Maximal induced matchings in triangle-free graphs

An induced matching in a graph is a set of edges whose endpoints induce a $1$-regular subgraph. It is known that any $n$-vertex graph has at most $10^{n/5} \approx 1.5849^n$ maximal induced matchings, and this bound is best possible. We prove that any $n$-vertex triangle-free graph has at most $3^{n/3} \approx 1.4423^n$ maximal induced matchings, and this bound is attained by any disjoint union of copies of the complete bipartite graph $K_{3,3}$. Our result implies that all maximal induced matchings in an $n$-vertex triangle-free graph can be listed in time $O(1.4423^n)$, yielding the fastest known algorithm for finding a maximum induced matching in a triangle-free graph.Comment: 17 page

Freshwater diatom persistence on clothing II: Further analysis of species assemblage dynamics over investigative timescales

Diatoms are a useful form of environmental trace evidence, yielding a circumstantial link between persons and scenes of forensic interest. A developing empirical research base has sought to understand those factors affecting the transfer and persistence of freshwater diatoms on clothing and footwear surfaces. Although an initial study has demonstrated that diatoms can persist on clothing following weeks of wear, no previous research has explored the temporal dynamics of a persistent species assemblage over timescales pertinent to forensic investigations. This study therefore aimed to determine if: (1) valve morphology (size and shape) influences diatom persistence, (2) the relative abundance of taxa within an assemblage affects retention, and (3) a persistent diatom assemblage retrieved from clothing after one month can reliably be compared to the site of initial transfer. To build on previous research findings which highlighted the impact of substrate and environmental seasonality on diatom transfer and persistence, here, nine clothing materials were tested in spring before a seasonal comparison in the winter. Fabric swatches were immersed in a freshwater river, worn attached to clothing, and subsamples retrieved at regular intervals (hours, days, weeks) up to one month post-immersion. Diatoms were extracted using a H2O2 technique and analysed via microscopy. The results indicated that smaller diatoms (< 10 µm) are retained in significantly greater abundance, with no statistically significant difference between centric and pennate diatom loss over time. Although a persistent species assemblage was relatively stable over the one month of wear, significant differences were identified between clothing substrate in the spring and between the seasonal samples. The most abundant environmental taxa were consistently identified in the forensic samples, with greater variability attributed to the retention of relatively less common species. The findings suggest that, despite a loss in the abundance and species-richness of diatoms retrieved from clothing over time, a persistent assemblage may provide a useful circumstantial link to the site of initial transfer. The complex relationships between clothing type, environmental seasonality, and time since wear on retention, emphasise the need for diatom trace evidence to be carefully interpreted within an exclusionary framework, and the significance of any casework findings to be determined with reference to empirical evidence bases

Freshwater diatom persistence on clothing I: A quantitative assessment of trace evidence dynamics over time

Freshwater diatoms offer valuable circumstantial forensic indicators, with a growing empirical research base aiming to identify and understand some of the spatial and temporal factors affecting their validity as trace evidence. Previous studies demonstrated that recipient surface characteristics, environmental variability, and individual species traits influence the initial transfer of freshwater diatoms to clothing. However, no previous research has sought to consider the impact of these and other variables on the persistence of transferred diatoms over investigative timescales. Therefore, this study aimed to identify and explore diatom retention dynamics on clothing following wear over time (hours to weeks). A series of experiments were designed to examine the impact of clothing material, seasonality, and time since wear (persistence interval) on the total number and species-richness of diatoms recovered and their relative retention (%) over time. Nine clothing swatches were immersed in a freshwater environment and then worn for one month in the spring. Subsamples were retrieved at regular intervals (e.g. 30 mins, 1 h, 8 h, 24 h) up to one month, diatoms were extracted using a H2O2 method, and examined microscopically. Three clothing materials were subject to the same experiment in the winter to generate a seasonal comparison. The results broadly identified three stages of diatom persistence on clothing - rapid initial loss, variable intermediate decay, and sustained long-term presence. Clothing material significantly impacted the number of diatoms recovered and retention dynamics over time, with complex interactions identified with seasonality. Although fewer diatoms were recovered in the winter, overall retention trends were consistent at the different times of year. The findings demonstrate that diatoms can be recovered from clothing, even weeks or months after an initial transfer, yielding a useful environmental trace indicator for forensic reconstructions over investigative timescales. The impact of clothing material and seasonality on persistence identified cotton, acrylic, and viscose clothing as the most reliable temporal repository of diatom trace evidence, with a more abundant forensic assemblage available for forensic comparisons in the spring

Robust Estimation for Linear Panel Data Models

In different fields of applications including, but not limited to, behavioral, environmental, medical sciences and econometrics, the use of panel data regression models has become increasingly popular as a general framework for making meaningful statistical inferences. However, when the ordinary least squares (OLS) method is used to estimate the model parameters, presence of outliers may significantly alter the adequacy of such models by producing biased and inefficient estimates. In this work we propose a new, weighted likelihood based robust estimation procedure for linear panel data models with fixed and random effects. The finite sample performances of the proposed estimators have been illustrated through an extensive simulation study as well as with an application to blood pressure data set. Our thorough study demonstrates that the proposed estimators show significantly better performances over the traditional methods in the presence of outliers and produce competitive results to the OLS based estimates when no outliers are present in the data set

