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arXiv 2024年

作者： He, Zhijuan Huang, Jin Jiang, Kai Shi, An-Chang School of Mathematics and Computational Science Xiangtan University Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing Ministry of Education 411105 China Laboratory of Mathematics and Complex Systems Ministry of Education School of Mathematical Sciences Beijing Normal University Beijing100875 China Department of Physics and Astronomy McMaster University HamiltonONL8S 4M1 Canada

The phase behavior of symmetric diblock copolymers under three-dimensional (3D) soft confinement is investigated using the self-consistent field theory. The soft confinement is realized in binary blends composed AB diblock copolymers and C homopolymers, where the copolymers self-assemble to form a droplet embedded in the homopolymer matrix. The phase behavior of the confined block copolymers is regulated by the degree of confinement and the selectivity of the homopolymers, resulting in a rich variety of novel structures. When the C homopolymers are neutral to the A- and B-blocks, stacked lamellae (SL) are formed where the number of layers increases with the droplet volume, resulting in a morphological transition sequence from Janus particle to square SL. When the C homopolymers are strongly selective to the B-blocks, a series of non-lamellar morphologies, including onion-, hamburger-, cross-, ring-, and cookie-like structures, are observed. A detailed free energy analysis reveals a first-order reversible transformation between SL and onion-like (OL) structures when the selectivity of the homopolymers is changed. Our results provide a comprehensive understanding of how various factors, such as the copolymer concentration, homopolymer chain length, degree of confinement, homopolymer selectivity, affect the self-assembled structures of diblock copolymers under soft 3D confinement. Copyright © 2024, The Authors. All rights reserved.

关键词： Free energy

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An Interpretable MRI Reconstruction Network with Two-grid-cycle Correction and Geometric Prior Distillation

arXiv

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arXiv 2022年

作者： Fan, Xiaohong Yang, Yin Chen, Ke Zhang, Jianping Dong, Ke The School of Mathematics and Computational Science Xiangtan University Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education Xiangtan411105 China The School of Mathematics and Computational Science Xiangtan University Hunan National Applied Mathematics Center Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan411105 China Centre for Mathematical Imaging Techniques Department of Mathematical Sciences The University of Liverpool Merseyside LiverpoolL6972L United Kingdom The School of Mathematics and Computational Science Xiangtan University Hunan National Applied Mathematics Center Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education Xiangtan411105 China Department of Radiation Oncology Xiangtan Central Hospital Xiangtan411101 China

Although existing deep learning compressed-sensing-based Magnetic Resonance Imaging (CS-MRI) methods have achieved considerably impressive performance, explainability and generalizability continue to be challenging for such methods since the transition from mathematical analysis to network design not always natural enough, often most of them are not flexible enough to handle multi-sampling-ratio reconstruction assignments. In this work, to tackle explainability and generalizability, we propose a unifying deep unfolding multi-sampling-ratio interpretable CS-MRI framework. The combined approach offers more generalizability than previous works whereas deep learning gains explainability through a geometric prior module. Inspired by the multigrid algorithm, we first embed the CSMRI-based optimization algorithm into correction-distillation scheme that consists of three ingredients: pre-relaxation module, correction module and geometric prior distillation module. Furthermore, we employ a condition module to learn adaptively step-length and noise level, which enables the proposed framework to jointly train multi-ratio tasks through a single model. The proposed model not only compensates for the lost contextual information of reconstructed image which is refined from low frequency error in geometric characteristic k-space, but also integrates the theoretical guarantee of model-based methods and the superior reconstruction performances of deep learning-based methods. Therefore, it can give us a novel perspective to design biomedical imaging networks. Numerical experiments show that our framework outperforms state-of-the-art methods in terms of qualitative and quantitative evaluations. Our method achieves 3.18 dB improvement at low CS ratio 10% and average 1.42 dB improvement over other comparison methods on brain dataset using Cartesian sampling mask. Copyright © 2022, The Authors. All rights reserved.

