On some fundamental results about higher-rank graphs and their C*-algebras

Results of Fowler and Sims show that every k-graph is completely determined by its k-coloured skeleton and collection of commuting squares. Here we give an explicit description of the k-graph associated to a given skeleton and collection of squares and show that two k-graphs are isomorphic if and only if there is an isomorphism of their skeletons which preserves commuting squares. We use this to prove directly that each k-graph {\Lambda} is isomorphic to the quotient of the path category of its skeleton by the equivalence relation determined by the commuting squares, and show that this extends to a homeomorphism of infinite-path spaces when the k-graph is row finite with no sources. We conclude with a short direct proof of the characterisation, originally due to Robertson and Sims, of simplicity of the C*-algebra of a row-finite k-graph with no sources.Comment: 21 pages, two pictures prepared using TiK

Adaptation and acclimatization to ocean acidification in marine ectotherms: an in situ transplant experiment with polychaetes at a shallow CO₂ vent system

Metabolic rate determines the physiological and life-history performances of ectotherms. Thus, the extent to which such rates are sensitive and plastic to environmental perturbation is central to an organism's ability to function in a changing environment. Little is known of long-term metabolic plasticity and potential for metabolic adaptation in marine ectotherms exposed to elevated pCO₂. Consequently, we carried out a series of in situ transplant experiments using a number of tolerant and sensitive polychaete species living around a natural CO₂ vent system. Here, we show that a marine metazoan (i.e. Platynereis dumerilii) was able to adapt to chronic and elevated levels of pCO₂. The vent population of P. dumerilii was physiologically and genetically different from nearby populations that experience low pCO₂, as well as smaller in body size. By contrast, different populations of Amphiglena mediterranea showed marked physiological plasticity indicating that adaptation or acclimatization are both viable strategies for the successful colonization of elevated pCO₂ environments. In addition, sensitive species showed either a reduced or increased metabolism when exposed acutely to elevated pCO₂. Our findings may help explain, from a metabolic perspective, the occurrence of past mass extinction, as well as shed light on alternative pathways of resilience in species facing ongoing ocean acidification

Determination of metal ion concentrations by SERS using 2,2’-bipyridyl complexes

Surface enhanced Raman scattering (SERS) can generate characteristic spectral “fingerprints” from metal complexes, thus providing the potential for the development of methods of analysis for the identification and quantitation of a range of metal ions in solution. The advantages include sensitivity and the use of one ligand for several metals without the need for a specific chromophore. Aqueous solutions of Fe(II), Ni(II), Zn(II), Cu(II), Cr(III) and Cd(II) in the presence of excess 2,2′-bipyridyl (bipy) were analysed using SERS. Specific marker bands enabled the identification of each metal ion and the limit of detection for each metal ion was estimated. Two of the ions, Zn(II) and Cu(II), could be detected below the World Health Organisation's (WHO) recommended limits for drinking water at levels of 0.22 and 0.6 mg L−1, respectively

Detection of potentially toxic metals by SERS using salen complexes

Surfaced enhanced Raman scattering (SERS) can discriminate between metal complexes due to the characteristic “spectral fingerprints” obtained. As a result, SERS has the potential to develop relatively simple and sensitive methods of detecting and quantifying a range of metal ions in solution. This could be beneficial for the environmental monitoring of potentially toxic metals (PTMs). Here, salen (C16H16N2O2) was used as a ligand to form complexes of Ni(II), Cu(II), Mn(II) and Co(II) in solution. The SERS spectra showed characteristic spectral differences specific to each metal complex, thus allowing the identification of each of these metal ions. This method allows a number of metal ions to be detected using the same ligand and an identical preparation procedure. The limit of detection (LOD) was determined for each metal ion, and it was found that Ni(II), Cu(II) and Mn(II) could be detected below the WHO’s recommended limits in drinking water at 1, 2 and 2 µg L-1, respectively. Co(II) was found to have an LOD of 20 µg L-1, however no limit has been set for this ion by the WHO as the concentration of Co(II) in drinking water is generally <1-2 μg L-1. A contaminated water sample was also analysed where Mn(II) was detected at a level of 800 µg L-1

Identification of liver metastases with probe-based confocal laser endomicroscopy at two excitation wavelengths.

BACKGROUND: Metastasis of colorectal cancer to the liver is the most common indication for hepatic resection in a western population. Incomplete excision of malignancy due to residual microscopic disease normally results in worse patient outcome. Therefore, a method aiding in the real time discrimination of normal and malignant tissue on a microscopic level would be of benefit. MATERIAL AND METHODS: The ability of fluorescent probe-based confocal laser endomicroscopy (pCLE) to identify normal and malignant liver tissue was evaluated in an orthotopic murine model of colorectal cancer liver metastasis (CRLM). To maximise information yield, two clinical fluorophores, fluorescein and indocyanine green (ICG) were injected and imaged in a dual wavelength approach (488 and 660 nm, respectively). Visual tissue characteristics on pCLE examination were compared with histological features. Fluorescence intensity in both tissues was statistically analysed to elucidate if this can be used to differentiate between normal and malignant tissue. RESULTS: Fluorescein (488 nm) enabled good visualisation of normal and CRLM tissue, whereas ICG (660 nm) visualisation was limited to normal liver tissue only. Fluorescence intensity in areas of CRLM was typically 53-100% lower than normal hepatic parenchyma. Using general linear mixed modelling and receiver operating characteristic analysis, high fluorescence intensity was found to be statistically more likely in normal hepatic tissue. CONCLUSION: Real time discrimination between normal liver parenchyma and metastatic tissue with pCLE examination of fluorescein and ICG is feasible. Employing two (rather than a single) fluorophores allows a combination of qualitative and quantitative characteristics to be used to distinguish between hepatic parenchyma and CRLM. Lasers Surg. Med. © 2016 Wiley Periodicals, Inc

