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Asymmetry and Condition Number of an Elliptic-Parabolic System for Biological Network Formation

应用数学与计算数学学报 2025年第1期7卷 78-94页

作者： Clarissa Astuto Daniele Boffi Jan Haskovec Peter Markowich Giovanni Russo Applied Mathematics and Computational Sciences Department King Abdullah University of Science and Technology4700 ThuwalSaudi Arabia Applied Mathematics and Computational Sciences Department King Abdullah University of Science and Technology4700 ThuwalSaudi Arabia Department of Mathematics"F.Casorati" University of Pavia27100 PaviaItaly Applied Mathematics and Computational Sciences Department King Abdullah University of Science and Technology4700 ThuwalSaudi Arabia Department of Mathematics University of Vienna1090 ViennaAustria Department of Mathematics and Computer Science University of Catania95125 CataniaItaly

We present results of numerical simulations of the tensor-valued elliptic-parabolic PDE model for biological network *** numerical method is based on a nonlinear finite difference scheme on a uniform Cartesian grid in a two-dimensional(2D)*** focus is on the impact of different discretization methods and choices of regularization parameters on the symmetry of the numerical *** particular,we show that using the symmetric alternating direction implicit(ADI)method for time discretization helps preserve the symmetry of the solution,compared to the(non-symmetric)ADI ***,we study the effect of the regularization by the isotropic background perme-ability r＞0,showing that the increased condition number of the elliptic problem due to decreasing value of r leads to loss of *** show that in this case,neither the use of the symmetric ADI method preserves the symmetry of the ***,we perform the numerical error analysis of our method making use of the Wasserstein distance.

关键词： Bionetwork formation Cai-Hu model Leaf venation Asymmetry Conditioning number Finite-difference scheme Semi-implicit Symmetric alternating direction implicit(ADI) Wasserstein distance

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Deep bed filtration model for cake filtration and erosion

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applied mathematics and Mechanics(English Edition) 2024年第2期45卷 355-372页

作者： L.I.KUZMINA Y.V.OSIPOV A.R.PESTEREV Department of Applied Mathematics HSE UniversityMoscow 101000Russia Department of Computer Science and Applied Mathematics Moscow State University of Civil EngineeringMoscow 129337Russia

Many phenomena in nature and technology are associated with the filtration of suspensions and colloids in porous media. Two main types of particle deposition,namely, cake filtration at the inlet and deep bed filtration throughout the entire porous medium, are studied by different models. A unified approach for the transport and deposition of particles based on the deep bed filtration model is proposed. A variable suspension flow rate, proportional to the number of free pores at the inlet of the porous medium, is considered. To model cake filtration, this flow rate is introduced into the mass balance equation of deep bed filtration. For the cake filtration without deposit erosion,the suspension flow rate decreases to zero, and the suspension does not penetrate deep into the porous medium. In the case of the cake filtration with erosion, the suspension flow rate is nonzero, and the deposit is distributed throughout the entire porous medium. An exact solution is obtained for a constant filtration function. The method of characteristics is used to construct the asymptotics of the concentration front of suspended and retained particles for a filtration function in a general form. Explicit formulae are obtained for a linear filtration function. The properties of these solutions are studied in detail.

关键词： deep bed filtration cake filtration porous medium particle deposition and erosion analytical solution concentration front

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Context-aware reinforcement learning for cooling operation of data centers with an Aquifer Thermal Energy Storage

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Energy and AI 2024年第3期17卷 233-246页

作者： Lukas Leindals Peter Grønning Dominik Franjo Dominković Rune Grønborg Junker Department of Applied Mathematics and Computer Science Technical University of DenmarkDenmark

Data centers are often equipped with multiple cooling units. Here, an aquifer thermal energy storage (ATES) system has shown to be efficient. However, the usage of hot and cold-water wells in the ATES must be balanced for legal and environmental reasons. Reinforcement Learning has been proven to be a useful tool for optimizing the cooling operation at data centers. Nonetheless, since cooling demand changes continuously, balancing the ATES usage on a yearly basis imposes an additional challenge in the form of a delayed reward. To overcome this, we formulate a return decomposition, Cool-RUDDER, which relies on simple domain knowledge and needs no training. We trained a proximal policy optimization agent to keep server temperatures steady while minimizing operational costs. Comparing the Cool-RUDDER reward signal to other ATES-associated rewards, all models kept the server temperatures steady at around 30 °C. An optimal ATES balance was defined to be 0% and a yearly imbalance of −4.9% with a confidence interval of [−6.2, −3.8]% was achieved for the Cool 2.0 reward. This outperformed a baseline ATES-associated reward of 0 at −16.3% with a confidence interval of [−17.1, −15.4]% and all other ATES-associated rewards. However, the improved ATES balance comes with a higher energy consumption cost of 12.5% when comparing the relative cost of the Cool 2.0 reward to the zero reward, resulting in a trade-off. Moreover, the method comes with limited requirements and is applicable to any long-term problem satisfying a linear state-transition system.

