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IEEE Transactions on Energy Markets, Policy and Regulation 2023年第2期1卷 131-144页

作者： Tsaousoglou, Georgios Technical University of Denmark Department of Applied Mathematics and Computer Science Lyngby2800 Denmark

Modern power systems face important demand uncertainties due to increasing penetration of behind-the-meter renewable generation. System operators need to account for such uncertainties when solving the unit commitment and economic dispatch problem. The research literature has proposed advanced methods for decision making under uncertainty but, in practice, actual system operators put more trust in the tried-and-true approach of dealing with future uncertainty by committing reserves. In this paper, the unit commitment and economic dispatch problem is formulated for a system with high penetration of storage and the inadequacy of methods based on the traditional notion of reserves is exposed. Namely, in contrast to a generator, a storage unit can provide reserve capacity in a number of timeslots but it cannot provide an analogous reserve activation in all of those timeslots due to the battery's energy being depleted. After discussing two plausible but inadequate approaches, a new, generalized notion of reserves is proposed, which addresses these issues while not abandoning the practical, reserve-based approach for the operator's problem, thus making the best of both worlds. The proposed scheme enables storage units to provide reserves, without putting the system at risk of energy scarcity, which is shown to result in substantial cost savings. © 2023 IEEE.

关键词： Decision making

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Improved Bounds on the Size of Permutation Codes Under Kendall τ-Metric

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IEEE Transactions on Information Theory 2025年第6期71卷 4156-4166页

作者： Parvaresh, Farzad Sobhani, Reza Abdollahi, Alireza Bagherian, Javad Jafari, Fatemeh Khatami, Maryam University of Isfahan Faculty of Engineering Department of Electrical Engineering Isfahan81746-73441 Iran School of Mathematics Tehran19395-5746 Iran University of Isfahan Faculty of Mathematics and Statistics Department of Applied Mathematics and Computer Science Isfahan81746-73441 Iran University of Isfahan Faculty of Mathematics and Statistics Department of Pure Mathematics Isfahan81746-73441 Iran

In order to overcome the challenges caused by flash memories and also to protect against errors related to reading information stored in DNA molecules in the shotgun sequencing method, the rank modulation method has been proposed. In the rank modulation framework, codewords are permutations. In this paper, we study the largest size P(n, d) of permutation codes of length n, i.e., subsets of the set Sn of all permutations on {1, . . . , n} with the minimum distance at least d ∈ {1, . . . ,(Formula presented)} under the Kendall τ-metric. By presenting an algorithm and two theorems, we improve the known lower and upper bounds for P(n,d) . In particular, we show that P(n,d)=4 for all n ≥ 6 and (Formula presented) (Formula presented) © 1963-2012 IEEE.

关键词： Flash memory

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Examining finite-time behaviors in the fractional Gray–Scott model: Stability, synchronization, and simulation analysis

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International Journal of Cognitive Computing in Engineering 2025年 6卷 380-390页

作者： Momani, Shaher Batiha, Iqbal M. Bendib, Issam Ouannas, Adel Hioual, Amel Mohamed, Dalah Department of Mathematics Faculty of Science The University of Jordan Amman11942 Jordan Ajman University Ajman United Arab Emirates Department of Mathematics Al Zaytoonah University of Jordan Amman11733 Jordan Applied Mathematics & Modeling Laboratory Department of Mathematics Faculty of Exact Sciences University of Brothers Mentouri Constantine25000 Algeria Department of Mathematics and Computer Science University of Oum El Bouaghi Oum El Bouaghi04000 Algeria

This paper investigates the behavior and stability of the fractional-order Gray–Scott model, with a specific focus on achieving finite-time stability and synchronization. It introduces essential concepts, including the Gamma function, the Riemann–Liouville fractional-order integral operator, the Caputo fractional derivative, and the Mittag-Leffler function, to establish a foundational framework for subsequent analysis. Equilibrium points are defined, distinguishing between initial and finite-time equilibria, and the conditions for finite-time stability, including settling time, are precisely outlined. Stability results for this model are presented through theorems with detailed proofs, elucidating the roles of Lyapunov functions, class functions, and other system parameters. Furthermore, the paper explores finite-time synchronization schemes in master–slave systems, providing a mathematical framework for understanding and achieving synchronization within a finite time frame. This framework illuminates synchronization dynamics and their practical implications for controlling complex systems. Additionally, numerical examples illustrate finite-time stability and synchronization within the Gray–Scott reaction–diffusion model. © 2025 The Authors

