Random walks on stochastic hyperbolic half planar triangulations

We study the simple random walk on stochastic hyperbolic half planar triangulations constructed in (Angel and Ray, Ann Probab, in press). We show that almost surely the walker escapes the boundary of the map in positive speed and that the return probability to the starting point after n steps scales like © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 49, 213–234, 2016     

The structure of the Mitchell order—I

We isolate here a wide class of well-founded orders called tame orders, and show that each such order of cardinality at most κ can be realized as the Mitchell order on a measurable cardinal κ, from a consistency assumption weaker than o(κ) = κ⁺.     

Electrochemistry, spectroscopy, and electrogenerated chemiluminescence of some star-shaped truxene-oligofluorene compounds

We report electrochemical studies, spectroscopy, and electrogenerated chemiluminescence (ECL) of four monodisperse star-shaped truxene core-oligofluorene compounds (T1-T4). All oligomers produced stable radical anions and radical cations and showed blue ECL by ion annihilation with an intensity that could be seen with the naked eye. ECL spectra showed that all ECL emissions were at the same position as the fluorescence emission, except for T1, the compound with the shortest fluorene arms that produced some longer wavelength emission in addition to that seen in the fluorescence spectrum. When tetra-n-butylammonium oxalate was used as a coreactant for T1, the emission was much weaker than that in ion annihilation with the same long-wavelength emission observed, making it unlikely that this emission can be ascribed to excimer formation. The ECL intensity of T4 was about 80% of the common blue ECL emitter, 9,10-diphenylanthracene (DPA), under similar conditions.     

Directed reductive amination of beta-hydroxy-ketones: convergent assembly of the ritonavir/lopinavir core

An efficient procedure for the directed reductive amination of beta-hydroxy-ketones (3) for the stereoselective preparation of 1,3-syn-amino alcohols (6) is reported. The operationally simple protocol uses Ti(iOPr)4 for coordination of the intermediate imino alcohol (5) and PMHS as the reducing agent. The method was expanded to an asymmetric aldol reductive amination sequence to allow a highly convergent synthesis of the hydroxy-amine core of the HIV-protease inhibitors ritonavir and lopinavir. [reaction: see text].     

An extension of a Bourgain-Lindenstrauss-Milman inequality

Let ‖⋅‖ be a norm on Rn. Averaging ‖(ε₁x₁,…,εnxn)‖ over all the n² choices of , we obtain an expression |||x||| which is an unconditional norm on Rn. Bourgain, Lindenstrauss and Milman [J. Bourgain, J. Lindenstrauss, V.D. Milman, Minkowski sums and symmetrizations, in: Geometric Aspects of Functional Analysis (1986/1987), Lecture Notes in Math., vol. 1317, Springer, Berlin, 1988, pp. 44-66] showed that, for a certain (large) constant η>1, one may average over ηn (random) choices of and obtain a norm that is isomorphic to |||⋅|||. We show that this is the case for any η>1.     

Structure and energetics of the hydronium hydration shells

Proton solvation and proton mobility are both subjects of great interest in chemistry and biology. Here we have studied the hydration shells of H3O+ at temperatures ranging from 260 to 340 K using the multistate empirical valence-bond methodology (MS-EVB2). We have calculated the radial distribution functions for the protonium and its solvation shells. Furthermore, we have determined the Gibbs energy and the enthalpy for hydrogen bonds donated or accepted by the first two solvation shells, in comparison to bulk water. We find systematic bond-energy differences that appear to agree with a recent IR study on proton hydration. Implications of our results to various proton mobility mechanisms are discussed.     

