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arXiv 2024年

作者： Akrivis, Georgios Chen, Minghua Yu, Fan Department of Computer Science and Engineering University of Ioannina Ioannina451 10 Greece Institute of Applied and Computational Mathematics FORTH Heraklion Crete700 13 Greece School of Mathematics and Statistics Gansu Key Laboratory of Applied Mathematics and Complex Systems Lanzhou University Lanzhou730000 China

Stability of the BDF methods of order up to five for parabolic equations can be established by the energy technique via Nevanlinna–Odeh multipliers. The nonexistence of Nevanlinna–Odeh multipliers makes the six-step BDF method special;however, the energy technique was recently extended by the authors in [Akrivis et al., SIAM J. Numer. Anal. 59 (2021) 2449–2472] and covers all six stable BDF methods. The seven-step BDF method is unstable for parabolic equations, since it is not even zero-stable. In this work, we construct and analyze a stable linear combination of two non zero-stable schemes, the seven-step BDF method and its shifted counterpart, referred to as WSBDF7 method. The stability regions of the WSBDFq, q 6 7, with a weight ϑ > 1, increase as ϑ increases, are larger than the stability regions of the classical BDFq, corresponding to ϑ = 1. We determine novel and suitable multipliers for the WSBDF7 method and establish stability for parabolic equations by the energy technique. The proposed approach is applicable for mean curvature flow, gradient flows, fractional equations and nonlinear equations. Copyright © 2024, The Authors. All rights reserved.

关键词： Nonlinear equations

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A Stochastic–Geometrical Framework for Object Pose Estimation based on Mixture Models Avoiding the Correspondence Problem

arXiv

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arXiv 2023年

作者： Hoegele, Wolfgang Munich University of Applied Sciences HM Department of Computer Science and Mathematics Lothstraße 64 München80335 Germany

Background: Pose estimation of rigid objects is a practical challenge in optical metrology and computer vision. This paper presents a novel stochastic–geometrical modeling framework for object pose estimation based on observing multiple feature points. Methods: This framework utilizes mixture models for feature point densities in object space and for interpreting real measurements. Advantages are the avoidance to resolve individual feature correspondences and to incorporate correct stochastic dependencies in multi–view applications. First, the general modeling framework is presented, second, a general algorithm for pose estimation is derived, and third, two example models (camera and lateration setup) are presented. Results: Numerical experiments show the effectiveness of this modeling and general algorithm by presenting four simulation scenarios for three observation systems, including the dependence on measurement resolution, object deformations and measurement noise. Probabilistic modeling utilizing mixture models shows the potential for accurate and robust pose estimations while avoiding the correspondence problem. Copyright © 2023, The Authors. All rights reserved.

关键词： computer vision

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Modeling and Nonlinear Predictive Control of Solar Thermal Systems in District Heating

SSRN

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SSRN 2023年

作者： Svensen, Jan Lorenz Bergsteinsson, Hjörleifur G. Madsen, Henrik Department of Applied Mathematics and Computer Science Technical University of Denmark Richard Petersens Plads 324 Kongens Lyngby2800 Denmark

In the future, district heating systems include portfolio of different renewable heating sources, e.g. solar thermal plants. Due to the intermittent nature of renewable heating sources, data-driven methods are required to make the system as efficient and flexible as possible. Therefore, when a District Heating System(DHS) is supported by a solar thermal plant, then predictions and control of the additional heat is necessary to reach optimal operation of the system. This paper presents a data-driven digital-twin model of a real-world solar thermal plant, and the design of nonlinear model predictive controllers for the plant. The performances show that the model is able to describe the dynamics of the system during operation, and that NMPC provided operational improvements in comparison to the historical control;showing an increse in transported power up to 28% . © 2023, The Authors. All rights reserved.

关键词： District heating

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IMPLEMENTING JACOBI ALGORITHM VERSUS GAUSS-SEIDEL ALGORITHM IN SOLVING A DISCRETIZED PROBLEM 10th

IMPLEMENTING JACOBI ALGORITHM VERSUS GAUSS-SEIDEL ALGORITHM ...

引用

10th International Conference on Advanced Materials and Systems, ICAMS 2024

作者： Sbîrnă, Sebastian Sbîrnă, Liana-Simona DTU Compute Department Institute of Applied Mathematics and Computer Science Technical University of Denmark Anker Engelunds Vej 1 Building 101A Kongens Lyngby Denmark Department of Chemistry Faculty of Sciences University of Craiova 107i Bucharest Way Craiova Romania

As it is well known that performance of algorithms generally relies both on the hardware that they are run on and on the way that they are implemented and executed the present paper aims to show that the executions’ wall-clock time might be affected by parallelizing the code, although this could sometimes become a hard task. Within this work, based on Poisson partial differential equation, we shall present different aspects of a comparison between implementing Jacobi algorithm in solving a discretized problem and implementing Gauss-Seidel algorithm in solving the same. On one hand, the results obtained by implementing the Jacobi algorithm benefited very much from the parallelization, so the first case has shown both good performance and scalability when introducing supplementary threads;as its structure always needed to exhibit a complete data copy computed in its former iterations, it became easier for us to have the code parallelly executed, because there was an insignificant risk of data races’ hitting. On the other hand, the results obtained by implementing the Gauss-Seidel algorithm managed to solve the discretized problem, although its performance was not as good as the one of the Jacobi algorithm, so the second case has shown a good execution performance in varying sizes of sequentially executed data, taking into account that, as far as parallelizing was concerned, the performance was unreliable and random. © 2024, Institute National Cercetare-Dezvoltare Textiles Pielarie. All rights reserved.

