Extending Whitney's extension theorem: nonlinear function spaces

We consider a global, nonlinear version of the Whitney extension problem for manifold-valued smooth functions on closed domains $C$, with non-smooth boundary, in possibly non-compact manifolds. Assuming $C$ is a submanifold with corners, or is compact and locally convex with rough boundary, we prove that the restriction map from everywhere-defined functions is a submersion of locally convex manifolds and so admits local linear splittings on charts. This is achieved by considering the corresponding restriction map for locally convex spaces of compactly-supported sections of vector bundles, allowing the even more general case where $C$ only has mild restrictions on inward and outward cusps, and proving the existence of an extension operator.Comment: 37 pages, 1 colour figure. v2 small edits, correction to Definition A.3, which makes no impact on proofs or results. Version submitted for publication. v3 small changes in response to referee comments, title extended. v4 crucial gap filled, results not affected. v5 final version to appear in Annales de l'Institut Fourie

Caffeine Withdrawal and Dependence: A Review

With the prevalence of caffeine use increasing in modern lifestyles, it is important to look at the symptoms of caffeine use, including withdrawal and dependence, and whether these symptoms have implications for addiction. A limited number of assessments have been developed to assess caffeine withdrawal. In order to make a call for more assessments and programs to be developed to assist with healthy caffeine use, this literature review observed recent studies focusing on withdrawal and dependence. Ozsunger et al. (2009) classified caffeine withdrawal into three categories of symptoms. Three years later, Juliano et al. (2012) used an experimental approach to develop a larger classification with seven clusters of withdrawal symptoms. Rogers et al. (2013) observed the effects of withdrawal on daily functionality. Juliano et al. (2012) assessed and interviewed participants who were physically dependent on caffeine in order to suggest further treatments for caffeine dependence. Evatt et al. (2015) developed a program for treatment for an individual problematically consuming caffeine

Investigating the pharmacology of novel 5-HT3 receptor ligands; with the potential to treat neuropsychiatric and gastrointestinal disorders

The 5-hydroxytryptamine (5-HT; serotonin) 5-HT3 receptor is an excitatory ligand-gated ion channel expressed in for example the brain and the gastrointestinal tract. Two major subtypes of the receptor have been studied in the most detail; the homomeric 5-HT3A receptor and the heteromeric 5-HT3AB receptor. 5-HT3 receptor antagonists are used clinically to treat chemotherapy induced and post-operative nausea and vomiting, and demonstrate symptomatic relief in diarrhoea-predominant irritable bowel syndrome (IBS-d); but unfortunately, these medications cause adverse effects such as constipation or rarely ischemic colitis in the latter condition. This study has characterised the pharmacology of two structurally distinct 5-HT3 receptor partial agonists (vortioxetine and CSTI-300); and identified the unique binding properties of the cryptic orthosteric modulator 5-chloroindole (Cl-indole) for the human (h) 5-HT3 receptor. Vortioxetine is a multi-modal antidepressant, which displays affinity for the 5-HT transporter as well as a multitude of 5-HT receptors, including the 5-HT3 receptor. The first part of this study has identified vortioxetine as a relatively high affinity, competitive 5-HT3 receptor partial agonist with an intrinsic efficacy of approximately 40-50% that of 5-HT. Given the safety of vortioxetine in patients, it has the potential to be trialled in other conditions for which 5-HT3 receptor antagonists demonstrate efficacy but cause adverse effects, such as IBS-d or even schizophrenia. The second section of this study has identified CSTI-300 as a selective, high affinity 5-HT3 receptor partial agonist (intrinsic activity 30-40% that of 5-HT). Moreover, in a rodent model of IBS-d, CSTI-300 demonstrated comparable efficacy to alosetron, a 5-HT3 receptor antagonist with established efficacy in treating IBS-d. CSTI-300 is predicted to be able to relieve symptoms of IBS-d in patients without eliciting the side effect profile associated with 5-HT3 receptor antagonism. The final part of this study has demonstrated that the binding mechanism of Cl-indole for the 5-HT3A receptor is modulated by 5-HT3 receptor agonists, but not 5-HT3 receptor antagonists. This could have implications in designing 5-HT3 receptor allosteric ligands for potentially treating conditions such as IBS-d

