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Categorification of Integrable Representations of Quantum Groups

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Acta Mathematica Sinica,English Series 2014年第6期30卷 899-932页

作者： hao zheng Department of Mathematics Zhongshan University School of Mathematical Sciences Peking University

We categorify the highest weight integrable representations and their tensor products of a symmetric quantum Kac–Moody algebra. As a byproduct, we obtain a geometric realization of Lusztig＇s canonical bases of these representations as well as a new positivity result. The main ingredient in the underlying geometric construction is a class of micro-local perverse sheaves on quiver varieties.

关键词： Categorification quantum groups canonical basis

Proof of the Volume Conjecture for Whitehead Doubles of a Family of Torus Knots

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Chinese Annals of Mathematics,Series B 2007年第4期28卷 375-388页

作者： hao zheng Department of Mathematics zhongshan University Guangzhou 510275 China

A technique to compute the colored Jones polynomials of satellite knots, illustrated by the Whitehead doubles of knots, is presented. Then the author proves the volume conjecture for Whitehead doubles of a family of t... 详细信息

关键词： Volume conjecture Whitehead double Torus knots Whitehead link

Design and Control of a Pneumatically Actuated Transtibial Prosthesis

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Journal of Bionic Engineering 2015年第2期12卷 217-226页

作者： hao zheng Xiangrong Shen Department of Mechanical Engineering University of Alabama 359 H.M. Comer Hall Box 870276 Tuscaloosa AL 35487-0276 USA

This paper presents the design and control of a pneumatically actuated transtibial prosthesis, which utilizes a pneumatic cylinder-type actuator to power the prosthetic ankle joint to support the user＇s locomotion. The pneumatic actuator has multiple advantages over the traditional electric motor, such as light weight, low cost, and high power-to-weight ratio. The objective of this work is to develop a compact and lightweight transtibial prosthesis, leveraging the multiple advantages provided by this highly competitive actuator. In this paper, the design details of the prosthesis are described, including the determination of performance specifications, the layout of the actuation mechanism, and the calculation of the torque capacity. Through the authors＇ design calculation, the prosthesis is able to provide sufficient range of motion and torque capacity to support the lo- comotion of a 75 Kg individual. The controller design is also described, including the underlying biomechanical analysis and the formulation of the finite-state impedance controller. The testing results of human subject indicate that the prosthesis is able to generate a natural walking gait and sufficient power output for its amputee user.

关键词： lower limb prosthesis powered prosthesis rehabilitation robotics assistive robotic devices

Facial expression recognition via weighted group sparsity

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Frontiers of Computer Science 2017年第2期11卷 266-275页

作者： hao zheng Xin GENG Key Laboratory of Trusted Cloud Computing and Big Data Analysis School of Information Engineering Nanjing Xiaozhuang University Nanjing 211171 China School of Computer Science and Engineering Southeast University Nanjing 211189 China

Considering the distinctiveness of different group features in the sparse representation, a novel joint multi- task and weighted group sparsity （JMT-WGS） method is pro- posed. By weighting popular group sparsity, not only the rep- resentation coefficients from the same class over their asso- ciate dictionaries may share some similarity, but also the rep- resentation coefficients from different classes have enough di- versity. The proposed method is cast into a multi-task frame- work with two-stage iteration. In the first stage, representa- tion coefficient can be optimized by accelerated proximal gra- dient method when the weights are fixed. In the second stage, the weights are computed via the prior information about their entropy. The experimental results on three facial expres- sion databases show that the proposed algorithm outperforms other state-of-the-art algorithms and demonstrate the promis- ing performance of the proposed algorithm.

关键词： facial expression recognition multi-task learning group sparsity

Categorical computation

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Frontiers of physics 2023年第2期18卷 181-187页

作者： Liang Kong hao zheng Shenzhen Institute for Quantum Science and Engineering Southern University of Science and TechnologyShenzhen 518055China International Quantum Academy Shenzhen 518048China Guangdong Provincial Key Laboratory of Quantum Science and Engineering Southern University of Science and TechnologyShenzhen 518055China Institute for Applied Mathematics Tsinghua UniversityBeijing 100084China Beijing Institute of Mathematical Sciences and Applications Beijing 101408China Department of Mathematics Peking UniversityBeijing 100871China

In quantum computing, the computation is achieved by linear operators in or between Hilbert spaces. In this work, we explore a new computation scheme, in which the linear operators in quantum computing are replaced by (higher) functors between two (higher) categories. If from Turing computing to quantum computing is the first quantization of computation, then this new scheme can be viewed as the second quantization of computation. The fundamental problem in realizing this idea is how to realize a (higher) functor physically. We provide a theoretical idea of realizing (higher) functors physically based on the physics of topological orders.

