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

Determinations of form factors for semileptonic D→KD\rightarrow K decays and leptoquark constraints

By analyzing all existing measurements for $D\rightarrow K \ell^+ \nu_{\ell}$ ( $\ell=e,\ \mu$ ) decays, we find that the determinations of both the vector form factor $f_+^K(q^2)$ and scalar form factor $f_0^K(q^2)$ for semileptonic $D\rightarrow K$ decays from these measurements are feasible. By taking the parameterization of the one order series expansion of the $f_+^K(q^2)$ and $f_0^K(q^2)$, $f_+^K(0)|V_{cs}|$ is determined to be $0.7182\pm0.0029$, and the shape parameters of $f_+^K(q^2)$ and $f_0^K(q^2)$ are $r_{+1}=-2.16\pm0.007$ and $r_{01}=0.89\pm3.27$, respectively. Combining with the average $f_+^K(0)$ of $N_f=2+1$ and $N_f=2+1+1$ lattice calculaltion, the $|V_{cs}|$ is extracted to be $0.964\pm0.004\pm0.019$ where the first error is experimental and the second theoretical. Alternatively, the $f_+^K(0)$ is extracted to be $0.7377\pm0.003\pm0.000$ by taking the $|V_{cs}|$ as the value from the global fit with the unitarity constraint of the CKM matrix. Moreover, using the obtained form factors by $N_f=2+1+1$ lattice QCD, we re-analyze these measurements in the context of new physics. Constraints on scalar leptoquarks are obtained for different final states of semileptonic $D \rightarrow K$ decays

Scale Invariance vs. Conformal Invariance: Holographic Two-Point Functions in Horndeski Gravity

We consider Einstein-Horndeski gravity with a negative bare constant as a holographic model to investigate whether a scale invariant quantum field theory can exist without the full conformal invariance. Einstein-Horndeski gravity can admit two different AdS vacua. One is conformal, and the holographic two-point functions of the boundary energy-momentum tensor are the same as the ones obtained in Einstein gravity. The other AdS vacuum, which arises at some critical point of the coupling constants, preserves the scale invariance but not the special conformal invariance due to the logarithmic radial dependence of the Horndeski scalar. In addition to the transverse and traceless graviton modes, the theory admits an additional trace/scalar mode in the scale invariant vacuum. We obtain the two-point functions of the corresponding boundary operators. We find that the trace/scalar mode gives rise to an non-vanishing two-point function, which distinguishes the scale invariant theory from the conformal theory. The two-point function vanishes in $d=2$, where the full conformal symmetry is restored. Our results indicate the strongly coupled scale invariant unitary quantum field theory may exist in $d\ge 3$ without the full conformal symmetry. The operator that is dual to the bulk trace/scalar mode however violates the dominant energy condition.Comment: Latex, 28 pages, comments and references adde