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...

We describe a general-purpose method for finding high-quality solutions to hard optimization problems, inspired by self-organized critical models of co-evolution such as the Bak-Sneppen model. The method, called Extremal Optimization, successively eliminates extremely undesirable components of sub-optimal solutions, rather than “breeding” better components. In contrast to Genetic Algorithms whi...

In the paper we consider a matrix version of the extremal Nehary problem [1],[4]. Our approach is based on the notion of a matrix analogue of the eigenvalue ρ2min. The notion of ρ 2 min was used in a number of the extremal interpolation problems [2],[3],[7]. We note that ρ2min is a solution of a nonlinear matrix inequality of the Riccati type [2],[6], [7]. Our approach coincides with the Adamja...

S-extremal strongly modular lattices maximize the minimum of the lattice and its shadow simultaneously. They are a direct generalization of the s-extremal unimodular lattices defined in [6]. If the minimum of the lattice is even, then the dimension of an s-extremal lattices can be bounded by the theory of modular forms. This shows that such lattices are also extremal and that there are only fin...

In this paper, binary extremal singly even self-dual codes of length 40 and extremal odd unimodular lattices in dimension 40 are studied. We give a classification of extremal singly even self-dual codes of length 40. We also give a classification of extremal odd unimodular lattices in dimension 40 with shadows having 80 vectors of norm 2 through their relationships with extremal doubly even sel...

S-extremal strongly modular lattices maximize the minimum of the lattice and its shadow simultaneously. They are a direct generalization of the s-extremal unimodular lattices defined in [6]. If the minimum of the lattice is even, then the dimension of an s-extremal lattices can be bounded by the theory of modular forms. This shows that such lattices are also extremal and that there are only fin...

A new extremal distance tracking algorithm is presented for convex parametric curves and surfaces undergoing rigid body motion. The geometric extremization problem is differentiated with respect to time to produce a dynamical system that incorporates dependence on both surface shape and rigid body motion. Extremization then takes place by integrating these dynamical equations, but with a feedba...

We review the recently discovered ansatz that describes non-extremal charged dilatonic branes of string/M-theory with a transverse circle. The ansatz involves a new coordinate system that interpolates between the spherical and cylindrical case, and reduces the equations of motion to a set of equations on one unknown function of two variables. The function is independent of the charge, so that t...

The paper presents a valid model and a solution method named population-based extremal optimization algorithm (PEOA) to solve the hot rolling scheduling problem (HRSP). Firstly, the problem is formulated as a prize-collecting vehicle problem (PCVRP), which considers two major requirements: (a) selecting a subset of slabs from manufacturing slabs to be processed; (b) determining the optimal prod...

Pairwise testing, which requires that every combination of valid values of each pair of system factors be covered by at lease one test case, plays an important role in software testing since many faults are caused by unexpected 2-way interactions among system factors. Although meta-heuristic strategies like simulated annealing can generally discover smaller pairwise test suite, they may cost mo...