Partial inner product spaces: Some categorical aspects

We make explicit in terms of categories a number of statements from the theory of partial inner product spaces (PIP spaces) and operators on them. In particular, we construct sheaves and cosheaves of operators on certain PIP spaces of practical interest.Comment: 21 page

The synthesis of monomers with pendent ethynyl group for modified high performance thermoplastics

The objectives of this project were to develop synthetic schemes for the following classes of modified monomers: (1) difunctional triarylethanes with pendent acetylenic groups; and (2) tertiary aspartimides with terminal acetylene groups at the two ends. Our efforts have resulted in the successful development of high yield schemes for the syntheses of several diamino and bisphenolic analogs of difunctional triarylethanes with pendent ethynyl group. A scheme for one new tertiary aspartimide was also established. Multi-gram samples of all prepared new monomers were provided to our technical contact at NASA-LaRC and preliminary polymerization studies were encouraging. Details of the accomplished work within the last four years are described

Simulating full-sky interferometric observations

Aperture array interferometers, such as that proposed for the Square Kilometre Array (SKA), will see the entire sky, hence the standard approach to simulating visibilities will not be applicable since it relies on a tangent plane approximation that is valid only for small fields of view. We derive interferometric formulations in real, spherical harmonic and wavelet space that include contributions over the entire sky and do not rely on any tangent plane approximations. A fast wavelet method is developed to simulate the visibilities observed by an interferometer in the full-sky setting. Computing visibilities using the fast wavelet method adapts to the sparse representation of the primary beam and sky intensity in the wavelet basis. Consequently, the fast wavelet method exhibits superior computational complexity to the real and spherical harmonic space methods and may be performed at substantially lower computational cost, while introducing only negligible error to simulated visibilities. Low-resolution interferometric observations are simulated using all of the methods to compare their performance, demonstrating that the fast wavelet method is approximately three times faster that the other methods for these low-resolution simulations. The computational burden of the real and spherical harmonic space methods renders these techniques computationally infeasible for higher resolution simulations. High-resolution interferometric observations are simulated using the fast wavelet method only, demonstrating and validating the application of this method to realistic simulations. The fast wavelet method is estimated to provide a greater than ten-fold reduction in execution time compared to the other methods for these high-resolution simulations.Comment: 16 pages, 9 figures, replaced to match version accepted by MNRAS (major additions to previous version including new fast wavelet method

Dynamic regulation of quaternary organization of the M1 muscarinic receptor by subtype-selective antagonist drugs

Although rhodopsin-like G protein-coupled receptors can exist as both monomers and non-covalently associated dimers/oligomers, the steady-state proportion of each form and whether this is regulated by receptor ligands is unknown. Herein we address these topics for the M1 muscarinic acetylcholine receptor, a key molecular target for novel cognition enhancers, by employing Spatial Intensity Distribution Analysis. This method can measure fluorescent particle concentration and assess oligomerization states of proteins within defined regions of living cells. Imaging and analysis of the basolateral surface of cells expressing some 50 molecules.microm-2 of the human muscarinic M1 receptor identified an ~75/25 mixture of receptor monomers and dimers/oligomers. Both sustained and shorter-term treatment with the selective M1 antagonist pirenzepine resulted in a large shift in the distribution of receptor species to favor the dimeric/oligomeric state. Although sustained treatment with pirenzepine also resulted in marked upregulation of the receptor, simple mass-action effects were not the basis for ligand-induced stabilization of receptor dimers/oligomers. The related antagonist telenzepine also produced stabilization and enrichment of the M1 receptor dimer population but the receptor subtype non-selective antagonists atropine and N-methylscopolamine did not. In contrast, neither pirenzepine nor telenzepine altered the quaternary organization of the related M3 muscarinic receptor. These data provide unique insights into the selective capacity of receptor ligands to promote and/or stabilize receptor dimers/oligomers and demonstrate that the dynamics of ligand regulation of the quaternary organization of G protein-coupled receptors is markedly more complex than previously appreciated. This may have major implications for receptor function and behavior