We explore a new general-purpose heuristic for finding high-quality solutions to hard discrete optimization problems. The method, called extremal optimization, is inspired by self-organized criticality, a concept introduced to describe emergent complexity in physical systems. Extremal optimization successively updates extremely undesirable variables of a single suboptimal solution, assigning th...

We explore a new general-purpose heuristic for finding high-quality solutions to hard discrete optimization problems. The method, called extremal optimization, is inspired by self-organized criticality, a concept introduced to describe emergent complexity in physical systems. Extremal optimization successively updates extremely undesirable variables of a single suboptimal solution, assigning th...

In the large coupling regime of the 5-dimensional Einstein–Maxwell–Chern–Simons theory, charged and rotating cohomogeneity-1 black holes form sequences of extremal and non-extremal radially excited configurations. These asymptotically global Anti-de Sitter (AdS5) black holes form a discrete set of solutions, characterised by the vanishing of the total angular momenta, or the horizon angular vel...

In this paper, we investigate the existence of positive solutions for the ellipticequation $Delta^{2},u+c(x)u = lambda f(u)$ on a bounded smooth domain $Omega$ of $R^{n}$, $ngeq2$, with Navier boundary conditions. We show that there exists an extremal parameter$lambda^{ast}>0$ such that for $lambda< lambda^{ast}$, the above problem has a regular solution butfor $lambda> lambda^{ast}$, the probl...

There exist extremal p-brane solutions of D=11 supergravity for p=2 and 5. In this paper we investigate the zero modes of the membrane and the fivebrane solutions as a first step toward understanding the full quantum theory of these objects. It is found that both solutions possess the correct number of normalizable zero modes dictated by supersymmetry. Typeset using REVTEX 1