关键词： Lyapunov functions

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On Error-Based Step Size Control for Discontinuous Galerkin Methods for Compressible Fluid Dynamics

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应用数学与计算数学学报 2025年第1期7卷 3-39页

作者： Hendrik Ranocha Andrew R.Winters Hugo Guillermo Castro Lisandro Dalcin Michael Schlottke-Lakemper Gregor J.Gassner Matteo Parsani Applied Mathematics University of HamburgBundesstr.5520146 HamburgGermany Department of Mathematics Applied Mathematics Linköping UniversityLinköpingSweden Extreme Computing Research Center(ECRC) Computer Electrical and Mathematical Science and Engineering Division(CEMSE)King Abdullah University of Science and Technology(KAUST)Thuwal 23955-6900Saudi Arabia Applied and Computational Mathematics RWTH Aachen UniversityAachenGermany High-Performance Computing Center Stuttgart University of StuttgartStuttgartGermany Department of Mathematics and Computer Science University of CologneCologneGermany Center for Data and Simulation Science University of CologneCologneGermany Extreme Computing Research Center(ECRC) Computer Electrical and Mathematical Science and Engineering Division(CEMSE)King Abdullah University of Science and Technology(KAUST)Thuwal 23955-6900Saudi Arabia Physical Science and Engineering Division(PSE) King Abdullah University of Science and Technology(KAUST)Thuwal 23955-6900Saudi Arabia

We study a temporal step size control of explicit Runge-Kutta(RK)methods for com-pressible computational fluid dynamics(CFD),including the Navier-Stokes equations and hyperbolic systems of conservation laws such as the Euler *** demonstrate that error-based approaches are convenient in a wide range of applications and compare them to more classical step size control based on a Courant-Friedrichs-Lewy(CFL)*** numerical examples show that the error-based step size control is easy to use,robust,and efficient,e.g.,for(initial)transient periods,complex geometries,nonlinear shock captur-ing approaches,and schemes that use nonlinear entropy *** demonstrate these properties for problems ranging from well-understood academic test cases to industrially relevant large-scale computations with two disjoint code bases,the open source Julia pack-ages *** with *** and the C/Fortran code SSDC based on PETSc.

关键词： Explicit Runge-Kutta(RK)methods Step size control Compressible fluid dynamics Adaptivity in space and time Shock capturing

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Unsupervised Assessment of Landscape Shifts Based on Persistent Entropy and Topological Preservation 1st

Unsupervised Assessment of Landscape Shifts Based on Persi...

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1st International Workshop on Discovering Drift Phenomena in Evolving Landscapes, DELTA 2024

作者： Basterrech, Sebastián Department of Applied Mathematics and Computer Science Technical University of Denmark Kongens Lyngby Denmark

ISBN: (纸本)9783031823459

Concept drift typically refers to the analysis of changes in data distribution. A drift in the input data can have negative consequences on a learning predictor and the system’s stability. The majority of concept drift methods emphasize the analysis of statistical changes in non-stationary data over time. In this context, we consider a slightly different perspective, where concept drift also integrates significant changes in the topological characteristics of the data *** this article, we introduce a novel framework for monitoring changes in multi-dimensional data streams. We explore variations in the topological structures of the data, presenting another angle on the standard concept *** developed approach is based on persistent entropy and topology-preserving projections in a continual learning scenario. The framework operates in both unsupervised and supervised environments. To show the utility of the proposed framework, we analyze the model across three scenarios using data streams generated with MNIST samples. The obtained results reveal the potential of applying topological data analysis for shift detection and encourage further research in this area. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Concept Drift Dimensionality reduction Distribution shifts Persistent entropy Self-organizing maps

