Effect of interaction strength on the evolution of cooperation

Cooperative behaviors are ubiquitous in nature,which is a puzzle to evolutionary biology,because the defector always gains more benefit than the cooperator,thus,the cooperator should decrease and vanish over time.This typical "prisoners' dilemma" phenomenon has been widely researched in recent years.The interaction strength between cooperators and defectors is introduced in this paper(in human society,it can be understood as the tolerance of cooperators).We find that only when the maximum interaction strength is between two critical values,the cooperator and defector can coexist,otherwise, 1) if it is greater than the upper value,the cooperator will vanish, 2) if it is less than the lower value,a bistable state will appear

Secure Transmission to the Strong User with Optimal Power Allocation in NOMA

With non-orthogonal multiple access(NOMA), we tackle the maximization of the secrecy rate for the strong user subject to a maximum allowable secrecy outage probability, while guaranteeing a constraint on the transmission rate to the weak user. For the first time, the dependence between the eavesdropper's ability to conduct successive interference cancellation and her channel quality is considered. We determine the optimal power allocation and the redundancy rate, based on which the cost of security in terms of the reduction in the strong user's secrecy rate is examined and the benefits of NOMA for secure transmissions are explicitly revealed

On the minimal affinizations over the quantum affine algebras of type CnC_n

In this paper, we study the minimal affinizations over the quantum affine algebras of type $C_n$ by using the theory of cluster algebras. We show that the $q$-characters of a large family of minimal affinizations of type $C_n$ satisfy some systems of equations. These equations correspond to mutation equations of some cluster algebras. Furthermore, we show that the minimal affinizations in these equations correspond to cluster variables in these cluster algebras.Comment: arXiv admin note: substantial text overlap with arXiv:1501.00146, arXiv:1502.0242

Upper bounds for bar visibility of subgraphs and n-vertex graphs

A $t$-bar visibility representation of a graph assigns each vertex up to $t$ horizontal bars in the plane so that two vertices are adjacent if and only if some bar for one vertex can see some bar for the other via an unobstructed vertical channel of positive width. The least $t$ such that $G$ has a $t$-bar visibility representation is the bar visibility number of $G$, denoted by $b(G)$. We show that if $H$ is a spanning subgraph of $G$, then $b(H)\le b(G)+1$. It follows that $b(G)\le \lceil n/6\rceil+1$ when $G$ is an $n$-vertex graph. This improves the upper bound obtained by Chang et al. (SIAM J. Discrete Math. 18 (2004) 462).Comment: 6 pages,1 figur

Beamforming Design and Power Allocation for Secure Transmission with NOMA

In this work, we propose a novel beamforming design to enhance physical layer security of a non-orthogonal multiple access (NOMA) system with the aid of artificial noise (AN). The proposed design uses two scalars to balance the useful signal strength and interference at the strong and weak users, which is a generalized version of the existing beamforming designs in the context of physical layer security for NOMA. We determine the optimal power allocation among useful signals and AN together with the two optimal beamforming scalars in order to maximize the secrecy sum rate (SSR). Our asymptotic analysis in the high signal-to-noise ratio regime provides an efficient and near-optimal solution to optimizing the beamforming scalars and power allocation coefficients. Our analysis indicates that it is not optimal to form a beam towards either the strong user or the weak user in NOMA systems for security enhancement. In addition, the asymptotically optimal power allocation informs that, as the transmit power increases, more power should be allocated to the weak user or AN signals, while the power allocated to the strong user keeps constant. Our examination shows that the proposed novel beamforming design can significantly outperform two benchmark schemes

On groups all of whose Haar graphs are Cayley graphs

A Cayley graph of a group $H$ is a finite simple graph $\Gamma$ such that ${\rm Aut}(\Gamma)$ contains a subgroup isomorphic to $H$ acting regularly on $V(\Gamma)$, while a Haar graph of $H$ is a finite simple bipartite graph $\Sigma$ such that ${\rm Aut}(\Sigma)$ contains a subgroup isomorphic to $H$ acting semiregularly on $V(\Sigma)$ and the $H$-orbits are equal to the bipartite sets of $\Sigma$. A Cayley graph is a Haar graph exactly when it is bipartite, but no simple condition is known for a Haar graph to be a Cayley graph. In this paper, we show that the groups $D_6, \, D_8, \, D_{10}$ and $Q_8$ are the only finite inner abelian groups all of whose Haar graphs are Cayley graphs (a group is called inner abelian if it is non-abelian, but all of its proper subgroups are abelian). As an application, it is also shown that every non-solvable group has a Haar graph which is not a Cayley graph.Comment: 17 page

