Lower Bounds on the Size of Maximum Independent Sets and Matchings in Hypergraphs of Rank Three

In this paper, we study lower bounds on the size of a maximum independent set and a maximum matching in a hypergraph of rank three. The rank in a hypergraph is the size of a maximum edge in the hypergraph. A hypergraph is simple if no two edges contain exactly the same vertices. Let H be a hypergraph and let and be the size of a maximum independent set and a maximum matching, respectively, in H, where a set of vertices in H is independent (also called strongly independent in the literature) if no two vertices in the set belong to a common edge. Let H be a hypergraph of rank at most three and maximum degree at most three. We show that with equality if and only if H is the Fano plane. In fact, we show that if H is connected and different from the Fano plane, then and we characterize the hypergraphs achieving equality in this bound. Using this result, we show that that if H is a simple connected 3‐uniform hypergraph of order at least 8 and with maximum degree at most three, then and there is a connected 3‐uniform hypergraph H of order 19 achieving this lower bound. Finally, we show that if H is a connected hypergraph of rank at most three that is not a complete hypergraph on vertices, where denotes the maximum degree in H, then and this bound is asymptotically best possible. © 2012 Wiley Periodicals, Inc. J. Graph Theory     

Effectively controlled microfluidic trap for spatiotemporal analysis of the electrotaxis of Caenorhabditis elegans

C. elegans is a popular model organism with a well‐developed neural network. Approximately 60% of the genes in C. elegans have genomic counterparts in humans, including those involved in building neural circuits. Therefore, we can extend the study of human neural network mechanisms to C. elegans which is easy to genetically manipulate. C. elegans shows behavioural responses to various external physical and chemical stimuli. Electrotaxis is one of its distinct behavioural responses, which is defined as movement towards the cathode in an electric field. In this study, we developed an effective microfluidic trap system for analysing electrotaxis in C. elegans. In addition, two mutant strains (unc‐54(s74) and unc‐6(e78)) from wild‐type (N2) worms were screened using the system. Wild‐type (N2) worms and the two mutant strains clearly showed different behavioural responses to the applied electric field, thus enabling the effective screening of the mutant worms from the wild type (N2). This microfluidic system can be utilized as a platform for the study of behavioural responses, and for the sorting and mutant screening of C. elegans.     

Tm:Ho co-doped single mode optical fibre laser pumped by a 1600 nm Er fibre laser

An all-fibre Tm:Ho laser system is reported, using a 1600 nm Er fibre pump laser and 0.3 m length of the fibre through a two-stage optimization of both the pump source and laser configuration to achieve a low threshold operation. As a result a low threshold power of 33 mW and a slope efficiency of 0.6% have been achieved, in laser operation at a wavelength of 1870 nm and a cross-comparison with 785 nm laser diode pumping has been made.     

Concurrent correction of geometric distortion and motion using the map-slice-to-volume method in echo-planar imaging

The accuracy of measuring voxel intensity changes between stimulus and rest images in fMRI echo-planar imaging (EPI) data is severely degraded in the presence of head motion. In addition, EPI is sensitive to susceptibility-induced geometric distortions. Head motion causes image shifts and associated field map changes that induce different geometric distortion at different time points. Conventionally, geometric distortion is "corrected" with a static field map independently of image registration. That approach ignores all field map changes induced by head motion. This work evaluates the improved motion correction capability of mapping slice to volume with concurrent iterative field corrected reconstruction using updated field maps derived from an initial static field map that has been spatially transformed and resampled. It accounts for motion-induced field map changes for translational and in-plane rotation motion. The results from simulated EPI time series data, in which motion, image intensity and activation ground truths are available, show improved accuracy in image registration, field corrected image reconstruction and activation detection.     