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Matrix nearness problems with off-block-diagonal rank constraints

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Linear Algebra and Its Applications 2025年 721卷 635-673页

作者： Chen, Lujing Pedersen, Frederik H. Andersen, Martin S. Department of Applied Mathematics and Computer Science Technical University of Denmark Richard Petersens Plads Bldg. 324 Kgs. Lyngby2800 Denmark

This paper explores the problem of finding a rank-structured approximation to a given Hermitian positive definite matrix. We first study a fundamental matrix nearness problem which seeks an approximation whose off-diagonal block must have low rank. Our investigation focuses on three objective functions: the spectral norm, Frobenius divergence, and log-determinant divergence. We derive closed-form solutions for the fundamental nearness problem, extending our analysis to include problems with a range restriction on the off-diagonal block. Building upon these results, we propose a practical, scalable algorithm to compute a positive definite hierarchical off-diagonal low-rank approximation to a Hermitian positive definite matrix. Through numerical experiments, we explore the use of our approximation as a general-purpose preconditioner for the conjugate gradient method. Our results demonstrate that the log-determinant divergence-based approximation exhibits good performance across a diverse set of test problems. © 2024 The Author(s)

关键词： Conjugate gradient method

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Single-Timescale Multi-Sequence Stochastic Approximation Without Fixed Point Smoothness: Theories and Applications

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IEEE Transactions on Signal Processing 2025年 73卷 1939-1953页

作者： Huang, Yue Wu, Zhaoxian Ma, Shiqian Ling, Qing Sun Yat-Sen University School of Computer Science and Engineering Guangdong Provincial Key Laboratory of Computational Science Guangzhou510006 China Rice University Department of Computational Applied Mathematics and Operations Research Houston77251 United States Pazhou Lab Guangzhou510275 China

Stochastic approximation (SA) that involves multiple coupled sequences, also known as multiple-sequence SA (MSSA), finds diverse applications in the fields of signal processing and machine learning. However, existing theoretical understandings of MSSA are limited: the multi-timescale analysis implies a slow convergence rate, whereas the single-timescale analysis relies on a stringent fixed point smoothness assumption. In this paper, we establish tighter single-timescale analysis for MSSA, without assuming smoothness of the fixed points. Our theoretical findings reveal that, when all involved operators are strongly monotone, MSSA converges at a rate of O˜(K−1), where K denotes the total number of iterations. When all involved operators are strongly monotone except for the main one, MSSA converges at a rate of O(K− 1/2 ). These rates align with the ones established for single-sequence SA. Applying our novel theoretical findings to bilevel optimization and communication-efficient distributed learning offers relaxed assumptions and/or simpler algorithms with performance guarantees, as validated by numerical experiments. © 1991-2012 IEEE.

关键词： Approximation theory

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Arbitrary style transfer system with split-and-transform scheme

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Multimedia Tools and Applications 2024年第23期83卷 62497-62517页

作者： Tu, Ching-Ting Lin, Hwei Jen Tsai, Yihjia Lin, Zi-Jun Department of Applied Mathematics National Chung Hsing University Taichung Taiwan Department of Computer Science and Information Engineering Tamkang University New Taipei Taiwan

For the subject of arbitrary image style transfer, there have been some proposed architectures that directly compute the transformation matrix of the whitening and coloring transformation (WCT) to obtain more satisfactory transformation results. However, calculating the transformation matrix of WCT is time-consuming. Li et al. trained a linear transformation module to generate a WCT transformation matrix for any pair of images, i.e., content image and style image, to avoid complex calculations and improves time efficiency. In this work, we introduce a flexible arbitrary image style transfer framework based on the LST, which uses deep neural networks to train a linear transformation matrix as the standard matrix for WCT. For the first part, inverse relationship between the Whitening matrix and the Coloring matrix w.r.t. the same image is enforced during the training of the linear transformation matrix, so that the resulting matrix will be more accurate and closer to the standard matrix of WCT. For the second part, a split-and-transform scheme is proposed. Unlike LST, which transforms the block of feature maps as a whole, the split-and-transform scheme divides the feature block into several smaller blocks and transforms them individually, so that the transformation is more localized, and the more the number of divided blocks, the more localized. In addition, the proposed split-and-transform scheme allows users to determine the number of divided blocks to flexibly control the locality of the transformations. Experimental results demonstrate the effectiveness and flexibility of the proposed framework by the high-quality stylized images and adjustable balance between globality and locality of transformations. The use of the split-and-transform scheme can reduce the computational time while preserving or even improving the stylization results. © The Author(s), under exclusive licence to Springer science+Business Media, LLC, part of Springer Nature 2024.

