A note on model diagnostics in longitudinal data analysis

Longitudinal study has become one of the most commonly adopted designs in medical research. The generalized estimating equations (GEE) method and/or mixed effects models are employed very often in causal inferences. The related model diagnostic procedures are not yet fully formalized, and perhaps never will be. The potential causes of major problems are the high variety of the dependence within subjects and/or the number of repeated measurements. A single testing procedure, e.g., run test, is not possible to resolve all model diagnostics problems in longitudinal data analysis. Multiple quantitative indexes for model diagnostics are needed to take into account this variety. We propose eight testing procedures for randomness accompanied with some conventional and/or non-conventional plots to remedy model diagnostics in longitudinal data analysis. The proposed issue in this paper is well illustrated with four clinical studies in Taiwan.     

Biradicals/zwitterions from thermolysis of enyne-isocyanates. Application to the synthesis of 2(1H)-pyridones, benzofuro[3,2-c]pyridin-1(2H)-ones, 2,5-dihydro-1H-pyrido[4,3-b]indol-1-ones, and related compounds

Thermolysis of benzannulated enyne-isocyanates 13 and enyne-isocyanates 36 and 37 promoted the cycloaromatization reactions to generate in situ O,4-didehydro-2-hydroxyquinolines and O,4-didehydro-2-hydroxypyridines, respectively, as reactive intermediates. These cycloaromatized intermediates could be captured either as biradicals and/or as zwitterions depending on the nature of the substituent at the alkynyl terminus. The intermediate derived from cycloaromatization of 13a bearing a phenyl substituent could be regarded as biradical 14, which then abstracts hydrogen atoms from gamma-terpinene leading to 2(1H)-quinolinone 15. Alternatively, the same intermediate could also be regarded as zwitterion 14', which then undergoes an initial hydride abstraction from gamma-terpinene followed by protonation to produce 15. The presence of a 2-phenylethyl substituent in 13b and 37a or a 2-methylphenyl substituent in 37b also allowed the resulting intermediates to be captured intramolecularly either as biradicals or as zwitterions, producing 2(1H)-quinolinone 19, 2(1H)-pyridone 39, and benzopyranopyridine 43, respectively. On the other hand, with a 2-methoxyphenyl, a 2-(dimethylamino)phenyl, or a 3-methoxypropyl substituent, the chemical behavior of the cycloaromatized adduct could be best accounted for in terms of a zwitterionic intermediate leading to benzofuro[3,2-c]quinolin-6(5H)-one (20), 5,11-dihydro-11-methyl-6H-indolo[3,2-c]quinolin-6-one (25), benzofuro[3,2-c]pyridin-1(2H)-one 44, 2,5-dihydro-2,5-dimethyl-1H-pyrido[4,3-b]indol-1-one 46, and related compounds. Interestingly, thermolysis of 37f bearing a 2-(methoxymethyl)phenyl substituent at the alkynyl terminus produced the unexpected benzopyranopyridine 56 as the major product in a process involving the cleavage of the bond between the methoxyl oxygen and the adjacent methylene carbon. The efficiency and selectivity of the cycloaromatization reaction could also be enhanced by the introduction of 1.1 to 10 equiv of dimethylphenylsilyl chloride to the reaction mixture to capture the resulting zwitterion.     

The foam analogy: from phases to elasticity

By mapping the interactions of colloidal particles onto the problem of minimizing areas, the physics of foams can be used to understand the phase diagrams of both charged and fuzzy colloids. We extend this analogy to study the elastic properties of such colloidal crystals and consider the face-centered cubic, body-centered cubic and A15 lattices. We discuss two types of soft interparticle potentials corresponding to charged and fuzzy colloids, respectively, and we analyze the dependence of the elastic constants on density as well as on the parameters of the potential. We show that the bulk moduli of the three lattices are generally quite similar, and that the shear moduli of the two non-close-packed lattices are considerably smaller than in the face-centered cubic lattice. We find that in charged colloids, the elastic constants are the largest at a finite screening length, and we discuss a shear instability of the A15 lattice.     

