The Chess Monster Hydra

Bifurcation and fine structure phenomena in critical collapse of a self-gravitating σ-field

“…7a will be valid for higher dimensional systems as long as only a few largest eigenvalues of the perturbation matter. Recently, Donninger [13] has studied linear perturbations around the CSS solution and found that for coupling constants around the critical value η c the first three largest eigenvalues do in fact satisfy the above stated Shil'nikov conditions. Combining this property with the fact that the bifurcating DSS solution is a saddle limit cycle, we conjecture that the (one-dimensional) unstable manifold of the DSS solution lies on the stable manifold of the neighboring CSS solution.…”

Almost sharp nonlinear scattering in one-dimensional Born-Infeld equations arising in nonlinear electrodynamics

“…Additionally, the study of (1.1) has gained a large impulse in String theory in the last years because gauge fields on a D-brane (that arise from attached open strings) are described by the same type of Lagrangian as (1.3); see [11] and references therein for more details. The literature on the above subjects is huge; a fairly incomplete set of references on the "critical" submanifold problem from different points of view is given by [4,5,22,14,9].…”

Comparison of Bayesian move prediction systems for Computer Go

“…The number of legal positions in 19x19 Go is about 2 × 10 170 [11]. In more than 40 years of research no static evaluation function for intermediate game positions was found good enough to achieve strong performance with traditional depth limited alpha-beta search [12] or conspiracy number search [13]. The vast amount of positions paired with the absence of strong evaluation functions makes Go extremely challenging and made it a popular testbed for AI research in recent years.…”