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arXiv 2024年

作者： Bang-Jensen, Jørgen Wang, Yun Yeo, Anders Dept. of Math. and Computer Science University of Southern Denmark Odense Denmark Dept. of Math. and Computer Science University of Southern Denmark Odense Denmark School of Mathematics Shandong University Jinan250100 China Department of Mathematics and Applied Mathematics University of Johannesburg Auckland Park2006 South Africa

A digraph is semicomplete if it has no pair of non-adjacent vertices. It is complete if every pair of distinct vertices induce a 2-cycle. It is well-known and easy to show that even the following version of the directed travelling salesman problem is NP-complete: Given a strongly connected complete digraph D = (V, A), a cost function w: A → {0, 1} and a natural number K;decide whether D has a directed Hamiltonian cycle of cost at most K. We study the following variant of this problem for {0, 1}-weighted semicomplete digraphs where the set of arcs which have cost 1 form a collection of vertex-disjoint complete digraphs. A digraph is semicomplete multipartite if it can be obtained from a semicomplete digraph D by choosing a collection of vertex-disjoint subsets X1, . . ., Xc of V (D) and then deleting all arcs both of whose end-vertices lie inside some Xi. Let D be a semicomplete digraph with a cost function w as above, where w(a) = 1 precisely when a is an arc inside one of the subsets X1, . . ., Xc and let D∗ be the corresponding semicomplete multipartite digraph that we obtain by deleting all arcs inside the Xi’s. Then every cycle C of D corresponds to a generalized cycle Cg of D∗ which is either the cycle C itself if w(C) = 0 or a collection of two or more paths that we obtain by deleting all arcs of cost 1 on C. Similarly we can define a generalized path P g in a semicomplete multipartite digraph. The purpose of this paper is to study structural and algorithmic properties of generalized paths and cycles in semicomplete multipartite digraphs. This allows us to identify classes of directed {0, 1}-weighted TSP instances that can be solved in polynomial time as well as others for which we can get very close to the optimum in polynomial time. Along with these results we also show that two natural questions about properties of cycles meeting all partite sets in semicomplete multipartite digraphs are *** Codes 05C20, 05c38, 05c45, 05c85 © 2024, CC BY.

关键词： Cost functions

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Nonlinear Two-Level Schwarz Methods: A Parallel Implementation in FROSch

arXiv

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arXiv 2024年

作者： Heinlein, Alexander Ho, Kyrill Klawonn, Axel Lanser, Martin Delft University of Technology Delft Institute of Applied Mathematics Mekelweg 4 Delft2628 CD Netherlands Department of Mathematics and Computer Science Division of Mathematics University of Cologne Weyertal 86-90 Cologne50931 Germany Center for Data and Simulation Science University of Cologne Germany

Owing to the ability of nonlinear domain decomposition methods to improve the nonlinear convergence behavior of Newton’s method, they have experienced a rise in popularity recently in the context of problems for which Newton’s method converges slowly or not at all. This article introduces a novel parallel implementation of a two-level nonlinear Schwarz solver based on the FROSch (Fast and Robust Overlapping Schwarz) solver framework, part of Sandia’s Trilinos library. First, an introduction to the key concepts underlying two-level nonlinear Schwarz methods is given, including a brief overview of the coarse space used to build the second level. Next, the parallel implementation is discussed, followed by preliminary parallel results for a scalar nonlinear diffusion problem and a 2D nonlinear plane-stress Neo-Hooke elasticity problem with large *** Codes 65F08, 65F10, 65H10, 65N22, 65N55 Copyright © 2024, The Authors. All rights reserved.

关键词： Domain decomposition methods

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Generalized transversality conditions for fuzzy quantum-symmetric variational problems via granular approach

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Computational and applied mathematics 2025年第6期44卷 1-32页

作者： Bohner, Martin Girejko, Ewa Malinowska, Agnieszka B. Nguyen, Linh Schneider, Baruch Truong, Tri Missouri S&T Rolla USA Faculty of Computer Science Bialystok University of Technology Białystok Poland Applied Analysis Research Group Faculty of Mathematics and Statistics Ton Duc Thang University Ho Chi Minh City Vietnam Department of Mathematics University of Ostrava Ostrava Czech Republic Department of Applied Mathematics Faculty of Applied Science Ho Chi Minh City University of Technology (HCMUT) Ho Chi Minh City Vietnam Vietnam National University Ho Chi Minh City Ho Chi Minh City Vietnam

This paper investigates fuzzy q-symmetric variational problems with natural boundary conditions. Based on the relative distance measure fuzzy arithmetic and horizontal membership functions (HMFs), we propose novel concepts of differentiability and integrability for fuzzy functions on quantum geometric subsets of real numbers. Then, fundamental foundations of q-symmetric calculus of variations based on HMFs are provided. With the help of HMFs and granular q-symmetric differentiability, we derive necessary optimality conditions for fuzzy q-symmetric variational problems that depend on free endpoints. Moreover, sufficient conditions for minimizers of q-symmetric variational problems are obtained. Some numerical examples illustrating the proposed approach are presented.

