Dot plots and hat plots: supporting young students emerging understandings of distribution,center and variability through modeling

An important use of statistical models and modeling in education stems from the potential to involve students more deeply with conceptions of distribution, variation and center. As models are key to statistical thinking, introducing students to modeling early in their schooling will likely support the statistical thinking that underpins later, more advanced work with increasingly sophisticated statistical models. In this case study, a class of 10–11 year-old students are engaged in an authentic task designed to elicit modeling. Multiple data sources were used to develop insights into student learning: lesson videotape, work samples and field notes. Through the use of dot plots and hat plots as data models, students made comparisons of the data sets, articulated the sources of variability in the data, sought to minimize the variability, and then used their models to both address the initial problem and to justify the effectiveness of their attempts to reduce induced variation. This research has implications for statistics curriculum in the early formal years of schooling.     

Pricing and advertisement in a manufacturer–retailer supply chain

We use a game theoretical approach to study pricing and advertisement decisions in a manufacturer–retailer supply chain when price discounts are offered by both the manufacturer and retailer. When the manufacturer is the leader of the game, we obtained Stackelberg equilibrium with manufacturer’s local allowance, national brand name investment, manufacturer’s preferred price discount, retailer’s price discount, and local advertising expense. For the special case of two-stage equilibrium when the manufacturer’s price discount is exogenous, we found that the retailer is willing to increase local advertising expense if the manufacturer increases local advertising allowance and provides deeper price discount, or if the manufacturer decreases its brand name investment. When both the manufacturer and retailer have power, Nash equilibrium in a competition game is obtained. The comparison between the Nash equilibrium and Stackelberg equilibrium shows that the manufacturer always prefers Stackelberg equilibrium, but there is no definitive conclusion for the retailer. The bargaining power can be used to determine the profit sharing between the manufacturer and the retailer. Once the profit sharing is determined, we suggest a simple contract to help the manufacturer and retailer obtain their desired profit sharing.     

Structures of divalent transition metal salts of 4-aminonaphthalene-1-sulfonate: unexpected variations in layering pattern

Salts of 4-aminonaphthalene-1-sulfonate with divalent Mg, Mn, Co, and Ni cations have been crystallized and their structures determined by single crystal X-ray methods. The Mg and Mn salts are isostructural. Crystal data for hexa-aquamagnesium(II) 4-aminonaphthalene-1-sulfonate dihydrate, [Mg(H₂O)₆](H₂NC₁₀H₆SO₃)₂ 2H ₂O: monoclinic, P2₁/c, Z = 2, a = 8.622(3), b = 7.043(3), c = 23.178(3) Å, =93.78(2)°, V = 1404.3(7) ų; hexa-aquamanganese(II) 4-aminonaphthalene-1-sulfonate dihydrate, [Mn(H₂O)₆](H₂NC₁₀H₆SO₃)₂ 2H ₂O: monoclinic, P2₁/c, Z = 2, a = 8.652(3), b = 7.031(4), c = 23.402(2) Å, =93.09(2)°, V = 1421.5(9) ų. The structures are composed of alternating layers of octahedral metal–aqua complexes and sulfonate anions linked by an extensive network of hydrogen bonds. The extra water molecules of crystallization are located in the hexa-aquametal cation layers. The repeat unit along the c axis is a double layer. The Co and Ni compounds are isostructural with each other, but compared to the Mg and Mn compounds, have a strikingly different structure. Crystal data for hexa-aquacobalt(II) 4-aminonaphthalene-1-sulfonate trihydrate, [Co(H₂O)₆](H₂NC₁₀H₆SO₃)₂ 3H ₂O: orthorhombic, Pbca, Z = 8, a = 8.518(1), b = 14.327(2), c = 45.367(6) Å, V = 5536(1) ų; hexa-aquanickel(II) 4-aminonaphthalene-1-sulfonate trihydrate, [Ni(H₂O)₆](H₂NC₁₀H₆SO₃)₂ 3H ₂O: orthorhombic, Pbca, Z = 8, a = 8.4976(6), b = 14.288(1), c = 45.076(3) Å, V = 5472.9(7) ų. These structures also contain layers of octahedral hexa-aquametal complexes and additional water molecules of crystallization sandwiched by layers of sulfonate anions, however the stacking pattern is more complex with a quadruple layer repeat unit and two different types of anion layers.     

