检索结果-内蒙古大学图书馆

GLOBAL SOLVABILITY AND ASYMPTOTICAL BEHAVIOR IN A TWO-SPECIES CHEMOTAXIS MODEL WITH SIGNAL ABSORPTION

学校读者我要写书评

暂无评论

arXiv 2021年

作者： Ren, Guoqiang Xiang, Tian School of Mathematics and Statistics Huazhong University of Science and Technology Hubei Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Hubei Wuhan430074 China Institute for Mathematical Sciences Renmin University of China Bejing100872 China

In this work, we study global existence, eventual smoothness and asymptotical behavior of positive solutions for the following two-species chemotaxis consumption model: ut = ∆u - χ1∇ · (u∇w), x ∈ Ω, t > 0, {{{{{{{ vt = ∆v - χ2∇ · (u∇w), x ∈ Ω, t > 0, wt = ∆w - (αu + βv)w, x ∈ Ω, t > 0, in a bounded smooth but not necessarily convex domain Ω ⊂ Rn(n = 2, 3, 4, 5) with nonnegative initial data u0, v0, w0 and homogeneous Neumann boundary data. Here, the parameters χ1, χ2 are positive and α, β are nonnegative. Under a smallness condition max{χ1, χ2}kw0kL∞ MSC Codes 35K59, 35K57 © 2021, CC BY.

关键词： Biochemistry

GLOBAL SOLVABILITY IN A TWO-SPECIES CHEMOTAXIS SYSTEM WITH SIGNAL PRODUCTION

学校读者我要写书评

暂无评论

arXiv 2021年

In this paper, we study the following prototypical two-species chemotaxis system with Lotka-Volterra competition and signal production: (Equation presented). We show that if (Equation presented). the associated Neumann initial-boundary value problem for (∗) admits a global generalized solutions in a bounded and smooth domain Ω ⊂ N (N ≥ 2) under merely integrable initial *** Codes 35A01, 35K57, 35Q92, 92C17 © 2021, CC BY.

关键词： Initial value problems

Data-driven method to learn the most probable transition pathway and stochastic differential equations

学校读者我要写书评

暂无评论

arXiv 2021年

作者： Chen, Xiaoli Duan, Jinqiao Hu, Jianyu Li, Dongfang School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Department of Mathematics National University of Singapore 119077 Singapore Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China Department of Applied Mathematics College of Computing Illinois Institute of Technology ChicagoIL60616 United States

Transition phenomena between metastable states play an important role in complex systems due to noisy fluctuations. We introduce the Onsager-Machlup theory and the Freidlin-Wentzell theory to quantify rare events in stochastic differential equations. By the variational principle, the most probable transition pathway is the minimizer of the action functional, which is governed by the Euler-Lagrange equation. In this paper, the physics-informed neural networks (PINNs) are presented to compute the most probable transition pathway through computing the Euler-Lagrange equation. The convergence result for the empirical loss is obtained for the forward problem. Then we investigate the inverse problem to extract the stochastic differential equation from the most probable transition pathway data. Finally, several numerical experiments are presented to verify the effectiveness of our methods. Copyright © 2021, The Authors. All rights reserved.

关键词： Inverse problems

Arrhythmia Classification with Attention-Based Res-BiLSTM-Net 1st

学校读者我要写书评

暂无评论

Arrhythmia Classification with Attention-Based Res-BiLSTM-Ne...

1st International Workshop on Machine Learning and Medical engineering for Cardiovasvular Healthcare, MLMECH 2019, and the 8th International Joint Workshops on computing and Visualization for Intravascular Imaging and Computer Assisted Stenting, CVII-STENT 2019, held in conjunction with 22nd International Conference on Medical Image computing and Computer-Assisted Intervention, MICCAI 2019

作者： Huang, Chengbin Zhao, Renjie Chen, Weiting Li, Huazheng MOE Engineering Research Center for Hardware/Software Co-Design Technology and Application Shanghai Key Laboratory of Trustworthy Computing East China Normal University Shanghai China

ISBN: (纸本)9783030333263

In the modern clinical diagnosis, the 12-lead electrocardiogram (ECG) signal has proved effective in cardiac arrhythmias classification. However, the manual diagnosis for cardiac arrhythmias is tedious and error-prone through ECG signals. In this work, we propose an end-to-end deep neural network called attention-based Res-BiLSTM-Net for automatic diagnosis of cardiac arrhythmias. Our model is capable of classifying ECG signals with different lengths. The proposed network consists of two parts: the attention-based Resnet and the attention-based BiLSTM. At first, ECG signals are divided into several signal segments with the same length. Then multi-scale features are extracted by our attention-based Resnet through signal segments. Next, these multi-scale features from a same ECG signal are integrated in chronological order. In the end, our attention-based BiLSTM classifies cardiac arrhythmias according to combined features. Our method achieved a good result with an average F1score of 0.8757 on a multi-label arrhythmias classification problem in the First China ECG Intelligent Competition. © 2019, Springer Nature Switzerland AG.