Recovery of thick shear bands in atactic polystyrene

The DSC thermograms of the shear band material cut out by a diamond saw to include some undeformed material revealed two T_g's clearly separated by about 10°C. The first T_g was at the same temperature as the T_g of the undeformed material. The second T_g, which was at a higher temperature than the first T_g, appeared shortly after the shear strain recovery during the heating of the shear band material in the DSC. When the shear strain in the shear band was partially reversed by mechanical means before taking the DSC thermogram, the ΔT between the two T_g's decreased and when the shear strain was mechanically reversed to almost zero, the second T_g disappeared. The stored energy of shear band material was found to be similar to that of the bulk compressed material for large strains. Dimensional recovery during heating of specimens with thick and fine bands was similar, both taking place above T_g.     

Matchings and radon transforms in lattices. I. Consistent lattices

An element in a lattice is join-irreducible if x=ab implies x=a or x=b. A meet-irreducible is a join-irreducible in the order dual. A lattice is consistent if for every element x and every join-irreducible j, the element xj is a join-irreducible in the upper interval [x, î]. We prove that in a finite consistent lattice, the incidence matrix of meet-irreducibles versus join-irreducibles has rank the number of join-irreducibles. Since modular lattices and their order duals are consistent, this settles a conjecture of Rival on matchings in modular lattices.     

Direct evidence of oxidized gold on supported gold catalysts

Supported gold catalysts have drawn worldwide interest due to the novel properties and potential applications in industries. However, the origin of the catalytic activity in gold nanoparticles is still not well understood. In this study, time-of-flight secondary ion mass spectroscopy (TOF-SIMS) has been applied to investigate the nature of gold in Au (1.3 wt %)/gamma-Al2O3 and Au (2.8 wt %)/TiO2 catalysts prepared by the deposition-precipitation method. The SIMS spectrum of the supported gold catalysts presented AuO-, AuO2-, and AuOH- ion clusters. These measurements show direct evidence for oxidized gold on supported gold catalysts and may be helpful to gaining better understanding of the origin of the catalytic activity.     

Separation of Dyes from Aqueous Solutions by Paper Adsorption

Separation of the dyes methyl violet, methylene blue, and congo red from aqueous solutions by paper capillary permeation adsorption method was studied using paper. Nearly 100% of the investigated dyes could be separated under the optimum conditions. The effect of pH on the separation efficiency was studied in particular. At pH 5–9, 1.3–11, and 7–11, the maximum separation was achieved for methyl violet, methylene blue and congo red, respectively. The effects of dye concentration and some foreign ions on the separatability were examined. Moreover, the selective separation of some dyes was attempted by elution with chemical reagents.     

Discovery of New Glucose Uptake Inhibitors as Potential Anticancer Agents by Non-Radioactive Cell-Based Assays

Tumor cells rely on aerobic glycolysis to support growth and survival, thus require more glucose supply. Glucose transporters GLUTs, primarily GLUT1, are overexpressed in various cancers. Targeting GLUTs has been regarded as a promising anticancer strategy. In this study, we first evaluated 75 potential GLUT1 inhibitors obtained from virtual screening of the NCI chemical library by a high-throughput cell-based method using a fluorescent glucose analogue 2-(N-(7-nitrobenz-2-oxa-1,3-diazol-4-yl)amino)-2-deoxy-d-glucose (2-NBDG) in COS-7 and SKOV3 cells that express high levels of GLUT1. Four compounds, #12, #16, #43 and #69, that significantly inhibited glucose uptake were further evaluated using flow cytometry directly measuring 2-NBDG uptake at the single-cell level and a Glucose Uptake-Glo^TM assay indirectly measuring 2-deoxy-d-glucose uptake in SKOV3, COS-7 or MCF-7 cells. The inhibitory effect on cancer cell growth was also determined in SKOV3 and MCF-7 cells, and #12 exhibited the best growth inhibitory effect equivalent to a known GLUT1 inhibitor WZB117. Although the anticancer effect of the identified potential GLUT1 inhibitors was moderate, they may enhance the activity of other anticancer drugs. Indeed, we found that #12 synergistically enhanced the anticancer activity of metformin in SKOV3 ovarian cancer cells.