We explore a new general-purpose heuristic for finding high-quality solutions to hard 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 replaces extremely undesirable elements of a single sub-optimal solution with new, random ones...

We study asymptotically flat stationary solutions of four-dimensional supergravity theories via the associated G/H pseudo-Riemannian non-linear sigma models in three spatial dimensions. The Noether charge C associated to G is shown to satisfy a characteristic equation that determines it as a function of the four-dimensional conserved charges. The matrix C is nilpotent for non-rotating extremal ...

Decay of a near-extremal black hole down to the extremal state is studied in the background field approximation to determine the fate of injected matter and Hawking pairs. By examining the behavior of light rays and solutions to the wave equation it is concluded that the singularity at the origin is irrelevant. Furthermore, there is most likely an instability of the event horizon arising from t...

In this paper the static, spherically symmetric and electrically charged black hole solutions in Einstein-Born-Infeld gravity with massive dilaton are investigated numerically. The Continuous Analog of Newton Method (CANM) is used to solve the corresponding non-linear multipoint boundary value problems (BVPs). The linearized BVPs are solved numerically by means of collocation scheme of fourth o...

We prove that a large class of leading order string solutions which generalize both the plane-wave and fundamental string backgrounds are, in fact, exact solutions to all orders in α′. These include, in particular, the traveling waves along the fundamental string. The key features of these solutions are a null symmetry and a chiral coupling of the string to the background. Using dimensional red...

In this paper we study extremal functions for invariant subspaces Ji of the Dirichlet shift, i.e., solutions <p of the extremal problem »up{|/"»(0)|/||/||fl:/eur, /VO}. Here n is the smallest nonnegative integer such that the sup is positive. It is known that such a function <p generates J! . We show that the derivative (zip)' has a pseudocontinuation to the exterior disc. This pseudocontinuati...

This paper considers the degree-diameter problem for undirected circulant graphs. The focus is on extremal graphs of given (small) degree and arbitrary diameter. The published literature only covers graphs of up to degree 7. The approach used to establish the results for degree 6 and 7 has been extended successfully to degree 8 and 9. Candidate graphs are defined as functions of the diameter fo...

The classical problem of finding conditions on the entire coefficients A(z) and B(z) guaranteeing that all nontrivial solutions of f ′′+A(z)f ′+ B(z)f = 0 are of infinite order is discussed. Two distinct approaches are used. In the first approach the coefficient A(z) itself is a solution of a differential equation w′′ + P (z)w = 0, where P (z) is a polynomial. This assumption yields stability o...

A black hole and a black hyperboloid solutions in the space with the Schrödinger isometries are presented and their thermodynamics is examined. The on-shell action is obtained by the difference between the extremal and non-extremal ones with the unusual matching of the boundary metrics. This regularization method is first applied to the black brane solution in the space of the Schrödinger symme...