Hybrid Precoding Based on Non-Uniform Quantization Codebook to Reduce Feedback Overhead in Millimeter Wave MIMO Systems

In this paper, we focus on the design of the hybrid analog/digital precoding in millimeter wave multiple-input multiple-output (MIMO) systems. To reduce the feedback overhead, we propose two non-uniform quantization (NUQ) codebook based hybrid precoding schemes for two main hybrid precoding implementations, i.e., the full-connected structure and the sub-connected structure. Specifically, we firstly group the angles of the arrive/departure (AOAs/AODs) of the scattering paths into several spatial lobes by exploiting the sparseness property of the millimeter wave in the angular domain, which divides the total angular domain into effective spatial lobes' coverage angles and ineffective coverage angles. Then, we map the quantization bits non-uniformly to different coverage angles and construct NUQ codebooks, where high numbers of quantization bits are employed for the effective coverage angles to quantize AoAs/AoDs and zero quantization bit is employed for ineffective coverage angles. Finally, two low-complexity hybrid analog/digital precoding schemes are proposed based on NUQ codebooks. Simulation results demonstrate that, the proposed two NUQ codebook based hybrid precoding schemes achieve near-optimal spectral efficiencies and show the superiority in reducing the feedback overhead compared with the uniform quantization (UQ) codebook based works, e.g., at least 12.5% feedback overhead could be reduced for a system with 144/36 transmitting/receiving antennas.Comment: 29 pages, 12 figure

Localized nonlinear waves of the three-component coupled Hirota equation by the generalized Darboux transformation

In this paper, We extend the two-component coupled Hirota equation to the three-component one, and reconstruct the Lax pair with $4\times4$ matrixes of this three-component coupled system including higher-order effects such as third-order dispersion, self-steepening and delayed nonlinear response. Combining the generalized Darboux transformation and a specific vector solution of this $4\times4$ matrix spectral problem, we study higher-order localized nonlinear waves in this three-component coupled system. Then, the semi-rational and multi-parametric solutions of this system are derived in our paper. Owing to these more free parameters in the interactional solutions than those in single- and two-component Hirota equation, this three-component coupled system has more abundant and fascinating localized nonlinear wave solutions structures. Besides, in the first- and second-order localized waves, we get a variety of new and appealing combinations among these three components $q_1, q_2$ and $q_3$. Instead of considering various arrangements of the three potential functions, we consider the same combination as the same type solution. Moreover, the phenomenon that these nonlinear localized waves merge with each other observably, may appears by increasing the absolute values of two free parameters $\alpha, \beta$. These results further uncover some striking dynamic structures in multi-component coupled system

Synchronized Collective Behavior via Low-cost Communication

An important natural phenomenon surfaces that satisfactory synchronization of self-driven particles can be achieved via sharply reduced communication cost, especially for high density particle groups with low external noise. Statistical numerical evidence illustrates that a highly efficient manner is to distribute the communication messages as evenly as possible along the whole dynamic process, since it minimizes the communication redundancy. More surprisingly, it is discovered that there exist some abnormal regions where moderately decreasing the communication cost can even improve the synchronization performance. A phase diagram on the noise-density parameter space is given, where the dynamical behaviors can be divided into three qualitatively different phases: normal phase where better synchronization corresponds to higher communication cost, abnormal phase where moderately decreasing communication cost could even improve the synchronization, and the disordered phase where no coherence among individuals is observed.Comment: 4 pages, 4 figure

Predicting the evolution of complex networks via local information

Almost all real-world networks are subject to constant evolution, and plenty of evolving networks have been investigated to uncover the underlying mechanisms for a deeper understanding of the organization and development of them. Compared with the rapid expansion of the empirical studies about evolution mechanisms exploration, the future links prediction methods corresponding to the evolution mechanisms are deficient. Real-world information always contain hints of what would happen next, which is also the case in the observed evolving networks. In this paper, we firstly propose a structured-dependent index to strengthen the robustness of link prediction methods. Then we treat the observed links and their timestamps in evolving networks as known information. We envision evolving networks as dynamic systems and model the evolutionary dynamics of nodes similarity. Based on the iterative updating of nodes' network position, the potential trend of evolving networks is uncovered, which improves the accuracy of future links prediction. Experiments on various real-world networks show that the proposed index performs better than baseline methods and the spatial-temporal position drift model performs well in real-world evolving networks

Mixed interactions of localized waves in the three-component coupled derivative nonlinear Schr\"{o}dinger equations

The Darboux transformation of the three-component coupled derivative nonlinear Schr\"{o}dinger equations is constructed, based on the special vector solution elaborately generated from the corresponding Lax pair, various interactions of localized waves are derived. Here, we focus on the higher-order interactional solutions among higher-order rogue waves (RWs), multi-soliton and multi-breather. Instead of considering various arrangements among the three components $q_1$, $q_2$ and $q_3$, we define the same combination as the same type solution. Based on our method, these interactional solutions are completely classified into six types among these three components $q_1$, $q_2$ and $q_3$. In these six types interactional solutions, there are four mixed interactions of localized waves in three different components. In particular, the free parameters $\alpha$ and $\beta$ paly an important role in dynamics structures of the interactional solutions, for example, different nonlinear localized waves merge with each other by increasing the absolute values of $\alpha$ and $\beta$

