Gradient‐based solvent suppression methods on a benchtop spectrometer

Benchtop NMR emerges as an appealing alternative to widely extend the scope of NMR spectroscopy in harsh environments and for on‐line monitoring. Obviously, the use of low‐field magnets induces a dramatic reduction of the spectral resolution leading to frequent peak overlaps. This issue is even more serious because applications such as chemical process monitoring involve the use of non‐deuterated solvents, leading to intense and broad peaks overlapping with the signals of interest. In this article, we highlight the need for efficient suppression methods compatible with flowing samples, which is not the case of the common pre‐saturation approaches. Thanks to a gradient coil included in our benchtop spectrometer, we were able to implement modern and efficient solvent suppression blocks such as WET or excitation sculpting to deliver quantitative spectra in the conditions of the on‐line monitoring. While these methods are commonly used at high field, this is the first time that they are investigated on a benchtop setting. Their analytical performance is evaluated and compared under static and on‐flow conditions. The results demonstrate the superiority of gradient‐based methods, thus highlighting the relevance of implementing this device on benchtop spectrometers. The comparison of major solvent suppression methods reveals an optimum performance for the WET‐180‐NOESY experiment, both under static and on‐flow conditions. Copyright © 2016 John Wiley & Sons, Ltd.     

Efficient calculation of two-dimensional adiabatic and free energy maps: Application to the isomerization of the C13C14 and C15N16 bonds in the retinal of bacteriorhodopsin

Accurate calculation of potential energy and free-energy profiles along reaction coordinates of biological processes such as enzymatic reactions or conformational changes is fundamental to the obtention of theoretical insight into protein function. We describe here the practical implementation of the Automatic Map Refinement Procedure (AMRP) and two-dimensional Weighted Histogram Analysis Method (WHAM) for efficient computation of adiabatic potential energy and free-energy maps, respectively. Methods for efficiently sampling configuration space with high-energy barriers and for removing hysteresis in the case of periodic reaction coordinates are presented. The application of these techniques to the isomerization of the C13C14 and C15N16 bonds in the retinal of bacteriorhodopsin is described. In dark-adapted bacteriorhodopsin (bR), the retinal moiety exists in two conformers, all-trans and (13,15)cis, with the latter making ≃67% of the population. This experimental free energy difference is reproduced here to within k_BT. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1644–1658, 1999     

Fabrication of organic phase biosensors based on multilayered polyphenol oxidase protected by an alginate coating

We describe herein, the creation of an organic phase enzyme electrode (OPEE) via avidin–biotin interactions built over an electrogenerated polymer. Multilayered polyphenol oxidase (PPO) assemblies were transferred into an organic solvent (chloroform) for the catechol detection at −0.2 V. In conjunction with an alginate gel, as a hydrophilic additive, the biosensor performance was widely enhanced. The effects of biotinylated polypyrrole film and alginate gel on the diffusion process through the biosensor coating are studied by rotating disk electrode experiments carried out in chloroform with hydroquinone as electroactive permeant.     

On Tightness and Weak Convergence in the Approximation of the Occupation Measure of Fractional Brownian Motion

In this paper we consider approximations of the occupation measure of the Fractional Brownian motion by means of some functionals defined on regularizations of the paths. In a previous article Berzin and León proved a cylindrical convergence to a Wiener process of conveniently rescaled functionals. Here we show the tightness of the approximation in the space of continuous functions endowed with the topology of uniform convergence on compact sets. This allows us to simplify the identification of the limit.     

Isoperimetric Constants of Infinite Plane Graphs

   Abstract. Let G be an infinite locally finite plane graph with one end and let H be a finite plane subgraph of G . Denote by a(H) the number of finite faces of H and by l(H) the number of the edges of H that are on the boundary of the infinite face or a finite face not in H . Define the isoperimetric constant h (G) to be inf _H l(H) / a(H) and define the isoperimetric constant h (δ) to be inf _G h (G) where the infimum is taken over all infinite locally finite plane graphs G having minimum degree δ and exactly one end. We establish the following bounds on h (δ) for δ ≥ 7 :

Linearly χ-bounding (P6, C4)-free graphs*

Given two graphs and , a graph is -free if it contains no induced subgraph isomorphic to or . Let and be the path on vertices and the cycle on vertices, respectively. In this paper we show that for any -free graph it holds that , where and are the chromatic number and clique number of , respectively. Our bound is attained by several graphs, for instance, the 5-cycle, the Petersen graph, the Petersen graph with an additional universal vertex, and all -critical -free graphs other than (see Hell and Huang [Discrete Appl. Math. 216 (2017), pp. 211–232]). The new result unifies previously known results on the existence of linear -binding functions for several graph classes. Our proof is based on a novel structure theorem on -free graphs that do not contain clique cutsets. Using this structure theorem we also design a polynomial time -approximation algorithm for coloring -free graphs. Our algorithm computes a coloring with colors for any -free graph in time.     

Efficient Spatial Modeling Using the SPDE Approach With Bivariate Splines

Gaussian fields (GFs) are frequently used in spatial statistics for their versatility. The associated computational cost can be a bottleneck, especially in realistic applications. It has been shown that computational efficiency can be gained by doing the computations using Gaussian Markov random fields (GMRFs) as the GFs can be seen as weak solutions to corresponding stochastic partial differential equations (SPDEs) using piecewise linear finite elements. We introduce a new class of representations of GFs with bivariate splines instead of finite elements. This allows an easier implementation of piecewise polynomial representations of various degrees. It leads to GMRFs that can be inferred efficiently and can be easily extended to nonstationary fields. The solutions approximated with higher order bivariate splines converge faster, hence the computational cost can be alleviated. Numerical simulations using both real and simulated data also demonstrate that our framework increases the flexibility and efficiency. Supplementary materials are available online.     

Approximation of stationary solutions of Gaussian driven stochastic differential equations

We study sequences of empirical measures of Euler schemes associated to some non-Markovian SDEs: SDEs driven by Gaussian processes with stationary increments. We obtain the functional convergence of this sequence to a stationary solution to the SDE. Then, we end the paper by some specific properties of this stationary solution. We show that, in contrast to Markovian SDEs, its initial random value and the driving Gaussian process are always dependent. However, under an integral representation assumption, we also obtain that the past of the solution is independent of the future of the underlying innovation process of the Gaussian driving process.