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A New Method for Solving Nonlinear Partial Differential Equations Based on Liquid Time-Constant Networks

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Journal of Systems Science & Complexity 2024年第2期37卷 480-493页

作者： sun Jiuyun DONG Huanhe FANG yong College of Mathematics and Systems Science Shandong University of Science and TechnologyQingdao 266590China

In this paper,physics-informed liquid networks(PILNs)are proposed based on liquid time-constant networks(LTC)for solving nonlinear partial differential equations(PDEs).In this approach,the network state is controlled via ordinary differential equations(ODEs).The significant advantage is that neurons controlled by ODEs are more expressive compared to simple activation *** addition,the PILNs use difference schemes instead of automatic differentiation to construct the residuals of PDEs,which avoid information loss in the neighborhood of sampling *** this method draws on both the traveling wave method and physics-informed neural networks(PINNs),it has a better physical ***,the KdV equation and the nonlinear Schr¨odinger equation are solved to test the generalization ability of the *** the best of the authors’knowledge,this is the first deep learning method that uses ODEs to simulate the numerical solutions of PDEs.

关键词： Nonlinear partial differential equations numerical solutions physics-informed liquid networks physics-informed neural networks

Jointly optimizing user clustering,power management,and wireless channel allocation for NOMA-based Internet of Things

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Digital Communications and Networks 2021年第1期7卷 29-36页

作者： xiang sun Liangkun Yu Yin Yang Department of Electrical&Computer Engineering University of New MexicoAlbuquerqueNM87131USA School of Computing Clemson UniversityClemsonSC29634USA

In order to accommodate the large number of Internet of Things(IoT)connections in mobile networks,Non-Orthogonal Multiple Access(NOMA)has been applied as the resource sharing mechanism in mobile access networks to improve the spectrum *** NOMA-based resource management for uplink communications comprises two problems,i.e.,user clustering and power&wireless channel *** clustering refers to assigning users in terms of IoT devices to different clusters(where users in the same cluster are sharing the wireless channels to upload their data),and power&wireless channel allocation is to optimize the transmission power of the users and the number of wireless channels allocated to the users in a *** two problems are coupled together,thus making it difficult to solve the NOMA-based resource management *** this paper,we propose a QoS-aWarE resourcE managemenT(SWEET)for NOMA algorithm to jointly optimize the user clustering,power management,and wireless channel allocation such that the number of wireless channels is minimized and the data rate requirements of the users can be *** performance of SWEET is validated via extensive simulations.

关键词： NOMA Internet of Things Resource management

（e, 2e） Investigations of the Simultaneous Ionization and Excitation of Helium to He＋（n=2）

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Chinese Journal of Chemical Physics 2013年第5期26卷 576-579,I0004页

作者： Shi-yan sun xiang-fu Jia Centure for research of Molecule Science School of Physics and Information Engineering Shanxi NormalUniversitj4 Linfen 041004 China

Three-Coulomb-wave method is employed to treat the process of （e, 2e） simultaneous ion- ization and excitation to the n=2 state of helium, with radial and angular correlated wave-function of He target. The triple differential cross sections are calculated and analyzed in very asymmetric coplanar geometry at incident energies of 5.50, 1.50 and 0.57 keV. Results are compared with the absolute measurements and the theoretical first and second Born approximation. The present triply differential cross section （TDCS） is found to be in good agreement with experimental data qualitatively. The distinguishing feature noted in TDCS structure is the presence of intense recoil peak that for certain parameters is even larger than the binary peak, an unusual feature for the single-ionization process at high and intermediate energies.

关键词： Excitation-ionization Three-Coulomb-wave model Triply differential crosssection

Adversarial data splitting for domain generalization

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Science China(Information Sciences) 2024年第5期67卷 28-42页

作者： xiang GU Jian sun Zongben XU School of Mathematics and Statistics Xi'an Jiaotong University

Domain generalization aims to learn a model that is generalizable to an unseen target domain,which is a fundamental and challenging task in machine learning for out-of-distribution generalization. This paper proposes a novel domain generalization approach that enforces the learned model to be able to generalize well over the train/val subset splitting of the training dataset. This idea is modeled herein as an adversarial data splitting framework, formulated as a min-max optimization problem inspired by the metalearning approach. The min-max optimization problem is solved by iteratively splitting the training dataset into the training and val subsets to maximize the domain shift measured by the objective function and updating the model parameters to enable the model to generalize well from the training subset to the val subset by minimizing the objective function. This adversarial training approach does not assume the known domain labels of the training data; instead, it automatically investigates the “hard” splitting of the train/val subsets to learn the generalizable model. Extensive experimental results using three benchmark datasets demonstrate the superiority of this approach. In addition, we derive a generalization error bound for the theoretical understanding of our proposed approach.

