Construction of a Lax Pair for the E6(1)E_6^{(1)} qq-Painlev\'e System

We construct a Lax pair for the $E^{(1)}_6$ $q$-Painlev\'e system from first principles by employing the general theory of semi-classical orthogonal polynomial systems characterised by divided-difference operators on discrete, quadratic lattices [arXiv:1204.2328]. Our study treats one special case of such lattices - the $q$-linear lattice - through a natural generalisation of the big $q$-Jacobi weight. As a by-product of our construction we derive the coupled first-order $q$-difference equations for the $E^{(1)}_6$ $q$-Painlev\'e system, thus verifying our identification. Finally we establish the correspondences of our result with the Lax pairs given earlier and separately by Sakai and Yamada, through explicit transformations

Insight into long-term ecological dynamics from the Lynn Brianne Observatory

Understanding the erosion of freshwater biodiversity has become a global imperative, but consistent series of long-term data from which to appraise changes are rare. In central Wales (UK), the Lynn Brianne Stream Observatory has provided unique insight into the complexity of biodiversity dynamics over four decades, revealing how apparent stasis in alpha- and beta-diversity might mask non-random functional changes in macroinvertebrate assemblages. Assessments of synchrony and stability at population and community levels reveal the effect of climatic variations in which warmer, wetter phases of the North Atlantic Oscillation (NAO) have been associated with large interannual changes in community composition. Moreover, these positive NAO periods have brought greater synchrony in species abundances within streams (community synchrony) and across streams (spatial population synchrony). Increasing synchrony can destabilise ecosystems with consequences for the persistence of populations. Preliminary analyses at Lynn Brianne suggest that species with greater spatial synchrony tend to decline in abundance over time. For instance, the abundance of cold-adapted species has declined by 40% since the 1980s reflecting the general increase in temperatures. Moreover, populations of these species displayed significantly higher spatial synchrony than warm-adapted species, which increased by 30% over the same time period. We suggest that both directional climate warming and the NAO contribute to the long-term reorganisation of benthic communities in temperate headwater

