Uniqueness Properties of Hardy Space Functions

We study the boundary uniqueness properties of Hardy space functions in several complex variables. Along the way, we develop properties of the Lumer Hardy space.     

Decision problems for inverse monoids presented by a single sparse relator

We study a class of inverse monoids of the form M=Inv 〈X∣w=1〉, where the single relator w has a combinatorial property that we call sparse. For a sparse word w, we prove that the word problem for M is decidable. We also show that the set of words in (X∪X ⁻¹)^* that represent the identity in M is a deterministic context free language, and that the set of geodesics in the Schützenberger graph of the identity of M is a regular language.     

Self-assembling cyclic peptides: molecular dynamics studies of dimers in polar and nonpolar solvents

The self-assembly of cyclic D,L-alpha-peptides into hollow nanotubes is a crucial mechanistic step in their application as antibacterial and drug-delivery agents. To understand this process, molecular dynamics (MD) simulations were performed on dimers of cyclic peptides formed from cyclo [(-L-Trp-D-N-MeLeu-)4-]2 and cyclo [(-L-Trp-D-Leu-)4-]2 subunits in nonpolar (nonane) and polar (water) solvent. The dimers were observed to be stable only in nonpolar solvent over the full 10 ns length of the MD trajectory. The behavior of the dimers in different solvents is rationalized in terms of the intersubunit hydrogen bonding, hydrogen bonding with the solvent, and planarity of the rings. It is shown that the phi and psi dihedral angles of a single uncapped ring in nonane lie in the beta-sheet region of the Ramachandran plot, and the ring stays in a flat conformation. Steered MD (SMD) simulations based on Jarzynski's equality were performed to obtain the potential of mean force as a function of the distance between the two rings of the capped dimer in nonane. It is also shown that a single peptide subunit prefers to reside close to the nonane/water interface rather than in bulk solvent because of the amphiphilic character of the peptide ring. The present MD results build the foundation for using MD simulations to study the mechanism of the formation of cyclic peptide nanotubes in lipid bilayers.     

Reversible activation of diblock copolymer monolayers at the interface by pH modulation, 2: Membrane interactions at the solid/liquid interface

A monolayer of the pH-responsive poly[2-(dimethylamino)ethyl methacrylate-block-methyl methacrylate] diblock copolymer [PDMAEMA-PMMA] was transferred from the air/water interface to a silicon substrate for evaluation as a tunable interlayer between biological material and solid substrates. Specular neutron reflectivity experiments revealed that the weak polyelectrolyte PDMAEMA chains at the solid/liquid interface can be reversibly activated by pH modulation. The thickness, scattering length density, and surface roughness of the polymer film can be systematically controlled by pH titration. As a simple model of plasma membranes, a lipid bilayer was deposited onto the polymer film. The membrane-substrate interaction was characterized by neutron reflectivity experiments, demonstrating that the membrane-substrate distance could be reversibly regulated by pH titration. These results confirm the potential of stimuli-responsive polymers for precise control of cell-surface interactions.     

Stereochemically general approach to adjacent bis(tetrahydrofuran) cores of annonaceous acetogenins

A series of six 2,5-disubstituted adjacent bis(tetrahydrofuran) stereoisomers with trans/erythro/cis, trans/threo/trans, or cis/threo/cis relative stereochemistry have been synthesized from known dihydroxycyclooctenes via ring opening/cross metathesis and Pd(0)-mediated asymmetric double cycloetherification. The stereochemistry of four of these isomers has been found in the biologically active annonaceous acetogenin natural products. [reaction: see text].     

Organogels derived from tetranitrated crown ethers

[reaction: see text] The 3,3',4'4'-tetranitrodibenzocrown ethers TNDB24C8 and TNDB30C10 form organogels with chloroalkanes at 3% w/v. Atomic force microscopy and scanning electron microscopy have been used to characterize the superstructure of the gels. Gels prepared using TNDB30C10 and CHCl(3) are more fibrous and are ordered into elongated domains attributable to exposed parts of intermingled fibers. Differential scanning calorimetry shows that the gel aids in the formation of supercooled CHCl(3) (DeltaT = 21 K, DeltaH(av) = 19.0 +/- 1.5 kJ mol(-)(1)) and that the gel liquefies at 307 K.     

Search for the Theta+ pentaquark in the reaction gammad --> pK-K+n

A search for the Theta+ in the reaction gammad --> pK-K+n was completed using the CLAS detector at Jefferson Lab. A study of the same reaction, published earlier, reported the observation of a narrow Theta+ resonance. The present experiment, with more than 30 times the integrated luminosity of our earlier measurement, does not show any evidence for a narrow pentaquark resonance. The angle-integrated upper limit on Theta+ production in the mass range of 1.52-1.56 GeV/c2 for the gammad --> pK-Theta+ reaction is 0.3 nb (95% C.L.). This upper limit depends on assumptions made for the mass and angular distribution of Theta+ production. Using Lambda(1520) production as an empirical measure of rescattering in the deuteron, the cross section upper limit for the elementary gamman --> K-Theta+ reaction is estimated to be a factor of 10 higher, i.e., approximately 3 nb (95% C.L.).     

Azimuthal angle correlations for rapidity separated Hadron pairs in d+Au collisions at square root of sNN=200 GeV

Deuteron-gold (d+Au) collisions at the Relativistic Heavy Ion Collider provide ideal platforms for testing QCD theories in dense nuclear matter at high energy. In particular, models suggesting strong saturation effects for partons carrying small nucleon momentum fraction (x) predict modifications to jet production at forward rapidity (deuteron-going direction) in d+Au collisions. We report on two-particle azimuthal angle correlations between charged hadrons at forward/backward (deuteron/gold going direction) rapidity and charged hadrons at midrapidity in d+Au and p+p collisions at square root of sNN=200 GeV. Jet structures observed in the correlations are quantified in terms of the conditional yield and angular width of away-side partners. The kinematic region studied here samples partons in the gold nucleus with x~0.1 to ~0.01. Within this range, we find no x dependence of the jet structure in d+Au collisions.     

A modern Bayesian look at the multi‐armed bandit

A multi‐armed bandit is an experiment with the goal of accumulating rewards from a payoff distribution with unknown parameters that are to be learned sequentially. This article describes a heuristic for managing multi‐armed bandits called randomized probability matching, which randomly allocates observations to arms according the Bayesian posterior probability that each arm is optimal. Advances in Bayesian computation have made randomized probability matching easy to apply to virtually any payoff distribution. This flexibility frees the experimenter to work with payoff distributions that correspond to certain classical experimental designs that have the potential to outperform methods that are ‘optimal’ in simpler contexts. I summarize the relationships between randomized probability matching and several related heuristics that have been used in the reinforcement learning literature. Copyright © 2010 John Wiley & Sons, Ltd.     

Spatial epidemics and local times for critical branching random walks in dimensions 2 and 3

The behavior at criticality of spatial SIR epidemic models in dimensions two and three is investigated. In these models, finite populations of size N are situated at the sites of the integer lattice, and infectious contacts are limited to individuals at the same or at neighboring sites. Susceptible individuals, once infected, remain contagious for one unit of time and then recover, after which they are immune to further infection. It is shown that the measure-valued processes associated with these epidemics, suitably scaled, converge, in the large-N limit, either to a standard Dawson–Watanabe process (super-Brownian motion) or to a Dawson–Watanabe process with location-dependent killing, depending on the size of the the initially infected set. A key element of the argument is a proof of Adler’s 1993 conjecture that the local time processes associated with branching random walks converge to the local time density process associated with the limiting super-Brownian motion.