior, Anna Kulakowski, Konrad AGH University of Science and Technology Faculty of Applied Mathematics Krak Poland AGH University of Science and Technology Faculty of Electrical Engineering Automatics Computer Science and Biomedical Engineering Krak Poland

One of the most widespread multi-criteria decision-making methods is the Analytic Hierarchy Process (AHP). AHP successfully combines the pairwise comparisons method and the hierarchical approach. It allows the decision-maker to set priorities for all ranked alternatives. But what if, for some of them, their ranking value is known (e.g., it can be determined differently)? The Heuristic Rating Estimation (HRE) method proposed in 2014 tried to bring the answer to this question. However, the considerations were limited to a model that did not consider many criteria. In this work, we go a step further and analyze how HRE can be used as part of the AHP hierarchical framework. The theoretical considerations are accompanied by illustrative examples showing HRE as a multiple-criteria decision-making method. Copyright © 2022, The Authors. All rights reserved.

关键词： Analytic hierarchy process

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An Improved Unbiased Particle Filter

arXiv

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arXiv 2023年

作者： Jasra, Ajay Maama, Mohamed Ombao, Hernando Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Statistics Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia

In this paper we consider the filtering of partially observed multi-dimensional diffusion processes that are observed regularly at discrete times. We assume that, for numerical reasons, one has to time-discretize the diffusion process which typically leads to filtering that is subject to discretization bias. The approach in [16] establishes that when only having access to the time discretized diffusion it is possible to remove the discretization bias with an estimator of finite variance. We improve on the method in [16] by introducing a modified estimator based on the recent work of [17]. We show that this new estimator is unbiased and has finite variance. Moreover, we conjecture and verify in numerical simulations that substantial gains are obtained. That is, for a given mean square error (MSE) and a particular class of multi-dimensional diffusion, the cost to achieve the said MSE falls. Copyright © 2023, The Authors. All rights reserved.

关键词： Mean square error

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Using Symmetries to Investigate the Complete Integrability, Solitary Wave Solutions and Solitons of the Gardner Equation

arXiv

引用

arXiv 2024年

作者： Hereman, Willy Göktaş, Ünal Department of Applied Mathematics and Statistics Colorado School of Mines GoldenCO80401-1887 United States Department of Computer Science and Engineering Texas A&M University College StationTX77843-3112 United States

In this paper, using a scaling symmetry, it is shown how to compute polynomial conservation laws, generalized symmetries, recursion operators, Lax pairs, and bilinear forms of polynomial nonlinear partial differential equations, thereby establishing their complete integrability. The Gardner equation is chosen as the key example, as it comprises both the Korteweg–de Vries and modified Korteweg–de Vries equations. The Gardner and Miura transformations, which connect these equations, are also computed using the concept of scaling homogeneity. Exact solitary wave solutions and solitons of the Gardner equation are derived using Hirota’s method and other direct methods. The nature of these solutions depends on the sign of the cubic term in the Gardner equation and the underlying mKdV equation. It is shown that flat (table-top) waves of large amplitude only occur when the sign of the cubic nonlinearity is negative (defocusing case), whereas the focusing Gardner equation has standard elastically colliding solitons. This paper’s aim is to provide a review of the integrability properties and solutions of the Gardner equation and to illustrate the applicability of the scaling symmetry approach. The methods and algorithms used in this paper have been implemented in Mathematica, but can be adapted for major computer algebra *** Codes Primary 35Q51, 35Q53. Secondary 37K10, 37K40 © 2024, CC BY.

关键词： Solitons

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UNet with Two-Fold Training for Effective Segmentation of Lung Section in Chest X-Ray 3

UNet with Two-Fold Training for Effective Segmentation of Lu...

引用

3rd International Conference on Intelligent Computing, Instrumentation and Control Technologies, ICICICT 2022

作者： Rajinikanth, Venkatesan Kadry, Seifedine Damasevicius, Robertas Gnanasoundharam, J. Abed Mohammed, Mazin Glan Devadhas, G. Noroff University College Faculty of Applied Computing and Technology Kristiansand94612 Norway Silesian University of Technology Faculty of Applied Mathematics Gliwice44-100 Poland St. Joseph's College of Engineering Omr Department of Electronics and Instrumentation Engineering Chennai600119 India University of Anbar College of Computer Science and Information Technology Ramadi31001 Iraq Vimal Jyothi Engineering College Department of Electronics and Instrumentation Engineering Chemperi India

ISBN: (数字)9781665410052

ISBN: (纸本)9781665410052

Segmentation and evaluation of the Region of Interest (ROI) in medical imaging is a prime task for disease screening and decision-making. Due to accuracy, Convolutional-Neural-Network (CNN) based ROI segmentation has been widely employed in recent years to evaluate a class of medical images recorded using chosen modality. The proposed work aims to demonstrate the segmentation performance of the UNet scheme with a one-fold and two-fold training process. To experimentally verify the merit of the proposed scheme, segmentation of the lung section from the chest X-ray is studied. This research includes the following parts;(i) Resizing the test image and image mask to pixels, (ii) Training the UNet with one-fold and two-fold approaches, (iii) Extracting the ROI, (iv) Comparing the ROI with the mask to compute the image metrics and (v) Validating and confirming the segmentation performance of UNet. The performance of UNet is then verified with UNet+ and UNet++. The investigational ending substantiates that the proposed approach helps to get better Jaccard (>95%), Dice ((>97%), and Accuracy (>98%) in two-fold training compared to other methods considered in this study. © 2022 IEEE.