Socio-economic predictors of stunting in preschool children – a population-based study from Johannesburg and Soweto

Background. Stunting continues to be a child public health concern in many African countries, including South Africa. This study uses data from the Birth to Twenty study, held in Johannesburg, to investigate a range of household-level socioeconomic and social support predictors of stunting in children aged less than 30 months.Design. Logistical regression models were constructed using aconceptual framework to investigate the association between early life measures of socio-economic status and stunting

Group 2 Innate Lymphoid Cells Are Redundant in Experimental Renal Ischemia-Reperfusion Injury.

Acute kidney injury (AKI) can be fatal and is a well-defined risk factor for the development of chronic kidney disease. Group 2 innate lymphoid cells (ILC2s) are innate producers of type-2 cytokines and are critical regulators of homeostasis in peripheral organs. However, our knowledge of their function in the kidney is relatively limited. Recent evidence suggests that increasing ILC2 numbers by systemic administration of recombinant interleukin (IL)-25 or IL-33 protects against renal injury. Whilst ILC2s can be induced to protect against ischemic- or chemical-induced AKI, the impact of ILC2 deficiency or depletion on the severity of renal injury is unknown. Firstly, the phenotype and location of ILC2s in the kidney was assessed under homeostatic conditions. Kidney ILC2s constitutively expressed high levels of IL-5 and were located in close proximity to the renal vasculature. To test the functional role of ILC2s in the kidney, an experimental model of renal ischemia-reperfusion injury (IRI) was used and the severity of injury was assessed in wild-type, ILC2-reduced, ILC2-deficient, and ILC2-depleted mice. Surprisingly, there were no differences in histopathology, collagen deposition or mRNA expression of injury-associated (Lcn2), inflammatory (Cxcl1, Cxcl2, and Tnf) or extracellular matrix (Col1a1, Fn1) factors following IRI in the absence of ILC2s. These data suggest the absence of ILC2s does not alter the severity of renal injury, suggesting possible redundancy. Therefore, other mechanisms of type 2-mediated immune cell activation likely compensate in the absence of ILC2s. Hence, a loss of ILC2s is unlikely to increase susceptibility to, or severity of AKI

Identifying wellbeing challenges and solutions in the police service using the World Café method

Police work presents risks to mental and physical health for officers and civilian staff. We report a project that involved police employees in identifying wellbeing challenges and potential solutions. We facilitated ‘World Café’ events in which approximately 180 officers and civilian staff participated. Qualitative data were collected and thematically analysed drawing upon the Job Demands-Resources model. We identified themes relating to workload, management practices, occupational health processes, and continuing mental health stigma. Our analyses suggest an environment in which resources are insufficient to meet demands. The resulting pressures may contribute to management behaviours that can impair subordinate wellbeing

Observation of spin Coulomb drag in a two-dimensional electron gas

An electron propagating through a solid carries spin angular momentum in addition to its mass and charge. Of late there has been considerable interest in developing electronic devices based on the transport of spin, which offer potential advantages in dissipation, size, and speed over charge-based devices. However, these advantages bring with them additional complexity. Because each electron carries a single, fixed value (-e) of charge, the electrical current carried by a gas of electrons is simply proportional to its total momentum. A fundamental consequence is that the charge current is not affected by interactions that conserve total momentum, notably collisions among the electrons themselves. In contrast, the electron's spin along a given spatial direction can take on two values, "up" and "down", so that the spin current and momentum need not be proportional. Although the transport of spin polarization is not protected by momentum conservation, it has been widely assumed that, like the charge current, spin current is unaffected by electron-electron (e-e) interactions. Here we demonstrate experimentally not only that this assumption is invalid, but that over a broad range of temperature and electron density, the flow of spin polarization in a two-dimensional gas of electrons is controlled by the rate of e-e collisions

A simple approach to the visible-light photoactivation of molecular metal oxides

This study explores a new method to maximize the visible-light-driven photocatalytic performance of organic–inorganic hybrid polyoxometalates (POMs). Experimental and theoretical investigations of a family of phosphonate-substituted POMs show that modification of grafted organic moieties can be used to tune the electronic structure and photoactivity of the metal oxide component. Unlike fully inorganic polyoxotungstates, these organic–inorganic hybrid species are responsive to visible light and function as photocatalysts (λ > 420 nm) in the decomposition of a model environmental pollutant. The degree of photoactivation is shown to be dependent on the nature of the inductive effect exerted by the covalently grafted substituent groups. This study emphasizes the untapped potential that lies in an orbital engineering approach to hybrid-POM design and helps to underpin the next generation of bespoke, robust, and cost-effective molecular metal oxide photoactive materials and catalysts