From the social learning theory to a social learning algorithm for global optimization

Traditionally, the Evolutionary Computation (EC) paradigm is inspired by Darwinian evolution or the swarm intelligence of animals. Bandura's Social Learning Theory pointed out that the social learning behavior of humans indicates a high level of intelligence in nature. We found that such intelligence of human society can be implemented by numerical computing and be utilized in computational algorithms for solving optimization problems. In this paper, we design a novel and generic optimization approach that mimics the social learning process of humans. Emulating the observational learning and reinforcement behaviors, a virtual society deployed in the algorithm seeks the strongest behavioral patterns with the best outcome. This corresponds to searching for the best solution in solving optimization problems. Experimental studies in this paper showed the appealing search behavior of this human intelligence-inspired approach, which can reach the global optimum even in ill conditions. The effectiveness and high efficiency of the proposed algorithm has further been verified by comparing to some representative EC algorithms and variants on a set of benchmarks

Lifshitz Scaling Effects on Holographic Superconductors

Via numerical and analytical methods, the effects of the Lifshitz dynamical exponent $z$ on holographic superconductors are studied in some detail, including $s$ wave and $p$ wave models. Working in the probe limit, we find that the behaviors of holographic models indeed depend on concrete value of $z$. We obtain the condensation and conductivity in both Lifshitz black hole and soliton backgrounds with general $z$. For both $s$ wave and $p$ wave models in the black hole backgrounds, as $z$ increases, the phase transition becomes more difficult and the growth of conductivity is suppressed. For the Lifshitz soliton backgrounds, when $z$ increases ($z=1,~2,~3$), the critical chemical potential decreases in the $s$ wave cases but increases in the $p$ wave cases. For $p$ wave models in both Lifshitz black hole and soliton backgrounds, the anisotropy between the AC conductivity in different spatial directions is suppressed when $z$ increases. The analytical results uphold the numerical results.Comment: Typos corrected; Footnote added; References added; To be published in Nuclear Physics

Five-dimensional generalized f(R)f(R) gravity with curvature-matter coupling

The generalized $f(R)$ gravity with curvature-matter coupling in five-dimensional (5D) spacetime can be established by assuming a hypersurface-orthogonal spacelike Killing vector field of 5D spacetime, and it can be reduced to the 4D formulism of FRW universe. This theory is quite general and can give the corresponding results to the Einstein gravity, $f(R)$ gravity with both no-coupling and non-minimal coupling in 5D spacetime as special cases, that is, we would give the some new results besides previous ones given by Ref.\cite{60}. Furthermore, in order to get some insight into the effects of this theory on the 4D spacetime, by considering a specific type of models with $f_{1}(R)=f_{2}(R)=\alpha R^{m}$ and $B(L_{m})=L_{m}=-\rho$, we not only discuss the constraints on the model parameters $m$, $n$, but also illustrate the evolutionary trajectories of the scale factor $a(t)$, the deceleration parameter $q(t)$ and the scalar field $\epsilon(t)$, $\phi(t)$ in the reduced 4D spacetime. The research results show that this type of $f(R)$ gravity models given by us could explain the current accelerated expansion of our universe without introducing dark energy.Comment: arXiv admin note: text overlap with arXiv:0912.4581, arXiv:gr-qc/0411066 by other author

Topolgical Charged Black Holes in Generalized Horava-Lifshitz Gravity

As a candidate of quantum gravity in ultrahigh energy, the $(3+1)$-dimensional Ho\v{r}ava-Lifshitz (HL) gravity with critical exponent $z\ne 1$, indicates anisotropy between time and space at short distance. In the paper, we investigate the most general $z=d$ Ho\v{r}ava-Lifshitz gravity in arbitrary spatial dimension $d$, with a generic dynamical Ricci flow parameter $\lambda$ and a detailed balance violation parameter $\epsilon$. In arbitrary dimensional generalized HL$_{d+1}$ gravity with $z\ge d$ at long distance, we study the topological neutral black hole solutions with general $\lambda$ in $z=d$ HL$_{d+1}$, as well as the topological charged black holes with $\lambda=1$ in $z=d$ HL$_{d+1}$. The HL gravity in the Lagrangian formulation is adopted, while in the Hamiltonian formulation, it reduces to Dirac$-$De Witt's canonical gravity with $\lambda=1$. In particular, the topological charged black holes in $z=5$ HL$_6$, $z=4$ HL$_5$, $z=3,4$ HL$_4$ and $z=2$ HL$_3$ with $\lambda=1$ are solved. Their asymptotical behaviors near the infinite boundary and near the horizon are explored respectively. We also study the behavior of the topological black holes in the $(d+1)$-dimensional HL gravity with $U(1)$ gauge field in the zero temperature limit and finite temperature limit, respectively. Thermodynamics of the topological charged black holes with $\lambda=1$, including temperature, entropy, heat capacity, and free energy are evaluated.Comment: 51 pages, published version. The theoretical framework of z=d HL gravity is set up, and higher curvature terms in spatial dimension become relevant at UV fixed point. Lovelock term, conformal term, new massive term, and Chern-Simons term with different critical exponent z are studie