关键词： quantum computation categorical computation topological order

De-noising of radiation pressure signal generated by bubble oscillation based on ensemble empirical mode decomposition

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Journal of Hydrodynamics 2022年第5期34卷 849-863页

作者： Xiang-hao zheng Yu-ning Zhang Key Laboratory of Power Station Energy Transfer Conversion and System(Ministry of Education) School of EnergyPower and Mechanical EngineeringNorth China Electric Power UniversityBeijing102206China

The radiation pressure signals generated by the bubble oscillation are often utilized to recognize the characteristics of the target objects in many ***,these signals are easily contaminated by complex background *** order to accurately extract the effective components of the radiation pressure signal generated by the bubble oscillation,this paper proposes a de-noising procedure for the radiation pressure signal,based on the ensemble empirical mode decomposition(EEMD),the autocorrelation function and the modified wavelet soft-threshold de-noising *** order to verify the effectiveness of the procedure,the typical radiation pressure signal generated based on the Keller-Miksis model under the acoustic excitation is employed for the subsequent de-noising *** results of the qualitative analysis show that the amplitude and the period of the bubble oscillation can be clearly observed in the time-domain diagram of the de-noised signal based on the *** the quantitative analysis,the de-noised signal based on the EEMD has better performance with higher signal-to-noise ratio(SNR),smaller root-mean-square error,and larger correlation coefficient than that based on the wavelet transform(WT)and the empirical mode decomposition(EMD).Furthermore,with the increase of the complexity of the radiation pressure signal(e.g.,the increase of the dimensionless pressure amplitude of the acoustic wave and the decrease of the SNR of the input signal),the above three evaluation indexes of the de-noised signal based on the EEMD are all better than those based on the other two *** the signal is more complex,the de-noising capabilities of the WT,the EMD are greatly reduced,but the EEMD can still maintain the good de-noising capability,which shows the superiority of the signal de-noising procedure proposed in the present paper.

关键词： Radiation pressure cavitation bubble oscillation signal de-noising ensemble empirical mode decomposition(EEMD) autocorrelation function wavelet soft-threshold de-noising

Bumblebees with the socially transmitted microbiome:A novel model organism for gut microbiota research

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Insect Science 2022年第4期29卷 958-976页

作者： Zi-Jing Zhang hao zheng College of Food Science and Nutritional Engineering China Agricultural UniversityBeijingChina

Eusocial bumble and honey bees are important pollinators for global ecology and the agricultural *** both the bumble and honey bees possess similar and host-restricted gut microbiota,they differ in aspects of morphology,autonomy,physiology,behavior,and life *** social bee gut bacteria exhibit host specificity that is likely a result of long-term *** unique life cycle of bumblebees is key for the acquisition and development of their gut microbiota,and affects the strain-level diversity of the core bacterial *** on bumblebee gut bacteria show that they retain less functional capacity for carbohydrate metabolism compared with that of the *** discuss the potential roles of the bumblebee gut microbiota against pathogenic threats and the application of host-specific probiotics for *** the advantages of the bumblebee microbiome,including the simple structure and host specificity,and the ease of manipulating bumblebee colonies,we propose that bumblebees may provide a valuable system for understanding the general principles of host-microbe interactions,gut-brain axis,and vertical transmission.

关键词： bumblebee gut microbiota host-microbe interaction model organism

An Algorithm to Analyze Electron Backscatter Diffraction Data for Grain Reconstruction:from Methodology to Application

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Acta Metallurgica Sinica(English Letters) 2016年第5期29卷 491-499页

作者： Xue-hao zheng Hong-Wang Zhang Shenyang National Laboratory for Materials Science Institute of Metal Research Chinese Academy of Sciences National Engineering Research Center for Equipment and Technology of Cold Strip Rolling College of Mechanical Engineering Yanshan University

An algorithm for grain reconstruction based on electron backscatter diffraction data was proposed in this paper. This algorithm can well record the original data arrangement when an external file for the reconstructed grain（s） was exported for further post-processing. Assisted by an in-house MATLAB program, grain reconstruction, lattice rotations, orientation spreads, and slip system analysis can be performed. The validity of this algorithm has been successfully tested by polycrystalline Ni before and after channel die compression.

关键词： Grain reconstruction Algorithm Electron backscatter diffraction Deformation Nickle

Topological superconductivity in a Bi2Te3/NbSe2 heterostructure:A review

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Chinese Physics B 2019年第6期28卷 5-15页

作者： hao zheng Jin-Feng Jia School of Physics and Astronomy Shanghai Jiao Tong University

Topological superconductors carry globally protected gapless boundary excitations, which are robust under local perturbations, and thus exhibit both fundamental and applicational importance. An unconventional pairing with p-wave symmetry, such as a nontrivial topology in the superconductor’s wavefunction, is required to generate a non-zero Berry phase. Until now, the Bi2 Te3/2 H–NbSe2 heterostructure has proven to be a practical way to realize a topological superconductor in real materials. This complex system, where odd numbers of spin-momentum locked Dirac cone surface states on the topological insulator Bi2 Te3 become superconducting, induced by the proximate effect from the underlying s-wave superconductor 2 H–NbSe2, realizes an effective two-dimensional(2 D) spinless px + i py topological superconductor. In this review article, we summarize the recent experimental progress of the successful synthesis of Bi2 Te3/2 H–NbSe2 heterostructures using molecular beam epitaxy, determining the thickness limit of the heterostructure, detecting the long thought Majorana quasiparticle inside a magnetic vortex core state by means of scanning tunneling microscopy and demonstration of the unique spatial and spin properties of a Majorana zero mode.

关键词： topological insulator topological superconductor Majorana zero mode scanning tunneling microscopy molecular beam epitaxy