关键词： Electrocardiograms

Convergence rate of inertial forward-backward splitting algorithms based on the local error bound condition

学校读者我要写书评

暂无评论

arXiv 2020年

作者： Liu, Hongwei Wang, Ting Liu, Zexian School Of Mathematics And Statistics Xidian University Xi'An710126 China State Key Laboratory Of Scientific And Engineering Computing Institute Of Computational Mathematics And Scientific/Engineering Computing AMSS Chinese Academy Of Sciences Beijing100190 China School Of Mathematics And Statistics Guizhou University Guiyang550025 China

The " Inertial Forward-Backward algorithm " (IFB) is a powerful tool for convex nonsmooth minimization problems, and under the local error bound condition, the R-linear convergence rates for the sequences of objective values and iterates have been proved if the inertial parameter γksatisfies supkγkkγk= 1 is not know. In this paper, based on the local error bound condition, we exploit a new assumption condition for the important parameter tkin IFB, which implies that limk→∞γk= 1, and establish the convergence rate of function values and strong convergence of the iterates generated by the IFB algorithms with six tksatisfying the above assumption condition in Hilbert space. It is remarkable that, under the local error bound condition, we show that the IFB algorithms with some tkcan achieve sublinear convergence rate of o(1/kp) for any positive integer p > 1. In addition, we propose a class of Inertial Forward-Backward algorithm with adaptive modification and show it has same convergence results as IFB under the error bound condition. Some numerical experiments are conducted to illustrate our results. Copyright © 2020, The Authors. All rights reserved.

关键词： Parameter estimation

ANALYSIS ON THE STEADY EULER FLOWS WITH STAGNATION POINTS IN AN INFINITELY LONG NOZZLE

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Li, Congming Lü, Yingshu Shahgholian, Henrik Xie, Chunjing School of Mathematical Sciences CMA-Shanghai Shanghai Jiao Tong University Shanghai200240 China Institute of Natural Sciences CMA-Shanghai Shanghai Jiao Tong University Shanghai200240 China Department of Mathematics Royal Institute of Technology Stockholm Sweden School of Mathematical Sciences Institute of Natural Sciences Ministry of Education Key Laboratory of Scientific and Engineering Computing CMA-Shanghai Shanghai Jiao Tong University Shanghai200240 China

A recent prominent result asserts that steady incompressible Euler flows strictly away from stagnation in a two-dimensional infinitely long strip must be shear flows. On the other hand, flows with stagnation points, very challenging in analysis, are interesting and important phenomenon in fluids. In this paper, we not only prove the uniqueness and existence of steady flows with stagnation points, but also obtain the regularity of the boundary of stagnation set, which is a class of obstacle type free boundary. First, we prove a global uniqueness theorem for steady Euler system with Poiseuille flows as upstream far field state in an infinitely long strip. Due to the appearance of stagnation points, the nonlinearity of the semilinear equation for the stream function becomes non- Lipschitz. This creates a challenging analysis problem since many classical analysis methods do not apply directly. Second, the existence of steady incompressible Euler flows, tending to Poiseuille flows in the upstream, are established in an infinitely long nozzle via variational approach. A very interesting phenomenon is the regularity of the boundary of non-stagnant region, which can be regarded as an obstacle type free boundary and is proved to be globally C1. Finally, the existence of stagnation region is proved as long as the nozzle is wider than the width of the nozzle at upstream where the flows tend to Poiseuille flows. Copyright © 2022, The Authors. All rights reserved.

