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arXiv 2023年

作者： Reiter, Sean Gosea, Ion Victor Gugercin, Serkan Department of Mathematics Division of Computational Modeling and Data Analytics Academy of Data Science Virginia Tech BlacksburgVA24061 United States Max Planck Institute for Dynamics of Complex Technical Systems Sandtorstr. 1 Magdeburg39106 Germany

The Quadrature-based Balanced Truncation (QuadBT) framework of [14] is a "non-intrusive" reformulation of balanced truncation;a classical projection-based model-order reduction technique for linear systems. QuadBT is non-intrusive in the sense that it builds approximate balanced reduced-order models entirely from system response data (e.g., transfer function measurements) without the need to reference an explicit state-space realization of the underlying full-order model. In this work, we generalize and extend QuadBT to other types of balanced truncation model reduction. Namely, we develop non-intrusive implementations for balanced stochastic truncation, positive-real balanced truncation, and bounded-real balanced truncation. We show that the data-driven construction of these balanced reduced-order models requires sampling certain spectral factors associated with the system of interest. Numerical examples are included in each case to validate our *** Codes 93B15 (Primary) 93A15, 37M99, 65D30, 65K99, 15A24 (Secondary) Copyright © 2023, The Authors. All rights reserved.

关键词： Linear systems

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A CFL condition for the finite cell method

arXiv

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arXiv 2025年

作者： Bürchner, Tim Radtke, Lars Kopp, Philipp Computational Modeling and Simulation Technische Universität München Germany Institute for Ship Structural Design and Analysis Technische Universität Hamburg Germany Chair of Data Science in Civil Engineering Bauhaus-Universität Weimar Germany

Immersed boundary finite element methods allow the user to bypass the potentially troublesome task of boundary-conforming mesh generation. However, they suffer from the influence of cut elements, i.e., elements that are intersected by the physical domain boundaries. When combined with explicit time integration, poorly cut elements with little support in the physical domain have a detrimental effect on the critical time step size, thereby hampering the application of immersed boundary methods to wave propagation simulations. In this paper, we investigate the stabilizing effect of the finite cell method concerning explicit time integration. Starting with an analytical solution of an example with one degree of freedom, we systematically study the influence of α-stabilization on the maximum eigenvalue and thus on the critical time step size. The analysis is then complemented by a numerical study of an example with one element and an increasing polynomial degree. We demonstrate that the critical time step size does not decrease below a certain limit, even when further reducing the cut fraction of the element. This minimum critical time step size is controlled by the chosen α value and becomes less severe for higher dimensions. Increasing the polynomial degree has little effect on the degradation of the minimum critical time step size. Finally, we provide an estimate of the minimum critical time step size depending on the chosen stabilization parameter α and the dimension of the problem. Based on this estimate, we propose a modified CFL condition for the finite cell method, the validity of which we demonstrate on a numerical example of a perforated plate. © 2025, CC BY.

关键词： Boundary element method

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Robust WCET Estimation via Ensemble Learning with Fractional-Order Legendre Function Kernels

Robust WCET Estimation via Ensemble Learning with Fractional...

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Applied Research in Electrical Engineering (AREE), National and International Conference on

作者： Amir Hussein Ataei Monfared Mahdi Movahedian Moghaddam Sheedeh Sharif-Bakhtiar Kourosh Parand Keivan Borna Department of Computer Science Faculty of Mathematics and Computer Science Kharazmi University Tehran Iran Department of Computer and Data Sciences Faculty of Mathematical Sciences Shahid Beheshti University Tehran Iran Department of Cognitive Modeling Institute for Cognitive and Brain Sciences Shahid Beheshti University Tehran Iran

ISBN: (数字)9798350377170

ISBN: (纸本)9798350377187

Estimating Worst-Case Execution Time (WCET) as a regression problem has become increasingly challenging due to the complexity of modern hardware and software systems. Traditional statistical methods often fall short of providing accurate and reliable estimates. To address these limitations, ensemble learning methods have emerged as a promising approach for capturing edge cases in execution scenarios. This paper proposes a novel ensemble model that integrates fractional-order Legendre functions (FLF) to enrich feature representation. This integration reduces correlations between individual models within the ensemble, enhancing generalization capabilities. Our method achieves significant reductions in Mean Squared Error (MSE) for WCET estimates while maintaining high levels of safeness. Specifically, the proposed model maintained an error below one across most benchmarks, with safeness levels of $\% 100$ in 13 out of 16 benchmarks. These findings underscore the efficacy of our approach and its potential to provide robust and accurate WCET estimates for complex systems.

关键词： Support vector machines Accuracy Upper bound Estimation Benchmark testing Real-time systems Complexity theory Ensemble learning Time factors Kernel

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Omics data Analysis Tools for Biomarker Discovery and the Tutorial

Omics Data Analysis Tools for Biomarker Discovery and the Tu...

