Congruences for sequences analogous to Euler numbers

For a given real number $a$ we define the sequence $\{E_{n,a}\}$ by $E_{0,a}=1$ and $E_{n,a}=-a\sum_{k=1}^{[n/2]} \binom n{2k}E_{n-2k,a}$ $(n\ge 1)$, where $[x]$ is the greatest integer not exceeding $x$. Since $E_{n,1}=E_n$ is the n-th Euler number, $E_{n,a}$ can be viewed as a natural generalization of Euler numbers. In this paper we deduce some identities and an inversion formula involving $\{E_{n,a}\}$, and establish congruences for $E_{2n,a}\mod{2^{{\rm ord}_2n+8}}$, $E_{2n,a}\pmod{3^{{\rm ord}_3n+5}}$ and $E_{2n,a}\pmod{5^{{\rm ord}_5n+4}}$ provided that $a$ is a nonzero integer, where ${\rm ord}_pn$ is the least nonnegative integer $\alpha$ such that p^{\a}\mid n but p^{\a+1}\nmid n.Comment: 16 page

Collaborative similarity analysis of multilayer developer-project bipartite network

To understand the multiple relations between developers and projects on GitHub as a whole, we model them as a multilayer bipartite network and analyze the degree distributions, the nearest neighbors' degree distributions and their correlations with degree, and the collaborative similarity distributions and their correlations with degree. Our results show that all degree distributions have a power-law form, especially, the degree distribution of projects in watching layer has double power-law form. Negative correlations between nearest neighbors' degree and degree for both developers and projects are observed in both layers, exhibiting a disassortative mixing pattern. The collaborative similarity of both developers and projects negatively correlates with degree in watching layer, while a positive correlations is observed for developers in forking layer and no obvious correlation is observed for projects in forking layer

Emergence of cooperation induced by preferential learning

The evolutionary Prisoner's Dilemma Game (PDG) and the Snowdrift Game (SG) with preferential learning mechanism are studied in the Barab\'asi-Albert network. Simulation results demonstrate that the preferential learning of individuals remarkably promotes the cooperative behavior for both two games over a wide range of payoffs. To understand the effect of preferential learning on the evolution of the systems, we investigate the time series of the cooperator density for different preferential strength and payoffs. It is found that in some specific cases two games both show the $1/f$-scaling behaviors, which indicate the existence of long range correlation. We also figure out that when the large degree nodes have high probability to be selected, the PDG displays a punctuated equilibrium-type behavior. On the contrary, the SG exhibits a sudden increase feature. These temporary instable behaviors are ascribed to the strategy shift of the large degree nodes.Comment: 10 pages, 5 figure

Secure quantum key distribution network with Bell states and local unitary operations

We propose a theoretical scheme for secure quantum key distribution network following the ideas in quantum dense coding. In this scheme, the server of the network provides the service for preparing and measuring the Bell states, and the users encodes the states with local unitary operations. For preventing the server from eavesdropping, we design a decoy when the particle is transmitted between the users. It has high capacity as one particle carries two bits of information and its efficiency for qubits approaches 100%. Moreover, it is not necessary for the users to store the quantum states, which makes this scheme more convenient for application than others.Comment: 5 pages, 2 figures. The decoy-photon technique is presented in a clear way for preventing a potentially dishonest server on a network from eavesdropping quantum communication freely. This technique may be useful in quantum secret sharing (of classical information or quantum information), controlled teleportation, and so o

The effect of social welfare system based on the complex network

With the passage of time, the development of communication technology and transportation broke the isolation among people. Relationship tends to be complicated, pluralism, dynamism. In the network where interpersonal relationship and evolved complex net based on game theory work serve respectively as foundation architecture and theoretical model, with the combination of game theory and regard public welfare as influencing factor, we artificially initialize that closed network system. Through continual loop operation of the program, we summarize the changing rule of the cooperative behavior in the interpersonal relationship, so that we can analyze the policies about welfare system about whole network and the relationship of frequency of betrayal in cooperative behavior. Most analytical data come from some simple investigations and some estimates based on internet and environment and the study put emphasis on simulating social network and analyze influence of social welfare system on Cooperative Behavio

