Additive Function-on-Function Regression

We study additive function-on-function regression where the mean response at a particular time point depends on the time point itself, as well as the entire covariate trajectory. We develop a computationally efficient estimation methodology based on a novel combination of spline bases with an eigenbasis to represent the trivariate kernel function. We discuss prediction of a new response trajectory, propose an inference procedure that accounts for total variability in the predicted response curves, and construct pointwise prediction intervals. The estimation/inferential procedure accommodates realistic scenarios, such as correlated error structure as well as sparse and/or irregular designs. We investigate our methodology in finite sample size through simulations and two real data applications. Supplementary material for this article is available online.     

Analytic Perturbation Theory for Bound States in the Transfer Matrix Spectrum of Weakly Correlated Lattice Ferromagnetic Spin Systems

We consider general d-dimensional lattice ferromagnetic spin systems with nearest neighbor interactions in the high temperature region (β≪1). Each model is characterized by a single site apriori spin distribution taken to be even. We also take the parameter α=〈s ⁴〉−3〈s ²〉²>0, i.e. in the region which we call Gaussian subjugation, where 〈s ^k 〉 denotes the kth moment of the apriori distribution. Associated with the model is a lattice quantum field theory known to contain a particle of asymptotic mass −lnβ and a bound state below the two-particle threshold. We develop a β analytic perturbation theory for the binding energy of this bound state. As a key ingredient in obtaining our result we show that the Fourier transform of the two-point function is a meromorphic function, with a simple pole, in a suitable complex spectral parameter and the coefficients of its Laurent expansion are analytic in β.     

Unprecedented alkene complex of zinc(II): structures and bonding of divinylzinc complexes

This report describes the solid-state structures of a series of divinylzinc complexes, one of which represents the only structurally characterized zinc(II) pi-complex. Vinylzinc reagents, Zn[C(Me)=CH2]2 (1) and Zn[C(H)=CMe2]2 (2), have been synthesized and isolated as white crystalline solids in 66 and 72% yield, respectively. Each compound exhibits an infinite polymeric architecture in the solid state via a series of zinc-pi (1) and zinc-sigma-bonded (2) bridging interactions. Addition of chelating ligands to these divinylzinc compounds allowed isolation of the monomeric adducts (bipy)Zn[C(Me)=CH2]2 (1.bipy), (tmeda)Zn[C(Me)=CH2]2 (1*tmeda), (bipy)Zn[C(H)=CMe2]2 (2*bipy), and (tmeda)Zn[C(H)=CMe2]2 (2*tmeda), of which 1*bipy, 2*bipy, and 2*tmeda have been characterized crystallographically.     

cis-3,5-Dibenzylidene-1,2,4-tritellurole,a novel organotellurium heterocycle

The reaction of sodium phenylethynyltellurolate with ethereal hydrogen chloride afforded, in addition to $\text{trans}$-2,4-dibenzylidene-1,3-di telluretane, a product shown to be the title compound by an X-ray crystallographic analysis.     

Oligomers of a 5-carboxy-methanopyrrolidine β-amino acid. A search for order

CD spectra for homooligomers (n = 4, 6, 8) of (1S,4R,5R)-5-syn-carboxy-2-azabicyclo[2.1.1]hexane (MPCA), a methano-bridged pyrrolidine β-carboxylic acid, suggest an ordered secondary structure. Even in the absence of internal hydrogen bonding, solution NMR, X-ray, and in silico analyses of the tetramer are indicative of conformations with trans-amides and C(5)-amide-carbonyls oriented toward the C(4) bridgehead. This highly constrained β-amino acid could prove useful in the ongoing development of well-defined foldamers.     

Novel diastereoselective synthesis of (E)- and (Z)-allylsilanes via organoboranes

A simple, novel diastereoselective synthesis of both (E)- and (Z)-allylsilanes via organoboranes is developed. (E)-1-Alkenylboronate esters easily prepared from the corresponding terminal alkynes via hydroboration with dibromoborane-methyl sulfide complex followed by treatment with 1,3-propane diol readily react with trimethylsilylmethyllithium at −78 °C in methanol followed by reaction with iodine in methanol to produce the corresponding (Z)-allylsilanes in high yields (72-80%) and in high stereochemical purities (98% as evidenced by CMR spectral data). Similarly, the (Z)-1-alkenylboronate esters react with trimethylsilylmethyllithium at −78 °C in methanol followed by treatment with iodine in methanol to produce the corresponding (E)-allylsilanes in moderate yields (57-65%) in high stereochemical purities (>98% as revealed by CMR spectral data).     