关键词： Distillation

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Nucleation and phase transition of decagonal quasicrystals

arXiv

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arXiv 2024年

作者： Zhou, Tiejun Zhang, Lei Zhang, Pingwen Shi, An-Chang Jiang, Kai Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing Ministry of Education School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China Beijing International Center for Mathematical Research Peking University Beijing100871 China School of Mathematics and Statistics Wuhan University Wuhan430072 China School of Mathematical Sciences Peking University Beijing100871 China Department of Physics and Astronomy McMaster University HamiltonL8S 4M1 Canada

In this work, we study the nucleation of quasicrystals from liquid or periodic crystals by developing an efficient order-order phase transition algorithm, namely the nullspace-preserving saddle search method. Specifically, we focus on nucleation and phase transitions of the decagonal quasicrystal (DQC) based on the Lifshitz-Petrich model. We present the nucleation path of DQC from the liquid and demonstrate one- and two-stage transition paths between DQC and periodic crystals. We provide a perspective of the group-subgroup phase transition and nucleation rates to understand the nucleation and phase transition mechanisms involving DQC. These results reveal the one-step and stepwise modes of symmetry breaking or recovery in the phase transition from DQC, where the stepwise modes are more probable. Copyright © 2024, The Authors. All rights reserved.

关键词： Quasicrystals

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Multifractal analyses of daily rainfall time series in Pearl River basin of China

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Physica A: Statistical Mechanics and its Applications 2014年 405卷 193-202页

作者： Zu-Guo Yu Yee Leung Yongqin David Chen Qiang Zhang Vo Anh Yu Zhou Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan Hunan 411105 China Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Xiangtan Hunan 411105 China School of Mathematical Sciences Queensland University of Technology GPO Box 2434 Brisbane Q4001 Australia Department of Geography and Resource Management The Chinese University of Hong Kong Hong Kong China Institute of Environment Energy and Sustainability The Chinese University of Hong Kong Hong Kong China Department of Water Resources and Environment Sun Yat-sen University Guangzhou 510275 China Key Laboratory of Water Cycle and Water Security in Southern China of Guangdong High Education Institute Sun Yat-sen University Guangzhou 510275 China

The multifractal properties of daily rainfall time series at the stations in Pearl River basin of China over periods of up to 45 years are examined using the universal multifractal approach based on the multiplicative cascade model and the multifractal detrended fluctuation analysis (MF-DFA). The results from these two kinds of multifractal analyses show that the daily rainfall time series in this basin have multifractal behavior in two different time scale ranges. It is found that the empirical multifractal moment function K ( q ) of the daily rainfall time series can be fitted very well by the universal multifractal model (UMM). The estimated values of the conservation parameter H from UMM for these daily rainfall data are close to zero indicating that they correspond to conserved fields. After removing the seasonal trend in the rainfall data, the estimated values of the exponent h ( 2 ) from MF-DFA indicate that the daily rainfall time series in Pearl River basin exhibit no long-term correlations. It is also found that K ( 2 ) and elevation series are negatively correlated. It shows a relationship between topography and rainfall variability.

关键词： Daily rainfall time series Multifractal property Universal multifractal model Multifractal detrended fluctuation analysis

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The improved Hagedorn wavepacket method for semiclassical Schrödinger equation

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International Journal of Modeling, simulation, and Scientific Computing 2014年第4期5卷

作者： Xueyang Li Aiguo Xiao Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Xiangtan Hunan P. R. China

The Hagedorn wavepacket method is an important numerical method for solving the semiclassical time-dependent Schrödinger equation. In this paper, a new semi-discretization in space is obtained by wavepacket operator. In a sense, such semi-discretization is equivalent to the Hagedorn wavepacket method, but this discretization is more intuitive to show the advantages of wavepacket methods. Moreover, we apply the multi-time-step method and the Magnus-expansion to obtain the improved algorithms in time-stepping computation. The improved algorithms are of the Gauss–Hermite spectral accuracy to approximate the analytical solution of the semiclassical Schrödinger equation. And for the given accuracy, the larger time stepsize can be used for the higher oscillation in the semiclassical Schrödinger equation. The superiority is shown by the error estimation and numerical experiments.

