Carbohydrate particles as protein carriers and scaffolds: physico-chemical characterization and collagen stability

We report a simple and effective supercritical fluid route to uniformly load ultrafine metal nanoparticles on the hydrophobic surfaces of graphene sheets. In the presence of supercritical carbon dioxide, PtRu alloy nanoparticles are decorated evenly on functionalized graphene sheets (FGSs) upon the reduction of organic platinum (II) and ruthenium (III) precursors, and its application as an electrocatalyst for methanol oxidation is studied. Transmission electron microscopy observation shows that highly dispersed PtRu metallic nanoparticles with an average size of about 3.11?nm are uniformly and densely distributed on the hydrophobic surface of FGSs. X-ray diffraction patterns demonstrate that the particles had a face-centered cubic crystal structure, and X-ray photoelectron spectroscopy analysis indicates the existence of zero-valence metals. Compared with the widely used Vulcan XC-72 carbon black, the PtRu/FGS composites exhibit superior catalytic activity and stability for methanol oxidation. The huge surface area of graphene and uniform distribution of nanosized metal particles are two critical factors for the significantly enhanced electrocatalytic efficiency. The findings suggest that the supercritical fluid method is highly efficient in preparing graphene-supported metallic catalysts, and FGSs serve as a favorable electrocatalytic carrier for direct methanol fuel cells.     

Trees and Markov Convexity

We show that an infinite weighted tree admits a bi-Lipschitz embedding into Hilbert space if and only if it does not contain arbitrarily large complete binary trees with uniformly bounded distortion. We also introduce a new metric invariant called Markov convexity, and show how it can be used to compute the Euclidean distortion of any metric tree up to universal factors. The research of the first author was conducted while he was at U. C. Berkeley and the Institute for Advanced Study.     

Chemical composition of mate tea leaves (Ilex paraguariensis): a study of extraction methods

The objective of this work was to investigate the extraction of Ilex paraguariensis leaves by means of three extraction techniques: pressurized liquid extraction (PLE, also called accelerated solvent extraction – ASE), maceration, and sonication. Samples of mate tea leaves were collected from an experiment conducted under agronomic control at Indústria e Comércio de Erva‐Mate Bar?o LTDA, Brazil. Six solvents with increasing polarities (n‐hexane, toluene, dichloromethane, ethyl acetate, acetone, and methanol) were used in this investigation. Chemical analysis of the extracts was performed by GC coupled with a mass spectrometer detector. The identification and quantification were accomplished by coinjections of certified standards. The results showed that no significant differences in the qualities of the extracts were noticed regarding the extraction methods. On the other hand, the PLE technique was found to be more effective for the extractions of caffeine, phytol, palmitic, and stearic acid. The use of PLE led to a significant decrease in the total extraction time, amount of solvent consumption, and manipulation of samples compared to maceration and ultrasound‐assisted extraction methods.     

How many matrices can be spectrally balanced simultaneously?

We prove that any ? positive definite d × d matrices, M₁,...,M_?, of full rank, can be simultaneously spectrally balanced in the following sense: for any k < d such that ? ≤ \(\ell \leqslant \left\lfloor {\frac{{d - 1}}{{k - 1}}} \right\rfloor \), there exists a matrix A satisfying \(\frac{{{\lambda _1}\left( {{A^T}{M_i}A} \right)}}{{Tr\left( {{A^T}{M_i}A} \right)}} < \frac{1}{k}\) 1/k for all i, where λ₁(M) denotes the largest eigenvalue of a matrix M. This answers a question posed by Peres, Popov and Sousi ([PPS13]) and completes the picture described in that paper regarding sufficient conditions for transience of self-interacting random walks. Furthermore, in some cases we give quantitative bounds on the transience of such walks.     