Stability and state of aggregation of aqueous fibrinogen and dipalmitoylphosphatidylcholine lipid vesicles

The stability and state of aggregation of aqueous fibrinogen (FB) and dipalmitoylphosphatidylcholine (DPPC) vesicles in water or buffer at 25 degrees C were studied with dynamic light scattering (DLS), UV-vis spectroturbidimetry (ST), and cryo-transmission electron microscopy (cryo-TEM). In water, when 1000 ppm (0.10 wt %) DPPC dispersions were prepared with a protocol including extensive sonication, they contained mostly vesicles and were quite clear, transparent, and stable for at least 30 days. FB mixtures with water (0.075 wt %) were quite unstable and biphasic. They formed large aggregates which eventually precipitated. The addition of DPPC vesicles into these unstable FB dispersions reversed FB aggregation and precipitation and produced stable translucent microdispersions. The inferred lipid/protein aggregates were limited in size, with average diameters ranging from 200 to 300 nm. In buffer, DPPC dispersions were also clear and quite stable, with average dispersed particles diameter of ca. 90 nm. FB dissolved in aqueous buffer and formed transparent and stable solutions. Adding salt to an aggregated FB dispersion in water reversed the aggregation. FB aggregated and redissolved in the presence of the citrate and after the citrate was removed. There was no effect of citrate (present in FB initially) in the FB aggregation or redissolution. FB molecules in buffer form dimers or higher aggregates. Their average aggregation number is 2, determined with Rayleigh scattering analysis of turbidity data. The average hydrodynamic diameter of FB solutions from DLS was 30 nm. Mixing a stable FB solution in buffer and a stable DPPC dispersion in buffer produced highly unstable mixtures, in which large aggregates precipitated. These results have implications in understanding the interactions of lipids and proteins in many biological applications and food processing applications.     

Multicanonical procedure for continuum peptide models

The multicanonical (Muca) Monte Carlo method enables simulating a system over a wide range of temperatures and thus has become an efficient tool for studying spin glasses, first‐order phase transitions, the helix–coil transition of polypeptides, and protein folding. However, implementation of the method requires calculating the multicanonical weights by an iterative procedure that is not straightforward and is a stumbling block for newcomers. A recursive procedure that takes into account the statistical errors of all previous iterations and thus enables an automatic calculation of the weights without the need for human intervention after each iteration has been proposed. This procedure, which has already been tested successfully for lattice systems, is extended here to continuum models of peptides and proteins. The method is examined in detail and tested for models of the pentapeptide Leu‐enkephalin (Tyr‐Gly‐Gly‐Phe‐Leu) described by the potential energy function ECEPP. Because of the great interest in the structural mapping of the low‐energy region of biomolecules, the energy of structures selected from the Muca trajectory is minimized. The extent of conformational coverage provided by the method is examined and found to be very satisfactory. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 1251–1261, 2000     

Line Profile Measure as a Stopping Criterion in CG-SENSE Algorithm

Conjugate gradient SENSE (CG-SENSE) is a parallel magnetic resonance imaging reconstruction algorithm which solves the inversion problem of SENSE iteratively. One major limitation of CG-SENSE is the appropriate choice of the number of iterations required for good reconstruction results. Fewer iterations result in aliasing artifacts and too many iterations result in an increased noise level. This paper proposes a novel method to define the stopping criterion of CG-SENSE algorithm which is based on the use of correlation measure between the line profiles of the reconstructed images in the current and the previous iterations. The results are compared with Bregman distance-stopping criterion. Artifact power and peak signal-to-noise ratio are used to quantify the quality of the reconstructed images. The results demonstrate that the line profile correlation measure acts as an effective stopping criterion in CG-SENSE.     

The effects of the intense laser field on the optical properties of the asymmetric parabolic quantum well

We have calculated the effects of the intense laser field on the total optical absorption coefficient (the linear and third-order nonlinear) for transition between two lower-lying electronic levels in the asymmetric parabolic \({\text{GaAs/ Ga}}_{{ 1 {\text{ - x}}}} {\text{Al}}_{\text{x}} {\text{As}}\) quantum well. Total absorption coefficient (linear and nonlinear absorption coefficient) for the transitions between any two electronic states was calculated by using density matrix formalism and the perturbation expansion method. Our results show that the effects of intense laser field and the well dimensions on the optical transitions are more pronounced. If well center is changed to be \({\text{L}}_{\text{c}} < 0 \, ({\text{L}}_{\text{c}} > 0)\), effective well width decreases (increases) and thus we can obtain the red or blue shift in the peak position of the absorption coefficient by changing the intensities of the non-resonant intense laser field as well as dimensions of the well.