关键词： Membership functions

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Path Planning for Autonomous Robot Navigation: Present Approaches 1

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3rd International Conference on Futuristic Trends in Network and Communication Technologies, FTNCT 2020

作者： Verma, Shagun Kumar, Neerendra Department of Computer Science IT Central University of Jammu Jammu181143 India Doctoral School of Applied Informatics and Applied Mathematics Óbuda University Budapest Hungary

ISBN: (数字)9789811614835

ISBN: (纸本)9789811614828

An intelligent autonomous robot is in demand for robotic operations in the fields such as industry, medical, bionics, military. For any machine, designed to follow a precise sequence of instructions, self-positioning, path framing, map architecture, and obstacle prevention are the prerequisites of navigation. This paper presents a survey about the key navigation approaches explored by various authors in the last decade. The survey has a brief insight into the various approaches used for robot navigation concerning to the variable and invariable nature of the vicinity and the obstacle. The comprehensive look-over presented in this paper provides an in-depth analysis and assessment of the discrete classical and heuristic approaches used by the researchers. The research assessment is finally concluded by aggregating the complete knowledge of the various path planning techniques by reviewing the literature. © 2021, Springer Nature Singapore Pte Ltd.

关键词： Motion planning

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Understanding the learning mechanism of convolutional neural network applied to fluorescence spectra 4

Understanding the learning mechanism of convolutional neural...

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AI and Optical Data sciences IV 2023

作者： Venturini, Francesca Michelucci, Umberto Sperti, Michela Gucciardi, Arnaud Deriu, Marco A. Institute of Applied Mathematics and Physics Zurich University of Applied Sciences Technikumstrasse 9 Winterthur8401 Switzerland TOELT llc Machine Learning Research and Development Birchlenstr. 25 Dübendorf8600 Switzerland Lucerne University of Applied Sciences and Arts Computer Science Department Lucerne Switzerland PolitoBIOMed Lab Department of Mechanical and Aerospace Engineering Politecnico di Torino Turin Italy Artificial Intelligence Laboratory University of Ljubljana Ljubljana Slovenia

ISBN: (纸本)9781510659810

The power of artificial neural networks to determine the quality and properties of olive oil was proven by several studies in the last years. Less clear is, however, how the neural network is able to extract useful information from the input data. This work investigates the learning mechanism of one-dimensional convolutional neural networks (1D-CNNs) trained to predict the physicochemical properties of olive oil from single fluorescence spectra. Such a 1D-CNN can successfully predict the parameters relevant to the quality assessment: acidity, peroxide value, and UV absorbance. To go beyond a simple quality assessment algorithm, it is important to identify which spectral features in the measured spectra are correlated with each chemical parameter and therefore with the quality of olive oil. To obtain this information, explainability techniques can be used by studying the latent feature space generated by the intermediate layers of the one-dimensional trained convolutional neural network. This work analyses in detail the common features that are used by the 1D-CNN to predict the two physicochemical parameters: acidity and K232 © 2023 SPIE.

关键词： Olive oil

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An Assessment of the Supremizer and Aggregation Methods of Stabilization for Reduced-Order Models

arXiv

引用

arXiv 2023年

作者： Davie, Kayla D. Elman, Howard C. Applied Mathematics & Statistics Scientific Computation Program University of Maryland College ParkMD20742 United States Department of Computer Science Institute for Advanced Computer Studies University of Maryland College ParkMD20742 United States

MSC Codes 65N22, 65K10, 65F45We explore the features of two methods of stabilization, aggregation and supremizer methods, for reduced-order modeling of parametrized optimal control problems. In both methods, the reduced basis spaces are augmented to guarantee stability. For the aggregation method, the reduced basis approximation spaces for the state and adjoint variables are augmented in such a way that the spaces are identical. For the supremizer method, the reduced basis approximation space for the state-control product space is augmented with the solutions of a supremizer equation. We implement both of these methods for solving several parametrized control problems and assess their performance. Results indicate that the number of reduced basis vectors needed to approximate the solution space to some tolerance with the supremizer method is much larger, possibly double, that for aggregation. There are also some cases where the supremizer method fails to produce a converged solution. We present results to compare the accuracy, efficiency, and computational costs associated with both methods of stabilization which suggest that stabilization by aggregation is a superior stabilization method for control problems. © 2023, CC BY.

