Artificial General Intelligence (AGI) seeks theories, models and techniques to endow machines with the kinds of intellectual abilities exemplified by humans. Yet, the predominant instance-driven approach in AI appears antithetical to this goal. This situation raises a question: What (if any) general principles underlie general intelligence? We approach this question from a (mathematical) catego...

Following a suggestion by Vafa, we present a quantum–mechanical model for S–duality symmetries observed in the quantum theories of fields, strings and branes. Our formalism may be understood as the topological limit of Berezin’s metric quantisation of the upper half–plane H, in that the metric dependence of Berezin’s method has been removed. Being metric–free, our prescription makes no use of g...

The dynamics of abelian vector and antisymmetric tensor gauge fields can be described in terms of twisted self-duality equations. The latter play an important role in exposing the duality symmetries of the theory. I this contribution I review recent progress in the construction of action principles for these equations and in particular their non-abelian generalizations.

In this paper, we show that the anisotropic nonlocal total variation involved in the image regularization model of Gilboa and Osher [15] as well as in the perceptual color correction model of Bertalmı́o et al. [4] possesses a dual formulation. We then obtain novel formulations of their solutions, which provide new insights on these models. In particular, we show that the model of Bertalmı́o et al...

De Vrijer has presented a proof of the finite developments theorem which, in addition to showing that all developments are finite, gives an effective reduction strategy computing longest developments as well as a simple formula computing their length. We show that by applying a rather simple and intuitive principle of duality to de Vrijer’s approach one arrives at a proof that some developments...

By resolving the Riemann curvature relative to a unit timelike vector into electric and magnetic parts, we define a duality transformation which interchanges active and passive electric parts. It implies interchange of roles of Ricci and Einstein curvatures. Further by modifying the vacuum/flat equation we construct spacetimes dual to the Schwarzschild solution and flat spacetime. The dual spac...

Abstract. Frames in Hilbert spaces generalize orthonormal bases and allow stable representation of all the elements of the space via a given frame and its dual frame. Frames are not only interesting from theoretical point of view, but play significant role in signal and image processing, which leads to many applications in informatics, engineering, medicine, and many other fields. In this paper...

Let • • • C K_ ] c Vq c Vx c • • • be a multiresolution analysis of L2 generated by the mth order 5-spline Nm{x). In this paper, we exhibit a compactly supported basic wavelet i//m(x) that generates the corresponding orthogonal complementary wavelet subspaces .quently, the two finite sequences that describe the two-scale relations of Nm(x) and i//m(x) in terms of Nm(2x-j), ;6Z, yield an efficie...