Imperfect targeted immunization in scale-free networks

Scale-free networks are prone to epidemic spreading. To provide cost-effective protection for such networks, targeted immunization was proposed to selectively immunize the hub nodes. In many real-life applications, however, the targeted immunization may not be perfect, either because some hub nodes are hidden and consequently not immunized, or because the vaccination simply cannot provide perfect protection. We investigate the effects of imperfect targeted immunization in scale-free networks. Analysis and simulation results show that there exists a linear relationship between the inverse of the epidemic threshold and the effectiveness of targeted immunization. Therefore, the probability of epidemic outbreak cannot be significantly lowered unless the protection is reasonably strong. On the other hand, even a relatively weak protection over the hub nodes significantly decreases the number of network nodes ever getting infected and therefore enhances network robustness against virus. We show that the above conclusions remain valid where there exists a negative correlation between nodal degree and infectiousness.     

Implementing a Multi-Qubit Quantum Phase Gate Encoded by Photonic Qubit

A protocol is proposed to implement a three-qubit phase gate for photonic qubits in a three-mode cavity. The idea can be extended to directly implement a N-qubit phase gate. We also show that the interaction time remains unchanged with the increasing number of qubits. In addition, the influence of cavity decay and atomic spontaneous emission on the gate fidelity and photon loss probability is also discussed by numerical calculation.     

Bose--Einstein Condensates with Two- and Three-Body Interactions in an Anharmonic Trap at Finite Temperature

The transition temperature, the depletion of the condensate atoms and the collective excitations of a Bose-Einstein condensation （BEC） with two- and three-body interactions in an anharmonic trap at finite temperature are studied in detail. By using the Popov version of the Hartree-Fock-Bogoliubov （HFB） approximation, an extended self-consistent model describing BEC with both two- and three-body interactions in a distorted harmonic potential at finite temperature is obtained and solved numerically. The results show that the transition temperature, the condensed atom number and the collective excitations are modified dramatically by the atomic three-body interactions and the distortion of the harmonic trap.     

Clockwise vs Counter-Clockwise I-V Hysteresis of Point-Contact Metal-Tip/Pr0.7 Ca0.3MnO3/Pt Devices

Metal-tip/Pr0.7Ca0.3MnO3/Pt devices possess two types of I-V hysteresis： clockwise vs counter clockwise depending on the tip materials. The criteria for categorization of these two types of devices can be simply based on whether the Gibbs free energy of oxidation for the metal tip is lower or higher than that of PCMO, respectively. While the clockwise hysteresis can be attributed to electric field induced oxidation/reduction, the counter clockwise hysteresis can be explained by oxygen vacancy migration in an electrical field. Alternating-current conductance spectra also reveal distinct hopping barriers between these two categories of devices at high resistive states.     

Locally Rotationally Symmetric Bianchi Type-I Model with Time Varying Λ Term

We investigate the locally rotationally symmetric (LRS) Bianchi type-I cosmological model for stiff matter and a vacuum solution with a cosmological term proportional to R^-m (R is the scale factor and m is a positive constant). The cosmological term decreases with time. We obtain that for both the cases the present universe is accelerating with a large fraction of cosmological density in the form of a cosmological term.     

Improved Quantum Evolutionary Computation Based on Particle SwarmOptimization and Two-Crossovers

A quantum evolutionary computation （QEC） algorithm with particle swarm optimization （PSO） and two-crossovers is proposed to overcome identified limitations. PSO is adopted to update the Q-bit automatically, and two-crossovers are applied to improve the convergence quality in the basic QEC model. This hybrid strategy can effectively employ both the ability to jump out of the local minima and the capacity of searching the global optimum. The performance of the proposed approach is compared with basic QEC on the standard unconstrained scalable benchmark problem that numerous hard combinatorial optimization problems can be formulated. The experimental results show that the proposed method outperforms the basic QEC quite significantly.     

Another Conserved Quantity by Mei Symmetry of Tzénoff Equation for Non-Holonomic Systems

As a direct result of Mei symmetry of the Ténoff equation for non-holonomic mechanical systems, another conserved quantity is studied. The expression and the determining equations of the above conserved quantity are also presented. Using this method, it is easier to find out conserved quantity than ever. In the last, an example is presented to illustrate applications of the new results.     

