Gaussian graphical models with toric vanishing ideals

Annals of the Institute of Statistical Mathematics - Gaussian graphical models are semi-algebraic subsets of the cone of positive definite covariance matrices. They are widely used throughout...     

Titanatranes derailed: static and dynamic triethanolamine slippage induced by polyphenoxide chelation

Aryloxytitanatranes [N(CH(2)CH(2)O)(3)]Ti[OC(6)H(2)-2,4-(t)()Bu(2)-6-CHPh(3)(-)(n)()(C(6)H(2)-3,5-(t)()Bu(2)-2-OH)(n)(-)(1)] (1, n = 1; 2, n = 2; 3, n = 3) containing aryloxides derived from substituted triphenylmethanes are formed in high yield in the reactions of the corresponding phenols with tert-butoxytitanatrane [N(CH(2)CH(2)O)(3)]Ti(O(t)()Bu). The aryloxytitanatranes adopt monomeric, trigonal bipyramidal structures, as confirmed by X-ray crystallography for 1 and 2. The compounds with pendant phenol groups display fluxional behavior due to interchange of the bound phenoxide with the free phenol groups, most likely via a mechanism involving displacement of one arm of the nitrilotriethoxide by the dangling phenol group. The amidotitanatrane [[N(CH(2)CH(2)O)(3)]Ti(NEt(2))](2) reacts with the bisphenol PhCH(C(6)H(2)-3,5-(t)()Bu(2)-2-OH)(2) to give a crystallographically characterized fully metalated cyclic octatitanium complex of the formula [PhCH(C(6)H(2)-3,5-(t)()Bu(2)-2-O)(2)Ti(2)[(OCH(2)CH(2))(3)N](2)](4) (4). The structure of 4 reveals a metallamacrocycle (minimum ring size = 28 members) consisting of four repeating unsymmetrical dititanium units. In each dititanium unit, there is an unprecedented slippage of the nitrilotriethoxide ligand such that both triethanolamine nitrogens coordinate to only one of the two titaniums, while the bisphenoxide is coordinated only to the other titanium. The propensity of the polyphenoxide ligands to chelate is attributed to favorable pi-bonding interactions attainable in the eight-membered chelate rings.     

THERMAL REQUIREMENTS OF PHOTOSENSITIZED PYRIMIDINE DIMER SPLITTING

Abstract— A cis, syn -pyrimidine dimer (derived from thymine and orotate) covalently linked to 5-methoxyindole has been studied as a mechanistic model of photosensitized pyrimidine dimer splitting. In this dimer-indole, photoinitiated electron transfer to the dimer causes splitting in a manner that parallels the mechanism by which the DNA photolyases are thought to act. Dissolved in EPA (diethyl ether-isopentane-ethyl alcohol, 5: 5: 1, by vol) at room temperature, the dimer-indole exhibited indole fluorescence quenching and underwent splitting upon irradiation at 300 nm. In an EPA glass at 77 K, however, no splitting was detectable. To distinguish the effects of temperature and immobilization, photolysis experiments were performed on PMM [poly(methyl methacrylate)] films containing dimer-indole. In PMM at room temperature, dimer-indole underwent splitting when irradiated at 300 nm, which indicated that immobilization per se was not responsible for the failure of dimer-indole to split at low temperature. Furthermore, no splitting was observed when dimer-indole was irradiated in PMM at 77 K. These results imply that a step following photoinitiated, intramolecular electron transfer from indole to dimer has an insurmountable activation barrier at 77 K. The mechanistic implications for the photolyases are considered.     

Subwavelength position sensing using nonlinear feedback and wave chaos

We demonstrate a position-sensing technique that relies on the inherent sensitivity of chaos, where we illuminate a subwavelength object with a complex structured radio-frequency field generated using wave chaos and nonlinear feedback. We operate the system in a quasiperiodic state and analyze changes in the frequency content of the scalar voltage signal in the feedback loop. This allows us to extract the object's position with a one-dimensional resolution of ~λ/10,000 and a two-dimensional resolution of ~λ/300, where λ is the shortest wavelength of the illuminating source.     

The topological theory of current graphs

W. Gustin's introduction of combinatorial current graphs as a device for obtaining orientable imbeddings of Cayley “color” graphs was fundamental to the solution of the Heawood map-coloring problem by G. Ringel, J. W. T. Youngs, C. M. Terry, and L. R. Welch. The topological current graphs of this paper lead to a construction that generalizes the method of Gustin and its augmentation to “vortex” graphs by Youngs, extending the scope of current graph theory from Cayley graphs alone to the much larger class of graphs that are covering spaces.     

