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3-Lie bialgebras and 3-pre-lie algebras induced by involutive derivations

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arXiv 2019年

作者： Bai, Ruipu Hou, Shuai Kang, Chuangchuang College of Mathematics and Information Science Hebei University Key Laboratory of Machine Learning and Computational Intelligence of Hebei Province Baoding071002 China College of Mathematics and Information Science Hebei University Baoding071002 China

In this paper, we study the structure of 3-Lie algebras with involutive derivations. We prove that if A is an m-dimensional 3-Lie algebra with an involutive derivation D, then there exists a compatible 3-pre-Lie algebra (A, -⋯ }D) such that A is the sub-adjacent 3-Lie algebra, and there is a local cocycle 3-Lie bialgebraic structure on the 2m-dimensional semi- direct product 3-Lie algebra A ad∗ A∗, which is associated to the adjoint representation (A, ad). By means of involutive derivations, the skew-symmetric solution of the 3-Lie classical Yang- Baxter equation in the 3-Lie algebra A ad∗ A∗, a class of 3-pre-Lie algebras, and eight and ten dimensional local cocycle 3-Lie bialgebras are constructed. Copyright © 2019, The Authors. All rights reserved.

关键词：

MANIN TRIPLES OF 3-LIE ALGEBRAS INDUCED BY INVOLUTIVE DERIVATIONS

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arXiv 2019年

作者： Hou, Shuai Bai, Ruipu College of Mathematics and Information Science Hebei University Baoding071002 China College of Mathematics and Information Science Hebei University Key Laboratory of Machine Learning and Computational Intelligence of Hebei Province Baoding071002 China

For any n-dimensional 3-Lie algebra A over a field of characteristic zero with an involutive derivation D, we investigate the structure of the 3-Lie algebra B1 = A ad∗ A∗ associated with the coadjoint representation (A∗, ad∗). We then discuss the structure of the dual 3-Lie algebra B2 of the local cocycle 3-Lie bialgebra (A ad∗ A∗, ∆). By means of the involutive derivation D, we construct the 4n-dimensional Manin triple (B1 B2, [·, ·, ·]1, [·, ·, ·]2, B1, B2) of 3-Lie algebras, and provide concrete multiplication in a special basis Π1 ∪ Π2. We also construct a sixteen dimensional Manin triple (B, [·, ·, ·]) with dim B1 = 12 using an involutive derivation on a four dimensional 3-Lie algebra A with dim A1 = 2. Copyright © 2019, The Authors. All rights reserved.

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DeePMD-kit v2: A software package for Deep Potential models

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arXiv 2023年

作者： Zeng, Jinzhe Zhang, Duo Lu, Denghui Mo, Pinghui Li, Zeyu Chen, Yixiao Rynik, Marián Huang, Li'ang Li, Ziyao Shi, Shaochen Wang, Yingze Ye, Haotian Tuo, Ping Yang, Jiabin Ding, Ye Li, Yifan Tisi, Davide Zeng, Qiyu Bao, Han Xia, Yu Huang, Jiameng Muraoka, Koki Wang, Yibo Chang, Junhan Yuan, Fengbo Bore, Sigbjørn Løland Cai, Chun Lin, Yinnian Wang, Bo Xu, Jiayan Zhu, Jia-Xin Luo, Chenxing Zhang, Yuzhi Goodall, Rhys E.A. Liang, Wenshuo Singh, Anurag Kumar Yao, Sikai Zhang, Jingchao Wentzcovitch, Renata Han, Jiequn Liu, Jie Jia, Weile York, Darrin M. Weinan, E. Car, Roberto Zhang, Linfeng Wang, Han Laboratory for Biomolecular Simulation Research Institute for Quantitative Biomedicine Department of Chemistry and Chemical Biology Rutgers University PiscatawayNJ08854 United States AI for Science Institute Beijing100080 China DP Technology Beijing100080 China Academy for Advanced Interdisciplinary Studies Peking University Beijing100871 China HEDPS CAPT College of Engineering Peking University Beijing100871 China College of Electrical and Information Engineering Hunan University Changsha China Yuanpei College Peking University Beijing100871 China Program in Applied and Computational Mathematics Princeton University PrincetonNJ08540 United States Department of Experimental Physics Comenius University Mlynská Dolina F2 Bratislava842 48 Slovakia Center for Quantum Information Institute for Interdisciplinary Information Sciences Tsinghua University Beijing100084 China Center for Data Science Peking University Beijing100871 China ByteDance Research Zhonghang Plaza No. 43 North 3rd Ring West Road Haidian District Beijing China College of Chemistry and Molecular Engineering Peking University Beijing100871 China Baidu Inc. Beijing China Key Laboratory of Structural Biology of Zhejiang Province School of Life Sciences Westlake University Zhejiang Hangzhou China Westlake AI Therapeutics Lab Westlake Laboratory of Life Sciences and Biomedicine Zhejiang Hangzhou China Department of Chemistry Princeton University PrincetonNJ08544 United States SISSA Scuola Internazionale Superiore di Studi Avanzati Trieste34136 Italy Laboratory of Computational Science and Modeling Institute of Materials École Polytechnique Fédérale de Lausanne Lausanne1015 Switzerland Department of Physics National University of Defense Technology Hunan Changsha410073 China State Key Lab of Processors Institute of Computing Technology Chinese Academy of Sciences Beijing China University of Chinese Academy of Sciences Beijing China School of Electronics Engineerin