The Fractal Dimensions of Complex Networks

It is shown that many real complex networks share distinctive features, such as the small-world effect and the heterogeneous property of connectivity of vertices, which are different from random networks and regular lattices. Although these features capture the important characteristics of complex networks, their applicability depends on the style of networks. To unravel the universal characteristics many complex networks have in common, we study the fractal dimensions of complex networks using the method introduced by Shanker. We find that the average ＇density＇ （p（r ） ） of complex networks follows a better power-law function as a function of distance r with the exponent dl, which is defined as the fractal dimension, in some real complex networks. Furthermore, we study the relation between df and the shortcuts Nadd in small-world networks and the size N in regular lattices. Our present work provides a new perspective to understand the dependence of the fractal dimension df on the complex network structure.     

Entanglement Evolution of a Two-Qubit System beyond Rotating-Wave Approximation

Two noninteracting qubits, initially entangled in Bell states, are coupled to a one-mode cavity and evolve under its influence. The entanglement evolution of the two qubits is investigated beyond the rotating-wave approximation. It is shown that the counter-rotating wave terms have a great influence on the disentanglement behavior.     

Coarse-Grained Molecular Dynamics Simulation of a Red Blood Cell

A worm-like chain model based on a spectrin network is employed to study the biomechanics of red blood cells. Coarse-grained molecular dynamics simulations are performed to obtain a stable configuration free of external loadings. We also discuss the influence of two parameters： the average bending modulus and the persistence length. The change in shape of a malaria-infected red blood cell can contribute to the change in its molecular-based structure. As the persistence length of the membrane network in the infected red blood cell decreases, the deformability decreases and the biconcave shape is destroyed. The numerical results are comparable with previously reported experimental results. The coarse-grained model can be used to study the relationship between macro-mechanical properties and molecular-scale structures of cells.     

A Wide Band Strong Acoustic Absorption in a Locally Network Anechoic Coating

Composite materials with interpenetrating network structures usually exhibit unexpected merit due to the cooperative interaction. Locally resonant phononic crystals （LRPC） exhibit excellent sound attenuation performance based on a periodical arrangement of sound wave scatters. Inspired by the interpenetrating network structure and the LRPC concept, we develop a locally network anechoic coating （LNAC） that can achieve a wide band of underwater strong acoustic absorption. The experimental results show that the LNAC possesses an excellent underwater acoustic absorbing capacity in a wide frequency range. Moreover, in order to investigate the impact of the interpenetrating network structure, we fabricate a faultage structure sample and the network is disconnected by hard polyurethane （PU）. The experimental comparison between the LNAC and the fanltage structure sample shows that the interpenetrating network structure of the LNAC plays an important role in achieving a wide band strong acoustic absorption.     

Effect of Eliminating Edges on Robustness of Scale-Free Networks under Intentional Attack

We study the robustness of complex networks under edge elimination. We propose three different edge elimination strategies and investigate their effects on the robustness of scale-free networks under intentional attack. We show that deleting a proper fraction of edges connecting hub nodes and hub nodes can enhance the robustness of scale-free networks under intentional attack.     

Lattice Waves in Two-Dimensional Hexagonal Quantum Plasma Crystals

Lattice waves including a longitudinal wave and a transverse wave in two-dimensional hexagonal quantum plasma crystals are investigated by using the modified Debye-Hückel screening potential. It is shown that there exists an unstable region of lattice parameters, where the system will melt. The general dispersion relations are derived, and the waves propagating parallel to a primitive translation vector are discussed. We find that both the longitudinal and transverse waves are acoustic-like, and the longitudinal wave has a greater sound speed than that of the transverse wave in the long wavelength limit region.     

A Toy Model for Magnetic Field Configurations in Black Hole Accretion Discs

We discuss the feature of the magnetic field configuration arising from double counter oriented electric currentrings in the accretion disc around a Kerr black hole （BH）. We discuss the relevant physical quantities corresponding to this configuration： （1） the power and torque transferred by the large-scale magnetic field, （2） the angular momentum and energy fluxes transferred from the BIt to the inner disc, （3） the radiation flux from the disc. In addition, we discuss the possibility that the closed magnetic field anchored at the disc probably evolves to the open magnetic field, which is helpful to produce the jet from the disc.     