Production and Harvest of Microalgae in Wastewater Raceways with Resource Recycling

Microalgae can be grown on municipal wastewater media to both treat the wastewater and produce feedstock for algae biofuel production. However the reliability of treatment must be demonstrated, as well as high areal algae productivity on recycled wastewater media and efficient sedimentation harvesting. This processes was studied at pilot scale in the present research. A pilot facility was operated with nine CO2-supplemented raceway ponds, each with a 33-m2 surface area and a 0.3-m depth, continuously from March 6, 2013 through September 24, 2014. The ponds were operated as three sets of triplicates with two sets continuously fed primary-clarified municipal wastewater at either a 2-day or 3-day hydraulic residence time (HRT), and one set fed the clarified effluent of the 3-day pond set. This second pond-in-series was operated with a 3-day HRT. Areal biomass productivity is reported as gross and net, the former based only on biomass in the pond effluents and the latter subtracting the volatile suspended solids in the influent from those in the effluent. An estimate was also made of autotrophic biomass productivity, as differentiated from heterotrophic growth. Over a year, net productivity averaged 83 metric tons per hectare per year (MT/ha-yr) for the 2-day HRT ponds, 52 MT/ha-yr for the 3-day HRT ponds, and 44 MT/ha-yr for the 3-day HRT ponds receiving clarified effluent of the first set of 3-day HRT ponds (i.e., recycled water). The lower net productivity of the pond receiving water recycling was attributed to two factors. First, the relatively high influent suspended solids concentrations were subtracted from the effluent suspended solids concentrations before net productivity was calculated. Second, the recycled water contained less soluble organic matter than the primary-clarified wastewater leading to less heterotrophic biomass production. The accumulation of inhibitory allelochemicals is a possible third cause of lower productivity , but no specific information was collected on allelopathy. Algae were harvested from pond effluent by sedimentation, with harvest efficiency most affected by the extent of natural bioflocculation occurring in the ponds. Some forms of bioflocculation are thought to be mediated by bacteria, which often make-up a substantial fraction of the settled flocs. Pond samples settled in 1-L Imhoff cones averaged/L total suspended solids after 24 hours of settling; but all ponds fell short of meeting an averaged/L total suspended solids after a 2 hour interval which would be ideally achieved for wastewater effluent. No relationship was seen between settling performance and the bacterial content of flocs. Soluble carbonaceous biochemical oxygen demand (scBOD5) removal by the raceway ponds was sufficient to meet wastewater treatment requirements year around. Influent scBOD5 concentrations averaged 83 mg/L, and the effluent averaged 5.1 mg/L and 4.2 mg/L for the 2-day and 3-day HRT pond sets, respectively. The variable with the greatest influence on productivity in all pond sets, and settling performance in the recycled water pond set, was season (i.e., co-correlated variables of solar insolation and pond temperature). Neither productivity nor settling appeared to be related to prominent algae genera or prevalence of grazers. The high net productivity achieved with a growth medium of primary clarifier effluent and the generally high settleability of algal-bacterial flocs indicate a good potential for algae wastewater treatment and biofuel production. However, the settling of algae grown on recycled water needs improvement to achieve the full potential of wastewater-grown algae biofuel production

Development of human C-peptide LC-MS isotope-dilution assay : optimization of C-peptide isolation from biological fluids and with ion exchange chromatography

Human C-peptide is an effective marker of insulin secretion in diabetes diagnostics, as it is produced in equimolar amounts with insulin. Little metabolism of C-peptide by the liver also enables its concentrations to be three to five times higher than insulin in the plasma. Although there exists a current demand for higher sensitivity, the method of C-peptide quantitative analysis by Isotope-dilution assays allows for greater specificity as compared to current immunoassay methods