Randomness Extraction in AC0 and with Small Locality

Randomness extractors, which extract high quality (almost-uniform) random bits from biased random sources, are important objects both in theory and in practice. While there have been significant progress in obtaining near optimal constructions of randomness extractors in various settings, the computational complexity of randomness extractors is still much less studied. In particular, it is not clear whether randomness extractors with good parameters can be computed in several interesting complexity classes that are much weaker than P. In this paper we study randomness extractors in the following two models of computation: (1) constant-depth circuits (AC0), and (2) the local computation model. Previous work in these models, such as [Vio05a], [GVW15] and [BG13], only achieve constructions with weak parameters. In this work we give explicit constructions of randomness extractors with much better parameters. As an application, we use our AC0 extractors to study pseudorandom generators in AC0, and show that we can construct both cryptographic pseudorandom generators (under reasonable computational assumptions) and unconditional pseudorandom generators for space bounded computation with very good parameters. Our constructions combine several previous techniques in randomness extractors, as well as introduce new techniques to reduce or preserve the complexity of extractors, which may be of independent interest. These include (1) a general way to reduce the error of strong seeded extractors while preserving the AC0 property and small locality, and (2) a seeded randomness condenser with small locality.Comment: 62 page

A study of allosteric binding behaviour of a 1,3-alternate thiacalix[4]arene-based receptor using fluorescence signal

A novel heteroditopic thiacalix[4]arene receptor L possessing 1,3-alternate conformation, which contains two pyrene moieties attached to the lower rim via urea linkages together with a crown ether moiety appended at the opposite side of the thiacalix[4]arene cavity, has been synthesized. The complexation behaviour of receptor L was studied by means of fluorescence spectra and ¹H NMR titration experiments in the presence of K⁺ ions and a variety of other anions. The results suggested that receptor L can complex efficiently via the urea cavity or the crown ether moiety, and a positive/negative allosteric effect operating in receptor L was observed