Effect of pumping methods on transmembrane pressure, fluid balance and relative recovery in microdialysis

There is a growing interest in using large pore size probes for microdialysis of macromolecular markers to monitor cell and tissue functions. Fluid balance could be an important issue when using large pore size microdialysis probes, which are affected by the mode of operation. In this study, the effect of pumping systems, push, pull, push-and-pull, and the resulting transmembrane pressure on the fluid balance, as well as, the relative recovery of small molecular nutrients and metabolites and macromolecules (proteins) were examined. The validity of the internal reference in situ calibration was examined in detail. It is concluded that a push-and-pull system is the only effective method of eliminating fluid loss or gain. The relative recovery of small solutes is not affected much by the applied pumping methods; however, the relative recovery of macromolecules is significantly influenced by them. The in situ calibration technique using Phenol Red can provide reliable results for small molecules including glucose and lactic acid. Using 10 and 70-kDa fluorescent dextrans as the internal standard for large molecules in situ calibration of similar size does not work for the pull pump system, but does work well when using a push-and-pull pumping method.     

Carbon nanotube-modified microelectrodes for simultaneous detection of dopamine and serotonin in vivo

Dopamine and serotonin are important neurotransmitters that interact in the brain. While dopamine is easily detected with electrochemical sensors, the detection of serotonin is more difficult because reactive species formed after oxidation can adsorb to the electrode, reducing sensitivity. Carbon nanotube treatments of electrodes have been used to increase the sensitivity, promote electron transfer, and reduce fouling. Most methods have focused on nanotube coatings of large electrodes and slower electrochemical techniques that are not conducive to measurements in vivo. In this study, we investigated carbon-fiber microelectrodes modified with single-walled carbon nanotubes for the co-detection of dopamine and serotonin in vivo. Using fast-scan cyclic voltammetry, S/N ratios for the neurotransmitters increased after nanotube coating. Electrocatalytic effects of nanotubes were not apparent at fast scan rates but faster kinetics were observed with slower scanning. Nanotube-modified microelectrodes showed significantly less fouling after exposure to serotonin than bare electrodes. The nanotube-modified electrodes were used to monitor stimulated dopamine and serotonin changes simultaneously in the striatum of anesthetized rat after administration of a serotonin synthetic precursor. These studies show that nanotube-coated microelectrodes can be used with fast scanning techniques and are advantageous for in vivo measurements of neurotransmitters because of their greater sensitivity and resistance to fouling.     

An electrochemiluminescence-based competitive displacement immunoassay for the type-2 brevetoxins in oyster extracts

A new competitive electrochemiluminescence-based immunoassay for the type-2 brevetoxins in oyster extracts was developed. The assay was verified by spiking known amounts of PbTx-3 into 80% methanol extracts of Gulf Coast oysters. We also provide preliminary data demonstrating that 100% acetone extracts, aqueous homogenates, and the clinical matrixes urine and serum can also be analyzed without significant matrix interferences. The assay offers the advantages of speed ( 2 h analysis time); simplicity (only 2 additions, one incubation period, and no wash steps before analysis); low limit of quantitation (conservatively, 50 pg/mL = 1 ng/g tissue equivalents); and a stable, nonradioactive label. Due to the variety of brevetoxin metabolites present and the lack of certified reference standards for liquid chromatography-mass spectrometry confirmation, a true validation of brevetoxins in shellfish extracts is not possible at this time. However, our assay correlated well with another brevetoxin immunoassay currently in use in the United States. We believe this assay could be useful as a regulatory screening tool and could support pharmacokinetic studies in animals and clinical evaluation of neurotoxic shellfish poisoning victims.     

