One-Step Generalized Estimating Equations With Large Cluster Sizes

Medical studies increasingly involve a large sample of independent clusters, where the cluster sizes are also large. Our motivating example from the 2010 Nationwide Inpatient Sample (NIS) has 8,001,068 patients and 1049 clusters, with average cluster size of 7627. Consistent parameter estimates can be obtained naively assuming independence, which are inefficient when the intra-cluster correlation (ICC) is high. Efficient generalized estimating equations (GEE) incorporate the ICC and sum all pairs of observations within a cluster when estimating the ICC. For the 2010 NIS, there are 92.6 billion pairs of observations, making summation of pairs computationally prohibitive. We propose a one-step GEE estimator that (1) matches the asymptotic efficiency of the fully iterated GEE; (2) uses a simpler formula to estimate the ICC that avoids summing over all pairs; and (3) completely avoids matrix multiplications and inversions. These three features make the proposed estimator much less computationally intensive, especially with large cluster sizes. A unique contribution of this article is that it expresses the GEE estimating equations incorporating the ICC as a simple sum of vectors and scalars.     

Molecular Design Principles for Near‐Infrared Absorbing and Emitting Indolizine Dyes

Desirable components for dye‐sensitzed solar cell (DSC) sensitizers and fluorescent imaging dyes include strong donating building blocks coupled with well‐balanced acceptor functionalities for absorption beyond the visible range. We have evaluated the effects of increasing acceptor strengths and incorporation of dye morphology controlling groups on molar absorptivity and absorption breadth with indolizine donor‐based dyes. Indolizine‐based D –A and D –π–A sensitizers incorporating bis‐rhodanine, tricyanofuran (TCF), and cyanoacrylic acid functionalities were analyzed for performance in DSC devices. The TCF derivatives were also evaluated as near‐infrared (NIR)‐emissive materials with the AH25 emissions extending past 1000 nm.     

Construction of the 17-Thiasteroid Ring System by the Diene-Sulfur Dioxide Cycloaddition Reaction

Abstract

We recently showed² that the steroid ring system can be constructed with a phosphorus atom replacing a carbon in the D-ring by the cycloaddition of a phosphorus (III) halide with a diene that is a vinyl dihydrophenanthrene derivative, such as (1). The phosphine oxide (3) resulting from the hydrolysis of the initial cycloadduct (2) has some resemblance to the hormone equilenin, which also has rings A and B in naphthalene form.     

THERMAL DEGRADATION OF DIMERS OF PHOSPHOLES

Abstract

The pathway followed by dimers of P-methylphospholes in their thermal degradation in solution is strongly dependent on the concentration. At low concentrations (around 0.04 M) in n-decane or toluene as solvent, decomposition is extensive after 17 h in the range 120–130°C. The major product is the P-methylphosphole from de-dimerization. At concentrations above 1.0 M, decomposition is faster and intermolecular interactions are more important. These interactions dominate over de-dimerization and lead to the loss of the bridging P in the 7-phosphanorbornene moiety to yield the cis-3a,7a-dihydrophosphindole system. From the dimer of 1,3-dimethylphosphole, isomeric dihydrophosphindoles are formed, which differ in location of the methyl group on the 6-membered ring and in configuration at phosphorus. These seem to result from attack by a phosphine group as a nucleophile on the bridging P, followed by bond rearrangements in the resulting phosphoranide ion. Decomposition was faster in the presence of tri-n-butylphosphine, which apparently acted as a catalyst through a similar mechanism. By using appropriate conditions each dihydrophosphindole isomer (1,3,5- or 1,3,7-trimethyl) could be made to predominate and this allowed their isolation. Characterization of the isomers and of some derivatives by ³¹P, ¹H, and ¹³C NMR techniques was performed. Most of the thermolysis products were highly complex mixtures and many minor products remain unidentified. The dimer of 1-phenyl-3-methyl-phosphole did not decompose to the phosphole, but the product composition was dependent on concentration.     

The Use of 18-Crown-6 As Phase Transfer Catalyst in the Reissert Reaction

Solid-liquid phase transfer of cyanide ion by 18-cro'wn-6 increases the yield of the Reissert reaction and eliminates the undesirable pseudo-base formation.     