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International Symposium on Fusion of Mathematics and Biology, 2020

作者： Nojima, Yosui Takeda, Yoshito Center for Mathematical Modeling and Data Science Osaka University Toyonaka Japan Department of Respiratory Medicine and Clinical Immunology Osaka University Graduate School of Medicine Suita Japan

ISBN: (纸本)9789811648656

Given the current progress in next-generation sequencing and mass spectrometry, considerable attention has been given to omics approaches and biomarker discovery to understand heterogeneous diseases. However, it is difficult to analyze them in the biological experimental community because the analysis processes are complicated. To address this problem, we have introduced and explained in this chapter the tools used for omics data analysis and how they are used. © 2021, Springer Nature Singapore Pte Ltd.

关键词： Biomarkers

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Trade Execution Games in a Markovian Environment

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Applied Mathematical Finance 2025年第4期31卷

作者： Ohnishi, Masamitsu Shimoshimizu, Makoto Faculty of Informatics Yamato University Osaka Suita City Japan Center for Mathematical Modeling and Data Science Osaka University Osaka Toyonaka City Japan Department of Industrial and Systems Engineering Tokyo University of Science Noda City Chiba Japan

This paper examines trade execution games for two large traders in a generalized price impact model. We incorporate a stochastic and sequentially dependent factor, called Markovian environment, that exogenously affects the market price into financial market modeling. Our model accounts for how strategic and environmental uncertainties affect the large traders' execution strategies. We formulate an expected utility maximization problem for two large traders as a Markov game model. Applying the backward induction method of dynamic programming, we provide an explicit closed-form execution strategy at a Markov perfect equilibrium. Our theoretical results reveal that the execution strategy generally lies in a dynamic and non-randomized class;it becomes deterministic if the Markovian environment is also deterministic. In addition, our simulation-based numerical experiments suggest that the execution strategy captures various features observed in financial markets. © 2025 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.

关键词： dynamic programming Markov perfect equilibrium Markovian environment Price impact trade execution game

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Decadal variations in near-surface wind speed across the Northern Hemisphere on a centennial timescale and their possible causes

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Advances in Climate Change Research 2024年第6期15卷 1003-1012页

作者： Lin-Wei LI Jin-Lin ZHA Ting CHUNA Jian WU De-Ming ZHAO Wen-Xuan FAN Yan-Jun LYU Hui-Ping JIANG Key Laboratory of Atmospheric Environment and Processes in the Boundary Layer Over the Low-Latitude Plateau Region Department of Atmospheric ScienceYunnan UniversityKunming 650091China Key Laboratory of Regional Climate and Environment for Temperate East Asia Institute of Atmospheric PhysicsChinese Academy of SciencesBeijing 100029China Center for Energy&Environmental Policy Research Beijing Institute of TechnologyBeijing 100081China Key Laboratory of Regional Sustainable Development Modeling Institute of Geographic Sciences and Natural Resources ResearchChinese Academy of SciencesBeijing 100101China International Research Center of Big Data for Sustainable Development Goals Beijing 100094China

The reduction in near-surface wind speed(NSWS),followed by its recent recovery,could be a feature of decadal ***,existing studies mainly analyse the characteristics and causes of NSWS changes on regional scales and over short *** decadal variations and underlying causes of global NSWS changes over long timescales remain *** this study,we investigated the characteristics of NSWS changes in the Northern Hemisphere(NH)on a centennial scale(1900–2010)and identify the potential causes of decadal variations by using an information flow *** results indicate that NSWS in the NH experienced a remarkable decadal variation,increasing during 1900–1945 and 1970–1980 and decreasing during 1945–1970 and 1980–***,regional differences in the distribution features and decadal variations of NSWS were *** and North America showed the highest data overlap compared to other regions,reaching 59.4%.The longest period of decadal variation in NSWS was found in North America(14 years),followed by Europe(11 years),with Asia showing the smallest period(10 years).When determining the effects of large-scale ocean–atmosphere circulation fields or internal climate models on NSWS changes,prioritising causality between the two variables and the study period is essential,rather than relying solely on simple correlation *** to the information flow technique,the decadal variations in NSWS over North America during 1950–2010 were linked with the Western Hemisphere Warm Pool,whereas the North Atlantic Oscillation influenced those in *** Tropical Northern Atlantic was the driver over *** study offers a scientific foundation for understanding NSWS characteristics on a centennial timescale and the primary causes of decadal variations in NSWS across the NH.