Rapid and simultaneous determination of capecitabine and its metabolites in mouse plasma, mouse serum, and in rabbit bile by high-performance liquid chromatography

A rapid high-performance liquid chromatography method has been developed for simultaneous determination of capecitabine and its metabolites: 5'-deoxy-5-fluorocytidine (5'-DFCR), 5'-deoxy-5-fluorouridine (5'-DFUR) and 5-fluorouracil (5-FU). 5'-DFCR was synthesized by hydrolyzing capecitabine using commercially available carboxyl esterase (CES) and characterized by NMR, mass spectrometry and elemental analysis. Base-line separations between capecitabine, 5'-DFCR, 5'-DFUR and 5-FU were found with symmetrical peak shapes on a Discovery RP-amide C16 column using 10 mM ammonium acetate at pH 4.0 and methanol as the mobile phase. The retention times of capecitabine, 5'-DFCR, 5'-DFUR and 5-FU were 8.9, 5.0, 5.3 and 3.0 min, respectively. Linear calibration curves were obtained for each compound across a range from 1 to 500 microg ml(-1). The intra- and inter-day relative standard deviations (%RSD) were <5%. A single-step protein precipitation method was employed for separation of the analytes from bio-matrices. Greater than 85% recoveries were obtained for capecitabine, 5'-DFCR, 5'-DFUR and 5-FU from bio-fluids including mouse plasma, mouse serum and rabbit bile.     

Chemistry of 4-alkylaryloxenium ion "precursors": sound and fury signifying something?

Quinol esters 2b, 2c, and 3b and sulfonamide 4c were investigated as possible precursors to 4-alkylaryloxenium ions, reactive intermediates that have not been previously detected. These compounds exhibit a variety of interesting reactions, but with one possible exception, they do not generate oxenium ions. The 4-isopropyl ester 2b predominantly undergoes ordinary acid- and base-catalyzed ester hydrolysis. The 4-tert-butyl ester 2c decomposes under both acidic and neutral conditions to generate tert-butanol and 1-acetyl-1,4-hydroquinone, 8, apparently by an SN1 mechanism. This is also a minor decomposition pathway for 2b, but the mechanism in that case is not likely to be SN1. Decomposition of 2c in the presence of N3- leads to formation of the explosive 2,3,5,6-tetraazido-1,4-benzoquinone, 14, produced by N3--induced hydrolysis of 8, followed by a series of oxidations and nucleophilic additions by N3-. No products suggestive of N3--trapping of an oxenium ion were detected. The 4-isopropyl dichloroacetic acid ester 3b reacts with N3- to generate the two adducts 2-azido-4-isopropylphenol, 5b, and 3-azido-4-isopropylphenol, 11b. Although 5b is the expected product of N3- trapping of the oxenium ion, kinetic analysis shows that it is produced by a kinetically bimolecular reaction of N3- with 3b. No oxenium ion is involved. The sulfonamide 4c predominantly undergoes a rearrangement reaction under acidic and neutral conditions, but a minor component of the reaction yields 4-tert-butylcresol, 17, and 2-azido-4-tert-butylphenol, 5c, in the presence of N3-. These products may indicate that 4c generates the oxenium ion 1c, but they are generated in very low yields (ca. 10%) so it is not possible to definitively conclude that 1c has been produced. If 1c has been generated, the N3--trapping data indicate that it is a very short-lived and reactive species in H2O. Comparisons with similarly reactive nitrenium ions indicate that the lifetime of 1c is ca. 20-200 ps if it is generated, so it must react by a preassociation process. Density functional theory calculations at the B3LYP/6-31G*//HF/6-31G* level coupled with kinetic correlations also indicate that the aqueous solution lifetimes of 1a-c are in the picosecond range.