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How many weights can a linear code have?

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arXiv 2018年

作者： Shi, Minjia Zhu, Hongwei Solé, Patrick Cohen, Gérard D. Key Laboratory of Intelligent Computing & Signal Processing Ministry of Education Anhui University No. 3 Feixi Road Hefei Anhui Province230039 China School of Mathematical Sciences Anhui University Hefei230601 China CNRS/LAGA University of Paris 8 2 rue de la Liberté Saint-Denis93 526 France TelecomParisTech 46 rue Barrault Paris75 013 France

We study the combinatorial function L(k, q), the maximum number of nonzero weights a linear code of dimension k over Fq can have. We determine it completely for q = 2, and for k = 2, and provide upper and lower bounds in the general case when both k and q are ≥ 3. A refinement L(n, k, q), as well as nonlinear analogues N(M, q) and N(n, M, q), are also introduced and studied. Copyright © 2018, The Authors. All rights reserved.

关键词： Codes (symbols)

Quasi-cyclic perfect codes in Doob graphs and special partitions of Galois rings

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arXiv 2023年

作者： Shi, Minjia Li, Xiaoxiao Krotov, Denis S. Özbudak, Ferruh Key Laboratory of Intelligent Computing and Signal Processing Ministry of Education School of Mathematical Sciences Anhui University Hefei230601 China School of Mathematical Sciences Anhui University Hefei230601 China Sobolev Institute of Mathematics pr. Akademika Koptyuga 4 Novosibirsk630090 Russia Faculty of Engineering and Natural Sciences Sabancı University Middle East Technical University 34956 Istanbul Ankara06800 Turkey

The Galois ring GR(4∆) is the residue ring Z4[x]/(h(x)), where h(x) is a basic primitive polynomial of degree ∆ over Z4. For any odd ∆ larger than 1, we construct a partition of GR(4∆)\{0} into 6-subsets of type {a, b, −a−b, −a, −b, a+b} and 3-subsets of type {c, −c, 2c} such that the partition is invariant under the multiplication by a nonzero element of the Teichmuller set in GR(4∆) and, if ∆ is not a multiple of 3, under the action of the automorphism group of GR(4∆). As a corollary, this implies the existence of quasi-cyclic additive 1-perfect codes of index (2∆ − 1) in D((2∆ − 1)(2∆ − 2)/6, 2∆ − 1) where D(m, n) is the Doob metric scheme on Z2m+n .MSC Codes 94B99 Copyright © 2023, The Authors. All rights reserved.

关键词： Algebra

Erratum to: Multi-party quantum key agreement with Bell states and Bell measurements

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Quantum Information processing 2012年第2期12卷 933-933页

作者： Shi, Run-Hua Zhong, Hong Key Laboratory of Intelligent Computing & Signal Processing of Ministry of Education Anhui University Hefei China School of Computer Science and Technology Anhui University Hefei China

The Graph Structure of Chebyshev Permutation Polynomials over Ring pk

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arXiv 2022年

作者： Li, Chengqing Lu, Xiaoxiong Tan, Kai Chen, Guanrong The School of Computer Science Xiangtan University Hunan Xiangtan411105 China The School of Mathematics and Computational Science Xiangtan University Xiangtan411105 China The Key Laboratory of Intelligent Computing & Information Processing Ministry of Education Xiangtan University Hunan Xiangtan411105 China The Department of Electrical Engineering City University of Hong Kong Hong Kong

Understanding the underlying graph structure of a nonlinear map over a particular domain is essential in evaluating its potential for real applications. In this paper, we investigate the structure of the associated functional graph of Chebyshev permutation polynomials over a ring pk, with p being a prime number greater than three, where every number in the ring is considered as a vertex and the existing mapping relation between two vertices is regarded as a directed edge. Based on some new properties of Chebyshev polynomials and their derivatives, we disclose how the basic structure of the functional graph evolves with respect to parameter k. First, we present a complete and explicit form of the length of a path starting from any given vertex. Then, we show that the strong patterns of the functional graph that the number of cycles of any given length always remains constant as k increases. Moreover, we rigorously prove the rules on the elegant structure of the functional graph and verify them experimentally. Our results could be useful for studying the emergence of the complexity of a nonlinear map in digital computers and security analysis of its cryptographic *** Codes 94A55 Copyright © 2022, The Authors. All rights reserved.