Brilliant Sm, Eu, Tb, and Dy chiral lanthanide complexes with strong circularly polarized luminescence

The synthesis, characterization, and luminescent behavior of trivalent Sm, Eu, Dy, and Tb complexes of two enantiomeric, octadentate, chiral, 2-hydroxyisophthalamide ligands are reported. These complexes are highly luminescent in solution. Functionalization of the achiral parent ligand with a chiral 1-phenylethylamine substituent on the open face of the complex in close proximity to the metal center yields complexes with strong circularly polarized luminescence (CPL) activity. This appears to be the first example of a system utilizing the same ligand architecture to sensitize four different lanthanide cations and display CPL activity. The luminescence dissymmetry factor, g(lum), recorded for the Eu(III) complex is one of the highest values reported, and this is the first time the CPL effect has been demonstrated for a Sm(III) complex with a chiral ligand. The combination of high luminescence intensity with CPL activity should enable new bioanalytical applications of macromolecules in chiral environments.     

A Series of Collaborations between Various Pharmaceutical Companies and Regulatory Authorities Concerning the Analysis of Biomolecules Using Capillary Electrophoresis: Additional Instruments/Buffer

An international project team (including members from US, Canada and UK) was formed from a number of interested biopharmaceutical companies and regulatory authorities to conduct a cross-organisation collaboration exercise. The results of the first comparison with eight different organisations that used instruments of the same equipment model, the same reagents, and the same methodology has been reported previously [1]. This report represents the addition of other instruments using a different run buffer. The relative migration times were different, as expected, prohibiting a direct comparison between companies. The within-organisation variability was low for both relative migration time (<0.34% RSD% for all companies save one) and the peak area (<5% RSD% for all companies save one) when measuring the purity of a representative IgG sample. The apparent molecular weight of bovine serum albumin was measured with good precision (less than 10% RSD% across all companies) to the theoretical value when all data is utilized (67.5 kDa compared to 66.4 kDa). For a representative IgG sample, the three main components, IgG Light Chain, IgG Non-glycosylated Heavy Chain, and IgG Heavy Chain, could not be separated, specifically the IgG Non-glycosylated Heavy Chain and IgG Heavy Chain. When the IgG Non-glycosylated Heavy Chain and IgG Heavy Chain were combined for all organisations, the fractional peak area for the IgG Light Chain and IgG Non-glycosylated Heavy Chain + IgG Heavy Chain peak also showed excellent agreement, with less than 7.5 and 3.5% RSD%, respectively. The value of this exercise is in demonstrating the reliability of CE for the determination of apparent size of biopharmaceutical proteins. This underpins the appropriate use of such CE data in support of regulatory submissions.

     

Formulation of magnetically perturbed time-dependent density functional theory

A formulation of time-dependent density functional theory (TDDFT) in the presence of a static imaginary perturbation is derived. A perturbational approach is applied leading to corrections to various orders in the quantities of interest, namely, the excitation energies and transition densities. The perturbed TDDFT equations are relatively straightforward to derive but the resulting expressions are rather cumbersome. Simplifications of these equations are suggested. Both the simplified and full expressions are used to obtain equations for first- and second-order corrections to the excitation energy, the first-order correction to the transition density, and the corrections for both quantities to first-order in two different perturbations. This formulation, called magnetically perturbed TDDFT, details how conventional TDDFT calculations can be corrected to allow for the inclusion of a static magnetic field and/or spin-orbit coupling.     

Direct measurement of the effective charge in nonpolar suspensions by optical tracking of single particles

The authors develop an ultrasensitive method for the measurement of the charge carried by a colloidal particle in a nonpolar suspension. The technique uses the phenomenon of the resonance of a particle held in an optical tweezer trap and driven by a sinusoidal electric field. The trapped particle forms a strongly damped harmonic oscillator whose fluctuations are a function of gamma, the ratio of the root-mean-square average of the electric and thermal forces on the particle. At low applied fields (gamma<1) the particle is confined to the optical axis, while at high fields (gamma>1) the probability distribution of the particle is double peaked. The periodically modulated thermal fluctuations are measured with nanometer sensitivity using an interferometric position detector. Charges, as low as a few elementary charges, can be measured with an uncertainty of about 0.25 e. This is significantly better than previous techniques and opens up new possibilities for the study of nonpolar suspensions.     

Cross-coupling for cross-conjugation: practical synthesis and Diels-Alder reactions of [3]dendralenes

The parent [3]dendralene and 2-substituted [3]dendralenes are made easily through cross-coupling reactions. Contrary to some earlier reports, [3]dendralene is sufficiently stable to be handled using standard synthetic methods. These compounds allow the one-step stereoselective construction of polycyclic frameworks through reactions with dienophiles. Site selectivity and stereoselectivity in Diels-Alder reactions with dienophiles are generally not influenced by the nature of the [3]dendralene's 2-substituent; these features can, however, be influenced with Lewis acids.