DeePMD-kit is a powerful open-source software package that facilitates molecular dynamics simulations using machine learning potentials (MLP) known as Deep Potential (DP) models. This package, which was released in 2017, has been widely used in the fields of physics, chemistry, biology, and material science for studying atomistic systems. The current version of DeePMD-kit offers numerous advanced features such as DeepPot-SE, attention-based and hybrid descriptors, the ability to fit tensile properties, type embedding, model deviation, Deep Potential - Range Correction (DPRc), Deep Potential Long Range (DPLR), GPU support for customized operators, model compression, non-von Neumann molecular dynamics (NVNMD), and improved usability, including documentation, compiled binary packages, graphical user interfaces (GUI), and application programming interfaces (API). This article presents an overview of the current major version of the DeePMD-kit package, highlighting its features and technical details. Additionally, the article benchmarks the accuracy and efficiency of different models and discusses ongoing developments. © 2023, CC BY-NC-ND.

关键词： Molecular dynamics

Multimodal Representation learning: Advances, Trends and Challenges

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Multimodal Representation Learning: Advances, Trends and Cha...

International Conference on machine learning and Cybernetics (ICMLC)

作者： Su-Fang Zhang Jun-Hai Zhai Bo-Jun Xie Yan Zhan Xin Wang Hebei Branch of China Meteorological Administration Training Center China Meteorological Administration Baoding China Hebei Key Laboratory of Machine Learning and Computational Intelligence College of Mathematics and Information Science Hebei University Baoding Hebei China

ISBN: (纸本)9781728128177

Representation learning is the base and crucial for consequential tasks, such as classification, regression, and recognition. The goal of representation learning is to automatically learning good features with deep models. Multimodal representation learning is a special representation learning, which automatically learns good features from multiple modalities, and these modalities are not independent, there are correlations and associations among modalities. Furthermore, multimodal data are usually heterogeneous. Due to the characteristics, multimodal representation learning poses many difficulties: how to combine multimodal data from heterogeneous sources; how to jointly learning features from multimodal data; how to effectively describe the correlations and associations, etc. These difficulties triggered great interest of researchers along with the upsurge of deep learning, many deep multimodal learning methods have been proposed by different researchers. In this paper, we present an overview of deep multimodal learning, especially the approaches proposed within the last decades. We provide potential readers with advances, trends and challenges, which can be very helpful to researchers in the field of machine, especially for the ones engaging in the study of multimodal deep machine learning.

关键词： Multimodal Representation learning machine learning Deep learning Multimodal deep learning learning machine learning Artificial Intelligence AUTOMATIC Association (Psychology)

An Acceleration Method for Computing Dominace Classes in Ordered Information System

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An Acceleration Method for Computing Dominace Classes in Ord...

International Conference on machine learning and Cybernetics (ICMLC)

作者： Yan Li Jing Zhang Qiang He Siyuan Liu Lujing Huo School of Applied Mathematics Beijing Normal University Zhuhai Zhuhai China Hebei Key Laboratory of Machine Learning and Computational Intelligence College of Mathematics and Information Science Hebei University Baoding Hebei China School of Science Beijing University of Civil Engineering and Architecture Beijing China

ISBN: (纸本)9781728128177

In rough set theory, two crisp sets (i.e., the lower and upper approximates of a target concept) is used to describe uncertainties in given information systems. However, the traditional rough set models are built based on equivalence relations which do not consider the preference relationship of attribute values. Dominance relation-based rough set approach effectively solve this problem which uses dominance relations to substitute equivalence relations to deal with ordered data. In this kind of approach, the computing of dominance class is a necessary step to attribute reduction which is very time-consuming. In order to reduce the computational cost in calculating dominance classes, this paper presents a method to compute dominance classes by gradually reducing the search space in the domain. The corresponding algorithm is proposed. In each step of the algorithm, the inferior classes of the objects in a given information system are removed in the universe with the increase of the attributes. Experiments using six UCI data show that the proposed method improves the efficiency of computing dominance classes with the increasing of attributes and objects.