关键词： High oscillation semiclassical Schrödinger equation Hagedorn wavepacket multi-time-step method Magnus-expansion

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Multifractal analysis for core-periphery structure of complex networks

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Journal of Statistical Mechanics: Theory and Experiment 2019年第7期2019卷 073405-073405页

作者： Liu, Jin-Long Yu, Zu-Guo Anh, Vo Key Lab. of Intelligent Comp. and Info. Proc. of Min. of Educ. and Hunan Key Lab. for Computation and Simulat. in Sci. and Eng. Xiangtan University Xiangtan HUNAN 411105 China School of Electrical Engineering and Computer Science Queensland University of Technology GPO Box 2434 Brisbane Q4001 Australia Faculty of Science Engineering and Technology Swinburne University of Technology PO Box 218 Hawthorn 3122 VIC Australia

Revealing the properties of the core-periphery structure of complex networks can help us to deeply understand their organized principle and function. Studies in recent years have indicated that the k-core and peripheral subnetworks of some model and real-world networks exhibit the fractal behavior, but it remains unclear whether they possess the multifractal behavior. In this paper, we study the multifractal property of these networks and their subnetworks. First, we obtain the sequence of k-cores and their corresponding k-peripheries of original networks by using the k-core decomposition method. We find that the multifractal property exists in these k-cores and k-peripheries of the generalized minimal model network and some Brain networks. Furthermore, the multifractality of the k-cores becomes weaker and that of k-peripheries becomes stronger with the increase of k. The result is consistent with the fact that the k-core becomes more homogenous or cohesive with increasing k. Then we decompose each of these original networks into a densely connected core and a sparsely connected periphery. Although the periphery and the original network have almost the same fractal behavior at the tail part of the resulting curves in the log-log plot for some fractal networks, their multifractality are very different. This means that a unique fractal dimension is not enough to characterize the complexity or spatial heterogeneity of these networks when they take a multifractal structure. Our results show that the multifractal analysis is more powerful than the fractal analysis in characterizing the complexity of the core-periphery structure of complex networks. © 2019 IOP Publishing Ltd and SISSA Medialab srl

关键词： fractal growth network dynamics nonlinear dynamics

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Superconvergence for General Convex Optimal Control Problems Governed by Semilinear Parabolic Equations

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International Scholarly Research Notices 2014年第1期2014卷

作者： Yongquan Dai Yanping Chen Hunan Key Laboratory for Computation and Simulation in Science and Engineering Department of Mathematics Xiangtan University Xiangtan Hunan 411105 *** School of Mathematical Sciences South China Normal University Guangzhou Guangdong 510631 ***

We will investigate the superconvergence for the semidiscrete finite element approximation of distributed convex optimal control problems governed by semilinear parabolic equations. The state and costate are approximated by the piecewise linear functions and the control is approximated by piecewise constant functions. We present the superconvergence analysis for both the control variable and the state variables.

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Inferring microRNA-disease association by hybrid recommendation algorithm and unbalanced bi-random walk on heterogeneous network

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Scientific reports 2019年第1期9卷 2474页

作者： Dong-Ling Yu Yuan-Lin Ma Zu-Guo Yu Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education and Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan Hunan 411105 P.R. China. Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education and Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan Hunan 411105 P.R. China. yuzuguo@***. School of Electrical Engineering and Computer Science Queensland University of Technology Brisbane Q4001 Australia. yuzuguo@***.

