LOWLAD: a locally weightedL 1 smoothing spline algorithm with cross validated choice of smoothing parameters

The computation ofL ₁ smoothing splines on large data sets is often desirable, but computationally infeasible. A locally weighted, LAD smoothing spline based smoother is suggested, and preliminary results will be discussed. Specifically, one can seek smoothing splines in the spacesW _m (D), with [0, 1] ⁿ D. We assume data of the formy _i =f(t _i )+ _i ,i=1,..., N with {t _i } _i=1 ^N D, the _i are errors withE( _i )=0, andf is assumed to be inW _m . An LAD smoothing spline is the solution,s , of the following optimization problem

AnL 1 smoothing spline algorithm with cross validation

We propose an algorithm for the computation ofL ₁ (LAD) smoothing splines in the spacesW _M (D), with . We assume one is given data of the formy _i =(f(t _i ) + _i , i=1,...,N with {itt_i} _i=1 ^{N D} , the _i are errors withE( _i )=0, andf is assumed to be inW _M . The LAD smoothing spline, for fixed smoothing parameter0, is defined as the solution,s , of the optimization problem (1/N) _i=1 ^N ¦y _i –g(t _i ¦+J _M (g), whereJ _M (g) is the seminorm consisting of the sum of the squaredL ₂ norms of theMth partial derivatives ofg. Such an LAD smoothing spline,s , would be expected to give robust smoothed estimates off in situations where the _i are from a distribution with heavy tails. The solution to such a problem is a thin plate spline of known form. An algorithm for computings is given which is based on considering a sequence of quadratic programming problems whose structure is guided by the optimality conditions for the above convex minimization problem, and which are solved readily, if a good initial point is available. The data driven selection of the smoothing parameter is achieved by minimizing aCV() score of the form .The combined LAD-CV smoothing spline algorithm is a continuation scheme in 0 taken on the above SQPs parametrized in, with the optimal smoothing parameter taken to be that value of at which theCV() score first begins to increase. The feasibility of constructing the LAD-CV smoothing spline is illustrated by an application to a problem in environment data interpretation.     

The theoretical basis of column chromatography in multicomponent separations. Part 2: Peak capacity. Column systems with good selectivity

The selectivity of a column system, S, defined by equation 28, includes a variation coefficient (β) of plate number with capacity ratio which has a large influence on the peak capacity, as shown in Fig. 18. Some typical chromatograms are given. In order to predict S for a column system from Kovat's Index, equations 40 and 41 are given to calculate the constant of the carbon number rule for squalane at different temperatures or for different stationary phases. The specific retention value of heptane on squalane at different temperatures can be calculated from equation 42. The nonpolarity index, defined by equation 43, was used to calculate the retention value of heptane on various stationary phases. In liquid chromatography, the order of elution may be reversed by changing the composition of the eluent on the same chemically bonded silica (manufactured in China). The linear relations between the log retention values of different kinds of solutes or of a single solute on the silicas of different surface areas when using the same eluent are given.     

Kinetics of the surface tension of micellar solutions: Comparison of different experimental techniques

The kinetics of the surface tension of micellar solutions of nonionic surfactant Triton X-100 is measured experimentally by means of three different techniques: oscillating jet, maximum bubble pressure and inclined plate. They allow to study the micellization kinetics at various time scales (from a few milliseconds to a few seconds) in fairly large concentration region up to 50 times CMC. The experimental data are satisfactorily explained by a theoretical model accounting for the kinetics of micellization, diffusion of surfactant species and expansion of the bubble interface. By this model are computed the characteristic times of diffusion and micellization, which are of comparable magnitude (about 5 to 200 ms), and the Gibbs' elasticity. The micellization time constant corresponds to the slow relaxation process known to coincide with the disintegration of micelles. Comparing our data with other data from literature one can conclude that more realistic information for the micellization kinetics is obtained by the maximum bubble pressure and the oscillating jet method. The inclined plate seems too slow to measure the relaxation processes in micellar solutions of this surfactant.     

A new approach for the sequential injection spectrophotometric determination of the total antioxidant activity

A sequential injection system based on the ABTS (2,2′-azino-bis-(3-ethylbenzothiazoline-6-sulphonic-acid) methodology was developed. The proposed method, incorporating a mixing chamber in the side port of the selection valve, was evaluated to measure the total antioxidant activity of several beverages and foods.The ABTS⁺ is generated by oxidation of ABTS with potassium persulfate and is reduced in presence of hydrogen-donating antioxidants converting into a colourless product. The applicability of the developed method was tested by measurement of the antioxidant activity of pure compounds as well as by analysing complex food and beverage samples. The antioxidant activity was presented as l(+) ascorbic acid equivalence. The values obtained by this methodology were not significantly different from the results obtained by the original spectrophotometric ABTS assay. For most of the studied antioxidants, antioxidant activity varied with pH and dilution. The proposed SIA system is suitable for screening direct or diluted total antioxidant activity of pure compounds or food samples.     

