Nonholonomic systems with symmetry allowing a conformally symplectic reduction

Non-holonomic mechanical systems can be described by a degenerate almost-Poisson structure (dropping the Jacobi identity) in the constrained space. If enough symmetries transversal to the constraints are present, the system reduces to a nondegenerate almost-Poisson structure on a ``compressed'' space. Here we show, in the simplest non-holonomic systems, that in favorable circumnstances the compressed system is conformally symplectic, although the ``non-compressed'' constrained system never admits a Jacobi structure (in the sense of Marle et al.).Comment: 8 pages. A slight edition of the version to appear in Proceedings of HAMSYS 200

Needle exchange services in Knowsley: An investigation into the needs and experiences of staff and service users

This work was commissioned by Knowsley Council to inform the development of needle exchange (NEX) services in Knowsley and to ensure that they meet the needs of people who inject drugs (PWID) locally. The views and experiences of both service users and staff from drug services and pharmacies offering needle exchange services in Knowsley were sought regarding the extent to which NEX are meeting the needs of PWID including their perceptions regarding the support available, NEX accessibility and service delivery. Findings are considered in the context of NICE guidelines on the optimal provision of needle and syringe programmes in England

Antibiotic-resistant Escherichia coli in wastewaters, surface waters, and oysters from an urban riverine system

antibiotic resistance (AR) patterns of 462 Escherichia coli isolates from wastewater, surface waters, and oysters were determined. Rates of AR and multiple-AR among isolates from surface water sites adjacent to wastewater treatment plant (WWTP) discharge sites were significantly higher (P < 0.05) than those among other isolates, whereas the rate of AR among isolates from oysters exposed to WWTP discharges was low (< lKc)

Can patterns of urban biodiversity be predicted using simple measures of green infrastructure?

Urban species and habitats provide important ecosystem services such as summertime cooling, recreation, and pollination at a variety of scales. Many studies have assessed how biodiversity responds to urbanization, but little work has been done to try and create recommendations that can be easily applied to urban planning, design and management practice. Urban planning often operates at broad spatial scales, typically using relatively simplistic targets for land cover mix to influence biodiversity and ecosystem service provision. Would more complicated, but still easily created, prescriptions for urban vegetation be beneficial? Here we assess the importance of vegetation measures (percentage vegetation cover, tree canopy cover and variation in canopy height) across four taxonomic groups (bats, bees, hoverflies and birds) at multiple spatial scales (100, 250, 500, 1000 m) within a major urban area (Birmingham, the United Kingdom). We found that small-scale (100–250-m radius) measures of vegetation were important predictors for hoverflies and bees, and that bats were sensitive to vegetation at a medium spatial-scale (250–500 m). In contrast, birds responded to vegetation characteristics at both small (100 m) and large (1000 m) scales. Vegetation cover, tree cover and variation in canopy height were expected to decrease with built surface cover; however, only vegetation height showed this expected trend. The results indicate the importance of relatively small patches of vegetation cover for supporting urban biodiversity, and show that relatively simple measures of vegetation characteristics can be useful predictors of species richness (or activity density, in the case of bats). They also highlight the danger of relying upon percentage built surface cover as an indicator of urban biodiversity potential

A Special Homotopy Continuation Method For A Class of Polynomial Systems

A special homotopy continuation method, as a combination of the polyhedral homotopy and the linear product homotopy, is proposed for computing all the isolated solutions to a special class of polynomial systems. The root number bound of this method is between the total degree bound and the mixed volume bound and can be easily computed. The new algorithm has been implemented as a program called LPH using C++. Our experiments show its efficiency compared to the polyhedral or other homotopies on such systems. As an application, the algorithm can be used to find witness points on each connected component of a real variety

Estimating trends and seasonality in Australian monthly lightning flash counts

We present the results of a statistical analysis of lightning characteristics in mainland Australia for the period from approximately 1988 to 2012, based on monthly lightning flash count (LFC) series obtained from a network of 19 Comité Internationale des Grands Réseaux Electriques, 500 Hz peak transmission filter circuit sensors. The temporal structures of the series are examined in terms of detecting and characterizing seasonal cycles, long-term trends, and changes in seasonality over time. A generalized additive modeling approach is used to ensure that the estimated structures are determined by the data, rather than by the constraints of any assumed mathematical form for the trends and seasonal cycle. Results indicate strong seasonality at all sites, the presence of long-term trends at 16 sites, and interactions between trend and seasonality (corresponding to changes in seasonality over time) at 13 sites. The most systematic change corresponds to a progressive deepening of the seasonal cycle (i.e., an ongoing decline in winter lightning flash counts) and is most noticeable across southern Australia (south of 30°S). These results are consistent with previous analyses that have detected decreasing atmospheric instability during the austral winter since the mid-1970s. This is associated with increasing mean sea level pressure and declining rainfall

Certifying reality of projections

Computational tools in numerical algebraic geometry can be used to numerically approximate solutions to a system of polynomial equations. If the system is well-constrained (i.e., square), Newton's method is locally quadratically convergent near each nonsingular solution. In such cases, Smale's alpha theory can be used to certify that a given point is in the quadratic convergence basin of some solution. This was extended to certifiably determine the reality of the corresponding solution when the polynomial system is real. Using the theory of Newton-invariant sets, we certifiably decide the reality of projections of solutions. We apply this method to certifiably count the number of real and totally real tritangent planes for instances of curves of genus 4.Comment: 9 page