Assembly, Elasticity, And Structure Of Lyotropic Chromonic Liquid Crystals And Disordered Colloids

This dissertation describes experiments which explore the structure and dynamics in two classes of soft materials: lyotropic chromonic liquid crystals and colloidal glasses and super-cooled liquids. The first experiments found that the achiral LCLCs, sunset yellow FCF (SSY) and disodium cromoglycate (DSCG) both exhibit spontaneous mirror symmetry breaking in the nematic phase driven by a giant elastic anisotropy of their twist modulus compared to their splay and bend moduli. Resulting structures of the confined LCLCs display interesting director configurations due to interplay of topologically required defects and twisted director fields. At higher concentrations, the LCLC compounds form columnar phases. We studied the columnar phase confined within spherical drops and discovered and understood configurations of the LC that sometimes led to non-spherical droplet shapes. The second experiments with SSY LCLCs confined in hollow cylinders uncovered director configurations which were driven in large measure by an exotic elastic modulus known as saddle-splay. We measured this saddle-splay modulus in a LCLC for the first time and found it to be more than 50 times greater than the twist elastic modulus. This large relative value of the saddle-splay modulus violates a theoretical result/assumption known as the Ericksen inequality. A third group of experiments on LCLCs explored the drying process of sessile drops containing SSY solutions, including evaporation dynamics, morphology, and deposition patterns. These drops differ from typical, well-studied evaporating colloidal drops primarily due to the LCLC\u27s concentration-dependent isotropic, nematic, and columnar phases. Phase separation occurs during evaporation, creating surface tension gradients and significant density and viscosity variation within the droplet. Thus, the drying multiphase drops exhibit new convective currents, drop morphologies, deposition patterns, as well as a novel ordered crystalline phase. Finally, experiments in colloidal glasses and super-cooled liquids were initiated to probe the relationship between structure and dynamics in their constituent particles. The displacements of individual particles in the colloids can be decomposed into small cage fluctuations and large rearrangements into new cages. We found a correlation between the rate of rearrangement and the local cage structure associated with each particle. Particle trajectories of a two-dimensional binary mixture of soft colloids are captured by video microscopy. We use a machine learning method to calculate particle ``softness\u27\u27, which indicates the likelihood of rearrangement based on many radial structural features for each particle. We measured the residence time between consecutive rearrangements and related probability distribution functions (PDFs). The softness-dependent conditional PDF is well fit by an exponential with decay time decreasing monotonically with increasing softness. Using these data and a simple thermal activation model, we determined activation energies for rearrangements

The kingdom in First Corinthians: reevaluating an underestimated Pauline theme

Despite the fact that scholars regularly overlook the theme of the kingdom in Paul’s letters, the thesis of this work is that the kingdom is a foundational component of God’s saving work in Christ in 1 Corinthians. This thesis can be demonstrated by observing three primarily lines of evidence: (1) the relationship of the kingdom to the effects of Christ’s death, resurrection, and saving reign, (2) the consistency of Paul’s kingdom references with respect to his inaugurated eschatological schema, and (3) the connection between the kingdom and Paul’s ethical teaching, or what might also be referred to as the transforming work of the Spirit. Chapter 1 provides a history of research concerning the different approaches to Paul’s theology of the kingdom in modern scholarship. Relatively few scholars have addressed the topic in a comprehensive way, and where the kingdom has been addressed, it has commonly been suggested that Paul has replaced it with another theme. Chapters 2 through 4 examine Paul’s references to the kingdom in the following texts: 1 Corinthians 4:8, 20; 6:2-3, 9-11; 15:20-28, 50. In addition to examining Paul’s use of words in the βασιλ– word group, these chapters also focus on Paul’s use of kingdom-related concepts, such as the reign of Christ, the reign of believers, and the future judgment of the saints. A number of connections are also drawn between the kingdom and related eschatological themes. Chapter 5 compares Paul’s kingdom theology in 1 Corinthians with the rest of his epistles. It is argued that there is a consistency to the apostle’s theology of the kingdom, even as different contexts require different aspects of the kingdom to be emphasized. The conclusion in chapter 6 provides a summary of the findings in the previous chapters, including a recap of how the thesis has been demonstrated. Also included are some limitations and implications of this work, along with suggestions for further study on this topic