检索结果-内蒙古大学图书馆

A HIGH-ORDER VELOCITY-BASED DISCONTINUOUS GALERKIN SCHEME FOR THE SHALLOW WATER EQUATIONS: LOCAL CONSERVATION, ENTROPY STABILITY, WELL-BALANCED PROPERTY, AND POSITIVITY PRESERVATION

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Fu, Guosheng Department of Applied and Computational Mathematics and Statistics University of Notre Dame United States

The nonlinear shallow water equations (SWEs) are widely used to model the unsteady water flows in rivers and coastal areas. In this work, we present a novel class of locally conservative, entropy stable and well-balanced discontinuous Galerkin (DG) methods for the nonlinear shallow water equation with a non-flat bottom topography. The major novelty of our work is the use of velocity field as an independent solution unknown in the DG scheme, which is closely related to the entropy variable approach to entropy stable schemes for system of conservation laws proposed by Tadmor [22] back in 1986, where recall that velocity is part of the entropy variable for the shallow water equations. Due to the use of velocity as an independent solution unknown, no specific numerical quadrature rules are needed to achieve entropy stability of our scheme on general unstructured meshes in two dimensions. The proposed DG semi-discretization is then carefully combined with the classical explicit strong stability preserving Runge-Kutta (SSP-RK) time integrators [13] to yield a locally conservative, well-balanced, and positivity preserving fully discrete scheme. Here the positivity preservation property is enforced with the help of a simple scaling limiter. In the fully discrete scheme, we re-introduce discharge as an auxiliary unknown variable. In doing so, standard slope limiting procedures can be applied on the conservative variables (water height and discharge) without violating the local conservation property. Here we apply a characteristic-wise TVB limiter [5] on the conservative variables using the Fu-Shu troubled cell indicator [10] in each inner stage of the Runge-Kutta time stepping to suppress numerical oscillations. This fully discrete can be readily applied to various SWEs simulations without dry areas where the water height is close to zero. The case with dry areas need further special attention, where the velocity approximation can be unphysically large near cells with a smal

关键词： Equations of motion

Multitask Classification of Antimicrobial Peptides for Simultaneous Assessment of Antimicrobial Property and Structural Fold

学校读者我要写书评

暂无评论

Multitask Classification of Antimicrobial Peptides for Simul...

International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： Michaela Areti Zervou Effrosyni Doutsi Yannis Pantazis Panagiotis Tsakalides Department of Computer Science University of Crete Heraklion Greece Institute of Computer Science-FORTH Heraklion Greece Institute of Applied and Computational Mathematics-FORTH Heraklion Greece

Antimicrobial peptides (AMPs) play a significant role in guiding drug design, advancing targeted therapies, and cancer treatment research. The function of peptides is highly associated with their three-dimensional structure. AMPs particularly favor alpha-helical structures, or alpha-folds, due to their ability to disrupt the protective layers that surround cells effectively and their structural stability. Existing classifiers mainly identify AMPs but overlook their structural fold which can provide valuable insights into their function. To address this limitation, we introduce an innovative multitask classifier that recognizes AMPs and predicts their alphahelical folds simultaneously. Our approach employs k-mers and Transformer networks for efficient, accurate multitask classification. Results on the datasets indicate comparable performance compared to single-task methods in half the time and complexity.

关键词：

Periodic propagation of singularities for heat equations with time delay

学校读者我要写书评

暂无评论

arXiv 2025年

作者： Wang, Gengsheng Yu, Huaiqiang Zhang, Yubiao Center for Applied Mathematics KL-AAGDM Tianjin University Tianjin300072 China School of Mathematics KL-AAGDM Tianjin University Tianjin300350 China Radon Institute for Computational and Applied Mathematics Austrian Academy of Sciences Altenbergerstraße 69 Upper Austria Linz4040 Austria Chair for Dynamics Control Machine Learning and Numerics Department of Mathematics Friedrich-Alexander-Universität Erlangen-Nürnberg Erlangen91058 Germany

This paper presents two remarkable phenomena associated with the heat equation with a time delay: namely, the propagation of singularities and periodicity. These are manifested through a distinctive mode of propagation of singularities in the solutions. Precisely, the singularities of the solutions propagate periodically in a bidirectional fashion along the time axis. Furthermore, this propagation occurs in a stepwise manner. More specifically, when propagating in the positive time direction, the order of the joint derivatives of the solution increases by 2 for each period;conversely, when propagating in the reverse time direction, the order of the joint derivatives decreases by 2 per period. Additionally, we elucidate the way in which the initial data and historical values impact such a propagation of singularities. The phenomena we have discerned not only corroborate the pronounced differences between heat equations with and without time delay but also vividly illustrate the substantial divergence between the heat equation with a time delay and the wave equation, especially when viewed from the point of view of singularity *** Codes 35K05 45K05 58J47 © 2025, CC BY.