关键词： Decision making

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Counting Nodes in Smolyak Grids

arXiv

引用

arXiv 2024年

作者： Minini, Jocelyn Wasem, Micha School of Engineering and Architecture HES-SO University of Applied Sciences and Arts Western Switzerland Pérolles 80 Fribourg1700 Switzerland Faculty of Mathematics and Computer Science UniDistance Suisse Schinerstrasse 18 Brig3900 Switzerland

Using generating functions, we are proposing a unified approach to produce explicit formulas, which count the number of nodes in Smolyak grids based on various univariate quadrature or interpolation rules. Our approach yields, for instance, a new formula for the cardinality of a Smolyak grid, which is based on Chebyshev nodes of the first kind and it allows to recover certain counting-formulas previously found by Bungartz-Griebel, Kaarnioja, Müller-Gronbach, Novak-Ritter and *** Codes 05A15, 05C69, 65D15 Copyright © 2024, The Authors. All rights reserved.

关键词： Differentiation (calculus)

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Heuristic Rating Estimation Method for the incomplete pairwise comparisons matrices

arXiv

引用

arXiv 2022年

作者： Kulakowski, Konrad Kędzior, Anna AGH University of Science and Technology Faculty of Electrical Engineering Automatics Computer Science and Biomedical Engineering Krak Poland AGH University of Science and Technology Faculty of Applied Mathematics Krak Poland

The Heuristic Rating Estimation Method enables decision-makers to decide based on existing ranking data and expert comparisons. In this approach, the ranking values of selected alternatives are known in advance, while these values have to be calculated for the remaining ones. Their calculation can be performed using either an additive or a multiplicative method. Both methods assumed that the pairwise comparison sets involved in the computation were complete. In this paper, we show how these algorithms can be extended so that the experts do not need to compare all alternatives pairwise. Thanks to the shortening of the work of experts, the presented, improved methods will reduce the costs of the decision-making procedure and facilitate and shorten the stage of collecting decision-making data. Copyright © 2022, The Authors. All rights reserved.

关键词： Decision making

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Study of fuzzy expert systems towards prediction and detection of fraud case in health care insurance

引用

Materials Today: Proceedings 2022年 56卷 477-480页

作者： Kalra, Gunjan Rajoria, Yogendra Kumar Boadh, Rahul Rajendra, P. Pandey, Pratibha Khatak, Naveen Kumar, Ajay Department of the Mathematics School of Basic and Applied Science K.R. Mangalam University Sohna Road Gurugram Haryana 122103 India Department of Mathematics CMR Institute of Technology Bengaluru India Department of Computer Application Uttaranchal Institute of Management Uttaranchal University Arcadia Grant P.O. Chandanwari Premnagar Uttarakhand Dehradun248007 India Department of Mechanical Engineering Faculty of Engineering and Technology Shree Guru Govind Singh Tricentenary University Haryana Gurugram122103 India Institute of Engineering and Technology Maharshi Dayanand University Rohtak Haryana Rohtak 124001 India

The size of this issue is sufficiently enormous to focus on it issue for wellbeing structures. Unseemly installments by protection associations or outsider payers happen due to mistakes, fraud and misrepresentation. Determined to pinpoint has been some property/loss protection inclusion that incorporates a medical consideration part. Fraud and misuse happen at many focuses in the medical services framework. Specialists, clinics, nursing homes, symptomatic offices, clinical gear providers, and lawyers have been referred to in tricks to dupe the framework. Medical care assumes a vital part in human existence and it should be reasonable. The rate of health care coverage extortion continues to expand each year, particularly during coronavirus. Extortion and maltreatment on clinical cases turned into a basic issue for the health care coverage industry. We have tracked down that large numbers of the distortions planned to bring about an unapproved advantage were made in the Medical health care coverage. Manual identification of fraud in medical coverage is an exceptionally intense undertaking. In this paper, Fuzzy expert system has been carried out to recognize medical coverage frauds. The point is to recognize extortion asserts precisely inside a brief timeframe. Extortion in medical coverage is truly exceptional and exorbitant for the two policyholders and insurance agencies in all areas of the protection area. © 2022

关键词： Health care

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