8,427 research outputs found

    Immunization for complex network based on the effective degree of vertex

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    The basic idea of many effective immunization strategies is first to rank the importance of vertices according to the degrees of vertices and then remove the vertices from highest importance to lowest until the network becomes disconnected. Here we define the effective degrees of vertex, i.e., the number of its connections linking to un-immunized nodes in current network during the immunization procedure, to rank the importance of vertex, and modify these strategies by using the effective degrees of vertices. Simulations on both the scale-free network models with various degree correlations and two real networks have revealed that the immunization strategies based on the effective degrees are often more effective than those based on the degrees in the initial network.Comment: 16 pages, 5 figure

    Effective Hamiltonian approach to the quantum phase transitions in the extended Jaynes-Cummings model

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    The study of phase transitions in dissipative quantum systems based on the Liouvillian is often hindered by the difficulty of constructing a time-local master equation when the system-environment coupling is strong. To address this issue, the complex discretization approximation for the environment is proposed to study the quantum phase transition in the extended Jaynes-Cumming model with an infinite number of boson modes. This approach yields a non-Hermitian effective Hamiltonian that can be used to simulate the dynamics of the spin. It is found that the ground state of this effective Hamiltonian determines the spin dynamics in the single-excitation subspace. Depending on the opening of the energy gap and the maximum population of excitations on the spin degree of freedom, three distinct phases can be identified: fast decaying, localized, and stretched dynamics of the spin. This approach can be extended to multiple excitations, and similar dynamics were found in the double-excitation subspace, indicating the robustness of the single-excitation phase.Comment: 12pages, published versio

    Reduced dynamics with renormalization in solid-state charge qubit measurement

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    Quantum measurement will inevitably cause backaction on the measured system, resulting in the well known dephasing and relaxation. In this report, in the context of solid--state qubit measurement by a mesoscopic detector, we show that an alternative backaction known as renormalization is important under some circumstances. This effect is largely overlooked in the theory of quantum measurement.Comment: 12 pages, 4 figure

    Complex Discretization approximation for the full dynamics of system-environment quantum models

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    The method of discretization approximation for the environment in continuum suffers from the recurrence, that makes the simulation of the open dynamics inefficient. In order to tackle this problem, the discretization approximation is generalized into the complex plane by introducing complex Gauss quadratures in this paper. The resulting effective Hamiltonian is thus non-Hermitian due to the dissipative dynamics of system. As illustrations, the open dynamics in two exactly solvable models, dephasing model and the single-excitation open dynamics in the generalized Aubry-Andr\'{e}-Harper model, is checked respectively by the method. It is found that the recurrence can be compressed greatly due to the occurrence of complex discrete modes in environment. Thus, the open dynamics in the two models can be simulated in high efficiency and precision.Comment: 13 pages. the statement has been improved and the references are updated. Comments are welcom

    Genome-wide linkage analysis for alcohol dependence: a comparison between single-nucleotide polymorphism and microsatellite marker assays

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    Both theoretical and applied studies have proven that the utility of single nucleotide polymorphism (SNP) markers in linkage analysis is more powerful and cost-effective than current microsatellite marker assays. Here we performed a whole-genome scan on 115 White, non-Hispanic families segregating for alcohol dependence, using one 10.3-cM microsatellite marker set and two SNP data sets (0.33-cM, 0.78-cM spacing). Two definitions of alcohol dependence (ALDX1 and ALDX2) were used. Our multipoint nonparametric linkage analysis found alcoholism was nominal linked to 12 genomic regions. The linkage peaks obtained by using the microsatellite marker set and the two SNP sets had a high degree of correspondence in general, but the microsatellite marker set was insufficient to detect some nominal linkage peaks. The presence of linkage disequilibrium between markers did not significantly affect the results. Across the entire genome, SNP datasets had a much higher average linkage information content (0.33 cM: 0.93, 0.78 cM: 0.91) than did microsatellite marker set (0.57). The linkage peaks obtained through two SNP datasets were very similar with some minor differences. We conclude that genome-wide linkage analysis by using approximately 5,000 SNP markers evenly distributed across the human genome is sufficient and might be more powerful than current 10-cM microsatellite marker assays
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