Raman Investigation of Sodium Titanate Nanotubes under Hydrostatic Pressures up to 26.9GPa

High pressure behavior of sodium titanate nanotubes （Na2Ti2O5） is investigated by Raman spectroscopy in a diamond anvil cell （DAC） at room temperature. The two pressure-induced irreversible phase transitions are observed under the given pressure. One occurs at about 4.2 GPa accompanied with a new Raman peak emerging at 834 cm-1 which results from the lattice distortion of the Ti-O network in titanate nanotubes. It can be can be assigned to Ti-O lattice vibrations within lepidocrocite-type （H0.7Ti1.825V0.175O4＆#12539;H2O）TiO6 octahedral host layers with V being vacancy. The structure of the nanotubes transforms to orthorhombic lepidocrocite structure. Another amorphous phase transition occurs at 16.7 GPa. This phase transition is induced by the collapse of titanate nanotubes. All the Raman bands shift toward higher wavenumbers with a pressure dependence ranging from 1.58-5.6 cm-1/GPa.     

Mechanical Properties and Anisotropy in PbWO4 Single Crystal

The mechanical properties of PbWO4 （PWO） crystals grown by the vertical Bridgman method are systematically investigated using the microindentation technique. In the present work, the Vickers microhardness Hν, fracture toughness Kc, yield strength σy and friability index Bi of PbWO4 crystals are measured. The Vickers microhardness Hν on the （100） wafer is about 140 MPa, which means that PWO is a little soft＇＇ scintillator. The anisotropy of mechanical properties is also investigated under a steady load of 0.5 kg. The （100） wafer of the crystal exhibits combined mechanical properties more excellent than those of （111） and （001） wafers, and the values of Kc, σy, and Bi are 0.538 MPa＆#12539;m1/2, 51.11 kg/mm2 and 284.96 νm-1/2, respectively.     

Immunization of susceptible-infected model on scale-free networks

In this paper, we investigate two major immunization strategies, random immunization and targeted immunization, of the susceptible-infected (SI) model on the Barabási-Albert (BA) networks. For the heterogeneous structure, the random strategy is quite ineffective if the vaccinated proportion is small, while the targeted one which prefers to vaccinate the individuals with the largest degree can sharply depress the epidemic spreading even only a tiny fraction of population are vaccinated. The analytical solution is also obtained, which can capture the trend of velocity change vs. the amount of vaccinated population.     

Periodic Wave of Epidemic Spreading in Community Networks

It was reported by Cummings ef al. [Nature 427 （2004） 344] that there are periodic waves in the spatiotemporal data of epidemics. For understanding the mechanism, we study the epidemic spreading on community networks by both the SIS model and the SIRS model. We find that with the increase of infection rate, the number of total infected nodes may be stabilized at a fixed point, oscillatory waves, and periodic cycles. Moreover, the epidemic spreading in the SIS model can be explained by an analytic map.     

Stability of the BA Network: a New Approach to Rigorous Proof

We propose a new approach to rigorously prove the existence of the steady-state degree distribution for the BA network. The approach is based on a vector Markov chain of vertex numbers in the network evolving process. This framework provides a rigorous theoretical basis for the rate equation approach which has been widely applied to many problems in the field of complex networks, e.g., epidemic spreading and dynamic synchronization.     

Comparison of immunization strategies in geographical networks

The epidemic spread and immunizations in geographically embedded scale-free (SF) and Watts-Strogatz (WS) networks are numerically investigated. We make a realistic assumption that it takes time which we call the detection time, for a vertex to be identified as infected, and implement two different immunization strategies: one is based on connection neighbors (CN) of the infected vertex with the exact information of the network structure utilized and the other is based on spatial neighbors (SN) with only geographical distances taken into account. We find that the decrease of the detection time is crucial for a successful immunization in general. Simulation results show that for both SF networks and WS networks, the SN strategy always performs better than the CN strategy, especially for more heterogeneous SF networks at long detection time. The observation is verified by checking the number of the infected nodes being immunized. We found that in geographical space, the distance preferences in the network construction process and the geographically decaying infection rate are key factors that make the SN immunization strategy outperforms the CN strategy. It indicates that even in the absence of the full knowledge of network connectivity we can still stop the epidemic spread efficiently only by using geographical information as in the SN strategy, which may have potential applications for preventing the real epidemic spread.