关键词： Chebyshev polynomials

A2J-Transformer: Anchor-to-Joint Transformer Network for 3D Interacting Hand Pose Estimation from a Single RGB Image

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A2J-Transformer: Anchor-to-Joint Transformer Network for 3D ...

Conference on Computer Vision and Pattern Recognition (CVPR)

作者： Changlong Jiang Yang Xiao Cunlin Wu Mingyang Zhang Jinghong Zheng Zhiguo Cao Joey Tianyi Zhou Key Laboratory of Image Processing and Intelligent Control Ministry of Education School of Artificial Intelligence and Automation Huazhong University of Science and Technology Wuhan China Alibaba Group Centre for Frontier AI Research Agency for Science Technology and Research (A*STAR) Singapore Institute of High Performance Computing Agency for Science Technology and Research (A*STAR) Singapore

3D interacting hand pose estimation from a single RGB image is a challenging task, due to serious self-occlusion and inter-occlusion towards hands, confusing similar appearance patterns between 2 hands, ill-posed joint position mapping from 2D to 3D, etc.. To address these, we propose to extend A2J-the state-of-the-art depth-based 3D single hand pose estimation method-to RGB domain under interacting hand condition. Our key idea is to equip A2J with strong local-global aware ability to well capture interacting hands' local fine details and global articulated clues among joints jointly. To this end, A2J is evolved under Transformer's non-local encoding-decoding framework to build A2J- Transformer. It holds 3 main advantages over A2J. First, self-attention across local anchor points is built to make them global spatial context aware to better capture joints' articulation clues for resisting occlusion. Secondly, each anchor point is regarded as learnable query with adaptive feature learning for facilitating pattern fitting capacity, instead of having the same local representation with the others. Last but not least, anchor point locates in 3D space instead of 2D as in A2J, to leverage 3D pose prediction. Experiments on challenging InterHand 2.6M demonstrate that, A2J-Transformer can achieve state-of-the-art model-free performance (3.38mm MPJPE advancement in 2-hand case) and can also be applied to depth domain with strong generalization. The code is avaliable at https://***/ChanglongJiangGit/A2J-Transformer.

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CSCL-DTI: predicting drug-target interaction through cross-view and self-supervised contrastive learning

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CSCL-DTI: predicting drug-target interaction through cross-v...

IEEE International Conference on Bioinformatics and Biomedicine (BIBM)

作者： Xuan Lin Xi Zhang Zu-Guo Yu Yahui Long Xiangxiang Zeng Philip S. Yu College of Computer Science Xiangtan University China Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University China Singapore Immunology Network (SIgN) Agency for Science Technology and Research (A*STAR) Singapore College of Information Science and Engineering Hunan University China Department of Computer Science University of Illinois Chicago USA

ISBN: (数字)9798350386226

ISBN: (纸本)9798350386233

Accurately predicting drug-target interactions (DTI) is a critical step in drug discovery. Existing methods of DTI prediction primarily employ Simplified Molecular-Input Line-Entry System (SMILES) sequences or molecular graphs to learn drug representations. However, the features learned by such single-view approach is prone to incomplete. While some multiview methods that consider the views of both SMILES sequences and molecular graphs have been developed, these methods often fall in short in capturing potential interactions between views. In this work, we propose a novel dual contrastive learning framework CSCL-DTI for DTI prediction. First, we design a contrastive-enhanced cross-view representation learning (CVRL) to learn representations for drugs. In this module, Transformer-based and graph convolutional network (GCN)-based encoders are separately adopted to learn view-specific representations, followed by contrastive learning to enrich the representations by accounting for the potential interplay between local chemical context and topological structure. Second, we combine Transformer with self-supervised contrastive learning (SSCL) to learn representations for targets by modelling protein amino acids sequences. The scheme allows to effectively preserve the intrinsic characteristics of the sequences. Finally, we introduce a bilinear attention network to obtain an integrated representation by adaptively incorporating drug and target representations. Benchmarking experiments on two datasets demonstrated that CSCL-DTI 1 outperforms six state-of-the-art methods.