关键词： Rough set Dominance relation Dominance class Rough sets Computer based information systems Equivalence relation dominance ordered data acceleration information Classes

Rotation Based Ensemble of One-Class Support Vector machines

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Rotation Based Ensemble of One-Class Support Vector Machines

International Conference on machine learning and Cybernetics (ICMLC)

作者： Wei-Tao Liu Hong-Jie Xing Key Laboratory of Machine Learning and Computational Intelligence College of Mathematics and Information Science Hebei University Baoding China

ISBN: (纸本)9781538652152

One-class support vector machine (OCSVM) is regarded as an important one-class classification method for tackling the problem of extreme class imbalance. However, combining several OCSVMs by the traditional ensemble approaches may not improve the performance of the single OCSVM because it is known as a strong classifier. In the paper, a rotation based ensemble method is proposed for integrating OCSVMs., The training data of different OCSVMs in the ensemble is transformed by different rotation matrices. Therefore, the diversity of training data for the ensemble of OCSVMs can be guaranteed. Experiments conducted on ten benchmark data sets to validate the effectiveness of the proposed ensemble strategy.

关键词： Training Support vector machines Training data Bagging Principal component analysis Forestry Diversity reception

Locality Correlation Preserving Based One-Class Support Vector machine 29

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Locality Correlation Preserving Based One-Class Support Vect...

第29届中国控制与决策会议

作者： Jian-Di Chang Hong-Jie Xing Key Laboratory of Machine Learning and Computational Intelligence College of Mathematics and Information ScienceHebei University

ISBN: (纸本)9781509046584

In order to fully utilize the local geometric information of the given training set consisting of the normal data,locality correlation preserving(LCP) is introduced into the traditional one-class support vector machine(OCSVM).The proposed method,named as locality correlation preserving based one-class support vector machine(LCP-OCSVM),inherits the merits of LCP and *** can keep locality correlation of the normal data and margin maximization between the normal data and the origin in the high-dimensional feature *** results on one synthetic data set and ten benchmark data sets demonstrate that the proposed method is superior to the traditional OCSVM and two related approaches.

关键词： Locality Correlation Preserving One-Class Support Vector machine One-Class Classification Local Geometric Structure

Adaptive-weighted One-Class Support Vector machine for Outlier Detection 29

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Adaptive-weighted One-Class Support Vector Machine for Outli...

第29届中国控制与决策会议

作者： Man Ji Hong-Jie Xing Key Laboratory of Machine Learning and Computational Intelligence College of Mathematics and Information ScienceHebei University

ISBN: (纸本)9781509046584

The classification performances of the traditional one-class support vector machine(OCSVM) and its variants are often not satisfying when outliers are *** deal with this case,assigning smaller weights to these outliers may alleviate their influence upon the classification boundary and enhance the robustness of *** this paper,a novel adaptive-weighted one-class support vector machine(AWOCSVM) is proposed for dealing with the outlier detection *** appropriate weights are assigned to training samples by considering both their local densities and distances between them to their *** results on two synthetic data sets and eight benchmark data sets demonstrate that the proposed AWOCSVM achieves more compact classification boundary and superior performance in comparison with the traditional OCSVM and one related approach.

关键词： One-Class Support Vector machine Classification Boundary Weighted One-Class Support Vector machine Support Vector machine

Uplink-downlink duality between multiple-access and broadcast channels with compressing relays

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arXiv 2020年

作者： Liu, Liang Liu, Ya-Feng Patil, Pratik Yu, Wei the Department of Electronic and Information Engineering The Hong Kong Polytechnic University Hong Kong the State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China The Edward S. Rogers Sr. Department of Electrical and Computer Engineering the University of Toronto the Department of Statistics and Data Science and the Machine Learning Department Carnegie Mellon University PittsburghPA15213 United States The Edward S. Rogers Sr. Department of Electrical and Computer Engineering University of Toronto 10 King’s College Road TorontoONM5S3G4 Canada

—Uplink-downlink duality refers to the fact that under a sum-power constraint, the capacity regions of a Gaussian multiple-access channel and a Gaussian broadcast channel with Hermitian transposed channel matrices are identical. This paper generalizes this result to a cooperative cellular network, in which remote access-points are deployed as relays in serving the users under the coordination of a central processor (CP). In this model, the users and the relays are connected over noisy wireless links, while the relays and the CP are connected over noiseless but rate-limited fronthaul links. Based on a Lagrangian technique, this paper establishes a duality relationship between such a multiple-access relay channel and broadcast relay channel, under the assumption that the relays use compression-based strategies. Specifically, we show that under the same total transmit power constraint and individual fronthaul rate constraints, the achievable rate regions of the Gaussian multiple-access and broadcast relay channels are identical, when either independent compression or Wyner-Ziv and multivariate compression strategies are used. The key observations are that if the beamforming vectors at the relays are fixed, the sum-power minimization problems under the achievable rate and fronthaul constraints in both the uplink and the downlink can be transformed into either a linear programming or a semidefinite programming problem depending on the compression technique, and that the uplink and downlink problems are Lagrangian duals of each other. Moreover, the dual variables corresponding to the downlink rate constraints become the uplink powers;the dual variables corresponding to the downlink fronthaul constraints become the uplink quantization noises. This duality relationship enables an efficient algorithm for optimizing the downlink transmission and relaying strategies based on the uplink. Copyright © 2020, The Authors. All rights reserved.

关键词： Linear programming