Critical percolation on random regular graphs

The behavior of the random graph G(n,p) around the critical probability p_c = is well understood. When p = (1 + O(n^1/3))p_c the components are roughly of size n^2/3 and converge, when scaled by n^?2/3, to excursion lengths of a Brownian motion with parabolic drift. In particular, in this regime, they are not concentrated. When p = (1 ‐ ?(n))p_c with ?(n)n^1/3 →∞ (the subcritical regime) the largest component is concentrated around 2?^?2 log(?³n). When p = (1 + ?(n))p_c with ?(n)n^1/3 →∞ (the supercritical regime), the largest component is concentrated around 2?n and a duality principle holds: other component sizes are distributed as in the subcritical regime. Itai Benjamini asked whether the same phenomenon occurs in a random d‐regular graph. Some results in this direction were obtained by (Pittel, Ann probab 36 (2008) 1359–1389). In this work, we give a complete affirmative answer, showing that the same limiting behavior (with suitable d dependent factors in the non‐critical regimes) extends to random d‐regular graphs. © 2009 Wiley Periodicals, Inc. Random Struct. Alg., 2010     

Glauber dynamics for the mean-field Ising model: cut-off, critical power law, and metastability

We study the Glauber dynamics for the Ising model on the complete graph, also known as the Curie–Weiss Model. For β < 1, we prove that the dynamics exhibits a cut-off: the distance to stationarity drops from near 1 to near 0 in a window of order n centered at [2(1 ? β)]^?1 n log n. For β = 1, we prove that the mixing time is of order n ^3/2. For β > 1, we study metastability. In particular, we show that the Glauber dynamics restricted to states of non-negative magnetization has mixing time O(n log n).     

Isotope ratio monitoring gas chromatography/Mass spectrometry of D/H by high temperature conversion isotope ratio mass spectrometry

Of all the elements, hydrogen has the largest naturally occurring variations in the ratio of its stable isotopes (D/H). It is for this reason that there has been a strong desire to add hydrogen to the list of elements amenable to isotope ratio monitoring gas chromatography/mass spectrometry (irm-GC/MS). In irm-GC/MS the sample is entrained in helium as the carrier gas, which is also ionized and separated in the isotope ratio mass spectrometer (IRMS). Because of the low abundance of deuterium in nature, precise and accurate on-line monitoring of D/H ratios with an IRMS requires that low energy helium ions be kept out of the m/z 3 collector, which requires the use of an energy filter. A clean mass 3 (HD(+.)) signal which is independent of a large helium load in the electron impact ion source is essential in order to reach the sensitivity required for D/H analysis of capillary GC peaks. A new IRMS system, the DELTA(plus)XL(trade mark), has been designed for high precision, high accuracy measurements of transient signals of hydrogen gas. It incorporates a retardation lens integrated into the m/z 3 Faraday cup collector. Following GC separation, the hydrogen bound in organic compounds must be quantitatively converted into H(2) gas prior to analysis in the IRMS. Quantitative conversion is achieved by high temperature conversion (TC) at temperatures >1400 degrees C. Measurements of D/H ratios of individual organic compounds in complicated natural mixtures can now be made to a precision of 2 per thousand (delta notation) or, better, with typical sample amounts of approximately 200 ng per compound. Initial applications have focused on compounds of interest to petroleum research (biomarkers and natural gas components), food and flavor control (vanillin and ethanol), and metabolic studies (fatty acids and steroids). Copyright 1999 John Wiley & Sons, Ltd.     

Robust ℋ∞-Filtering Design with Pole Placement Constraint via Linear Matrix Inequalities

The problem of robust filtering design for continuous-time systems with convex bounded uncertainties is addressed in this paper. The aim is to determine a stable linear filter such that the filtering error system remains quadratically stable within a prespecified -attenuation level. Necessary and sufficient conditions for the existence of such robust filter are provided in terms of linear matrix inequalities, which can be solved efficiently through standard convex optimization procedures guaranteeing global convergence. Furthermore, as an improvement of the strategy, the filter dynamics can be constrained to some specific regions inside the left-half complex plane.