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Cycle-tree guided attack of random K-core: Spin glass model and efficient message-passing algorithm

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Science China(Physics,Mechanics & Astronomy) 2022年第3期65卷 33-38页

作者： hai-Jun zhou CAS Key Laboratory for Theoretical Physics Institute of Theoretical PhysicsChinese Academy of SciencesBeijing 100190China MinJiang Innovative Center for Theoretical Physics MinJiang UniversityFuzhou 350108China School of Physical Sciences University of Chinese Academy of SciencesBeijing 100049China

The K-core of a graph is the maximal subgraph within which each vertex is connected to at least K other vertices. It is a fundamental network concept for understanding threshold cascading processes with a discontinuous percolation transition. A minimum attack set contains the smallest number of vertices whose removal induces complete collapse of the K-core. Here we tackle this prototypical optimal initial-condition problem from the spin-glass perspective of cycle-tree maximum packing and propose a cycle-tree guided attack(CTGA) message-passing algorithm. The good performance and time efficiency of CTGA are verified on the regular random and Erd?s-Rényi random graph ensembles. Our central idea of transforming a long-range correlated dynamical process to static structural patterns may also be instructive to other hard optimization and control problems.

关键词： K-core collapse spin glass model tree packing optimal initial condition random graph

Weak Convergence Theorems for Strict Pseudo-contractions in Banach Spaces

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Acta Mathematica Sinica,English Series 2014年第5期30卷 755-766页

作者： hai Yun zhou Department of Mathematics Shijiazhuang Mechanical Engineering College

In this paper, it is shown that there is a gap in the paper [Chidume, C. E., Shahzad, N.： Weak convergence theorems for a finite family of strict pseudo-contractions. Nonlinear Anal., 72, 1257–1265（2010）], consequently, the main results of the paper do not hold in uniformly smooth Banach spaces. Meanwhile, it is also shown that the main results（Lemma 3.4, Theorems 3.5–3.6, 3.8–3.9） in the paper [Cholamjiak, P., Suantai, S.： Weak convergence theorems for a countable family of strict pseudo-contractions in Banach spaces. Fixed Point Theory Appl., 2010, Article ID 632137, 16 pages（2010）] do not hold in Lpfor p 〉 3. Finally, some modified results are presented in the setting of uniformly smooth and uniformly convex Banach spaces which include Lpfor p ≥ 2 as special cases. Furthermore, our arguments are also different from the ones given by the authors above.

关键词： Fr′echet differentiable Banach spaces Reich's inequality a countable family of λ-strict pseudo-contractions normal Mann iteration algorithm weak convergence theorems

Convergence Theorems for λ-strict Pseudo-contractions in q-uniformly Smooth Banach Spaces

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Acta Mathematica Sinica,English Series 2010年第4期26卷 743-758页

作者： hai Yun zhou College of Mathematics and Information Science Hebei Normal University Shijiazhuang 050016 P. R. China Department of Mathematics Shijiazhuang Mechanical Engineering College Shijiazhuang 050003 P. R. China

In this paper, we continue to discuss the properties of iterates generated by a strict pseudo- contraction or a finite family of strict pseudo-contractions in a real q-uniformly smooth Banach space. The results presented in this paper are interesting extensions and improvements upon those known ones of Marino and Xu [Marino, G., Xu, H. K.： Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces. J. Math. Anal. Appl., 324, 336-349 （2007）]. In order to get a strong convergence theorem, we modify the normal Mann＇s iterative algorithm by using a suitable convex combination of a fixed vector and a sequence in C. This result extends a recent result of Kim and Xu [Kim, T. H., Xu, H. K.： Strong convergence of modified Mann iterations. Nonl. Anal., 61, 51- 60 （2005）] both from nonexpansive mappings to λ-strict pseudo-contractions and from Hilbert spaces to q-uniformly smooth Banach spaces.

关键词： convergence theorem λ-strict pseudo-contraction the normal Mann iteration the Ishika- wa-like iteration q-uniformly smooth Banach spaces

On Tame Kernels and Ideal Class Groups

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Acta Mathematica Sinica,English Series 2007年第10期23卷 1807-1812页

作者： hai Yan zhou Department of Mathematics Nanjing University Nanjing 210093 P. R. China Institute of Mathematics School of Mathematics and Computer Sciences Nanjing Normal University Nanjing 210097 P. R. China

It is well known that there is a close connection between tame kernels and ideal class groups of number fields. However, the latter is a very difficult subject in number theory. In this paper, we prove some results connecting the p^n-rank of the tame kernel of a cyclic cubic field F with the p^n-rank of the coinvariants of μp^n×CI（δE,T） under the action of the Galois group, where E = F（ζp^n ） and T is the finite set of primes of E consisting of the infinite primes and the finite primes dividing p. In particular, if F is a cyclic cubic field with only one ramified prime and p = 3, n = 2, we apply the results of the tame kernels to prove some results of the ideal class groups of E, the maximal real subfield of E and F（ζ3）.