关键词： Gauss-Seidel algorithm Jacobi algorithm Poisson partial differential equation

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The sine and cosine diffusive representations for the Caputo fractional derivative

arXiv

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arXiv 2023年

作者： Khosravian-Arab, Hassan Dehghan, Mehdi Department of Applied Mathematics and Computer Science Faculty of Mathematics and Statistics University of Isfahan Isfahan81746-73441 Iran No.424 Hafez Avenue Tehran Iran

As we are aware, various types of methods have been proposed to approximate the Caputo fractional derivative numerically. A common challenge of the methods is the non-local property of the Caputo fractional derivative which leads to the slow and memory consuming methods. Diffusive representation of fractional derivative is an efficient tool to overcome the mentioned challenge. This paper presents two new diffusive representations to approximate the Caputo fractional derivative of order 0 MSC Codes 26A33, 65D30, 65D25, 65D32 Copyright © 2023, The Authors. All rights reserved.

关键词： Error analysis

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Comparative sensitivity analysis of single and multiple modifications in multi-criteria decision analysis 28th

Comparative sensitivity analysis of single and multiple modi...

引用

28th International Conference on Knowledge Based and Intelligent information and Engineering Systems, KES 2024

作者： Wieckowski, Jakub Bialon, Pawel Salabun, Wojciech Research Team on Intelligent Decision Support Systems Department of Artificial Intelligence and Applied Mathematics Faculty of Computer Science and Information Technology West Pomeranian University of Technology Szczecin ul. Zolnierska 49 Szczecin71-210 Poland National Institute of Telecommunications ul. Szachowa 1 Warsaw04-894 Poland

In the area of decision-making, where complexities often exceed experts' analytical capabilities, this study addresses a critical gap by introducing a novel methodology for sensitivity analysis within the Multi-Criteria Decision Analysis (MCDA) problems. Current analytical frameworks struggle to comprehensively consider potential modifications to values within decision matrices, making it challenging to understand their impact in detail. To address this challenge, decision-makers need enhanced tools, and MCDA methods combined with systematic changes in selected elements of the decision matrix stand out as a promising approach. However, existing studies primarily focus on different criteria-weight scenarios, leaving an unexplored gap in the simultaneous modification of multiple values within the decision matrix. This paper integrates sensitivity analysis within the MCDA methods, extending its role in the comprehensive assessment of decision problems. Sensitivity analysis becomes crucial in offering decision-makers a broader perspective, aiding them in navigating the complexities of decision-making in dynamic environments. Recognizing the unexplored potential in sensitivity analysis, the study proposed a novel approach of simultaneous modification of multiple values in a decision matrix, offering an extension of conventional one-at-a-time modifications. As a Proof of Concept (PoC) research work, the study investigated whether the determined approach provides divergent preference scores compared to the traditional single-modification method across ten different MCDA techniques. The results showed that modifying multiple values simultaneously produced different preference scores of alternatives than in the case of a conventional single change, showing that additional insight knowledge could be extracted from this type of sensitivity analysis. © 2024 The Authors.

关键词： Sensitivity analysis

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TrafficKAN-GCN: Graph Convolutional-based Kolmogorov-Arnold Network for Traffic Flow Optimization

arXiv

引用

arXiv 2025年

作者： Zhang, Jiayi Zhang, Yiming Zheng, Yuan Wang, Yuchen You, Jinjiang Xu, Yuchen Jiang, Wenxing Dev, Soumyabrata School of Mathematics and Applied Mathematics University of Nottingham Ningbo China School of Computer Science University of Nottingham Ningbo China Department of Electrical and Computer Engineering University of Washington United States School of Computer Science Carnegie Mellon University United States School of Engineering University of Nottingham Ningbo China School of Computer Science University College Dublin Ireland The ADAPT SFI Research Centre Ireland

Urban traffic optimization is crucial for improving transportation efficiency and alleviating congestion. Traditional algorithms [1] like Dijkstra’s [2] and Floyd’s [3], along with Genetic Algorithms (GA) [4], are widely used for route planning but struggle with large-scale, dynamic traffic networks due to computational complexity and limited ability to capture nonlinear spatial-temporal dependencies [5]. To address these challenges, we propose a hybrid framework combining Kolmogorov-Arnold Networks (KAN) with Graph Convolutional Networks (GCN) [6, 7, 8] for urban traffic flow optimization. KAN’s ability to approximate nonlinear functions, along with GCN’s capacity to model spatial dependencies in graph-structured data, provides a more effective representation of traffic dynamics. We evaluate KAN-GCN on real-world datasets and compare it to traditional models like Multi-Layer Perceptrons (MLP) [9] and decision trees. While MLP-GCN shows higher accuracy, KAN-GCN excels in handling noisy and complex traffic patterns [7]. Results highlight challenges in applying KAN to large-scale networks and suggest potential improvements. Additionally, we explore extending the framework to Transformer models for scalable and dynamic traffic forecasting. Our findings indicate that combining KAN with GCN offers promising potential for intelligent traffic management, with further optimization possible for large-scale *** the spirit of reproducible research, the model code, dataset, and results of the experiments in this paper are available at: https://***/ZhangJiayi24/KAN_GCN_*** Codes 90B20, 68T07, 05C85, 90C90 © 2025, CC BY.