关键词： Stabilization

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Second-order nonstandard finite difference schemes for a class of models in bioscience

arXiv

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arXiv 2022年

作者： Anguelov, Roumen Lubuma, Jean M.-S. Department of Mathematics and Applied Mathematics University of Pretoria Pretoria South Africa School of Computer Science and Applied Mathematics University of the Witwatersrand Johannesburg South Africa

We consider a dynamical system, defined by a system of autonomous differential equations, on Ω ⊂ Rn. By using Mickens' rule on the nonlocal approximation of nonlinear terms, we construct an implicit Nonstandard Finite Difference (NSFD) scheme that, under an existence and uniqueness condition, is an explicit time reversible scheme. Apart from being elementary stable, we show that the NSFD scheme is of second-order and domain-preserving, thereby solving a pending problem on the construction of higher-order nonstandard schemes without spurious solutions, and extending the tangent condition to discrete dynamical systems. It is shown that the new scheme applies directly for mass action-based models of biological and chemical *** Codes 65L05 © 2022, CC BY.

关键词： Dynamical systems

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INVERSION SETS AND QUOTIENT ROOT SYSTEMS

arXiv

引用

arXiv 2023年

作者： Dimitrov, Ivan Gigliotti, Cole Ossip, Etan Paquette, Charles Wehlau, David Department of Mathematics and Statistics Queen’s University United Kingdom Department of Mathematics University of British Columbia Canada Faculty of Engineering and Applied Science Queen’s University United Kingdom Department of Mathematics and Computer Science Royal Military College of Canada Canada

We provide a recursive description of all decompositions of the positive roots R+ of a quotient root system R into disjoint unions of inversion sets. Our description is type-independent and generalizes the analogous result for type A root systems in [USRA]. The main tool is the notion of an inflation of a subset of a quotient root system. This new notion allows us to treat all root systems (and their quotients) uniformly. We also obtain some numerical results about the number of special decompositions. The new sequences we obtain may be considered as extensions of Catalan *** Codes 17B22 © 2023, CC BY.

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m−ACCRETIVE EXTENSIONS OF FRIEDRICHS OPERATORS

arXiv

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arXiv 2025年

作者： Burazin, Krešimir Erceg, Marko Soni, Sandeep Kumar School of Applied Mathematics and Computer Science J. J. Strossmayer University of Osijek Trg Ljudevita Gaja 6 Osijek31000 Croatia Department of Mathematics Faculty of Science University of Zagreb Bijenička cesta 30 Zagreb10000 Croatia

MSC Codes 35F45, 46C05, 46C20, 47B44The introduction of abstract Friedrichs operators in 2007—an operator-theoretic framework for studying classical Friedrichs operators—has led to significant developments in the field, including results on well-posedness, multiplicity, and classification. More recently, the von Neumann extension theory has been explored in this context, along with connections between abstract Friedrichs operators and skew-symmetric operators. In this work, we show that all m−accretive extensions of abstract Friedrichs operators correspond precisely to those satisfying (V)-boundary conditions. We also establish a connection between the m−accretive extensions of abstract Friedrichs operators and their skew-symmetric components. Additionally, the three equivalent formulations of boundary conditions are unified within a single interpretive framework. To conclude, we discuss a constructive relation between (V)- and (M)-boundary conditions and examine the multiplicity of the associated M-operators. We demonstrate our results on two examples, namely, the first order ordinary differential equation on an interval, with various boundary conditions, and the second-order elliptic partial differential equation with Dirichlet boundary conditions. © 2025, CC BY.

关键词： Ordinary differential equations

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Real-Time Credit Card Fraud Detection Surveillance System 2

Real-Time Credit Card Fraud Detection Surveillance System

引用

2nd International Conference on Cybernetics and Innovations, ICCI 2023

作者： Thongthawonsuwan, Pattarawan Ganokratanaa, Thittaporn Pramkeaw, Patiyuth Chumuang, Narumol Ketcham, Mahasak King Mongkut's University of Technology North Bangkok Department of Information Technology Management Bangkok Thailand King Mongkut's University of Technology Thonburi Applied Computer Science Program Bangkok Thailand King Mongkut's University of Technology Thonburi Media Technology Program Bangkok Thailand Department of Digital Media Technology Thailand Media Technology Program King Mongkut s University of Technology Thonburi Bangkok Thailand

ISBN: (纸本)9798350336573

In this research, the system that detects administrative behavior, credit card and developing corruption from credit cards through LINE applications. The objective of this research 1) To develop a risk notification system or suspect to be corruption of credit cards through the connection channels of LINE application 2) to measure the accuracy of the system developed. As for the notification to prevent the risk of credit card corruption The research methods are divided into 5 steps, namely Step 1, Step System analysis. Is a study and analysis to determine the needs of steps 2 steps, system design Is the process of designing tools used in research. Step 3 System development Is the process of developing the tools used in research. Step 4, the process of testing and correcting the system. Is the process of testing the tools used in research. Step 5 Summary Discuss results and suggestions. The research results are summarized as follows The results of the measurement and completeness of the data are very good as 86.67 percent. The results of the measurement of the correct conditions are as good as 80 percent and the performance measurement of time is in The criteria is as good as 86.67 percent. In conclusion, the corruption system from credit cards through the application alert. LINE can be used appropriately. © 2023 IEEE.

关键词： Systems analysis

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