关键词： Nozzles

Large deviations principle for stochastic delay differential equations with super-linearly growing coefficients

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Jin, Diancong Chen, Ziheng Zhou, Tau School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China School of Mathematics and Statistics Yunnan University Kunming650500 China Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

We utilize the weak convergence method to establish the Freidlin-Wentzell large deviations principle (LDP) for stochastic delay differential equations (SDDEs) with super-linearly growing coefficients, which covers a large class of cases with non-globally Lipschitz coefficients. The key ingredient in our proof is the uniform moment estimate of the controlled equation, where we handle the super-linear growth of the coefficients by an iterative argument. Our results allow both the drift and diffusion coefficients of the considered equations to super-linearly grow not only with respect to the delay variable but also to the state variable. This work extends the existing results which develop the LDPs for SDDEs with super-linearly growing coefficients only with respect to the delay *** Codes 60H10, 60F10, 60H30 Copyright © 2022, The Authors. All rights reserved.

关键词： Stochastic systems

Quantum algorithms for uncertainty quantification: application to partial differential equations

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Golse, Francois Jin, Shi Liu, Nana Ecole Polytechnique CMLS PalaiseauCedex 91128 France Institute of Natural Sciences Shanghai Jiao Tong University Shanghai200240 China School of Mathematical Sciences Shanghai Jiao Tong University Shanghai200240 China Ministry of Education Key Laboratory in Scientific and Engineering Computing Shanghai Jiao Tong University Shanghai200240 China University of Michigan Shanghai Jiao Tong University Joint Institute Shanghai200240 China

Most problems in uncertainty quantification, despite its ubiquitousness in scientific computing, applied mathematics and data science, remain formidable on a classical computer. For uncertainties that arise in partial differential equations (PDEs), large numbers M >> 1 of samples are required to obtain accurate ensemble averages. This usually involves solving the PDE M times. In addition, to characterise the stochasticity in a PDE, the dimension L of the random input variables is high in most cases, and classical algorithms suffer from curse-of-dimensionality. We propose new quantum algorithms for PDEs with uncertain coefficients that are more efficient in M and L in various important regimes, compared to their classical counterparts. We introduce transformations that transfer the original d-dimensional equation (with uncertain coefficients) into d + L (for dissipative equations) or d + 2L (for wave type equations) dimensional equations (with certain coefficients) in which the uncertainties appear only in the initial data. These transformations also allow one to superimpose the M different initial data, so the computational cost for the quantum algorithm to obtain the ensemble average from M different samples is then independent of M, while also showing potential advantage in d, L and precision ǫ in computing ensemble averaged solutions or physical observables. © 2022, CC BY.

关键词： Partial differential equations

Advanced Analysis of Arabidopsis thaliana Leaf Traits Using RGB Imaging and Machine Learning

学校读者我要写书评

暂无评论

Advanced Analysis of Arabidopsis thaliana Leaf Traits Using ...

International Symposium on Industrial Electronics (INDEL)

作者： Rijad Sarić Edhem Čustović Martin Trtílek Amila Akagić Mathew G. Lewsey James Whelan La Trobe Institute for Sustainable Agriculture & Food (LISAF) La Trobe University Melbourne VIC Australia Australian Research Council Research Hub for Medicinal Agriculture La Trobe University Melbourne VIC Australia School of Computing Engineering and Mathematical Sciences La Trobe University (LTU) Melbourne VIC Australia Scientific Instruments Australia (SIA) Melbourne VIC Australia Photon Systems Instruments (PSI) Plant Phenotyping Research Centre Drasov Brno Czech Republic Faculty of Electrical Engineering University of Sarajevo (UNSA) Sarajevo Bosnia and Herzegovina State Key Laboratory of Plant Environmental Resilience College of Life Science Zhejiang University (ZJU) P.R. China Provincial International Science and Technology Cooperation Base on Engineering Biology Zhejiang University P.R China

ISBN: (数字)9798350352320

ISBN: (纸本)9798350352337

Image-based high-throughput plant phenotyping utilises various imaging techniques to automatically and non-invasively understand the growth of different plant species. These innovative imaging infrastructures are implemented to monitor plant development over time in indoor or outdoor environments. However, understanding the relationship between genotype and phenotype interactions under different environments remains challenging. This research study demonstrates superior extraction of leaf morphological features of different Arabidopsis thaliana ecotypes by analysing leaf geometry using a sequence of RGB images. Upon successful extraction of anatomical features, leaf length and area are converted into physical coordinates. Furthermore, considering these leaf features as 1D signals, the Fourier Spectrum is analysed, and most descriptive features are selected using PCA. Finally, leaf shape classification is established by training and testing five distinct ML models. A thorough evaluation of selected models demonstrates superiority in classifying two common leaf shapes of Arabidopsis plants.

关键词： Training Shape Biological system modeling Imaging Machine learning Feature extraction Real-time systems Reliability Testing Principal component analysis