关键词： Linear transformations

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Unveiling the Power of Sparse Neural Networks for Feature Selection 27

Unveiling the Power of Sparse Neural Networks for Feature Se...

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27th European Conference on Artificial Intelligence, ECAI 2024

作者： Atashgahi, Zahra Liu, Tennison Pechenizkiy, Mykola Veldhuis, Raymond Mocanu, Decebal Constantin van der Schaar, Mihaela Faculty of Electrical Engineering Mathematics and Computer Science University of Twente Netherlands Department of Applied Mathematics and Theoretical Physics University of Cambridge United Kingdom Department of Mathematics and Computer Science Eindhoven University of Technology Netherlands Department of Computer Science University of Luxembourg Luxembourg

ISBN: (纸本)9781643685489

Sparse Neural Networks (SNNs) have emerged as powerful tools for efficient feature selection. Leveraging the dynamic sparse training (DST) algorithms within SNNs has demonstrated promising feature selection capabilities while drastically reducing computational overheads. Despite these advancements, several critical aspects remain insufficiently explored for feature selection. Questions persist regarding the choice of the DST algorithm for network training, the choice of metric for ranking features/neurons, and the comparative performance of these methods across diverse datasets when compared to dense networks. This paper addresses these gaps by presenting a comprehensive systematic analysis of feature selection with sparse neural networks. Moreover, we introduce a novel metric considering sparse neural network characteristics, which is designed to quantify feature importance within the context of SNNs. Our findings show that feature selection with SNNs trained with DST algorithms can achieve, on average, more than 50% memory and 55% FLOPs reduction compared to the dense networks, while outperforming them in terms of the quality of the selected features. © 2024 The Authors.

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Problems in Video Conferencing-Mediated Teaching: Experiences of Three User Roles of a University in Bangladesh

Problems in Video Conferencing-Mediated Teaching: Experience...

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2024 International Conference on Advances in Computing, Communication, Electrical, and Smart Systems, iCACCESS 2024

作者： Mansoor, Nafees Rozario, Anatte Kibria, Muhammad Golam Khalid, Md Saifuddin University of Liberal Arts Department of Computer Science and Engineering Bangladesh Department of Applied Mathematics and Computer Science Kongens Lyngby Denmark

ISBN: (纸本)9798350350289

Video-conferencing systems (VCS) became a defacto tool for online and hybrid teaching during COVID-19 and the gradual return to physical classrooms. As part of the EdViCon Erasmus+ project, towards defining the scenarios for improving teaching with additional portable tools by university teachers, this study reports users' problems in the context of the University of Liberal Arts Bangladesh (ULAB). Classroom observations, problem-tree analysis, interviews, and focus-group discussions with academics, e-learning and IT consultants, and students provide different perspectives on the central problems, underlying causes, and the effects of VCS use during live teaching sessions. While teachers emphasized the lack of resources and technical barriers, students' problem statement focused on the reduced quality of interactions due to the differences between VCS-mediated and physical classrooms, and the IT & e-learning professionals emphasized technological issues (audio, tone, lack of facial expression etc.), lack of collaboration, and differences in expectations among participants. The central contribution of this paper is three diagrams showing problem tree analysis from the perspectives of the three roles. Each of the causes, effects, and problem statements will be considered as point-of-view statements for generating ideas for supporting hardware and software tools and training on technology and pedagogy, © 2024 IEEE.

关键词： Students

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