The International Planning Competition has provided a means of comparing the performance of planners. It is supposed to be a driving-force for planning technology. As the competition has advanced, more and more complex domains have been introduced. However, the methods for generating the competition instances are typically simplistic. At best, this means that our planners are not tested on the ...

We investigate several tricritical models on the square lattice by means of Monte Carlo simulations. These include the Blume-Capel model, Baxter's hard-square model, and the q=1 , 3, and 4 Potts models with vacancies. We use a combination of the Wolff and geometric cluster methods, which conserves the total number of vacancies or lattice-gas particles and suppresses critical slowing down. Sever...

We show how certain diffeomorphism-invariant functionals on differential forms in dimensions 6, 7 and 8 generate in a natural way special geometrical structures in these dimensions: metrics of holonomy G2 and Spin(7), metrics with weak holonomy SU(3) and G2, and a new and unexplored example in dimension 8. The general formalism becomes a practical tool for calculating homogeneous or cohomogenei...

We show that the shape moduli associated with large extra dimensions can have a dramatic effect on the corresponding Kaluza-Klein spectra. Specifically, shape moduli can change the mass gap, induce level crossings, and even interpolate between theories with different numbers of compactified dimensions. We also show that in certain cases it is possible to maintain the ratio between the higher-di...

All isomorphisms of Plücker spaces on affine spaces with dimensions ≥ 3 arise from collineations of the underlying affine spaces.

A matrix T ∈ Mn(C) is UECSM if it is unitarily equivalent to a complex symmetric (i.e., self-transpose) matrix. We develop several techniques for studying this property in dimensions three and four. Among other things, we completely characterize 4×4 nilpotent matrices which are UECSM and we settle an open problem which has lingered in the 3×3 case. We conclude with a discussion concerning a cru...

Exploiting a Lagrangian strategy we present a numerical study for both perturbative and nonperturbative regions of the Kraichnan advection model. The major result is the numerical assessment of the first-order 1/d expansion by Chertkov, Falkovich, Kolokolov, and Lebedev [Phys. Rev. E 52, 4924 (1995)] for the fourth-order scalar structure function in the limit of high dimension d's. In addition ...

The study integrates two methodologies so that income-related inequality in general health can be decomposed into contributions from socio-demographic characteristics to each of the dimensions defining general health. It is found that these relative contributions vary substantially across dimensions. For policy purposes such information is valuable as it indicates at which population groups and...