In this article we give several new results on the complexity of algorithms that learn Boolean functions from quantum queries and quantum examples. • Hunziker et al. [17] conjectured that for any class C of Boolean functions, the number of quantum black-box queries which are required to exactly identify an unknown function from C is at most O( log |C| √ γ̂ ), where γ̂ is a combinatorial parameter...

Robert van Liere Centrum voor Wiskunde en Informatica P.O. Box 94079, 1090 GB Amsterdam The Netherlands E-mail: [email protected] Jurriaan D. Mulder Centrum voor Wiskunde en Informatica P.O. Box 94079, 1090 GB Amsterdam The Netherlands E-mail: [email protected] Jarke J. van Wijk Netherlands Energy Research Foundation ECN P.O. Box 1, 1755 ZG Petten The Netherlands Centrum voor Wiskunde en Informatica P...

We generalize a theorem of Nymann that the density of points in Z that are visible from the origin is 1/ζ(d), where ζ(a) is the Riemann zeta function P∞ i=1 1/i . A subset S ⊂ Z is called primitive if it is a Z-basis for the lattice Z ∩ spanR(S), or, equivalently, if S can be completed to a Z-basis of Z. We prove that if m points in Z are chosen uniformly and independently at random from a larg...

time-dependent schrödinger equation for a 1-d model of hydrogen molecular ion h2+ in intenselaser field linearly polarized along the molecular axis is solved. ionization rates are calculated for differentinitial states. the evolution of electronic wavefunction at fixed inter-nuclear separations are simulated andanalyzed. the results obtained for the ground state of this 1-d model of h2+ show ap...

Site-specific 2'-O-ribose methylation of eukaryotic rRNAs is guided by small nucleolar RNAs (snoRNAs). The methylation guide snoRNAs carry long perfect complementaries to rRNAs. These antisense elements are located either in the 5' half or in the 3' end region of the snoRNA, and are followed by the conserved D' or D box motifs, respectively. An uninterrupted helix formed between the rRNA and th...