Extremal optimization is a new general-purpose method for approximating solutions to hard optimization problems. We study the method in detail by way of the computationally hard (NP-hard) graph partitioning problem. We discuss the scaling behavior of extremal optimization, focusing on the convergence of the average run as a function of run time and system size. The method has a single free para...

We consider the class of semi-stable positive solutions to semilinear equations −∆u = f(u) in a bounded domain Ω ⊂ Rn of double revolution, that is, a domain invariant under rotations of the first m variables and of the last n−m variables. We assume 2 ≤ m ≤ n− 2. When the domain is convex, we establish a priori Lp and H1 0 bounds for each dimension n, with p = ∞ when n ≤ 7. These estimates lead...

It has recently been shown that there exist stable inhomogeneous neutral black strings in higher dimensional gravity. These solutions were motivated by the fact that the corresponding homogeneous solutions are unstable. We show that there exist new inhomogeneous black string and black p-brane solutions even when the corresponding translationally invariant solutions are stable. In particular, we...

We construct and study the electrically charged, rotating black hole solution in heterotic string theory compactified on a (10 − D) dimensional torus. This black hole is characterized by its mass, angular momentum, and a (36 − 2D) dimensional electric charge vector. One of the novel features of this solution is that for D > 5, its extremal limit saturates the Bogomol’nyi bound. This is in contr...

For −1 < α ≤ 0 and 0 < p < ∞, the solutions of certain extremal problems are known to act as contractive zerodivisors in the weighted Bergman space Aα. We show that for 0 < α ≤ 1 and 0 < p < ∞, the analogous extremal functions do not have any extra zeros in the unit disk and, hence, have the potential to act as zero-divisors. As a corollary, we find that certain families of hypergeometric funct...

On the occasion of Laurens de Haan’s 70th birthday, we discuss two aspects of the statistical inference on the extreme value behavior of time series with a particular emphasis on his important contributions. First, the performance of a direct marginal tail analysis is compared with that of a model-based approach using an analysis of residuals. Second, the importance of the extremal index as a m...

All extremal solutions of the truncated L-problem of moments in two real variables , with support contained in a given compact set, are described as characteristic functions of semi-algebraic sets given by a single polynomial inequality. An exponential kernel, arising as the determinantal function of a naturally associated hyponormal operator with rank-one self-commutator, provides a natural de...

We introduce a notion of universality classes for the Gregory-Laflamme instability and determine, in the supergravity approximation, the stability of a variety of solutions, including the non-extremal D3-brane, M2-brane, and M5-brane. These three non-dilatonic branes cross over from instability to stability at a certain non-extremal mass. Numerical analysis suggests that the wavelength of the s...

It is argued that many non-extremal black branes exhibit a classical Gregory-Laflamme instability if, and only if, they are locally thermodynamically unstable. For some black branes, the Gregory-Laflamme instability must therefore disappear near extremality. For the black p-branes of the type II supergravity theories, the Gregory-Laflamme instability disappears near extremality for p = 1, 2, 4 ...