Ecological indicators for abandoned mines, Phase 1: Review of the literature

Mine waters have been identified as a significant issue in the majority of Environment Agency draft River Basin Management Plans. They are one of the largest drivers for chemical pollution in the draft Impact Assessment for the Water Framework Directive (WFD), with significant failures of environmental quality standards (EQS) for metals (particularly Cd, Pb, Zn, Cu, Fe) in many rivers linked to abandoned mines. Existing EQS may be overprotective of aquatic life which may have adapted over centuries of exposure. This study forms part of a larger project to investigate the ecological impact of metals in rivers, to develop water quality targets (alternative objectives for the WFD) for aquatic ecosystems impacted by long-term mining pollution. The report reviews literature on EQS failures, metal effects on aquatic biota and effects of water chemistry, and uses this information to consider further work. A preliminary assessment of water quality and biology data for 87 sites across Gwynedd and Ceredigion (Wales) shows that existing Environment Agency water quality and biology data could be used to establish statistical relations between chemical variables and metrics of ecological quality. Visual representation and preliminary statistical analyses show that invertebrate diversity declines with increasing zinc concentration. However, the situation is more complex because the effects of other metals are not readily apparent. Furthermore, pH and aluminium also affect streamwater invertebrates, making it difficult to tease out toxicity due to individual mine-derived metals. The most characteristic feature of the plant communities of metal-impacted systems is a reduction in diversity, compared to that found in comparable unimpacted streams. Some species thrive in the presence of heavy metals, presumably because they are able to develop metal tolerance, whilst others consistently disappear. Effects are, however, confounded by water chemistry, particularly pH. Tolerant species are spread across a number of divisions of photosynthetic organisms, though green algae, diatoms and blue-green algae are usually most abundant, often thriving in the absence of competition and/or grazing. Current UK monitoring techniques focus on community composition and, whilst these provide a sampling and analytical framework for studies of metal impacts, the metrics are not sensitive to these impacts. There is scope for developing new metrics, based on community-level analyses and for looking at morphological variations common in some taxa at elevated metal concentrations. On the whole, community-based metrics are recommended, as these are easier to relate to ecological status definitions. With respect to invertebrates and fish, metals affect individuals, population and communities but sensitivity varies among species, life stages, sexes, trophic groups and with body condition. Acclimation or adaptation may cause varying sensitivity even within species. Ecosystem-scale effects, for example on ecological function, are poorly understood. Effects vary between metals such as cadmium, copper, lead, chromium, zinc and nickel in order of decreasing toxicity. Aluminium is important in acidified headwaters. Biological effects depend on speciation, toxicity, availability, mixtures, complexation and exposure conditions, for example discharge (flow). Current water quality monitoring is unlikely to detect short-term episodic increases in metal concentrations or evaluate the bioavailability of elevated metal concentrations in sediments. These factors create uncertainty in detecting ecological impairment in metal-impacted ecosystems. Moreover, most widely used biological indicators for UK freshwaters were developed for other pressures and none distinguishes metal impacts from other causes of impairment. Key ecological needs for better regulation and management of metals in rivers include: i) models relating metal data to ecological data that better represent influences on metal toxicity; ii) biodiagnostic indices to reflect metal effects; iii) better methods to identify metal acclimation or adaptation among sensitive taxa; iv) better investigative procedures to isolate metal effects from other pressures. Laboratory data on the effects of water chemistry on cationic metal toxicity and bioaccumulation show that a number of chemical parameters, particularly pH, dissolved organic carbon (DOC) and major cations (Na, Mg, K, Ca) exert a major influence on the toxicity and/or bioaccumulation of cationic metals. The biotic ligand model (BLM) provides a conceptual framework for understanding these water chemistry effects as a combination of the influence of chemical speciation, and metal uptake by organisms in competition with H+ and other cations. In some cases where the BLM cannot describe effects, empirical bioavailable models have been successfully used. Laboratory data on the effects of metal mixtures across different water chemistries are sparse, with implications for transferring understanding to mining-impacted sites in the field where mixture effects are likely. The available field data, although relatively sparse, indicate that water chemistry influences metal effects on aquatic ecosystems. This occurs through complexation reactions, notably involving dissolved organic matter and metals such as Al, Cu and Pb. Secondly, because bioaccumulation and toxicity are partly governed by complexation reactions, competition effects among metals, and between metals and H+, give rise to dependences upon water chemistry. There is evidence that combinations of metals are active in the field; the main study conducted so far demonstrated the combined effects of Al and Zn, and suggested, less certainly, that Cu and H+ can also contribute. Chemical speciation is essential to interpret and predict observed effects in the field. Speciation results need to be combined with a model that relates free ion concentrations to toxic effect. Understanding the toxic effects of heavy metals derived from abandoned mines requires the simultaneous consideration of the acidity-related components Al and H+. There are a number of reasons why organisms in waters affected by abandoned mines may experience different levels of metal toxicity than in the laboratory. This could lead to discrepancies between actual field behaviour and that predicted by EQS derived from laboratory experiments, as would be applied within the WFD. The main factors to consider are adaptation/acclimation, water chemistry, and the effects of combinations of metals. Secondary effects are metals in food, metals supplied by sediments, and variability in stream flows. Two of the most prominent factors, namely adaptation/ acclimation and bioavailability, could justify changes in EQS or the adoption of an alternative measure of toxic effects in the field. Given that abandoned mines are widespread in England and Wales, and the high cost of their remediation to meet proposed WFD EQS criteria, further research into the question is clearly justified. Although ecological communities of mine-affected streamwaters might be over-protected by proposed WFD EQS, there are some conditions under which metals emanating from abandoned mines definitely exert toxic effects on biota. The main issue is therefore the reliable identification of chemical conditions that are unacceptable and comparison of those conditions with those predicted by WFD EQS. If significant differences can convincingly be demonstrated, the argument could be made for alternative standards for waters affected by abandoned mines. Therefore in our view, the immediate research priority is to improve the quantification of metal effects under field circumstances. Demonstration of dose-response relationships, based on metal mixtures and their chemical speciation, and the use of better biological tools to detect and diagnose community-level impairment, would provide the necessary scientific information