关键词： Wave equations

Stochastic dynamics of two-compartment cell proliferation models with regulatory mechanisms for hematopoiesis

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Wang, Ren-Yi Kimmel, Marek Pang, Guodong Department of Statistics Rice University HoustonTX77005 United States Department of Computational Applied Mathematics and Operations Research Rice University HoustonTX77005 United States

We present an asymptotic analysis of a stochastic two-compartmental cell division system with regulatory mechanisms inspired by Getto et al. (2013). The hematopoietic system is modeled as a two-compartment system, where the first compartment consists of dividing cells in the bone marrow, referred to as type 0 cells, and the second compartment consists of post-mitotic cells in the blood, referred to as type 1 cells. Division and self-renewal of type 0 cells are regulated by the population density of type 1 cells. By scaling up the initial population, we demonstrate that the scaled dynamics converges in distribution to the solution of a system of ordinary differential equations (ODEs). This system of ODEs exhibits a unique non-trivial equilibrium that is globally stable. Furthermore, we establish that the scaled fluctuations of the density dynamics converge in law to a linear diffusion process with time-dependent coefficients. When the initial data is Gaussian, the limit process is a Gauss-Markov process. We analyze its asymptotic properties to elucidate the joint structure of both compartments over large times. This is achieved by proving exponential convergence in the 2-Wasserstein metric for the associated Gaussian measures on an L2 Hilbert space. Finally, we apply our results to compare the effects of regulating division and self-renewal of type 0 cells, providing insights into their respective roles in maintaining hematopoietic system stability. Copyright © 2024, The Authors. All rights reserved.

关键词： Stochastic systems

Voltage mapping in subcellular nanodomains using electro-diffusion modeling

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Paquin-Lefebvre, Frédéric Holcman, David Group of Data Modeling Computational Biology and Applied Mathematics École Normale Supérieure Université PSL Paris75005 France Department of Applied Mathematics and Theoretical Physics Churchill College University of Cambridge CambridgeCB3 0WA United Kingdom

Voltage distribution in sub-cellular micro-domains such as neuronal synapses, small protrusions or dendritic spines regulates the opening and closing of ionic channels, energy production and thus cellular homeostasis and excitability. Yet how voltage changes at such a small scale in vivo remains challenging due to the experimental diffraction limit, large signal fluctuations and the still limited resolution of fast voltage indicators. Here, we study the voltage distribution in nano-compartments using a computational approach based on the Poisson–Nernst–Planck equations for the electro-diffusion motion of ions, where inward and outward fluxes are generated between channels. We report a current–voltage (I–V) logarithmic relationship generalizing Nernst law that reveals how the local membrane curvature modulates the voltage. We further find that an influx current penetrating a cellular electrolyte can lead to perturbations from tens to hundreds of nanometers deep depending on the local channels organization. Finally, we show that the neck resistance of dendritic spines can be completely shunted by the transporters located on the head boundary, facilitating ionic flow. To conclude, we propose that voltage is regulated at a subcellular level by channels organization, membrane curvature and narrow *** Codes 35J05, 35J08, 35J25 Copyright © 2024, The Authors. All rights reserved.

关键词： Electrolytes

SPECIAL ORTHOGONAL, SPECIAL UNITARY, AND SYMPLECTIC GROUPS AS PRODUCTS OF GRASSMANNIANS

学校读者我要写书评

暂无评论

arXiv 2025年

作者： Lim, Lek-Heng Lu, Xiang Ye, Ke Computational and Applied Mathematics Initiative University of Chicago ChicagoIL60637 United States Department of Statistics University of Chicago ChicagoIL60637 United States KLMM Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

We describe a curious structure of the special orthogonal, special unitary, and symplectic groups that has not been observed, namely, they can be expressed as matrix products of their corresponding Grassmannians realized as involution matrices. We will show that SO(n) is a product of two real Grassmannians, SU(n) a product of four complex Grassmannians, and Sp(2n, R) or Sp(2n, C) a product of four symplectic Grassmannians over or ℂ *** Codes 14M15, 22E10, 22E15, 51A50 © 2025, CC BY.

