First and second moments for self‐similar couplings and Wasserstein distances

We study aspects of the Wasserstein distance in the context of self‐similar measures. Computing this distance between two measures involves minimising certain moment integrals over the space of couplings, which are measures on the product space with the original measures as prescribed marginals. We focus our attention on self‐similar measures associated to equicontractive iterated function systems consisting of two maps on the unit interval and satisfying the open set condition. We are particularly interested in understanding the restricted family of self‐similar couplings and our main achievement is the explicit computation of the 1st and 2nd moment integrals for such couplings. We show that this family is enough to yield an explicit formula for the 1st Wasserstein distance and provide non‐trivial upper and lower bounds for the 2nd Wasserstein distance for these self‐similar measures.     

Elements of Design‐Based Science Activities That Affect Students' Motivation

The primary purpose of this study was to examine the ways in which a 12‐week afterschool science and engineering program affected middle school students' motivation to engage in science and engineering activities. We used current motivation research and theory as a conceptual framework to assess 14 students' motivation through questionnaires, structured interviews, and observations. Students reported that during the activities they perceived that they were empowered to make choices in how to complete things, the activities were useful to them, they could succeed in the activities, they enjoyed and were interested in the hands‐on activities and some presentations, they felt cared for by the facilitators and received help when they were stuck or confused, and they put forth effort. Based on our examination of data across our three data sources, we identified motivating opportunities that were provided to students during the activities. These motivating opportunities can serve as examples to help both formal and informal science educators better connect motivation theory to practice so that they can create motivating opportunities for students. Furthermore, this study provides a methodological example of how students' motivation can be examined during the context of authentic science and engineering instruction.     

High angular-resolution automated visible-wavelength scanning angle Raman microscopy

A scanning angle (SA) Raman microscope with 532-nm excitation is reported for probing chemical content perpendicular to a sample interface. The instrument is fully automated to collect Raman spectra across a range of incident angles from 20.50 to 79.50° with an angular spread of 0.4 ± 0.2° and an angular uncertainty of 0.09°. Instrumental controls drive a rotational stage with a fixed axis of rotation relative to a prism-based sample interface mounted on an inverted microscope stage. Three benefits of SA Raman microscopy using visible wavelengths, compared to near infrared wavelengths are: (i) better surface sensitivity; (ii) increased signal due to the frequency to the fourth power dependence of the Raman signal, and the possibility for resonant enhancement; (iii) the need to scan a reduced angular range to shorten data collection times. These benefits were demonstrated with SA Raman measurements of thin polymer films of polystyrene or a diblock copolymer of polystyrene and poly(3-hexylthiophene-2,5-diyl). Thin film spectra were collected with a signal-to-noise ratio of 30 using a 0.25 s acquisition time.     

Rubber-based substrates modified with carbon nanotubes inks to build flexible electrochemical sensors

The development of a solid-contact potentiometric sensor based on conducting rubbers using a carbon nanotubes ink is described here. Commercial rubbers are turned into conductive ones by a simple and versatile method, i.e. painting an aqueous dispersion of single-walled carbon nanotubes on the polymer surface. On this substrate, both the working ion-selective electrode and the reference electrode are built in order to form an integrated potentiometric cell. As a proof-of-principle, selective potassium electrodes are fully characterized giving comparable performances to conventional electrodes (sensitivity, selectivity, stability, linear range, limit of detection and reproducibility). As an application of the rubber-based electrodes, a bracelet was constructed to measure potassium levels in artificial sweat. Since rubbers are ubiquitous in our quotidian life, this approach offers great promise for the generation of chemical information through daily objects.     

A flexible synthesis of C-6 and N-1 analogues of a 4-amino-1,3-dihydroimidazo[4,5-c]pyridin-2-one core

A flexible route which enables access to derivatives of 4-amino-1,3-dihydroimidazo[4,5-c]pyridin-2-ones is described. Issues of selectivity, reaction safety, and low yields in original routes are overcome with the key improvements to the route, including a Negishi cross-coupling and use of a carbamate as a protecting group and intrinsic carbonyl source. The new route enables variation of C-6 and N-1 substituents.     