Mean Field Voter Model of Election to the House of Representatives in Japan

In this study, we propose a mechanical model of a plurality election based on a mean field voter model. We assume that there are three candidates in each electoral district, i.e., one from the ruling party, one from the main opposition party, and one from other political parties. The voters are classified as fixed supporters and herding (floating) voters with ratios of $1-p$ and $p$, respectively. Fixed supporters make decisions based on their information and herding voters make the same choice as another randomly selected voter. The equilibrium vote-share probability density of herding voters follows a Dirichlet distribution. We estimate the composition of fixed supporters in each electoral district and $p$ using data from elections to the House of Representatives in Japan (43rd to 47th). The spatial inhomogeneity of fixed supporters explains the long-range spatial and temporal correlations. The estimated values of $p$ are close to the estimates obtained from a survey.Comment: 11 pages, 7 figure

Ecological science for ecosystem services and the stewardship of Natural Capital

1. National and international assessments are increasingly highlighting the unsustainable use of earth's natural resources in the face of population increase, growing material affluence and global change. In all likelihood, the use and degradation of natural resources will continue. 2. In contrast to resource depletion, the concept of natural capital emphasises how the environment is an asset to be managed, to ensure that the benefits which flow from it are sustained for future generations. These benefits are the ecosystem goods and services upon which all people rely for their continued survival and well-being both now and, ideally, in perpetuity. 3. Despite their importance, the evidence-base and quantitative understanding of links between biodiversity, ecosystem function and ecosystem services are insufficient to allow informed use and management. Moreover, the concepts of natural capital and ecosystem services are insufficiently mainstream to influence decisions that currently favour the production of food and fibre rather than less tangible services such as climate regulation, air and water purification, pollination or the contributions of environment to health. 4. There are specific challenges to ecological science in this interdisciplinary endeavour: specifically, to develop frameworks for identifying and monitoring natural capital; to parameterise factors affecting ecosystem services and their resilience to change; to integrate the complexity of ecological systems into ecosystem service valuation; and to characterise the synergies and trade-offs between ecosystem services in different management and policy scenarios. 5. Synthesis and applications. The five papers in this Special Profile exemplify just some of the leading work through which ecologists in the UK are contributing nationally and internationally to these needs, stemming from the UK National Ecosystem Assessment - the first national scale exercise of its type in the world. We expect a major, worldwide increase in work on ecosystem services and natural capital in future as decisions on ecosystem use of management are squeezed increasingly between the needs of exploitation and protection

Time to Dispense with the Mute of Malice Procedure

Assesses whether measures for establishing whether a defendant is "mute of malice" are anachronistic and obsolete, and should be repealed. Reviews the historical role of the mute of malice procedure, its significance, how it differs from unfitness to plead and how developments such as practice directions and procedural rule changes have rendered it unnecessary. Suggests how reforms involving repeal might be implemented

An observational prospective study of topical acidified nitrite for killing methicillin-resistant Staphylococcus aureus (MRSA) in contaminated wounds

Background Endogenous nitric oxide (NO) kills bacteria and other organisms as part of the innate immune response. When nitrite is exposed to low pH, NO is generated and has been used as an NO delivery system to treat skin infections. We demonstrated eradication of MRSA carriage from wounds using a topical formulation of citric acid (4.5%) and sodium nitrite (3%) creams co-applied for 5 days to 15 wounds in an observational prospective pilot study of 8 patients. Findings Following treatment with topical citric acid and sodium nitrite, 9 of 15 wounds (60%) and 3 of 8 patients (37%) were cleared of infection. MRSA isolates from these patients were all sensitive to acidified nitrite in vitro compared to methicillin-sensitive S. aureus and a reference strain of MRSA. Conclusions Nitric oxide and acidified nitrite offer a novel therapy for control of MRSA in wounds. Wounds that were not cleared of infection may have been re-contaminated or the bioavailability of acidified nitrite impaired by local factors in the tissue