Exact constructive dimension as a generalisation of Lutz’s [Lut00, Lut03] approach to constructive dimension was recently introduced in [Sta11]. It was shown that it is in the same way closely related to a priori complexity, a variant of Kolmogorov complexity, of infinite sequences as their constructive dimension is related to asymptotic Kolmogorov complexity. The aim of the present paper is to...

Wavelets on the sphere are re-introduced and further developed independently of the original group theoretic formalism, in an alternative and completely equivalent approach, as inverse stereographic projection of wavelets on the plane. These developments are motivated by the interest of the scale-space analysis of the cosmic microwave background (CMB) anisotropies on the sky. In addition to off...

A general principle is given for detection of the 3D structure and motion from an image sequence without using point-to-point correspondence. The procedure consists of two stages: ( i ) determination of the "flow parameters" from "features" without using correspondence and ( i i ) computation of the 3D structure and motion from these flow parameters. The f i r s t stage is done by solving equat...

Niels Bohr’s “correspondence principle” is typically believed to be the requirement that in the limit of large quantum numbers (n→∞) there is a statistical agreement between the quantum and classical frequencies. A closer reading of Bohr’s writings on the correspondence principle, however, reveals that this interpretation is mistaken. Specifically, Bohr makes the following three puzzling claims...

Informally speaking, the Furstenberg Correspondence [5, 6] shows that the “local behavior” of a dynamical system is controlled by the behavior of sufficiently large finite systems. By the local behavior of a dynamical system (X,B, μ,G), we mean the properties which can be stated using finitely many actions of G and the integral given by μ1. By a finite system, we just mean (S,P(S), c, G) where ...

We propose a correspondence between the physics of certain small charge black holes in AdSk × Sl and large charge black holes in AdSl × Sk. The curvature singularities of these solutions arise, following Myers and Tafjord, from a condensate of giant gravitons. When the number of condensed giants Ng is much greater than the number of background branes N , we propose that the system has an equiva...

The black hole combines in some sense both the “hydrogen atom” and the “black-body radiation” problems of quantum gravity. This analogy suggests that black-hole quantization may be the key to a quantum theory of gravity. During the last twenty-five years evidence has been mounting that black-hole surface area is indeed quantized, with uniformally spaced area eigenvalues. There is, however, no g...

Many programming languages can be studied by desugaring them into an intermediate language, namely, the simply-typed-calculus. In this manner Landin and Tennent discovered a \correspondence" between the semantics of deenition bindings and parameter bindings such that the semantics of free identiiers becomes independent of their mode of deenition. In this paper we consider programming languages ...

We discuss the correspondence point between a string state and a black hole, in a pp-wave background, and find that the answer is considerably different from that in a flat spacetime background.