Gate voltage controlled thermoelectric figure of merit in three-dimensional topological insulator nanowires

The thermoelectric properties of the surface states in three-dimensional topological insulator nanowires are studied. The Seebeck coefficients $S_c$ and the dimensionless thermoelectrical figure of merit $ZT$ are obtained by using the tight-binding Hamiltonian combining with the nonequilibrium Green's function method. They are strongly dependent on the gate voltage and the longitudinal and perpendicular magnetic fields. By changing the gate voltage or magnetic fields, the values of $S_c$ and $ZT$ can be easily controlled. At the zero magnetic fields and zero gate voltage, or at the large perpendicular magnetic field and nonzero gate voltage, $ZT$ has the large value. Owing to the electron-hole symmetry, $S_c$ is an odd function of the Fermi energy while $ZT$ is an even function regardless of the magnetic fields. $S_c$ and $ZT$ show peaks when the quantized transmission coefficient jumps from one plateau to another. The highest peak appears while the Fermi energy is near the Dirac point. At the zero perpendicular magnetic field and zero gate voltage, the height of $n$th peak of $S_C$ is $\frac{k_B}{e}\texttt{ln}2/(|n|+1/2)$ and $\frac{k_B}{e}\texttt{ln}2/|n|$ for the longitudinal magnetic flux $\phi_{\parallel} = 0$ and $\pi$, respectively. Finally, we also study the effect of disorder and find that $S_c$ and $ZT$ are robust against disorder. In particular, the large value of $ZT$ can survive even if at the strong disorder. These characteristics (that $ZT$ has the large value, is easily regulated, and is robust against the disorder) are very beneficial for the application of the thermoelectricity.Comment: 9 pages,10 figure

Energies and E1, M2 transition rates for Mo XXX

Based on relativistic wavefunctions from multiconfigurational Dirac-Hartree-Fock (MCDHF) and configuration interaction calculations, energy levels, radiative rates, and wavelengths are evaluated for all levels of 3s$^2$3p, 3s3p$^2$, 3s$^2$3d, 3p$^3$, 3s3p3d, 3p$^2$3d and 3s3d$^2$ configurations of Al-like Molybdenum ion (Mo XXX). Transition probabilities are reported for E1 and M2 transitions from the ground level. The valence-valence and core-valence correlation effects are accounted for in a systematic way. Breit interactions and quantum electrodynamics effects are estimated in subsequent relativistic configuration interaction calculations. Comparisons are made with the available data in the literature and good agreement has been found which confirms the reliability of our results.Comment: 13page

A nonlinear tracking algorithm with range-rate measurements based on unbiased measurement conversion

The three-dimensional CMKF-U with only position measurements is extended to solve the nonlinear tracking problem with range-rate measurements in this paper. A pseudo measurement is constructed by the product of range and range-rate measurements to reduce the high nonlinearity of the range-rate measurements with respect to the target state; then the mean and covariance of the converted measurement errors are derived by the measurement conditioned method, showing better consistency than the transitional nested conditioning method; finally, the sequential filter was used to process the converted position and range-rate measurements sequentially to reduce the approximation error in the second-order EKF. Monte Carlo simulations show that the performance of the new tracking algorithm is better than the traditional one based on CMKF-D

Arc-transitive cyclic and dihedral covers of pentavalent symmetric graphs of order twice a prime

A regular cover of a connected graph is called {\em cyclic} or {\em dihedral} if its transformation group is cyclic or dihedral respectively, and {\em arc-transitive} (or {\em symmetric}) if the fibre-preserving automorphism subgroup acts arc-transitively on the regular cover. In this paper, we give a classification of arc-transitive cyclic and dihedral covers of a connected pentavalent symmetric graph of order twice a prime. All those covers are explicitly constructed as Cayley graphs on some groups, and their full automorphism groups are determined