A High‐Barrier Molecular Balance for Studying Face‐to‐Face Arene–Arene Interactions in the Solid State and in Solution

An atropisomeric molecular balance was developed to study face‐to‐face arene–arene interactions. The balance has a large central 1,4,5,8‐naphthalene diimide surface that forms intramolecular arene–arene interactions with two pendent arms. The balance adopts distinct syn and anti isomers with varying numbers of intramolecular interactions. Thus, the strength of the arene–arene interaction could be quantitatively measured by NMR spectroscopy from the anti/syn ratios. The size of the arene arms was easily varied, which allowed examination of the relationship between arene size and strength of the interaction. A nonlinear size dependence was observed in solution with larger arene arms having a disproportionately stronger arene–arene interaction. The intramolecular arene–arene interactions were also characterized in the solid state by X‐ray crystallography. These studies were facilitated by the kinetic stability of the syn and anti isomers at room temperature due to the high isomerization barrier (ΔG=27.0 kcal mol^?1). Thus, the anti isomer could be selectively isolated and crystallized in its folded conformation. The X‐ray structures confirmed that the anti isomers formed two strong intramolecular arene–arene interactions with face‐to‐face geometries. The solid‐state structure analysis also reveals that the rigid framework may contribute to the observed nonlinear size trend. The acetate linker is slightly too long, which selectively destabilizes the balances with smaller arene arms. The larger arene arms are able to compensate for the longer linker and form effective intramolecular arene–arene interactions.     

Molecular recognition in a uradinyl-functionalized stable radical

Stable radical 2-(6-uradinyl)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazole-1-oxyl (1) binds to hydrogen-bonding complement 2,6-di(propylamido)pyridine (DAP) in chloroform with Ka=220 M(-1) at 33 degrees C; ESI-MS shows not only 1:DAP complementary dyad formation, but also 1:(DAP)2 formation at higher concentrations of DAP.     

Improved detection of the histamine receptor on human peripheral blood mononuclear cells by crosslinking using tritiated as compared with radioiodinated histamine

In order to detect histamine receptors on the surface of human peripheral blood mononuclear cells, the cells were incubated in the presence of radiolabelled histamine and then the bifunctional crosslinker disuccimidyl suberate was added in various concentrations. They were then solubilized with sodium dodecyl sulphate, boiled, reduced and the lysate separated by sodium dodecyl sulfate-polyacrylamide gel electrophoresis. Both 3H and 125I-radiolabelled ligands bound to a 16 kDa band, to be defined although a much clearer and obviously unequivocal signal was obtained with 3H-labelled histamine. This molecule migrated with the same mass on sodium dodecyl sulfate-polyacrylamide gel electrophoresis as a 16 kDa subunit which had been purified on a histamine affinity column from Triton X-100 solubilized mononuclear cells, indicating it to be the ligand-binding subunit for the histamine receptor on these cells. For 3H, fluorography with Entensify was required to obtain an autoradiographic signal. Although 3H took much longer to give a signal than 125I, the considerable background, artefacts and heavy lane trailing seen with [125I] histamine were completely abrogated when [3H]histamine was used. In addition, the distinction between specific and nonspecific binding was more clearly seen using [3H]histamine. The modifications reported here which improve signal detection for 3H should encourage the use of tritiated ligands in radioreceptor crosslinking, particularly those of low molecular weight which might otherwise undergo steric modification due to iodination, this having the potential for interfering with receptor ligand binding.     

Improved Synthesis of the ORL Antagonist 1-[(3R,4R)-1-Cyclooctylmethyl-3-ethoxycarbonyl-4-piperidinyl]-3-ethyl-1,3-dihydro-2H-benzimidazol-2-one (J-113397)

A practical synthesis of optically pure 1-[(3R,4R)-1-cyclooctylmethyl-3-ethoxycarbonyl-4-piperidinyl]-3-ethyl-1,3-dihydro-2H-benzimidazol-2-one (J-113397) was developed that avoids the use of chiral columns.