Modification of HPTLC-plates by in situ chemical bonding with non-polar and polar organosilanes

A method has been developed for the preparation of modified silica plates for high performance thin-layer chromatography (HPTLC). Some typical organosilanes were thus allowed to react in situ with the silica of Merck HPTLC-plates. This method was found to be highly reproducible, simple and cheap. Non-polar plates were prepared and compared with commercial plates from Merck, Whatman and Macherey-Nagel. Modification with cyanodecyltrichlorosilane resulted in plates that showed good coverage, efficiency and low residual silica activity. Silica modified with a multifunctional silane has different properties in different organic solvents. It will appear to be non-polar in a polar solvent and vice versa. New advantageous separation systems are thus made feasible by the presence of cyano groups on the plate. The utility of modified thin-layer plates is demonstrated by the separation of some homologues of p-hydroxybenzoic acid esters and of some polycyclic aromatic hydrocarbons.     

Development of the continuously variable volume reactor for flow injection analysis: Part 1. Design, capabilities and testing

A new apparatus for mixing sample and reagent in flow injection analysis (FIA) is described. The continuously variable volume reactor (CVVR) replaces the conventional mixing coil in a flow injection (FI) manifold to provide mixing and dilution. A linear actuator motor allows control of the chamber volume via LabVIEW software. The chamber volume can be incremented in steps of 1 μl over the range 68-1704 μl. In addition, the chamber has an integral variable-speed stirring unit that is also under computer control. Experiments were performed to evaluate the dispersion characteristics of this new device, evaluate the volume reproducibility, and understand the mixing characteristics. Use of the chamber is shown in the determination of iron(II) in pond water, and in NIST SRM 1643d with excellent results and a detection limit of 3.7 μg/l iron(II). Advantages of the CVVR and future research activities using the device are discussed.     

Self-organization of polymer particles on hydrophobic solid substrates in aqueous media. I. Self-organization of cationic polymer particles on alkylated glass plates

Monodisperse, cationic polymer particles bearing quaternary ammonium groups effectively self-organized on hydrophobic solid substrates such as alkylated glass plates and polymer films to form particle monolayers. With an increase of the particle surface charge density, the surface coverage decreased and the morphology of particle monolayers changed from aggregated type to dispersed type. The dispersed type of particle monolayers having a relatively regular particle distance was formed at higher temperature. The self-organization behaviors on alkylated glass plates were different from those on unmodified glass plates through electrostatic interaction. The formation of particle monolayers on alkylated glass plates occurred only over a certain latex concentration range in contrast with that on unmodified glass plate. The adhesive strength of particle monolayers was enhanced by annealing at temperatures above the glass transition temperature (T _g) of the particles. Lens-shaped particle monolayers were fabricated by annealing the dispersed type of particle monolayers.     

On the applicability of the “abt” concept

Kaiser's “abt” concept rests on the experimental establishment of a linear relation between band width at half height, b_0.5, and capacity ratio, k, according to His column specification quantity, h_real, is dependent on the square of the slope a, obtained from a linear regression analysis based on this relation. It is shown in the present paper that an improvement of the experimental conditions leading to a lower extra-column contribution to band broadening, b, introduces a tendency towards a negative curvature in the plot at low k values. The mean slope increases, and an uncritical linear regression would yield an h_real-value which is higher than before and which would be in the opposite direction to the requirements of a reliable column specification. Generally the linear regression analysis has to be moved to higher k regions in cases of curvature, especially as it is also shown that h_real is an estimation of the traditional HETP value, H∞, that would be obtained when k approaches infinity. This theoretically expected relation is a strong motivation for the use of h_real as a column specification, since the b_0.5-value associated with H∞ is expected to be practically independent of b.     

Self‐Assembly Film of Zeolite Y Nanocrystals Loading Palladium on an Au Electrode for Electrochemical Applications

Nano‐scale zeolite Y crystals were synthesized, and palladium nanoparticles were prepared in the supercage of the zeolite by “ship‐in‐a‐bottle” approach. A novel method to fabricate zeolite‐modified electrode (ZME) loading Pd nanoparticles was developed, in which the zeolite Y loading Pd²⁺ ions was self‐assembled on (3‐mercaptopropyl) trimethoxysilane‐attached Au surface to form the stable and density packed multilayers (SAM‐ZME). The structures of zeolite Y and the SAM‐ZME were investigated by using TEM, XRD and SEM techniques. Pd²⁺ ions in the SAM‐ZME were converted into Pd nanoparticles (Pd_n⁰) by two steps consisting of the electrochemical reduction as well as the succeeding admission and release of CO. The redox couple [Fe(CN)₆]^3?/4? was used to probe the electron‐transfer barrier properties during self‐assembling process. Moreover, the special properties of the SAM‐ZME loading Pd_n⁰ were studied by using cyclic voltammetry and CO‐probe in situ FTIR spectroscopy. The results illustrated that Pd_n⁰ in the SAM‐ZME exhibits higher electrocatalytic activity for oxidation of adsorbed CO than that of ZME prepared in our previous study by zeolite coating method. The present study is of importance in design and preparation of SAM‐ZME, which poccesseses excellent properties for the immobilization of electrocatalysts or biomolecules.