LC–MS/MS analysis of puerarin and 18β-glycyrrhetinic acid in human plasma after oral administration of Samso-eum and its application to pharmacokinetic study

The aim of this study was to confirm pharmacokinetic screening of multiple components in healthy Korean subjects after oral administration of Samso-eum and perform quantitation of active components in the human plasma. Thirteen potential bioactive components [puerarin (PRR), daidzin, nodakenin, ginsenoside Rb1, 18β-glycyrrhetinic acid (18β-GTA), 6-shogaol, naringin, glycyrrhizin, hesperidin, platycodin D, naringenin, hesperetin, and 6-gingerol] were screened based on literature. The results showed that three analytes (daidzin, naringenin, and hesperetin) were detected in trace amounts. In addition, PRR and 18β-GTA were detected in human plasma after the oral administration of Samso-eum. In this study, a liquid chromatography–electrospray ionization-tandem mass spectrometry method was validated for the simultaneous determination of PRR and 18β-GTA in human plasma. This was the first study to evaluate pharmacokinetics of PRR and 18β-GTA after the usual oral dose of Samso-eum (30 g containing 102.48 mg PRR, 48.18 mg glycyrrhizin) in human subjects.     

Evaluation of alumina slurry dispersion by nuclear magnetic resonance relaxation as a comparison to conventional dispersion evaluation methods

In this paper, we evaluated the particle dispersion degree of alumina slurry containing a dispersant by solvent nuclear magnetic resonance (NMR) relaxation and compared it with conventional dispersion evaluation methods such as viscosity, particle size, and sedimentation height measurements. The dispersion of slurry was evaluated via numerical analysis of the transverse relaxation time (T₂). The effect of the changes in different parameters of the experiment in terms of milling time, solid loading, and dispersant amount was investigated by NMR relaxation as well as conventional methods. The results of NMR relaxation measurements revealed that T₂ correlates well with other dispersion evaluation methods; thus, it is an efficient technique to evaluate the dispersion of alumina slurry, specifically, when studying the effect of the change in milling time and dispersion amount.     

A Kinetic Study for the Noncatalytic Esterification of Palm Fatty Acid Distillate

In this work, the reaction scheme for the esterification of palm fatty acid distillate performed under the noncatalytic and high‐temperature condition (230–290°C) was investigated with a rigorous mathematical modeling. The esterification reaction was assumed to be the pseudo–homogeneous second‐order reversible reaction, and the mass transfer effectiveness factor (η) was introduced in the modeling framework to systematically and collectively consider both evaporation and reaction, which are simultaneously and competitively occurred in the liquid phase. The nonlinear programming problem was constructed with the objective function consisting of the errors between experimental data and the estimated values from the reaction model. The problem was solved by using the Nelder–Mead simplex algorithm to identify kinetic parameters, reaction rate constants, and mass transfer coefficients. The values of mass transfer coefficients were found to follow the Hertz–Knudsen relation and expressed as a function of reaction temperature. From the reaction rate constants obtained from the proposed kinetic models, the apparent activation energy was estimated to be 43.98 kJ/mol, which is lower than the value obtained from the reaction using heterogeneous catalysts. This low value indicates that reactants and products behave as an acid catalyst at relatively high operating temperature and constant pressure.     

Recent advances in understanding mechanisms for the electrochemical reduction of carbon dioxide

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Hydrophobic‐Force‐Driven Removal of Organic Compounds from Water by Reduced Graphene Oxides Generated in Agarose Hydrogels

Hydrophobic reduced graphene oxides (rGOs) were generated in agarose hydrogel beads (AgarBs) by NaBH₄ reduction of graphene oxides (GOs) initially loaded in the AgarBs. The resulting rGO‐loaded AgarBs were able to effectively adsorb organic compounds in water as a result of the attractive hydrophobic force between the rGOs in the AgarBs and the organic compounds dissolved in aqueous media. The adsorption capacity of the rGOs was fairly high even toward reasonably water‐soluble organic compounds such as rhodamine B (321.7 mg g^?1) and aspirin (196.4 mg g^?1). Yet they exhibited salinity‐enhanced adsorption capacity and preferential adsorption of organic compounds with lower solubility in water. Such peculiar adsorption behavior highlights the exciting possibility for adopting an adsorption strategy, driven by hydrophobic forces, in practical wastewater treatment processes.