关键词： Data centers ATES Smart energy systems Reinforcement learning Delayed rewards

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Modified DS np Chart Using Generalized Multiple Dependent State Sampling under Time Truncated Life Test

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computer Modeling in Engineering & sciences 2024年第3期138卷 2471-2495页

作者： Wimonmas Bamrungsetthapong Pramote Charongrattanasakul Division of Applied Statistics Department of Mathematics and Computer ScienceFaculty of Science and TechnologyRajamangala University of Technology ThanyaburiPathum Thani12110Thailand Division of Mathematics Department of Mathematics and Computer ScienceFaculty of Science and TechnologyRajamangala University of Technology KrungthepBangkok10120Thailand

This study presents the design of a modified attributed control chart based on a double sampling(DS)np chart applied in combination with generalized multiple dependent state(GMDS)sampling to monitor the mean life of the product based on the time truncated life test employing theWeibull *** control chart developed supports the examination of the mean lifespan variation for a particular product in the process of *** control limit levels are used:the warning control limit,inner control limit,and outer control ***,they enhance the capability for variation detection.A genetic algorithm can be used for optimization during the in-control process,whereby the optimal parameters can be established for the proposed control *** control chart performance is assessed using the average run length,while the influence of the model parameters upon the control chart solution is assessed via sensitivity analysis based on an orthogonal experimental design withmultiple linear regression.A comparative study was conducted based on the out-of-control average run length,in which the developed control chart offered greater sensitivity in the detection of process shifts while making use of smaller samples on average than is the case for existing control ***,to exhibit the utility of the developed control chart,this paper presents its application using simulated data with parameters drawn from the real set of data.

关键词： Modified DS np chart generalizedmultiple dependent state sampling time truncated life test Weibull distribution average run length average sample size

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ILAPU-Q: An Improved Lightweight Authentication Protocol for IoT Based on U-quark Hash Function

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Recent Advances in computer science and Communications 2024年第2期17卷 78-87页

作者： Jebrane, Jihane Lazaar, Saiida Mathematics and Computer Science Department Mathematics Computer Science and Applications ERMIA-Team National School of Applied Science-ENSA of Tangier AbdelMalek Essaadi University Tetouan Morocco

Background: In the last decades, the development of Internet activities has been significantly accelerated, particularly with the emergence of the Internet of Things (IoT). Heterogeneous devices in the IoT can seamlessly and feasibly inter-connect with each other with-out human interaction. Due to this revolution, many applications have been adopted in the are-na of smart healthcare, e-commerce, environmental and habitat monitoring, etc. In order to promote and facilitate people's standards of living around the world. However, these unbound-ed applications bring more challenges to the storage capabilities of devices, and their security and privacy preservation. Moreover, security issues suffer from weak authentication protocols. Methods: To address these issues, suitable and secure lightweight mutual authentication schemes based on Elliptic Curve Cryptography (ECC) are required for the approval of Identity Management (IDM) of devices in the IoT. In this paper, we will propose an improved mutual authentication scheme based on ECC, coupled with a relevant seminal work considered as a reference in the field. This scheme is combined with U-quark, a lightweight hash function, to guarantee the security needed in the IoT environment. Results: We will compare our amended protocol with a seminal scheme as an established reference in terms of computation cost, storage cost, and executing CPU time to demonstrate that our version can ensure the most favorable performance during the authentication process. Conclusion: Finally, our proposed mutual authentication scheme has demonstrated its effectiveness in enhancing the security of IoT devices when compared to the seminal work in the same computational environment. © 2024, Bentham science Publishers. All rights reserved.

关键词： Hash functions

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Quantum spin systems: Toroidal classification and geometric duality

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Physical Review B 2024年第14期110卷 L140403页

作者： Vahid Azimi-Mousolou Anders Bergman Anna Delin Olle Eriksson Manuel Pereiro Danny Thonig Erik Sjöqvist Department of Applied Mathematics and Computer Science Faculty of Mathematics and Statistics Department of Physics and Astronomy Department of Applied Physics School of Engineering Sciences (SeRC) Wallenberg Initiative Materials Science for Sustainability (WISE) Wallenberg Initiative Materials Science WISE School of Science and Technology

We demonstrate a toroidal classification for quantum spin systems, revealing an intrinsic geometric duality within this structure. Through our classification and duality, we reveal that various bipartite quantum features in magnon systems can manifest equivalently in both bipartite ferromagnetic and antiferromagnetic materials, based upon the availability of relevant Hamiltonian parameters. Additionally, the results highlight the antiferromagnetic regime as an ultrafast dual counterpart to the ferromagnetic regime, both exhibiting identical capabilities for quantum spintronics and technological applications. Concrete illustrations are provided, demonstrating how splitting and squeezing types of two-mode magnon quantum correlations can be realized across ferro- and antiferromagnetic regimes.

