Computing devices,mathematics education and mathematics: Sexton’s omnimetre in its time

Material objects can tell us much about mathematical practice. In 1899, Albert Sexton, a Philadelphia mechanical engineer, received the John Scott Medal of the Franklin Institute for his invention of the omnimetre. This inexpensive circular slide rule was one of a host of computing devices that became common in the United States around 1900. It is inscribed “NUMERI MUNDUM REGUNT”. In part because of instruments such as the omnimetre, numbers increasingly ruled the practical world of the late 19th and early 20th century. This changed not only engineering, but mathematics education and mathematical work.     

The impact of the natural sciences on archaeology

This article reviews some of the applications of physics to the solution of archaeological problems. The use of magnetic, resistivity and electromagnetic surveying techniques for the location of buried features is described. Various methods of age determination are outlined while the problems associated with radiocarbon dating of organic material and thermoluminescent dating of pottery are discussed in detail. The techniques, including petrological examination, chemical analysis and isotopic analysis, employed in the physical examination of archaeological artefacts are described. Examples of the application of these techniques in establishing the source of the raw materials used in pottery, metal and stone implements and in elucidating the techniques of manufacture of pottery and metal objects are also given.     

Quantitative model for prediction of hydrodynamic size of nonionic reverse micelles

The sizes of nonionic reverse micelles were investigated as a function of the molecular structure of the surfactant, the type of oil, the total concentration of surfactant [NP], the ratio of surfactant to total surfactant (r), the water to surfactant molar ratio (omega), temperature, salt concentration, and polar phase. The basis of our investigation was a mixture of nonylphenol polyethoxylates--NP4 and NP7, various polar phases, and several oils. Micelle sizes were determined using dynamic light scattering (DLS). A central composite experimental design was used to quantitatively model micelle size as a function of omega, surfactant concentration, and r. The model has demonstrated the capability of predicting the mean diameter of micelles from 4 to 13 with a precision of +/-2 nm as measured by DLS. This quantitative correlation between the size of reverse micelles and the synthetic variables provides the foundation for choosing experimental conditions to control reverse micelle size. In turn, this allows control of the size of nanoparticles synthesized within them.     

Phenolic compounds,essential oil composition,and antioxidant activity of Angelica purpurascens (Avé-Lall.) Gill

In this study, methanol extracts (MEs) and essential oil (EO) of Angelica purpurascens (Avé-Lall.) Gill obtained from different parts (root, stem, leaf, and seed) were evaluated in terms of antioxidant activity, total phenolics, compositions of phenolic compound, and essential oil with the methods of 2,2-azino-bis(3ethylbenzo-thiazoline-6-sulfonic acid (ABTS•⁺), 2,2-diphenyl-1-picrylhydrazil (DPPH•) radical scavenging activities, and ferric reducing/antioxidant power (FRAP), the Folin–Ciocalteu, liquid chromatography−tandem mass spectrometry (LC−MS/MS), and gas chromatography-mass spectrometry (GC−MS), respectively. The root extract of A. purpurascens exhibited the highest ABTS•⁺, DPPH•, and FRAP activities (IC₅₀: 0.05 ± 0.0001 mg/mL, IC₅₀: 0.06 ± 0.002 mg/mL, 821.04 ± 15.96 µM TEAC (Trolox equivalent antioxidant capacity), respectively). Moreover, EO of A. purpurascens root displayed DPPH• scavenging activity (IC₅₀: 2.95 ± 0.084 mg/mL). The root extract had the highest total phenolic content (438.75 ± 16.39 GAE (gallic acid equivalent), µg/mL)). Twenty compounds were identified by LC−MS/MS. The most abundant phenolics were ferulic acid (244.39 ± 15.64 μg/g extract), benzoic acid (138.18 ± 8.84 μg/g extract), oleuropein (78.04 ± 4.99 μg/g extract), and rutin (31.21 ± 2.00 μg/g extract) in seed, stem, root, and leaf extracts, respectively. According to the GC−MS analysis, the major components were determined as α-bisabolol (22.93%), cubebol (14.39%), α-pinene (11.63%), and α-limonene (9.41%) among 29 compounds. Consequently, the MEs and EO of A. purpurascens can be used as a natural antioxidant source.     

Transition Metal Ion-binding Properties of a 14-Membered N2O2S2- Macrobicyclic Ligand

The selective liquid–liquid extraction of various transition metal cations from the aqueous phase to the organic phase was carried out using a 14-membered N₂O₂S₂-macrobicycle. Metal picrates such as Pb²⁺, Co²⁺, Zn²⁺, Ni²⁺,Cu²⁺ and Cd²⁺ were used in this extraction studies. It was found that the ligand showed moderate selectivity towards Pb²⁺ only among the other metals. The extraction constant (log K _ex) was determined to be 13.8 for Pb²⁺ complex.     

Separation and characterisation of five polar herbicides using countercurrent chromatography with detection by negative ion electrospray ionisation mass spectrometry.

Five polar herbicides were separated and characterised using high-speed analytical countercurrent chromatography (HSACCC) in conjunction with online electrospray mass spectrometry (ESI-MS). The countercurrent chromatography used a standard isocratic biphasic solvent system of hexane/ethyl acetate/methanol/water in reverse phase to effect the separation of these five environmentally important compounds. The chromatograph was coupled to a triple quadrupole mass spectrometer via a standard electrospray liquid chromatography interface that was able to give mass spectra in negative ion mode of each compound. Limits of detection are reported for this series of compounds along with representative negative ion ESI-MS data and calibrations for the separation.     

Efficient delivery of Cre-recombinase to neurons in vivo and stable transduction of neurons using adeno-associated and lentiviral vectors

Background

As development proceeds the human embryo attains an ever more complex three dimensional (3D) structure. Analyzing the gene expression patterns that underlie these changes and interpreting their significance depends on identifying the anatomical structures to which they map and following these patterns in developing 3D structures over time. The difficulty of this task greatly increases as more gene expression patterns are added, particularly in organs with complex 3D structures such as the brain. Optical Projection Tomography (OPT) is a new technology which has been developed for rapidly generating digital 3D models of intact specimens. We have assessed the resolution of unstained neuronal structures within a Carnegie Stage (CS)17 OPT model and tested its use as a framework onto which anatomical structures can be defined and gene expression data mapped.

Results

Resolution of the OPT models was assessed by comparison of digital sections with physical sections stained, either with haematoxylin and eosin (H&E) or by immunocytochemistry for GAP43 or PAX6, to identify specific anatomical features. Despite the 3D models being of unstained tissue, peripheral nervous system structures from the trigeminal ganglion (~300 μm by ~150 μm) to the rootlets of cranial nerve XII (~20 μm in diameter) were clearly identifiable, as were structures in the developing neural tube such as the zona limitans intrathalamica (core is ~30 μm thick). Fourteen anatomical domains have been identified and visualised within the CS17 model. Two 3D gene expression domains, known to be defined by Pax6 expression in the mouse, were clearly visible when PAX6 data from 2D sections were mapped to the CS17 model. The feasibility of applying the OPT technology to all stages from CS12 to CS23, which encompasses the major period of organogenesis for the human developing central nervous system, was successfully demonstrated.

Conclusion

In the CS17 model considerable detail is visible within the developing nervous system at a minimum resolution of ~20 μm and 3D anatomical and gene expression domains can be defined and visualised successfully. The OPT models and accompanying technologies for manipulating them provide a powerful approach to visualising and analysing gene expression and morphology during early human brain development.