STEREOCHEMICAL PROPERTIES OF THE 1-CHLORO-1- PHENYL-2,5-DIMETHYL-2-PHOSPHOLENIUM ION AND DERIVED OXIDE AND PHOSPHINE

Abstract

The cycloaddition of phenylphosphonous dichloride and trans, trans-2,4-hexadiene, or the addition of chlorine to trans-1-phenyl-cis-2,5-dimethyl-3-phospholene, gave 1-chloro-1-phenyl-2,5-dimethyl-2-phospholenium chloride. This compound shows no evidence in its ³¹P and ¹H nmr spectra for the existence of cis, trans isomers, yet on hydrolysis or dehalogenation with magnesium the resulting oxide and phosphine, respectively, are seen to be isomer mixtures. This phenomenon is explained by a rapid equilibration of the cis, trans form of the I-chloro ion through a pentacovalent species. Structures of the oxides and phosphines were assigned by ¹H and ¹³C nmr relations. The 1-phenyl-cis-2,5-dimethyl-3-phospholenium ion and related compounds were also characterized.     

Self-assembly and aggregation of ATRP prepared amphiphilic BAB tri-block copolymers contained nonionic ethylene glycol and fluorescent 9,10-di(1-naphthalenyl)-2-vinyl-anthracene/1-vinyl-pyrene segments

Two novel amphiphilic BAB-type block copolymers, ADN-PEG3400-ADN and Py-PEG3400-Py containing deep blue and bluish-green fluorescent moieties were prepared using atom transfer radical polymerization (ATRP) (where, ADN = poly(9,10-di(1-naphthalenyl)-2-vinylanthracene), Py = poly(1-vinyl pyrene) and PEG3400 = poly(ethylene glycol) with M_n = 3400 g/mol). The GPC number averaged molecular weights (MW) of the block copolymers were M_n = 9600 and 13,800 g/mol, respectively, based on polystyrene MW standards. The PEG3400 segment has a melting temperature (T_m peak) at 64–65 °C, whereas the glass transition temperatures (T_g midpoint) of the ADN and Py segments were found to be 230 °C and 193 °C, respectively, and are similar to their respective homopolymers indicating complete microphase segregration. The photoluminescence (PL) emission of the copolymers ADN-PEG3400-ADN exhibited two maxima at 423.5 nm and 441.5 nm while Py-PEG3400-Py has a maximum at 488.5 nm. Both copolymers form individual spherical micelles with diameter from 30 to 90 nm for Py-PEG3400-Py and 40–160 nm for ADN-PEG3400-ADN. The micelles, however, transform into cross-linked pearl-necklace-like aggregates at polymer concentrations above 1000 ppm, which may be attributed to the physical cross-linking between adjacent spherical micelles caused by the PEG3400 segments.     

Natural bond orbital analysis in the ONETEP code: Applications to large protein systems

First principles electronic structure calculations are typically performed in terms of molecular orbitals (or bands), providing a straightforward theoretical avenue for approximations of increasing sophistication, but do not usually provide any qualitative chemical information about the system. We can derive such information via post‐processing using natural bond orbital (NBO) analysis, which produces a chemical picture of bonding in terms of localized Lewis‐type bond and lone pair orbitals that we can use to understand molecular structure and interactions. We present NBO analysis of large‐scale calculations with the ONETEP linear‐scaling density functional theory package, which we have interfaced with the NBO 5 analysis program. In ONETEP calculations involving thousands of atoms, one is typically interested in particular regions of a nanosystem whilst accounting for long‐range electronic effects from the entire system. We show that by transforming the Non‐orthogonal Generalized Wannier Functions of ONETEP to natural atomic orbitals, NBO analysis can be performed within a localized region in such a way that ensures the results are identical to an analysis on the full system. We demonstrate the capabilities of this approach by performing illustrative studies of large proteins—namely, investigating changes in charge transfer between the heme group of myoglobin and its ligands with increasing system size and between a protein and its explicit solvent, estimating the contribution of electronic delocalization to the stabilization of hydrogen bonds in the binding pocket of a drug‐receptor complex, and observing, in situ, the n → π* hyperconjugative interactions between carbonyl groups that stabilize protein backbones. © 2012 Wiley Periodicals, Inc.