关键词： Magnons Quantum correlations in quantum information Quantum information processing Quantum information theory Spintronics

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An infrastructure software perspective toward computation offloading between executable specifications and foundation models

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science China(Information sciences) 2025年第4期68卷 380-382页

作者： Dezhi RAN Mengzhou WU Yuan CAO Assaf MARRON David HAREL Tao XIE Key Laboratory of High Confidence Software Technologies (PKU) Ministry of Education School of Computer SciencePeking University School of Electronics Engineering and Computer Science Peking University Department of Computer Science and Applied Mathematics Weizmann Institute of Science

Foundation models(FMs) [1] have revolutionized software development and become the core components of large software systems. This paradigm shift, however, demands fundamental re-imagining of software engineering theories and methodologies [2]. Instead of replacing existing software modules implemented by symbolic logic, incorporating FMs' capabilities to build software systems requires entirely new modules that leverage the unique capabilities of ***, while FMs excel at handling uncertainty, recognizing patterns, and processing unstructured data, we need new engineering theories that support the paradigm shift from explicitly programming and maintaining user-defined symbolic logic to creating rich, expressive requirements that FMs can accurately perceive and implement.

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Correlation-aware probabilistic data summarization for large-scale multi-block scientific data visualization

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computational Visual Media 2023年第3期9卷 513-529页

作者： Yang Yang Kecheng Lu Yu Wu Yunhai Wang Yi Cao Institute of Applied Physics and Computational Mathematics Beijing 100094China School of Computer Science and Technology Shandong UniversityQingdao 266237China

In this paper,we propose a correlationaware probabilistic data summarization technique to efficiently analyze and visualize large-scale multi-block volume data generated by massively parallel scientific *** core of our technique is correlation modeling of distribution representations of adjacent data blocks using copula functions and accurate data value estimation by combining numerical information,spatial location,and correlation distribution using Bayes’*** effectively preserves statistical properties without merging data blocks in different parallel computing nodes and repartitioning them,thus significantly reducing the computational ***,this enables reconstruction of the original data more accurately than existing *** demonstrate the effectiveness of our technique using six datasets,with the largest having one billion grid *** experimental results show that our approach reduces the data storage cost by approximately one order of magnitude compared to state-of-the-art methods while providing a higher reconstruction accuracy at a lower computational cost.

关键词： correlation-awareness large-scale data multi-block methods probabilistic data summarization

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Radial solution of the Logarithmic Laplacian system

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applied mathematics(A Journal of Chinese Universities) 2024年第1期39卷 114-124页

作者： ZHANG Li-hong NIE Xiao-feng WANG Guo-tao Bashir Ahmad School of Mathematics and Computer Science Shanxi Normal UniversityLinfen 041004China Nonlinear Analysis and Applied Mathematics(NAAM)Research Group Department of MathematicsFaculty of ScienceKing Abdulaziz UniversityJeddah 21589Saudi Arabia.

The paper generalizes the direct method of moving planes to the Logarithmic Laplacian ***,some key ingredients of the method are discussed,for example,Narrow region principle and Decay at ***,the radial symmetry of th... 详细信息

关键词： the Logarithmic Laplacian system radial symmetry the direct method of moving planes

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Domination based graph neural networks

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International Journal of computers and Applications 2024年第11期46卷 998-1005页

作者： Meybodi, Mohsen Alambardar Safari, Mahdi Davoodijam, Ensieh Department of Applied Mathematics and Computer Science Faculty of Mathematics and Statistics University of Isfahan Isfahan Iran Department of Software Engineering University of Kashan Kashan Iran

Graph Neural Networks (GNNs) have emerged as a widely used and effective method across various domains for learning from graph data. Despite the abundance of GNN variants, many struggle with effectively propagating messages over long distances. This paper introduces a novel hierarchical message passing framework for graph learning, specifically designed to address the challenge of long-distance message propagation in graphs. By constructing smaller graphs from the main graph using the concept of domination, a fundamental principle in graph theory, we facilitate more efficient message passing within each subgraph. Subsequently, we employ a Graph Attention Network (GAT) to aggregate these features and propagate them to distant nodes across the graph. Experimental results on standard node classification datasets validate that the proposed architecture achieves performance comparable to or better than conventional GNNs. Additionally, our model consistently performs better on graphs with missing edges. © 2024 Informa UK Limited, trading as Taylor & Francis Group.

关键词： Neural network models

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