Conservation laws of some lattice equations

We derive infinitely many conservation laws for some multi-dimensionally consistent lattice equations from their Lax pairs. These lattice equations are the Nijhoff-Quispel-Capel equation, lattice Boussinesq equation, lattice nonlinear Schr\"{o}dinger equation, modified lattice Boussinesq equation, Hietarinta's Boussinesq-type equations, Schwarzian lattice Boussinesq equation and Toda-modified lattice Boussinesq equation

Bringing Reference Groups Back: Agent-based Modeling of the Spiral of Silence

The purpose of this study is threefold: first, to bring reference groups back into the framework of spiral of silence (SOS) by proposing an extended framework of dual opinion climate; second, to investigate the boundary conditions of SOS; third, to identify the characteristics of SOS in terms of spatial variation and temporal evolution. Modeling SOS with agent-based models, the findings suggest (1) there is no guarantee of SOS with reference groups being brought back; (2) Stable existence of SOS is contingent upon the comparative strength of mass media over reference groups; (3) SOS is size-dependent upon reference groups and the population; (4) the growth rate of SOS decreases over time. Thus, this research presents an extension of the SOS theory.Comment: 31 pages, 1 figur

Tracing the Attention of Moving Citizens

With the widespread use of mobile computing devices in contemporary society, our trajectories in the physical space and virtual world are increasingly closely connected. Using the anonymous smartphone data of $1 \times 10^5$ users in 30 days, we constructed the mobility network and the attention network to study the correlations between online and offline human behaviours. In the mobility network, nodes are physical locations and edges represent the movements between locations, and in the attention network, nodes are websites and edges represent the switch of users between websites. We apply the box-covering method to renormalise the networks. The investigated network properties include the size of box $l_B$ and the number of boxes $N(l_B)$. We find two universal classes of behaviours: the mobility network is featured by a small-world property, $N(l_B) \simeq e^{-l_B}$, whereas the attention network is characterised by a self-similar property $N(l_B) \simeq l_B^{-\gamma}$. In particular, with the increasing of the length of box $l_B$, the degree correlation of the network changes from positive to negative which indicates that there are two layers of structure in the mobility network. We use the results of network renormalisation to detect the community and map the structure of the mobility network. Further, we located the most relevant websites visited in these communities, and identified three typical location-based behaviours, including the shopping, dating, and taxi-calling. Finally, we offered a revised geometric network model to explain our findings in the perspective of spatial-constrained attachment.Comment: 15 pages, 8 figure

Coherent dynamics of a qubit-oscillator system in a noisy environment

We investigate the non-Markovian dynamics of a qubit-oscillator system embedded in a noisy environment by employing the hierarchical equations of motion approach. It is found that the decoherence rate of the whole qubit-oscillator-bath system can be significantly suppressed by enhancing the coupling strength between the qubit and the harmonic oscillator. Moreover, we find that the non-Markovian memory character of the bath is able to facilitate a robust quantum coherent dynamics in this qubit-oscillator-bath system. Our findings may be used to engineer some tunable coherent manipulations in mesoscopic quantum circuits

Predict Forex Trend via Convolutional Neural Networks

Deep learning is an effective approach to solving image recognition problems. People draw intuitive conclusions from trading charts; this study uses the characteristics of deep learning to train computers in imitating this kind of intuition in the context of trading charts. The three steps involved are as follows: 1. Before training, we pre-process the input data from quantitative data to images. 2. We use a convolutional neural network (CNN), a type of deep learning, to train our trading model. 3. We evaluate the model's performance in terms of the accuracy of classification. A trading model is obtained with this approach to help devise trading strategies. The main application is designed to help clients automatically obtain personalized trading strategies.Comment: 30 pages, 41 figure

Deriving conservation laws for ABS lattice equations from Lax pairs

In the paper we derive infinitely many conservation laws for the ABS lattice equations from their Lax pairs. These conservation laws can algebraically be expressed by means of some known polynomials. We also show that H1, H2, H3, Q1, Q2, Q3 and A1 equation in ABS list share a generic discrete Riccati equation.Comment: 16 page

The ργ∗→π(ρ)\rho \gamma^* \to \pi (\rho) transition form factors in the Perturbative QCD factorization approach

In this paper, we studied the $\rho \gamma^* \to \pi$ and $\rho\gamma^*\to \rho$ transition processes and made the calculations for the $\rho\pi$ transition form factor $Q^4 F_{\rho\pi}(Q^2)$ and the $\rho$ meson electromagnetic form factors, $F_{\rm LL, LT,TT}(Q^2)$ and $F_{1,2,3}(Q^2)$, by employing the perturbative QCD (PQCD) factorization approach. For the $\rho \gamma^* \to \pi$ transition, we found that the contribution to form factor $Q^4 F_{\rho\pi}(Q)$ from the term proportional to the distribution amplitude combination $\phi^T_{\rho}(x_1)\phi^P_{\pi}(x_2)$ is absolutely dominant, and the PQCD predictions for both the size and the $Q^2$-dependence of this form factor $Q^4 F_{\rho\pi}(Q^2)$ agree well with those from the extended ADS/QCD models or the light-cone QCD sum rule. For the $\rho \gamma^* \to \rho$ transition and in the region of $Q^2\geq 3$ GeV$^2$, further more, we found that the PQCD predictions for the magnitude and their $Q^2$-dependence of the $F_1(Q^2)$ and $F_2(Q^2)$ form factors agree well with those from the QCD sum rule, while the PQCD prediction for $F_3(Q^2)$ is much larger than the one from the QCD sum rule.Comment: 11 pages, 3 figure

On the classification of fractal squares

In \cite{LaLuRa13}, the authors completely classified the topological structure of so called {\it fractal square} $F$ defined by $F=(F+{\mathcal D})/n$, where ${\mathcal{D}}\subsetneq\{0,1,\dots,n-1\}^2, n\ge 2$. In this paper, we further provide simple criteria for the $F$ to be totally disconnected, then we discuss the Lipschitz classification of $F$ in the case $n=3$, which is an attempt to consider non-totally disconnected sets.Comment: 16 pages, 12 figure

Tune-out wavelengths for the alkaline earth atoms

The lowest 3 tune-out wavelengths of the four alkaline-earth atoms, Be, Mg, Ca and Sr are determined from tabulations of matrix elements produced from large first principles calculations. The tune-out wavelengths are located near the wavelengths for $^3P^o_1$ and $^1P^o_1$ excitations. The measurement of the tune-out wavelengths could be used to establish a quantitative relationship between the oscillator strength of the transition leading to existence of the tune-out wavelength and the dynamic polarizability of the atom at the tune-out frequency. The longest tune-out wavelengths for Be, Mg, Ca, Sr, Ba and Yb are 454.9813 nm, 457.2372 nm, 657.446 nm, 689.200 nm, 788.875 nm and 553.00 nm respectively

Signature Design of Sparsely Spread CDMA Based on Superposed Constellation Distance Analysis

Sparsely spread code division multiple access (SCDMA) is a non-orthogonal superposition coding scheme that permits a base station simultaneously communicates with multiple users over a common channel. The detection performance of an SCDMA system is mainly determined by its signature matrix, which should be sparse to guarantee large Euclidean distance for the equivalent signal constellation after spreading and superposition. Good signature matrices that perform well under both belief prorogation and the maximum likelihood detections are designed. The proposed design applies to several similar well-documented schemes, including trellis code multiple access (TCMA), low density spreading, and superposition modulation systems.Comment: Submitted to IEEE Transactions on Information Theor