Dimers, tilings and trees

Generalizing results of Temperley (London Mathematical Society Lecture Notes Series 13 (1974) 202), Brooks et al. (Duke Math. J. 7 (1940) 312) and others (Electron. J. Combin. 7 (2000); Israel J. Math. 105 (1998) 61) we describe a natural equivalence between three planar objects: weighted bipartite planar graphs; planar Markov chains; and tilings with convex polygons. This equivalence provides a measure-preserving bijection between dimer coverings of a weighted bipartite planar graph and spanning trees of the corresponding Markov chain. The tilings correspond to harmonic functions on the Markov chain and to “discrete analytic functions” on the bipartite graph.The equivalence is extended to infinite periodic graphs, and we classify the resulting “almost periodic” tilings and harmonic functions.     

Evidence for the quantum birth of our universe

We present evidence for a nonsingular origin of the Universe with intial conditions determined by quantum physics and relativistic gravity. In particular, we establish that the present temperature of the microwave background and the present density of the Universe agree well with our predictions from these intial conditions, after evolution to the present age using the Einstein-Friedmann equation. Remarkably, the quantum origin for the Universe naturally allows its evolution at exactly the critical density. We also discuss the consequences of these results to some fundamental aspects of quantum physics in the early Universe.     

The conversion of isotopically labeled glycine to 1-methyl-2-amino-2-imidazolin-4-one (creatinine)

A procedure is presented which allows the conversion of glycine to creatinine (1-methyl-2-amino-2-imidazolin-4-one). The scheme was devised to optimize the yield based on the amount of glycine used so that the relatively readily available isotopically labeled glycines could be efficiently converted to the correspondingly labeled creatinines. In this case 1-(¹³C)-glycine was converted to 4-(¹³C)-1-methyl-2-amino-2-imidazolin-4-one.     

Changes in adsorbed fibrinogen upon conversion to fibrin

The conversion of adsorbed fibrinogen to fibrin in the presence of the enzyme thrombin was studied using surface plasmon resonance (SPR), a quartz crystal microbalance (QCM), sum frequency generation (SFG), atomic force microscopy (AFM), and an elutability assay. Exposure of adsorbed fibrinogen to thrombin resulted in a mass loss at the surface consistent with fibrinopeptide release and conversion to fibrin. Changes in hydration upon conversion of adsorbed fibrinogen to fibrin were determined from comparisons of acoustic (QCM) and optical (SPR) mass adsorption data. Conversion to fibrin also resulted in the adsorbed layer becoming more strongly bound to the surface and more compact. The elutability of adsorbed fibrinogen by Triton X-100, studied with SPR, decreased from 90 +/- 5 to 6 +/- 2% after conversion to fibrin. The height of the adsorbed monolayer, as determined by AFM, decreased from 5.5 +/- 2.2 to 1.7 +/- 0.8 nm. We conclude that thrombin-catalyzed fibrinopeptide release triggers significant changes in fibrinogen conformation beyond peptide cleavage.     

Representation type of the blocks of category in types and

In this paper a complete classification of the representation type of the infinitesimal blocks of the parabolic category for the complex simple Lie algebras of types F₄ and G₂ is given.