Notes on nonlocal dispersal equations in a periodic habitat

In this paper, we prove that the solution maps of a large class of nonlocal dispersal equations are $\alpha$-contractions, where $\alpha$ is the Kuratowski measure of noncompactness. Then we give some remarks on the spreading speeds and traveling waves for such evolution equations in a periodic habitat

Bistable Traveling Waves for Monotone Semiflows with Applications

This paper is devoted to the study of traveling waves for monotone evolution systems of bistable type. Under an abstract setting, we establish the existence of bistable traveling waves for discrete and continuous-time monotone semiflows. This result is then extended to the cases of periodic habitat and weak compactness, respectively. We also apply the developed theory to four classes of evolution systems

Traveling waves and spreading speeds for time-space periodic monotone systems

The theory of traveling waves and spreading speeds is developed for time-space periodic monotone semiflows with monostable structure. By using traveling waves of the associated Poincar\'e maps in a strong sense, we establish the existence of time-space periodic traveling waves and spreading speeds. We then apply these abstract results to a two species competition reaction-advection-diffusion model. It turns out that the minimal wave speed exists and coincides with the single spreading speed for such a system no matter whether the spreading speed is linearly determinate. We also obtain a set of sufficient conditions for the spreading speed to be linearly determinate.Comment: arXiv admin note: text overlap with arXiv:1410.459

Fidelity approach to quantum phase transitions: finite size scaling for quantum Ising model in a transverse field

We analyze the scaling parameter, extracted from the fidelity for two different ground states, for the one-dimensional quantum Ising model in a transverse field near the critical point. It is found that, in the thermodynamic limit, the scaling parameter is singular, and the derivative of its logarithmic function with respect to the transverse field strength is logarithmically divergent at the critical point. The scaling behavior is confirmed numerically by performing a finite size scaling analysis for systems of different sizes, consistent with the conformal invariance at the critical point. This allows us to extract the correlation length critical exponent, which turns out to be universal in the sense that the correlation length critical exponent does not depend on either the anisotropic parameter or the transverse field strength.Comment: 5 pages, 5 figure

Identifying a set of influential spreaders in complex networks

Identifying a set of influential spreaders in complex networks plays a crucial role in effective information spreading. A simple strategy is to choose top-$r$ ranked nodes as spreaders according to influence ranking method such as PageRank, ClusterRank and $k$-shell decomposition. Besides, some heuristic methods such as hill-climbing, SPIN, degree discount and independent set based are also proposed. However, these approaches suffer from a possibility that some spreaders are so close together that they overlap sphere of influence or time consuming. In this report, we present a simply yet effectively iterative method named VoteRank to identify a set of decentralized spreaders with the best spreading ability. In this approach, all nodes vote in a spreader in each turn, and the voting ability of neighbors of elected spreader will be decreased in subsequent turn. Experimental results on four real networks show that under Susceptible-Infected-Recovered (SIR) model, VoteRank outperforms the traditional benchmark methods on both spreading speed and final affected scale. What's more, VoteRank is also superior to other group-spreader identifying methods on computational time.Comment: 13 pages, 6 Figures, 37 reference

Proton radioactivity described by covariant density functional theory with Similarity Renormalization Group method

Half-life of proton radioactivity of spherical proton emitters is studied within the scheme of covariant density functional (CDF) theory, and for the first time the potential barrier that prevents the emitted proton is extracted with the similarity renormalization group (SRG) method, in which the spin-orbit potential along with the others that turn out to be non-negligible can be derived automatically. The spectroscopic factor that is significant is also extracted from the CDF calculations. The estimated half-lives are found in good agreement with the experimental values, which not only confirms the validity of the CDF theory in describing the proton-rich nuclei, but also indicates the prediction power of present approach to calculate the half-lives and in turn to extract the structural information of proton emitters.Comment: 6 pages, 2 figure

Singularities in ground state fidelity and quantum phase transitions for the Kitaev model

The ground state fidelity per lattice site is shown to be able to detect quantum phase transitions for the Kitaev model on the honeycomb lattice, a prototypical example of quantum lattice systems with topological order. It is found that, in the thermodynamic limit, the ground state fidelity per lattice site is non-analytic at the phase boundaries: the second-order derivative of its logarithmic function with respect to a control parameter describing the interaction between neighboring spins is logarithmically divergent. A finite size scaling analysis is performed, which allows us to extract the correlation length critical exponent from the scaling behaviors of the ground state fidelity per lattice site.Comment: 4+ pages, 3 figure

Graded Projected Entangled-Pair State Representations and An Algorithm for Translationally Invariant Strongly Correlated Electronic Systems on Infinite-Size Lattices in Two Spatial Dimensions

An algorithm to find a graded Projected Entangled-Pair State representation of the ground state wave functions is developed for translationally invariant strongly correlated electronic systems on infinite-size lattices in two spatial dimensions. It is tested for the two-dimensional t-J model at and away from half filling, with truncation dimensions up to 6. We are able to locate a line of phase separation, which qualitatively agrees with the results based on the high-temperature expansions. We find that the model exhibits an extended s-wave superconductivity for J=0.4t at quarter filling. However, we emphasize that the currently accessible truncation dimensions are not large enough, so it is necessary to incorporate the symmetry of the system into the algorithm, in order to achieve results with higher precision.Comment: 5 pages, 5 figure

Propagation dynamics of a reaction-diffusion equation in a time-periodic shifting environment

This paper concerns the nonautonomous reaction-diffusion equation $$u_t=u_{xx}+ug(t,x-ct,u), \quad t>0,x\in\mathbb{R},$$ where $c\in\mathbb{R}$ is the shifting speed, and the time periodic nonlinearity $ug(t,\xi,u)$ is asymptotically of KPP type as $\xi \to-\infty$ and is negative as $\xi\to+\infty$. Under a subhomogeneity condition, we show that there is $c^*>0$ such that a unique forced time periodic wave exists if and only $|c|< c^*$ and it attracts other solutions in a certain sense according to the tail behavior of initial values. In the case where $|c|\ge c^*$, the propagation dynamics resembles that of the limiting system as $\xi\to\pm \infty$, depending on the shifting direction.Comment: 28 page

DyNet: Dynamic Convolution for Accelerating Convolutional Neural Networks

Convolution operator is the core of convolutional neural networks (CNNs) and occupies the most computation cost. To make CNNs more efficient, many methods have been proposed to either design lightweight networks or compress models. Although some efficient network structures have been proposed, such as MobileNet or ShuffleNet, we find that there still exists redundant information between convolution kernels. To address this issue, we propose a novel dynamic convolution method to adaptively generate convolution kernels based on image contents. To demonstrate the effectiveness, we apply dynamic convolution on multiple state-of-the-art CNNs. On one hand, we can reduce the computation cost remarkably while maintaining the performance. For ShuffleNetV2/MobileNetV2/ResNet18/ResNet50, DyNet can reduce 37.0/54.7/67.2/71.3% FLOPs without loss of accuracy. On the other hand, the performance can be largely boosted if the computation cost is maintained. Based on the architecture MobileNetV3-Small/Large, DyNet achieves 70.3/77.1% Top-1 accuracy on ImageNet with an improvement of 2.9/1.9%. To verify the scalability, we also apply DyNet on segmentation task, the results show that DyNet can reduce 69.3% FLOPs while maintaining Mean IoU on segmentation task