Prospectus, January 26, 2000

https://spark.parkland.edu/prospectus_2000/1002/thumbnail.jp

Quantum Algorithms for Learning and Testing Juntas

In this article we develop quantum algorithms for learning and testing juntas, i.e. Boolean functions which depend only on an unknown set of k out of n input variables. Our aim is to develop efficient algorithms: - whose sample complexity has no dependence on n, the dimension of the domain the Boolean functions are defined over; - with no access to any classical or quantum membership ("black-box") queries. Instead, our algorithms use only classical examples generated uniformly at random and fixed quantum superpositions of such classical examples; - which require only a few quantum examples but possibly many classical random examples (which are considered quite "cheap" relative to quantum examples). Our quantum algorithms are based on a subroutine FS which enables sampling according to the Fourier spectrum of f; the FS subroutine was used in earlier work of Bshouty and Jackson on quantum learning. Our results are as follows: - We give an algorithm for testing k-juntas to accuracy $\epsilon$ that uses $O(k/\epsilon)$ quantum examples. This improves on the number of examples used by the best known classical algorithm. - We establish the following lower bound: any FS-based k-junta testing algorithm requires $\Omega(\sqrt{k})$ queries. - We give an algorithm for learning $k$-juntas to accuracy $\epsilon$ that uses $O(\epsilon^{-1} k\log k)$ quantum examples and $O(2^k \log(1/\epsilon))$ random examples. We show that this learning algorithms is close to optimal by giving a related lower bound.Comment: 15 pages, 1 figure. Uses synttree package. To appear in Quantum Information Processin

Energy Dependence of the Delta Resonance: Chiral Dynamics in Action

There is an important connection between the low energy theorems of QCD and the energy dependence of the Delta resonance in pi-N scattering, as well as the closely related gamma^{*} N -> pi N reaction. The resonance shape is due not only to the strong pi-N interaction in the p wave but the small interaction in the s wave; the latter is due to spontaneous chiral symmetry breaking in QCD (i.e. the Nambu-Goldstone nature of the pion). A brief overview of experimental tests of chiral perturbation theory and chiral based models is presentedComment: 11 pages, 6 figures, Festschrift for S.N. yan

Quantum algorithm for the Boolean hidden shift problem

The hidden shift problem is a natural place to look for new separations between classical and quantum models of computation. One advantage of this problem is its flexibility, since it can be defined for a whole range of functions and a whole range of underlying groups. In a way, this distinguishes it from the hidden subgroup problem where more stringent requirements about the existence of a periodic subgroup have to be made. And yet, the hidden shift problem proves to be rich enough to capture interesting features of problems of algebraic, geometric, and combinatorial flavor. We present a quantum algorithm to identify the hidden shift for any Boolean function. Using Fourier analysis for Boolean functions we relate the time and query complexity of the algorithm to an intrinsic property of the function, namely its minimum influence. We show that for randomly chosen functions the time complexity of the algorithm is polynomial. Based on this we show an average case exponential separation between classical and quantum time complexity. A perhaps interesting aspect of this work is that, while the extremal case of the Boolean hidden shift problem over so-called bent functions can be reduced to a hidden subgroup problem over an abelian group, the more general case studied here does not seem to allow such a reduction.Comment: 10 pages, 1 figur

AF-algebras and topology of mapping tori

A covariant functor from the category of mapping tori to a category of AF-algebras is constructed; the functor takes continuous maps between such manifolds to stable homomorphisms between the corresponding AF-algebras. We use this functor to develop an obstruction theory for the torus bundles of dimension 2, 3 and 4.Comment: to appear Czechoslovak Math.

Chiral Bosons Through Linear Constraints

We study in detail the quantization of a model which apparently describes chiral bosons. The model is based on the idea that the chiral condition could be implemented through a linear constraint. We show that the space of states is of indefinite metric. We cure this disease by introducing ghost fields in such a way that a BRST symmetry is generated. A quartet algebra is seen to emerge. The quartet mechanism, then, forces all physical states, but the vacuum, to have zero norm.Comment: 9 page

Global nucleosome occupancy in yeast

BACKGROUND: Although eukaryotic genomes are generally thought to be entirely chromatin-associated, the activated PHO5 promoter in yeast is largely devoid of nucleosomes. We systematically evaluated nucleosome occupancy in yeast promoters by immunoprecipitating nucleosomal DNA and quantifying enrichment by microarrays. RESULTS: Nucleosome depletion is observed in promoters that regulate active genes and/or contain multiple evolutionarily conserved motifs that recruit transcription factors. The Rap1 consensus was the only binding motif identified in a completely unbiased search of nucleosome-depleted promoters. Nucleosome depletion in the vicinity of Rap1 consensus sites in ribosomal protein gene promoters was also observed by real-time PCR and micrococcal nuclease digestion. Nucleosome occupancy in these regions was increased by the small molecule rapamycin or, in the case of the RPS11B promoter, by removing the Rap1 consensus sites. CONCLUSIONS: The presence of transcription factor-binding motifs is an important determinant of nucleosome depletion. Most motifs are associated with marked depletion only when they appear in combination, consistent with a model in which transcription factors act collaboratively to exclude nucleosomes and gain access to target sites in the DNA. In contrast, Rap1-binding sites cause marked depletion under steady-state conditions. We speculate that nucleosome depletion enables Rap1 to define chromatin domains and alter them in response to environmental cues

Prospectus, February 2, 2000

https://spark.parkland.edu/prospectus_2000/1003/thumbnail.jp