Algorithms that combat the curse of dimensionality take advantage of nonuniformity properties of the underlying functions, which may be rotational (e.g., grid alignment) or translational (e.g., near-singularities localized at certain points of the domain). The significance of such effects is explored for four different classes of algorithms: low-rank compression, quasi-Monte Carlo integration, ...

Abstract Statistical Isotropy of the Cosmic Microwave Background (CMB) radiation has been studied and debated extensively in recent years. Under this assumption, hot spots cold CMB are expected to be uniformly distributed over a 2-sphere. We use orientation matrix, first proposed by Watson (1965) Scheidegger associated shape strength parameters (Woodcock, 1977) analyse whether observed temperat...

There has been growing interest in the possibility of testing more precisely the assumption of statistical isotropy of primordial density perturbations. If it is to be tested with galaxy surveys at distance scales < ∼ 10 Mpc, then nonlinear evolution of anisotropic power must be understood. To this end, we calculate the angular dependence of the power spectrum to third order in perturbation the...