More and more research works have indicated that microRNAs (miRNAs) play indispensable roles in exploring the pathogenesis of diseases. Detecting miRNA-disease associations by experimental techniques in biology is expensive and time-consuming. Hence, it is important to propose reliable and accurate computational methods to exploring potential miRNAs related diseases. In our work, we develop a novel method (BRWHNHA) to uncover potential miRNAs associated with diseases based on hybrid recommendation algorithm and unbalanced bi-random walk. We first integrate the Gaussian interaction profile kernel similarity into the miRNA functional similarity network and the disease semantic similarity network. Then we calculate the transition probability matrix of bipartite network by using hybrid recommendation algorithm. Finally, we adopt unbalanced bi-random walk on the heterogeneous network to infer undiscovered miRNA-disease relationships. We tested BRWHNHA on 22 diseases based on five-fold cross-validation and achieves reliable performance with average AUC of 0.857, which an area under the ROC curve ranging from 0.807 to 0.924. As a result, BRWHNHA significantly improves the performance of inferring potential miRNA-disease association compared with previous methods. Moreover, the case studies on lung neoplasms and prostate neoplasms also illustrate that BRWHNHA is superior to previous prediction methods and is more advantageous in exploring potential miRNAs related diseases. All source codes can be downloaded from https://***/myl446/BRWHNHA .

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Multifractal temporally weighted detrended partial cross-correlation analysis of two non-stationary time series affected by common external factors

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Physica A: Statistical Mechanics and its Applications 2021年 573卷

作者： Bao-Gen Li Dian-Yi Ling Zu-Guo Yu Hunan Key Laboratory for Computation and Simulation in Science and Engineering and Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Xiangtan Hunan 411105 China School of Electrical Engineering and Computer Science Queensland University of Technology GPO Box 2434 Brisbane Q4001 Australia

When common factors strongly influence two cross-correlated time series recorded in complex natural and social systems, the results will be biased if we use multifractal detrended cross-correlation analysis (MF-DXA) without considering these common factors. In order to better study the time series of such cases, we extend the multifractal temporally weighted detrended cross-correlation analysis (MF-TWXDFA) proposed by our group (Wei et al., 2017) and propose multifractal temporally weighted detrended partial cross-correlation analysis (MF-TWDPCCA) to quantify intrinsic power-law cross-correlation of two non-stationary time series affected by common external factors in this paper. To test the performance of MF-TWDPCCA, we apply it and multifractal partial cross-correlation analysis (MF-DPXA) proposed by Qian et al. (2015) on simulated series. Numerical tests on artificially simulated series demonstrate that MF-TWDPCCA can more accurately detect the intrinsic cross-correlations for two simultaneously recorded series than MF-DPXA and MF-TWXDFA. To further show the utility of MF-TWDPCCA, we apply it on time series from stock markets and find that there exists significantly multifractal power-law cross-correlation between stock returns. In addition, a new partial cross-correlation coefficient is defined to quantify the level of intrinsic cross-correlation between two time series.

关键词： Partial cross-correlation Multifractal temporally weighted detrended partial cross-correlation analysis Partial cross-correlation coefficient

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Numerical homogenization of elastoplastic deformations of composite material with small proportion of inclusions

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Journal of Physics: Conference Series 2019年第1期1392卷

作者： Petr V. Sivtsev Aleksandr E. Kolesov Petr E. Zakharov Ying Yang Research Laboratory 'Multiscale Matheatical Modeling and Computing' Ammosov North-Eastern Federal University 58 Belinskogo 677000 Yakutsk Russia Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Xiangtan 411105 Hunan China

Numerical simulation of the stress-strain state of a composite material may be difficult due to large computational complexity associated with a grid resolution of a large number of inclusions. To overcome the problem one may use the homogenization method. But for material with plastic properties, proper modeling of yield stress and hardening may be overcomplicated. In this work we use some simplification associated with a small proportion of inclusions and restriction of stress values by matrix material strength. As model problem, we use deformation of concrete deep beam reinforced with steel or basalt fiber inclusions. For the numerical solution, the finite element method was applied using the FEniCS computing platform.

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