关键词： domain generalization adversarial learning data splitting meta-learning out of distribution

Upconversion Nanoparticles-Encoded Hydrogel Microbeads-Based Multiplexed Protein Detection

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Nano-Micro Letters 2018年第2期10卷 135-150页

作者： Swati Shikha xiang Zheng yong Zhang Department of Biomedical Engineering Faculty of Engineering National University of Singapore (NUS) NUS Graduate School for Integrative Sciences and Engineering Centre for Life Sciences (CeLS)

Fluorescently encoded microbeads are in demand for multiplexed applications in different *** to organic dye-based commercially available Luminex's x MAP technology, upconversion nanoparticles(UCNPs) are better alternatives due to their large antiStokes shift, photostability, nil background, and single wavelength excitation. Here, we developed a new multiplexed detection system using UCNPs for encoding poly(ethylene glycol) diacrylate(PEGDA) microbeads as well as for labeling reporter antibody. However, to prepare UCNPs-encoded microbeads, currently used swellingbased encapsulation leads to non-uniformity, which is undesirable for fluorescence-based multiplexing. Hence,we utilized droplet microfluidics to obtain encoded microbeads of uniform size, shape, and UCNPs distribution inside. Additionally, PEGDA microbeads lack functionality for probe antibodies conjugation on their *** to functionalize the surface of PEGDA microbeads(acrylic acid incorporation, polydopamine coating)reported thus far quench the fluorescence of UCNPs. Here,PEGDA microbeads surface was coated with silica followed by carboxyl modification without compromising the fluorescence intensity of UCNPs. In this study, droplet microfluidics-assisted UCNPs-encoded microbeads of uniform shape, size, and fluorescence were *** color codes were generated by mixing UCNPs emitting red and green colors at different ratios prior to encapsulation. UCNPs emitting blue color were used to label the reporter antibody. Probe antibodies were covalently immobilized on red UCNPs-encoded microbeads for specific capture of human serum albumin(HSA) as a model protein. The system was also demonstrated for multiplexed detection of both human C-reactive protein(hCRP) and HSA protein by immobilizing anti-h CRP antibodies on green UCNPs.

关键词： Upconversion nanoparticles PEGDA microbeads Encoding Multiplexed bio-detection Single wavelength excitation

Extensions of quantum enveloping algebras

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Applied Mathematics(A Journal of Chinese Universities) 2012年第3期27卷 290-304页

作者： HONG Yan-yong WU Zhi-xiang Department of Mathematics Zhejiang UniversityHangzhou 310027China

In this paper, we define a class of extended quantum enveloping algebras Uq （f（K, J）） and some new Hopf algebras, which are certain extensions of quantum enveloping algebras by a Hopf algebra H. This construction generalizes some well-known extensions of quantum enveloping algebras by a Hopf algebra and provides a large of new noncommutative and nonco- commutative Hopf algebras.

关键词： quantum enveloping algebra Kac-Moody algebra ambiskew polynomial ring.

DETECTING COMMUNITY STRUCTURE： FROM PARSIMONY TO WEIGHTED PARSIMONY

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Journal of Systems Science & Complexity 2010年第5期23卷 1024-1036页

作者： Junhua ZHANG Yuqing QIU xiang-sun ZHANG Key Laboratory of Random Complex Structures and Data Science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

Community detection has attracted a great deal of attention in recent years. A parsimony criterion for detecting this structure means that as minimal as possible number of inserted and deleted edges is needed when we make the network considered become a disjoint union of cliques. However, many small groups of nodes are obtained by directly using this criterion to some networks especially for sparse ones. In this paper we propose a weighted parsimony model in which a weight coefficient is introduced to balance the inserted and deleted edges to ensure the obtained subgraphs to be reasonable communities. Some benchmark testing examples are used to validate the effectiveness of the proposed method. It is interesting that the weight here can be determined only by the topological features of the network. Meanwhile we make some comparison of our model with maximizing modularity Q and modularity density D on some of the benchmark networks, although sometimes too many or a little less numbers of communities are obtained with Q or D, a proper number of communities are detected with the weighted model. All the computational results confirm its capability for community detection for the small or middle size networks.

关键词： Cliques community detection complex networks parsimony.

Loop quantum modified gravity and its cosmological application

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Frontiers of physics 2013年第1期8卷 80-93页

作者： xiang-Dong Zhang yong-Ge Ma Department of Physics South China University of Technology Guangzhou 510641 China Department of Physics Beijing Normal University Beijing 100875 China

A general nonperturvative loop quantization procedure for metric modified gravity is reviewed. As an example, this procedure is applied to scalar-tensor theories of gravity. The quantum kinematical framework of these theories is rigorously constructed. Both the Hamiltonian and master constraint operators are well defined and proposed to represent quantum dynamics of scalar-tensor theories. As an application to models, we set up the basic structure of loop quantum Brans-Dicke cosmology. The effective dynamical equations of loop quantum Brans-Dicke cosmology are also obtained, which lay a foundation for the phenomenological investigation to possible quantum gravity effects in cosmology.

关键词： loop quantum gravity scalar-tensor theories

Thermodynamics properties and thermal conductivity of Mg_2Pb at high pressure

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Science China(Physics,Mechanics & Astronomy) 2013年第10期56卷 1854-1860页

作者： DUAN yongHua sun yong Faculty of Material Science and Technology Kunming University of Science and Technology Key Lab of Advanced Materials of Yunnan Province Kunming University of Science and Technology

The thermodynamics properties and thermal conductivity of Mg2Pb at high pressures have been calculated by *** enthalpy of formation and heat capacity obtained at 0 GPa are in good agreement with the experiments and other theoretical *** thermal conductivity and coefficient of thermal expansion of Mg2 Pb at high pressure were *** thermal conductivity presents a second-order polynomial with *** calculated thermal conductivity of Mg2Pb indicates that it is suitable to be used as thermal conductor at 0 K.

关键词： thermodynamics properties thermal conductivity first-principles Mg2Pb