关键词： Decision trees

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A new class of distances on complex projective spaces

引用

Linear Algebra and Its Applications 2025年 721卷 577-611页

作者： Bistroń, Rafal Eckstein, Michal Friedland, Shmuel Miller, Tomasz Życzkowski, Karol Institute of Theoretical Physics Faculty of Physics Astronomy and Applied Computer Science Jagiellonian University ul. prof. Stanislawa Lojasiewicza 11 Krakow30-348 Poland Doctoral School of Exact and Natural Sciences Jagiellonian University ul. prof. Stanislawa Lojasiewicza 11 Krakow30-348 Poland Department of Mathematics Statistics and Computer Science University of Illinois at Chicago 851 S. Morgan Street ChicagoIL60607-7045 United States Copernicus Center for Interdisciplinary Studies Jagiellonian University ul. Mikolaja Kopernika 27 Krakow31-501 Poland Center for Theoretical Physics Polish Academy of Science aleja Lotników 32/46 Warsaw02-668 Poland

The complex projective space P(Cn) can be interpreted as the space of all quantum pure states of size n. A distance on this space, interesting from the perspective of quantum physics, can be induced from a classical distance defined on the n-point probability simplex by the ‘earth mover problem’. We show that this construction leads to a quantity satisfying the triangle inequality, which yields a true distance on complex projective space belonging to the family of quantum 2-Wasserstein distances. © 2024 Elsevier Inc.

关键词： State space methods

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Hyperbolic Polariton Lenses For Sub-Diffractive Imaging

Hyperbolic Polariton Lenses For Sub-Diffractive Imaging

引用

CLEO: Fundamental science, CLEO:FS 2024 - Part of Conference on Lasers and Electro-Optics, CLEO 2024

作者： Renzi, Enrico Maria Yves, Simon Strickland, Diana Erland, Sveinung Bachmat, Eitan Alù, Andrea Photonics Initiative Advanced Science Research Center City University of New York New YorkNY10031 United States Physics Program The Graduate Center City University of New York NY10026 United States Department of Maritime Studies Western Norway University of Applied Sciences Haugesund5528 Norway Department of Computer Science Ben-Gurion University of the Negev Beer Sheva84105 Israel

We introduce the design of lenses for hyperbolic surface phonon polaritons operated in the mid-infrared range. Based on Minkowski space considerations, these lenses offer unbounded numerical aperture and can largely o... 详细信息

ISBN: (纸本)9781957171395

关键词： Polariton

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HISTOGRAMICALLY COMPARING MATHEMATICAL SIMULATION RESULTS IN MODELING A STOCHASTIC PROCESS EXHIBITING BOTH CONTINUOUS AND DISCRETE VARIATIONS 10th

HISTOGRAMICALLY COMPARING MATHEMATICAL SIMULATION RESULTS IN...

引用

10th International Conference on Advanced Materials and Systems, ICAMS 2024

作者： Sbîrnă, Sebastian Sbîrnă, Liana-Simona DTU Compute Department Institute of Applied Mathematics and Computer Science Technical University of Denmark 1 Anker Engelunds Street Building 101A Kongens Lyngby Denmark Department of Chemistry Faculty of Sciences University of Craiova 107i Bucharest Way Craiova Romania

The current paper aims to present several mathematical simulation results which have been obtained by modeling a Lévy stochastic process, exhibiting two continuous variations followed by a discrete one. In modeling such a process, we surely had to decompose it into three sub-processes: the first one is a deterministic linear drift (a time-depending simple linear function);the second one is a standard (one dimensional) Wiener process (a stochastic process respecting three essential properties, namely: independence, stationarity and continuity);the third one is a CFD Poisson stochastic process, which is discrete (as formerly stated). The comparison was made by analyzing different sets of histograms. These sets have been plotted by histogramically comparing two jump distributions, namely Pareto distribution vs. normal distribution. The analyzed Lévy stochastic process, exhibiting both continuous and discrete variations, has been computed upon its discrete part, by using an appropriate skeleton structure, the main advantage of such a computation being the efficiency of it, although it is known that a weakness in using “discrete skeletons” is that the location of large jumps in the simulation model cannot be precisely identified. © 2024, Institute National Cercetare-Dezvoltare Textiles Pielarie. All rights reserved.

关键词： histogram Lévy stochastic process Wiener process

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