Characterization of the stimulated excitation in a driven Bose-Einstein condensate

We apply the time-dependent generalized Hartree-Fock-Bogoliubov (td-GHFB) theory to describe the stimulated excitation driven by periodically modulating the interactions in a Bose-Einstein condensate (BEC). A comparison with the results calculated from the typical Bogoliubov approximation indicates that the additional interaction terms contributed by the excited modes play a significant role to explain the dynamics of the stimulating process. The td-GHFB model has not only painted a clear picture of the density wave propagation, but also partly explained the generation of the second order harmonic of the excited modes. The theoretical framework can be directly employed to study similar driven processes.Comment: 6 pages, comments are welcom

Exact solution of the pairing problem for spherical and deformed systems

There has been increasing interest in studying the Richardson model from which one can derive the exact solution for certain pairing Hamiltonians. However, it is still a numerical challenge to solve the nonlinear equations involved. In this paper we tackle this problem by employing a simple hybrid polynomial approach. The method is found to be robust and is valid for both deformed and nearly spherical nuclei. It also provides important and convenient initial guesses for spherical systems with large degeneracy. As an example, we apply the method to study the shape coexistence in neutron-rich Ni isotopes.Comment: 5 pages, 6 figure

Once for All: a Two-flow Convolutional Neural Network for Visual Tracking

One of the main challenges of visual object tracking comes from the arbitrary appearance of objects. Most existing algorithms try to resolve this problem as an object-specific task, i.e., the model is trained to regenerate or classify a specific object. As a result, the model need to be initialized and retrained for different objects. In this paper, we propose a more generic approach utilizing a novel two-flow convolutional neural network (named YCNN). The YCNN takes two inputs (one is object image patch, the other is search image patch), then outputs a response map which predicts how likely the object appears in a specific location. Unlike those object-specific approach, the YCNN is trained to measure the similarity between two image patches. Thus it will not be confined to any specific object. Furthermore the network can be end-to-end trained to extract both shallow and deep convolutional features which are dedicated for visual tracking. And once properly trained, the YCNN can be applied to track all kinds of objects without further training and updating. Benefiting from the once-for-all model, our algorithm is able to run at a very high speed of 45 frames-per-second. The experiments on 51 sequences also show that our algorithm achieves an outstanding performance

Darboux transformation of nonisospectral coupled Gross-Pitaevskii equation and its multi-component generalization

We extend one component Gross-Pitaevskii equation to two component coupled case with the damping term, linear and parabolic density profiles, then give the Lax pair and infinitely-many conservations laws of this coupled system. The system is nonautonomous, that is, it admits a nonisospectral linear eigenvalue problem. In fact, the Darboux transformation for this kind of inhomogeneous system which is essentially different from the isospectral case, we reconstruct the Darboux transformation for this coupled Gross-Pitaevskii equation. Multi nonautonomous solitons, one breather and the first-order rogue wave are also obtained by the Darboux transformation. When $\beta >0$, the amplitudes and velocities of solitons decay exponentially as $t$ increases, otherwise, they increase exponentially as $t$ increases. Meanwhile, the real part $Re(\xi_j)$'s~$(j=1,2,3,\dots)$ of new spectral parameters determine the direction of solitions' propagation and $\alpha$ affects the localization of solitons. Choosing $Re(\xi_1)=Re(\xi_2)$, the two-soliton bound state is obtained. From nonzero background seed solutions, we construct one nonautonomous breather on curved background and find that this breather has some deformations along the direction of $t$ due to the exponential decaying term. Besides, $\beta$ determines the degree of this curved background, if we set $\beta>0$, the amplitude of the breather becomes small till being zero as $t$ increases. Through taking appropriate limit about the breather, the first-order rogue wave can be acquired. Finally, we give multi-component generalization of Gross-Pitaevskii equation and its Lax pair with nonisospectral parameter, meanwhile, Darboux transformation about this multi-component generalization is also constructed

Dynamics of Generalized Nevanlinna Functions

In the early 1980's, computers made it possible to observe that in complex dynamics, one often sees dynamical behavior reflected in parameter space and vice versa. This duality was first exploited by Douady, Hubbard and their students in early work on rational maps. See \cite{DH,BH} for example. Here, we continue to study these ideas in the realm of transcendental functions. In \cite{KK1}, it was shown that for the tangent family, $\lambda \tan z$, the way the hyperbolic components meet at a point where the asymptotic value eventually lands on infinity reflects the dynamic behavior of the functions at infinity. In the first part of this paper we show that this duality extends to a much more general class of transcendental meromorphic functions that we call {\em generalized Nevanlinna functions} with the additional property that infinity is not an asymptotic value. In particular, we show that in "dynamically natural" one dimensional slices of parameter space, there are "hyperbolic-like" components with a unique distinguished boundary point whose dynamics reflect the behavior inside an asymptotic tract at infinity. Our main result is that {\em every} parameter point in such a slice for which the asymptotic value eventually lands on a pole is such a distinguished boundary point. In the second part of the paper, we apply this result to the families $\lambda \tan^p z^q$, $p,q \in \mathbb Z^+$, to prove that all hyperbolic components of period greater than $1$ are bounded.Comment: 31 pages, 3 figure