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Spectral Gap of the Largest Eigenvalue of the Normalized Graph Laplacian

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Communications in mathematics and Statistics 2022年第3期10卷 371-381页

作者： Jürgen Jost Raffaella Mulas Florentin Münch max planck institute for mathematics in the sciences LeipzigGermany

We offer a new method for proving that the maxima eigenvalue of the normalized graph Laplacian of a graph with n vertices is at least n+1/n−1 provided the graph is not complete and that equality is attained if and only if the complement graph is a single edge or a complete bipartite graph with both parts of size n−1/*** the same method,we also prove a new lower bound to the largest eigenvalue in terms of the minimum vertex degree,provided this is at most n−1/2.

关键词： Spectral graph theory Normalized Laplacian Largest eigenvalue Sharp bounds

PREDICTIVE MODELS AND GENERATIVE COMPLEXITY

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Journal of Systems Science & Complexity 2012年第1期25卷 30-45页

作者： Wolfgang LHR max planck institute for mathematics in the sciences Inselstraβe 22D-04103 LeipziqGermany

The causal states of computational mechanics define the minimal sufficient memory for a given discrete stationary stochastic process. Their entropy is an important complexity measure called statistical complexity （or true measure complexity）. They induce the s-machine, which is a hidden Markov model （HMM） generating the process. But it is not the minimal one, although generative HMMs also have a natural predictive interpretation. This paper gives a mathematical proof of the idea that the s-machine is the minimal HMM with an additional （partial） determinism condition. Minimal internal state entropy of a generative HMM is in analogy to statistical complexity called generative complexity. This paper also shows that generative complexity depends on the process in a nice way. It is, as a function of the process, lower semi-continuous （w.r.t. weak-, topology）, concave, and behaves nice under ergodic decomposition of the process.

关键词： Causal states complexity s-machine generative complexity HMM partially deterministicHMM predictive model statistical.

Concurrence,tangle and fully entangled fraction

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Chinese Physics B 2010年第9期19卷 161-167页

作者：李明费少明李先清 College of mathematics and Computational Science China University of Petroleum Department of mathematics Capital Normal University max-planck-institute for mathematics in the sciences

We show that although we cannot distil a singlet frora many pairs of bound entangled states, the concurrence and the tangle of two entangled quantum states are always strictly larger than those of one of them, even both entangled quantum states are bound entangled. We present a relation between the concurrence and the fidelity of optimal teleportation. We also give new upper and lower bounds for concurrence and tangle.

关键词： concurrence entanglement teleportation

Time optimal quantum control of two-qubit systems

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Science China(Physics,Mechanics & Astronomy) 2013年第11期56卷 2116-2121页

作者： LI Bin YU ZuHuan FEI ShaoMing LI-JOST XianQing School of Mathematical sciences Capital Normal University School of mathematics and Statistics Northeast Normal University max-planck-institute for mathematics in the sciences

We study the optimal quantum control of heteronuclear two-qubit systems described by a Hamiltonian containing both nonlocal internal drift and local control *** derive an explicit formula to compute the minimum time required to steer the system from an initial state to a specified final *** applications the minimal time to implement Controlled-NOT gate,SWAP gate and Controlled-U gate is calculated in *** experimental realizations of these quantum gates are explicitly presented.

关键词： time optimal quantum control heteronuclear two-spin system local invariants

Variational Characterization of Multitype Galton-Watson Branching Processes

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Acta Mathematicae Applicatae Sinica 2014年第1期30卷 27-36页

作者： Ying Wang max-planck-institute for mathematics in the sciences Academy of mathematics and Systems Science Chinese Academy of Sciences Warwick Systems Biology Centre University of Warwick

In this paper, we give a variational characterization for the growth rate of a multitype population modelled by a multitype Galton-Watson branching process. In particular, the so-called retrospective process plays an important role in the description of the equilibrium state used in the variational characterization. We define the retrospective process associated with a multitype Galton-Watson branching process and identify it with the mutation process describing the type evolution along typical lineages of the multitype Galton-Watson branching process.

关键词： multitype branching processes retrospective processes variational analysis equilibrium states large deviations

Effects of Variant Rates and Noise on Epidemic Spreading

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Chinese Physics Letters 2011年第5期28卷 282-284页

作者： LI Wei GAO Zong-Mao GU Jiao Complexity Science Center and institute of Particle Physics Huazhong Normal UniversityWuhan 430079 max-planck-institute for mathematics in the sciences

We introduce variant rates,for both infection and recovery and noise into the susceptible-infected-removed(SIR)modelfor epidemic *** changing rates are taken mainly due to the changing profiles of an epidemic during its ***,the noise parameter which is taken from a given distribution,*** can describe the fluctuations of the infection and recovery *** numerical simulations show that the SIR model with variant rates and noise and can improve the fitting with real SARS data in the near-stationary stage.

关键词： evolution infection epidemic

Parameterized monogamy and polygamy relations of multipartite entanglement

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Chinese Physics B 2023年第12期32卷 231-240页

作者：沈中喜王珂珂费少明 School of Mathematical sciences Capital Normal UniversityBeijing 100048China max-planck-institute for mathematics in the sciences Leipzig 04103Germany

Monogamy and polygamy relations are important properties of entanglement,which characterize the entanglement distribution of multipartite *** explore monogamy and polygamy relations of entanglement in multipartite systems by using two newly derived parameterized mathematical inequalities,and establish classes of parameterized monogamy and polygamy relations of multiqubit entanglement in terms of concurrence and entanglement of *** show that these new parameterized monogamy and poelygamy inequalities are tighter than the existing ones by detailed examples.

关键词： monogamy polygamy concurrence entanglement of formation

Lower Bound of Concurrence Based on Generalized Positive Maps

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Communications in Theoretical Physics 2013年第12期60卷 663-666页

作者：秦慧慧费少明 Department of mathematics School of Science South China University of Technology School of Mathematical sciences Capital Normal University max-planck-institute for mathematics in the sciences

We study the concurrence of arbitrary dimensional bipartite quantum systems. By using a positive but not completely positive map, we present an anaJytical lower bound of concurrence. Detailed examples are used to show... 详细信息

关键词： lower bound of concurrence positive maps

Nonlocality of Two-Qubit and Three-Qubit Schmidt-Correlated States

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Communications in Theoretical Physics 2011年第8期56卷 253-257页

作者：赵明镜李宗国李波费少明王志玺李先清 School of Mathematical sciences Capital Normal University College of Science Tianjin University of Technology max-planck-institute for mathematics in the sciences

We investigate the nonlocality of Schmidt-correlated （SC） states, and present analytical expressions of the maximum violation value of Bell inequalities. It is shown that the violation of Clauser-Horne-Shimony-Holt （CHSH） inequality is necessary and sufficient for the nonlocality of two-qubit SC states, whereas the violation of the Svetlichny inequaJity is only a sumcient condition for the genuine nonlocality of three-qubit SC states. Furthermore, the relations among the maximum violation values, concurrence, and relative entropy entanglement are discussed.

关键词： separability entanglement Bell inequality