关键词： cyclic cubic fields tame kernels ideal class groups

Quantum transport in topological semimetals under magnetic fields (Ⅱ)

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Frontiers of physics 2019年第3期14卷 1-24页

作者： hai-Peng Sun hai-zhou Lu Department of Physics Harbin Institute of Technology Harbin 150001 China Shenzhen Institute for Quantum Science and Engineering and Department of Physics Southern University of Science and Technology Shenzhen 518055 China Shenzhen Key Laboratory of Quantum Science and Engineering Shenzhen 518055 China

We review our recent works on the quantum transport, mainly in topological semimetals and also in topological insulators, organized according to the strength of the magnetic field. At weak magnetic fields, we explain the negative magnetoresistance in topological semimetals and topological insulators by using the semiclassical equations of motion with the nontrivial Berry curvature. We show that the negative magnetoresistance can exist without the chiral anomaly. At strong magnetic fields, we establish theories for the quantum oscillations in topological Weyl, Dirac, and nodal-line semimetals. We propose a new mechanism of 3D quantum Hall effect, via the "wormhole" tunneling through the Weyl orbit formed by the Fermi arcs and Weyl nodes in topological semimetals. In the quantum limit at extremely strong magnetic fields, we find that an unexpected Hall resistance reversal can be understood in terms of the Weyl fermion annihilation. Additionally, in parallel magnetic fields, longitudinal resistance dips in the quantum limit can serve as signatures for topological insulators.

关键词： topological semimetai topological insulator quantum oscillation negative magne to resistance quantum Hall effect

Quantum transport in topological semimetals under magnetic fields (III)

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Frontiers of physics 2023年第2期18卷 63-87页

作者： Lei Shi hai-zhou Lu Shenzhen Institute for Quantum Science and Engineering and Department of Physics Southern University of Science and TechnologyShenzhen 518055China Shenzhen Key Laboratory of Quantum Science and Engineering Shenzhen 518055China

We review our most recent research on quantum transport,organizing the review according to the intensity of the magnetic field and focus mostly on topological semimetals and topological *** first describe the phenomenon of quantum transport when a magnetic field is not *** introduce the nonlinear Hall effect and its theoretical ***,we discuss Coulomb instabilities in 3D higher-order topological ***,we pay close attention to the surface states and find a function to identify the axion insulator in the antiferromagnetic topological insulator *** weak magnetic fields,we focus on the decaying Majorana oscillations which has the correlation with spin−orbit *** the section on strong magnetic fields,we study the helical edge states and the one-sided hinge states of the Fermi-arc mechanism,which are relevant to the quantum Hall *** extremely large magnetic fields,we derive a theoretical explanation of the negative magnetoresistance without a chiral ***,we show how magnetic responses can be used to detect relativistic ***,we introduce the 3D quantum Hall effect’s charge-density wave mechanism and compare it with the theory of 3D transitions between metal and insulator driven by magnetic fields.

关键词： topological semimetal topological insulator axion insulator nonlinear Hall effect(NHE) quantum oscillation quantum Hall effect(QHE) charge density wave(CDW)

3D quantum Hall effect

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National Science Review 2019年第2期6卷 208-210页

作者： hai-zhou Lu Shenzhen Institute for Quantum Science and Engineering and Department of Physics Southern University of Science and Technology (SUSTech) Shenzhen Key Laboratory of Quantum Science and Engineering

The discovery of the quantum Hall effect in 2D systems opens the door to topological phases of matter. A quantum Hall effect in three dimensions is a long-sought phase of matter and has inspired many efforts and claim... 详细信息

关键词： In quantum Hall effect

Active Online Learning in the Binary Perceptron Problem

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Communications in Theoretical Physics 2019年第2期71卷 243-252页

作者： hai-Jun zhou School of Physical Sciences University of Chinese Academy of SciencesBeijing 100049China

The binary perceptron is the simplest artificial neural network formed by N input units and one output unit, with the neural states and the synaptic weights all restricted to ±1 values. The task in the teacher-student scenario is to infer the hidden weight vector by training on a set of labeled patterns. Previous efforts on the passive learning mode have shown that learning from independent random patterns is quite inefficient. Here we consider the active online learning mode in which the student designs every new Ising training pattern. We demonstrate that it is mathematically possible to achieve perfect(error-free) inference using only N designed training patterns, but this is computationally unfeasible for large systems. We then investigate two Bayesian statistical designing protocols, which require 2.3N and 1.9N training patterns, respectively, to achieve error-free inference. If the training patterns are instead designed through deductive reasoning, perfect inference is achieved using N + log_2N samples. The performance gap between Bayesian and deductive designing strategies may be shortened in future work by taking into account the possibility of ergodicity breaking in the version space of the binary perceptron.

关键词： neural network perceptron online learning belief propagation statistical inference

Regularized canonical correlation analysis with unlabeled data

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2009年第4期10卷 504-511页

作者： Xi-chuan zhou hai-bin SHEN Institute of VLSI Design Zhejiang University Hangzhou 310027 China

In standard canonical correlation analysis (CCA), the data from definite datasets are used to estimate their canonical correlation. In real applications, for example in bilingual text retrieval, it may have a great portion of data that we do not know which set it belongs to. This part of data is called unlabeled data, while the rest from definite datasets is called labeled data. We propose a novel method called regularized canonical correlation analysis (RCCA), which makes use of both labeled and unlabeled samples. Specifically, we learn to approximate canonical correlation as if all data were labeled. Then, we describe a generalization of RCCA for the multi-set situation. Experiments on four real world datasets, Yeast, Cloud, Iris, and Haberman, demonstrate that, by incorporating the unlabeled data points, the accuracy of correlation coefficients can be improved by over 30%.

关键词： Canonical correlation analysis (CCA) Regularization Unlabeled data Generalized canonical correlation analysis(GCCA)