关键词： Matrix algebra

A Variational Spike-and-Slab Approach for Group Variable Selection

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Lin, Buyu Ge, Changhao Liu, Jun S. Department of Statistics Harvard University United States Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania United States

We introduce a class of generic spike-and-slab priors for high-dimensional linear regression with grouped variables and present a Coordinate-ascent Variational Inference (CAVI) algorithm for obtaining an optimal variational Bayes approximation. Using parameter expansion for a specific, yet comprehensive, family of slab distributions, we obtain a further gain in computational efficiency. The method can be easily extended to fitting additive models. Theoretically, we present general conditions on the generic spike-and-slab priors that enable us to derive the contraction rates for both the true posterior and the VB posterior for linear regression and additive models, of which some previous theoretical results can be viewed as special cases. Our simulation studies and real data application demonstrate that the proposed method is superior to existing methods in both variable selection and parameter estimation. Our algorithm is implemented in the R package GVSSB. Copyright © 2023, The Authors. All rights reserved.

关键词： computational efficiency

Securing Smart City Networks - Intelligent Detection Of DDoS Cyber Attacks

学校读者我要写书评

暂无评论

Securing Smart City Networks - Intelligent Detection Of DDoS...

International Conference on Contemporary Computing and Informatics (IC3I)

作者： Ms. Deepthi Tabitha Bennet Ms. Preethi Samantha Bennet D Anitha Department of Applied Mathematics and Computational Science Thiagarajar College of Engineering Madurai India

A distributed denial-of-service (DDoS) is a malicious attempt by attackers to disrupt the normal traffic of a targeted server, service or network. This is done by overwhelming the target and its surrounding infrastructure with a flood of Internet traffic. The multiple compromised computer systems (bots or zombies) then act as sources of attack traffic. Exploited machines can include computers and other network resources such as IoT devices. The attack results in either degraded network performance or a total service outage of critical infrastructure. This can lead to heavy financial losses and reputational damage. These attacks maximise effectiveness by controlling the affected systems remotely and establishing a network of bots called bot networks. It is very difficult to separate the attack traffic from normal traffic. Early detection is essential for successful mitigation of the attack, which gives rise to a very important role in cybersecurity to detect the attacks and mitigate the effects. This can be done by deploying machine learning or deep learning models to monitor the traffic data. We propose using various machine learning and deep learning algorithms to analyse the traffic patterns and separate malicious traffic from normal traffic. Two suitable datasets have been identified (DDoS attack SDN dataset and CICDDoS2019 dataset). All essential preprocessing is performed on both datasets. Feature selection is also performed before detection techniques are applied. 8 different Neural Networks/ Ensemble/ Machine Learning models are chosen and the datasets are analysed. The best model is chosen based on the performance metrics (DEEP NEURAL NETWORK MODEL). An alternative is also suggested (Next best - Hypermodel). Optimisation by Hyperparameter tuning further enhances the accuracy. Based on the nature of the attack and the intended target, suitable mitigation procedures can then be deployed.

关键词： Deep learning Smart cities computational modeling Neural networks Traffic control Denial-of-service attack Chatbots

Advancements on multi-fidelity random Fourier neural networks: application to hurricane modeling for offshore wind energy

学校读者我要写书评

暂无评论

Advancements on multi-fidelity random Fourier neural network...

AIAA Science and Technology Forum and Exposition, AIAA SciTech Forum 2025

作者： Davis, Owen Geraci, Gianluca Wentz, Jacqueline M. King, Ryan N. Cortiella, Alexandre Rybchuk, Alex Gomez, Miguel Sanchez Deskos, Georgios Motamed, Mohammad Optimization and Uncertainty Quantification Sandia National Laboratories AlbuquerqueNM United States Computational Data Science Sandia National Laboratories LivermoreCA United States National Wind Technology Center National Renewable Energy Laboratory GoldenCO United States Department of Applied Mathematics and Statistics University of New Mexico AlbuquerqueNM United States

ISBN: (数字)9781624107238

ISBN: (纸本)9781624107238

Multi-fidelity approaches are emerging as effective strategies in computational science to handle otherwise intractable tasks like Uncertainty Quantification (UQ), training of Machine Learning (ML) models, and optimization, for expensive high-fidelity applications in which the amount of available simulations or data is limited. The main idea is simple: large datasets generated for low-fidelity approximations of the problem at hand are fused with a much sparser dataset for the target (high-fidelity) system. In this paper, we build on our recent success in designing random Fourier Neural Networks (rFNNs) [1] to target problems arising in wind energy applications and in particular problems of interest for hurricane modeling. In this context, data for the high-fidelity models are limited and lower fidelity alternatives are needed. In this work, we introduce a novel multi-fidelity training approach for our rFNNs and demonstrate its use on a simple verification problem and on a hurricane modeling problem in which high-fidelity data are generated via Large-Eddy Simulations (LES), while low-fidelity data are given by a mesoscale model. Initial results demonstrate how the multi-fidelity training approach can improve the quality of the resulting surrogate. © 2025, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.

关键词： Large eddy simulation