关键词： Near-surface wind speed Centennial timescale Information flow Regional difference Northern Hemisphere

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Applying Satellite Sea Surface Temperature as Dirichlet-Type Surface Thermal Boundary Condition in an Ocean Model

SSRN

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SSRN 2024年

作者： Zhang, Tiecheng Wu, Xinrong Yin, Xunqiang Gao, Zhigang Liu, Kexiu Yang, Zhitong Chao, Guofang Key Laboratory of Marine Environmental Information Technology National Marine Data and Information Service Ministry ofNaturalResources Tianjin China Key Laboratory of Marine Science and Numerical Modeling First Institute of Oceanography Ministry ofNaturalResources Qingdao China

Following the Dirichlet-type boundary condition that specifies value at boundary of a system in mathematics and physics, this study suggests applying satellite sea surface temperature (SST) as Dirichlet-type surface thermal boundary condition (STBC) in ocean models. Numerical experiments with Dirichlet-type and combined-type STBC with different configures of satellite SST, for the period of January to April 2019 in the Northwest Pacific Ocean, were carried out based on the Princeton Ocean Model. The experiments were assessed using satellite and in situ observations of temperature, GOFS3.1 analysis and GLORYS12v1 reanalysis. Results show that applying satellite SST as Dirichlet-type STBC could constrain the modeled SST and near-surface temperature in upper 50m depth well, which is better than the scheme that uses satellite SST as the relaxation terms of combined-type STBC. The temperature section along the 137°E resulted from the Dirichlet-type STBC is comparable with GOFS3.1 analysis and better than GLORYS12v1 reanalysis in upper 50m depth. These results suggest that applying high-accuracy satellite SST as Dirichlet-type STBC in ocean models has a promising prospective in numerical simulation. © 2024, The Authors. All rights reserved.

关键词： Surface temperature

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Chemtrain: Learning Deep Potential Models Via Automatic Differentiation and Statistical Physics

SSRN

引用

SSRN 2024年

作者： Fuchs, Paul Thaler, Stephan Röcken, Sebastien Zavadlav, Julija Department of Engineering Physics and Computation TUM School of Engineering and Design Technical University of Munich Germany Valence Labs MontrealQC Canada Atomistic Modeling Center Munich Data Science Institute Technical University of Munich Germany

Neural Networks (NNs) are promising models for refining the accuracy of molecular dynamics, potentially opening up new fields of application. Typically trained bottom-up, atomistic NN potential models can reach first-principle accuracy, while coarse-grained implicit solvent NN potentials surpass classical continuum solvent models. However, overcoming the limitations of costly generation of accurate reference data and data inefficiency of common bottom-up training demands efficient incorporation of data from many sources. This paper introduces the framework chemtrain to learn sophisticated NN potential models through customizable training routines and advanced training algorithms. These routines can combine multiple top-down and bottom-up algorithms, e.g., to incorporate both experimental and simulation data or pre-train potentials with less costly algorithms. chemtrain provides an object-oriented high-level interface to simplify the creation of custom routines. On the lower level, chemtrain relies on JAX to compute gradients and scale the computations to use available resources. We demonstrate the simplicity and importance of combining multiple algorithms in the examples of parametrizing an all-atomistic model of titanium and a coarse-grained implicit solvent model of alanine dipeptide. © 2024, The Authors. All rights reserved.

关键词： Coarse-grained modeling

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Characterizing Zagreb Index Bounds in Trees with Specified Metric Dimension

arXiv

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arXiv 2024年

作者： Ali, Waqar Husin, Mohamad Nazri Bin Nadeem, Muhammad Faisal Special Interest Group on Modeling and Data Analytics Faculty of Computer Science and Mathematics Universiti Malaysia Terengganu Terengganu Kuala Nerus21030 Malaysia Department of Mathematics COMSATS University Islamabad Lahore Campus Lahore54000 Pakistan

Consider a simple graph G = (V, E), where V are the vertices and E are the edges. The first Zagreb index, M1(G) = Pv∈V ψG(v)2. The second Zagreb index, M2(G) = Puv∈E ψG(u)ψG(v). The metric dimension of a graph refers to the smallest subset of vertices in a resolving set such that the distances from these vertices to all others in the graph uniquely identify each vertex. In this paper, we characterize bounds for the Zagreb indices of trees, based on the order of the tree and its metric dimension. Furthermore, we identify the trees that achieve these extremal bounds, offering valuable insights into how the metric dimension influences the behavior of the Zagreb indices in tree structures. © 2024, CC BY.

关键词： Trees (mathematics)

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Extremal Values of the Atom-Bond Connectivity Index for Trees with Given Roman Domination Numbers

arXiv

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arXiv 2024年

Consider that G = (X, Y) is a simple, connected graph with X as the vertex set and Y as the edge set. The atom-bond connectivity (ABC) index is a novel topological index that Estrada introduced in Estrada et al. (1998). It is defined as ABC(G) = xy∈XY (G)s ζx +ζxζζyy− 2 where ζx and ζx represent the degrees of the vertices x and y, respectively. In this work, we explore the behavior of the ABC index for tree graphs. We establish both lower and upper bounds for the ABC index, expressed in terms of the graph’s order and its Roman domination number. Additionally, we characterize the tree structures that correspond to these extremal values, offering a deeper understanding of how the Roman domination number (RDN) influences the ABC index in tree graphs. © 2024, CC BY.

关键词： Trees (mathematics)

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