关键词： Drugs Proteins Representation learning Protein engineering Adaptation models Contrastive learning Predictive models Transformers Amino acids Diffusion tensor imaging

Error Analysis of Virtual Element Methods for the Time-dependent Poisson-Nernst-Planck Equations

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arXiv 2022年

作者： Yang, Ying Liu, Ya Shu, Shi School of Mathematics and Computational Science Guangxi Colleges Universities Key Laboratory of Data Analysis and Computation Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Guilin University of Electronic Technology Guangxi Guilin541004 China School of Mathematics and Computational Science Guilin University of Electronic Technology Guangxi Guilin541004 China School of Mathematics and Computational Science Xiangtan University Xiangtan411105 China

We discuss and analyze the virtual element method on general polygonal meshes for the time-dependent Poisson-Nernst-Planck equations, which are a nonlinear coupled system widely used in semiconductors and ion channels. The spatial discretization is based on the elliptic projection and the L2 projection operator, and for the temporal discretization, the backward Euler scheme is employed. After presenting the semi and fully discrete schemes, we derive the a priori error estimates in the L2 and H1 norms. Finally, a numerical experiment verifies the theoretical convergence results. Copyright © 2022, The Authors. All rights reserved.

关键词： Nonlinear equations

A Design of Hign Gain Wideband Circular Polarization Antenna Based on All-Metal Vivaldi Antenna

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Journal of Physics: Conference Series 2020年第1期1651卷

作者： Xuemei Li Zhixiang Huang Dui Liu Chao Wang Yi Cheng Key Lab of Intelligent Computing & Signal Processing Ministry of Education AnHui University AnHui University Heifei China AnHui 230000 China

This paper designs a broadband circularly polarized antenna covering the 25 GHz to 31 GHz band. The Vivaldi antenna is used as the basic structure to generate broadband electromagnetic waves; circular polarization is achieved by feeding through a circularly polarized bridge; a metal choke ring is used at the bottom to ensure the low side lobes of the antenna. The antenna consists of four basic Vivaldi antennas, a metal choke ring, a grounded substrate, and a feed network. The results show that the antenna covers the entire frequency band when the axial ratio is lower than 3 dB, and the impedance matching is better. The use of a choke ring structure ensures that the antenna electromagnetic waves are radiated upward, resulting in higher gain and lower side lobes. The highest gain in the included frequency band is 11.4 dB, and the simulation result is good. The antenna has high gain and low sidelobe characteristics.

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Compact Broadband Absorptive Bandstop Filter Based on Microstrip

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Journal of Physics: Conference Series 2020年第1期1651卷

作者： Qi Lu Xianliang Wu Chao Wang Key Lab of Intelligent Computing & Signal Processing Ministry of Education AnHui University AnHui University Heifei China AnHui 230000 China

A compact broadband absorptive band rejection filter (ABSF) based on microstrip line is proposed. The filter consists of a pair of coupled wires and is loaded with a resistor. The coupling line of the filter has an open stub. The transmission zero point can be adjusted by adjusting the width of the coupling line. The center frequency can be adjusted by changing the length of the intermediate coupling line. Absorption performance can be achieved through loaded resistors. In this way, the signal not input in the filter will be dissipated in the filter and will not be reflected. When F0=3.8 GHz, 26% of the 20 dB bandwidth covers 3.15 GHz-4.2 GHz, the rejection depth of the stopband is less than -40 dB, and the in-band absorption is less than -10 dB.

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