The Precise Formula in a Sine Function Form of the norm of the Amplitude and the Necessary and Sufficient Phase Condition for Any Quantum Algorithm with Arbitrary Phase Rotations

In this paper we derived the precise formula in a sine function form of the norm of the amplitude in the desired state, and by means of he precise formula we presented the necessary and sufficient phase condition for any quantum algorithm with arbitrary phase rotations. We also showed that the phase condition: identical rotation angles, is a sufficient but not a necessary phase condition.Comment: 16 pages. Modified some English sentences and some proofs. Removed a table. Corrected the formula for kol on page 10. No figure

A General SU(2) Formulation for Quantum Searching with Certainty

A general quantum search algorithm with arbitrary unitary transformations and an arbitrary initial state is considered in this work. To serach a marked state with certainty, we have derived, using an SU(2) representation: (1) the matching condition relating the phase rotations in the algorithm, (2) a concise formula for evaluating the required number of iterations for the search, and (3) the final state after the search, with a phase angle in its amplitude of unity modulus. Moreover, the optimal choices and modifications of the phase angles in the Grover kernel is also studied.Comment: 8 pages, 2 figure

Fidelity susceptibility in the two-dimensional spin-orbit models

We study the quantum phase transitions in the two-dimensional spin-orbit models in terms of fidelity susceptibility and reduced fidelity susceptibility. An order-to-order phase transition is identified by fidelity susceptibility in the two-dimensional Heisenberg XXZ model with Dzyaloshinsky-Moriya interaction on a square lattice. The finite size scaling of fidelity susceptibility shows a power-law divergence at criticality, which indicates the quantum phase transition is of second order. Two distinct types of quantum phase transitions are witnessed by fidelity susceptibility in Kitaev-Heisenberg model on a hexagonal lattice. We exploit the symmetry of two-dimensional quantum compass model, and obtain a simple analytic expression of reduced fidelity susceptibility. Compared with the derivative of ground-state energy, the fidelity susceptibility is a bit more sensitive to phase transition. The violation of power-law behavior for the scaling of reduced fidelity susceptibility at criticality suggests that the quantum phase transition belongs to a first-order transition. We conclude that fidelity susceptibility and reduced fidelity susceptibility show great advantage to characterize diverse quantum phase transitions in spin-orbit models.Comment: 11 pages. 11 figure

Magnetic Field Effect on the Phase Transition in AdS Soliton Spacetime

We investigate the scalar perturbations in an AdS soliton background coupled to a Maxwell field via marginally stable modes. In the probe limit, we study the magnetic field effect on the holographic insulator/superconductor phase transition numerically and analytically. The condensate will be localized in a finite circular region for any finite constant magnetic field. Near the critical point, we find that there exists a simple relation among the critical chemical potential, magnetic field, the charge and mass of the scalar field. This relation indicates that the presence of the magnetic field causes the phase transition hard.Comment: 15 pages, 3 figures, 2 tables. contents improved and references adde

Measurement-driven temporal analysis of information diffusion in online social networks

The rapid development of online social networks (OSN) renders them a popular mechanism for information diffusion. Studying the temporal characteristics is critical in understanding the diffusion process. However, due to the lack of well-defined propagation data, hardly any study addresses the temporal feature of information diffusion in OSN. In this paper, we present a measurement study on information diffusion in the Renren social network. We investigate the latency of information propagation along social links and define the 'activation time' for an OSN user, and find that the activation time follows the lognormal distribution. Based on this, we develop two new information diffusion models incorporating asynchronous activation times. Application of the models in the influence maximization problem shows that they capture the temporal diffusion behavior very well. This leads to fundamental ramifications to many related OSN applications. © 2012 IEEE.published_or_final_versio

Non-Gaussian Features of Transmitted Flux of QSO's Lyα\alpha Absorption: Intermittent Exponent

We calculate the structure function and intermittent exponent of the 1.) Keck data, which consists of 29 high resolution, high signal to noise ratio (S/N) QSO Ly$\alpha$ absorption spectra, and 2.)the Ly$\alpha$ forest simulation samples produced via the pseudo hydro scheme for the low density cold dark matter (LCDM) model and warm dark matter (WDM) model with particle mass $m_W=300, 600, 800$ and 1000 eV. These two measures detect not only non-gaussianities, but also the type of non-gaussianty in the the field. We find that, 1.) the structure functions of the simulation samples are significantly larger than that of Keck data on scales less than about 100 h$^{-1}$ kpc, 2.) the intermittent exponent of the simulation samples is more negative than that of Keck data on all redshifts considered, 3.) the order-dependence of the structure functions of simulation samples are closer to the intermittency of hierarchical clustering on all scales, while the Keck data are closer to a lognormal field on small scales. These differences are independent of noise and show that the intermittent evolution modeled by the pseudo-hydro simulation is substantially different from observations, even though they are in good agreement in terms of second and lower order statistics. (Abridged)Comment: 17 pages, 13 figures. Accepted by Ap

Experimental investigation on the enhancement of plenum window noise reduction using solid scatterers

The sound transmission across plenum windows installed with rigid non-resonant cylindrical scatterer arrays was investigated in detail using scale-down model measurements carried out inside a fully anechoic chamber. The arrays have manifested to some extent the acoustical behaviors of virtual sonic crystals. The maximum cross section blockage ratio was 0.6. The effects of plenum window gap, array configuration, and scatterer diameter on the sound transmission characteristics were also examined. Results indicate that the window cavity longitudinal modes and the gap modes control the sound transmission characteristics at low frequencies. The upper bound of this frequency range increases with decreasing gap width. Within this frequency range, the scatterers have negligible effect on the sound transmission. At higher frequencies, the array configurations with scatterer(s) attached to the window walls result in stronger sound reduction. There are relatively higher sound transmission loss improvements around the frequencies where a full bandgap is observed. There are wide bandgaps in various lattice directions, and the present results suggest that they play a role in the broadband improvement of sound reduction

Multi-Source-Driven Asynchronous Diffusion Model for Video-Sharing in Online Social Networks

Characterizing the video diffusion in online social networks (OSNs) is not only instructive for network traffic engineering, but also provides insights into the information diffusion process. A number of continuous-time diffusion models have been proposed to describe video diffusion under the assumption that the activation latency along social links follows a single parametric distribution. However, such assumption has not been empirically verified. Moreover, a user usually has multiple activated neighbors with different activation times, and it is hard to distinguish the different contributions of these multiple potential sources. To fill this gap, we study the multiple-source-driven asynchronous information diffusion problem based on substantial video diffusion traces. Specifically, we first investigate the latency of information propagation along social links and define the single-source (SS) activation latency for an OSN user. We find that the SS activation latency follows the exponential mixture model. Then we develop an analytical framework which incorporates the temporal factor and the influence of multiple sources to describe the influence propagation process. We show that one's activation probability decreases exponentially with time. We also show that the time shift of the exponential function is only determined by the most recent source (MRS) active user, but the total activation probability is the combination of influence exerted by all active neighbors. Based on these discoveries, we develop a multi-source-driven asynchronous diffusion model (MADM). Using maximum likelihood techniques, we develop an algorithm based on expectation maximization (EM) to learn model parameters, and validate our proposed model with real data. The experimental results show that the MADM obtains better prediction accuracy under various evaluation metrics.published_or_final_versio