Efficient quantum circuits for Schur and Clebsch-Gordan transforms

The Schur basis on n d-dimensional quantum systems is a generalization of the total angular momentum basis that is useful for exploiting symmetry under permutations or collective unitary rotations. We present efficient {size poly[n,d,log(1/epsilon)] for accuracy epsilon} quantum circuits for the Schur transform, which is the change of basis between the computational and the Schur bases. Our circuits provide explicit efficient methods for solving such diverse problems as estimating the spectrum of a density operator, quantum hypothesis testing, and communicating without a shared reference frame. We thus render tractable a large series of methods for extracting resources from quantum systems and for numerous quantum information protocols.     

Highly diastereoselective Diels-Alder cycloadditions of 9R-(1-methoxyethyl)anthracene with p-benzoquinone

Diels-Alder cycloadditions of p-benzoquinone with 9R-(1-methoxyethyl)anthracene provides a 60:40 ratio of cycloadducts when heated at reflux in xylene. Mechanistic studies to explore the origins of this selectivity have shown that at lower temperatures the kinetic product predominates, giving a 96:4 ratio of cycloadducts.     

Template-guided organization of chromonic liquid crystals into micropatterned anisotropic organic solids

We have developed an approach to generate micropatterns of anisotropic organic materials which exploits the self-organization, driven by pi-stacking and hydrophobic interactions, of an ionic perylenebis(dicarboximide) in aqueous solutions.     

Hindman’s theorem and idempotent types

Motivated by a question of Di Nasso, we show that Hindman’s theorem is equivalent to the existence of idempotent types in countable complete extensions of Peano Arithmetic.     

A new approach to center conditions for simple analytic monodromic singularities

In this paper we present an alternative algorithm for computing Poincaré-Lyapunov constants of simple monodromic singularities of planar analytic vector fields based on the concept of inverse integrating factor. Simple monodromic singular points are those for which after performing the first (generalized) polar blow-up, there appear no singular points. In other words, the associated Poincaré return map is analytic. An improvement of the method determines a priori the minimum number of Poincaré-Lyapunov constants which must cancel to ensure that the monodromic singularity is in fact a center when the explicit Laurent series of an inverse integrating factor is known in (generalized) polar coordinates. Several examples show the usefulness of the method.     

Quenching of IR luminescence of erbium, neodymium, and ytterbium beta-diketonate complexes by ligand C-H and C-D bonds

The effect of CH and CD quenching on the luminescence lifetime of Er(3+) Nd(3+) and Yb(3+) in the Cs[Ln(HFA)(4)] system has been quantified, and we have shown that for Er(3+) ions the quenching is dominated by the nearest neighbor CH oscillators, whereas for Nd(3+) ions the roles of more distant CH oscillators and nearest neighbor CD oscillators are important.     

Magnetic iron oxide nanoparticles for biorecognition: evaluation of surface coverage and activity

Modifying the surfaces of magnetic nanoparticles (MNPs) by the covalent attachment of biomolecules will enable their implementation as contrast agents for magnetic resonance imaging or as media for magnetically assisted bioseparations. In this paper we report both the surface coverage and the activity of IgG antibodies on MNPs. The antibodies were immobilized on gamma-Fe2O3 nanoparticles by conventional methods using aminopropyltriethoxy silane and subsequent activation by glutaraldehyde. Novel fluorescence methods were used to provide a quantitative evaluation of this well-known approach. Our results show that surface coverage can be stoichiometrically adjusted with saturated surface coverage occurring at approximately 36% of the theoretical limit. The saturated surface coverage corresponds to 34 antibody molecules bound to an average-sized MNP (32 nm diameter). We also show that the immobilized antibodies retain approximately 50% of their binding capacity at surface-saturated levels.     

Limitations of quantum simulation examined by simulating a pairing Hamiltonian using nuclear magnetic resonance

Quantum simulation uses a well-known quantum system to predict the behavior of another quantum system. Certain limitations in this technique arise, however, when applied to specific problems, as we demonstrate with a theoretical and experimental study of an algorithm proposed by Wu, Byrd, and Lidar [Phys. Rev. Lett. 89, 057904 (2002).10.1103/PhysRevLett.89.057904] to find the low-lying spectrum of a pairing Hamiltonian. While the number of elementary quantum gates required scales polynomially with the size of the system, it increases inversely to the desired error bound E. Making such simulations robust to decoherence using fault tolerance requires an additional factor of approximately 1/E gates. These constraints, along with the effects of control errors, are illustrated using a three qubit NMR system.     

Dotplot: A Program for Exploring Self-Similarity in Millions of Lines of Text and Code

Abstract

An interactive program, dotplot, has been developed for browsing millions of lines of text and source code, using an approach borrowed from biology for studying homology (self-similarity) in DNA sequences. With conventional browsing tools such as a screen editor, it is difficult to identify structures that are too big to fit on the screen. In contrast, with dotplots we find that many of these structures show up as diagonals, squares, textures, and other visually recognizable features, as will be illustrated in examples selected from biology and two new application domains, text (AP news, Canadian Hansards) and source code (5ESS®). In an attempt to isolate the mechanisms that produce these features, we have synthesized similar features in dotplots of artificial sequences. We also introduce an approximation that makes the calculation of dotplots practical for use in an interactive browser.     

Electron emission in superfluid and low temperature vapor phase helium

Tungsten filaments used as sources of electrons in a low-temperature liquid or gaseous helium environment have remarkable properties of operating at thousands of degrees kelvin in surroundings at temperatures of order 1 K. We provide an explanation of this performance in terms of important changes in the thermal transport mechanisms. The behavior can be cast as a first-order phase transition.