Gold nanoparticles deposited capillaries for in-capillary microextraction capillary zone electrophoresis of monohydroxy-polycyclic aromatic hydrocarbons

This article presents the first application of gold nanoparticles deposited capillaries as pre-concentration devices for in-capillary microextraction CZE and their use for the analysis of monohydroxy-polycyclic aromatic hydrocarbons in synthetic urine samples. The successful separation of 1-hydroxypyrene, 9-hydroxyphenanthrene, 3-hydroxybenzo[a]pyrene (3-OHbap), 4-hydroxybenzo[a]pyrene and 5-hydroxybenzo[a]pyrene under a single set of electrophoretic conditions is demonstrated as well as the feasibility to obtain competitive ultraviolet absorption LOD with commercial instrumentation. Enrichment factors ranging from 87 (9-OHphe) to 100 (3-OHbap) made it possible to obtain LOD ranging from 9 ng/mL (9-OHphe and 3-OHbap) to 14 ng/mL (4-hydroxybenzo[a]pyrene).     

Response analysis in biochemical chain reactions with negative feedforward and feedbackward loops

Finite difference equations can be used to study the responses of biochemical chain reactions at any step of the chain to an external stimulus. In this study, we developed mathematical models for two hypothetical chain reactions involving loops to study the responses in the chain as the length of the chain gets longer, so called transient and steady state responses. The first model is for a chain with a negative feedforward loop, and the second one is for a chain that has a negative feedback loop. Although both of the models have the same steady state equations and values, we showed that the chain with negative feedforward and negative feedback loops can produce significantly different behaviors. The former can bring the chain into oscillations with various periods and eventually chaos when the feedback is strong enough as the length of the reaction chain increases, whereas the latter is not capable of producing oscillations and more complicated dynamics.     

Polymeric cross-linked surface treatments for controlling block copolymer orientation in thin films

The orientation of cylinder-forming poly(styrene-block-methyl methacrylate) [P(S-b-MMA)] was investigated on two sets of polymeric surface treatments: 10 para-substituted polystyrene derivatives with <10 mol % poly(4-vinylbenzyl azide) and a series of poly(styrene-random-4-vinylbenzyl azide) [P(S-r-VBzAz)] copolymers with 5-100 mol % poly(4-vinylbenzyl azide). The copolymers were spin-coated to form thin films and then cross-linked by heating. The resulting films exhibited a range of surface tensions from 21 to 45 dyn/cm. Perpendicular orientation of P(S-b-MMA) cylinders was achieved with poly(p-bromostyrene) and all the [P(S-r-VBzAz)] copolymer surface treatments, most notably the homopolymer of poly(4-vinylbenzyl azide). Films made from these simple copolymers are as effective as random terpolymer alignment layers commonly made from both block monomers and a cross-linkable monomer.     

Ultrasonic frequency analysis of antibody-linked hydrogel biosensors for rapid point of care testing

Analyte quantification in highly scattering media such as tissue, blood, and other biological fluids is challenging using conventional spectroscopic methods. Ultrasound easily penetrates these opaque samples, yet currently provides little chemical information. We have developed a general approach for creating hydrogel biosensors based on antibody-linked cellulose polymers. Target recognition induces changes to the sensor stiffness and size, which is accompanied by characteristic changes to a measured ultrasonic frequency profile. Using this technique, nM sensitivity for acetaminophen is demonstrated in a series of biofluids including whole blood, blood plasma, saliva, and urine. Likewise, this methodology is attractive for point of care diagnostics due to the short measurement time, simple methodology which excludes pretreatment of samples, and has minimal chemical or buffer requirements.     

Diversity oriented synthesis: substitution at C5 in unreactive pyrimidines by Claisen rearrangement and reactivity in nucleophilic substitution at C2 and C4 in pteridines and pyrido[2,3-d]pyrimidines

Diversity oriented synthesis of fused pyrimidines leads to scaffolds with many biological activities. In the case of the preparation of pyrido[2,3-d]pyrimidines from 2-alkylthiopyrimidines, the formation of a new carbon-carbon bond at C5 is required, a reaction, that is, very limited in scope. However Claisen type rearrangement of simple 4-allylic ethers affords C5 substituted pyrimidines readily; in cases with an ester substituent, rearrangement occurs at room temperature. Subsequent cyclisation to afford 6-methylpyrido[2,3-d]pyrimidin-7(8H)-ones was achieved in high yield. Using allylic ethers derived from 3-chloromethyl-4-arylbut-3-en-2-ones as substrates, a new titanium[IV]chloride catalysed reaction affording 6-arylmethyl-7-methylpyrido[2,3-d]pyrimidines was discovered. In contrast, 2-alkylthiopteridines are readily available. In both cases, substitution at C2 and C4 to generate diversity has been carried out and the reactivity compared; yields of substitution products were generally higher with pteridine substrates. In biological assays unexpected hits were found for activity against the Gram positive bacterium, Nocardia farcinia, and against the parasite Trypanosoma brucei brucei, illustrating the value of diversity oriented synthesis in the discovery of biologically active compounds.