Dynamical Coarse Graining of Large Scale-Free Boolean networks

We present a renormalization-grouplike method performed in the state space for detecting the dynamical behaviors of large scale-free Boolean networks, especially for the chaotic regime as well as the edge of chaos. Numerical simulations with different coarse-graining level show that the state space networks of scale-free Boolean networks follow universal power-law distributions of in and out strength, in and out degree, as well as weight. These interesting results indicate scale-free Boolean networks still possess self-organized mechanism near the edge of chaos in the chaotic regime. The number of state nodes as a function of biased parameter for distinct coarse-graining level also demonstrates that the power-law behaviors are not the artifact of coarse-graining procedure. Our work may also shed some light on the investigation of brain dynamics.Comment: 5 pages, 6 figure

A New Type of Two-photon Forward Radiation in Pure Liquids

Unexpected spectral features are observed in the two photon spectrum of the pure water in the forward direction when an 80 femtosecond laser pulse is focused at 10^10Wcm-2 or less. Such intensity is much lower than the breakdown or stimulated threshold of the liquid water. The two broad features are about 2700cm-1 and 5000cm-1 red shifted from the hyper-Rayleigh wavelength, respectively, and they are quadratic with the laser intensity. They do not match the known Raman or hyper-Raman frequencies of water, and they are both centered at a narrow angle in the forward direction. Several other liquids also exhibited similar but molecular specific spectral features.Comment: 4 pages, 4 figure

Diffusion-limited-aggregation on a directed small world network

For real world systems, nonuniform medium is ubiquitous. Therefore, we investigate the diffusion-limited-aggregation process on a two dimensional directed small-world network instead of regular lattice. The network structure is established by rewiring connections on the two dimensional directed lattice. Those rewired edges are controlled by two parameters $\theta$ and $m$, which characterize the spatial length and the density of the long-range connections, respectively. Simulations show that there exists a maximum value of the fractal dimension when $\theta$ equals zero. Interestingly, we find that the symmetry of the aggregation pattern is broken when rewired connections are long enough, which may be an explanation for the formation of asymmetrical fractal in nature. Then, we perform multifractal analysis on the patterns further.Comment: 5 pages, 5 figure

Eigenvectors of Z-tensors associated with least H-eigenvalue with application to hypergraphs

Unlike an irreducible $Z$-matrices, a weakly irreducible $Z$-tensor $\mathcal{A}$ can have more than one eigenvector associated with the least H-eigenvalue. We show that there are finitely many eigenvectors of $\mathcal{A}$ associated with the least H-eigenvalue. If $\mathcal{A}$ is further combinatorial symmetric, the number of such eigenvectors can be obtained explicitly by the Smith normal form of the incidence matrix of $\mathcal{A}$. When applying to a connected uniform hypergraph $G$, we prove that the number of Laplacian eigenvectors of $G$ associated with the zero eigenvalue is equal to the the number of adjacency eigenvectors of $G$ associated with the spectral radius, which is also equal to the number of signless Laplacian eigenvectors of $G$ associated with the zero eigenvalue if zero is an signless Laplacian eigenvalue

A New Target-specific Object Proposal Generation Method for Visual Tracking

Object proposal generation methods have been widely applied to many computer vision tasks. However, existing object proposal generation methods often suffer from the problems of motion blur, low contrast, deformation, etc., when they are applied to video related tasks. In this paper, we propose an effective and highly accurate target-specific object proposal generation (TOPG) method, which takes full advantage of the context information of a video to alleviate these problems. Specifically, we propose to generate target-specific object proposals by integrating the information of two important objectness cues: colors and edges, which are complementary to each other for different challenging environments in the process of generating object proposals. As a result, the recall of the proposed TOPG method is significantly increased. Furthermore, we propose an object proposal ranking strategy to increase the rank accuracy of the generated object proposals. The proposed TOPG method has yielded significant recall gain (about 20%-60% higher) compared with several state-of-the-art object proposal methods on several challenging visual tracking datasets. Then, we apply the proposed TOPG method to the task of visual tracking and propose a TOPG-based tracker (called as TOPGT), where TOPG is used as a sample selection strategy to select a small number of high-quality target candidates from the generated object proposals. Since the object proposals generated by the proposed TOPG cover many hard negative samples and positive samples, these object proposals can not only be used for training an effective classifier, but also be used as target candidates for visual tracking. Experimental results show the superior performance of TOPGT for visual tracking compared with several other state-of-the-art visual trackers (about 3%-11% higher than the winner of the VOT2015 challenge in term of distance precision).Comment: 14pages,11figures, Submited to IEEE Transactions on Cybernetis