Information sheet 25: Elodea nutallii, Nuttall's Pondweed

Information sheet on control of Elodea specie

On the optimality of gluing over scales

We show that for every $\alpha > 0$, there exist $n$-point metric spaces (X,d) where every "scale" admits a Euclidean embedding with distortion at most $\alpha$, but the whole space requires distortion at least $\Omega(\sqrt{\alpha \log n})$. This shows that the scale-gluing lemma [Lee, SODA 2005] is tight, and disproves a conjecture stated there. This matching upper bound was known to be tight at both endpoints, i.e. when $\alpha = \Theta(1)$ and $\alpha = \Theta(\log n)$, but nowhere in between. More specifically, we exhibit $n$-point spaces with doubling constant $\lambda$ requiring Euclidean distortion $\Omega(\sqrt{\log \lambda \log n})$, which also shows that the technique of "measured descent" [Krauthgamer, et. al., Geometric and Functional Analysis] is optimal. We extend this to obtain a similar tight result for $L_p$ spaces with $p > 1$.Comment: minor revision

The structure of typical clusters in large sparse random configurations

The initial purpose of this work is to provide a probabilistic explanation of a recent result on a version of Smoluchowski's coagulation equations in which the number of aggregations is limited. The latter models the deterministic evolution of concentrations of particles in a medium where particles coalesce pairwise as time passes and each particle can only perform a given number of aggregations. Under appropriate assumptions, the concentrations of particles converge as time tends to infinity to some measure which bears a striking resemblance with the distribution of the total population of a Galton-Watson process started from two ancestors. Roughly speaking, the configuration model is a stochastic construction which aims at producing a typical graph on a set of vertices with pre-described degrees. Specifically, one attaches to each vertex a certain number of stubs, and then join pairwise the stubs uniformly at random to create edges between vertices. In this work, we use the configuration model as the stochastic counterpart of Smoluchowski's coagulation equations with limited aggregations. We establish a hydrodynamical type limit theorem for the empirical measure of the shapes of clusters in the configuration model when the number of vertices tends to $\infty$. The limit is given in terms of the distribution of a Galton-Watson process started with two ancestors

Emergence of communities on a coevolutive model of wealth interchange

We present a model in which we investigate the structure and evolution of a random network that connects agents capable of exchanging wealth. Economic interactions between neighbors can occur only if the difference between their wealth is less than a threshold value that defines the width of the economic classes. If the interchange of wealth cannot be done, agents are reconnected with another randomly selected agent, allowing the network to evolve in time. On each interaction there is a probability of favoring the poorer agent, simulating the action of the government. We measure the Gini index, having real world values attached to reality. Besides the network structure showed a very close connection with the economic dynamic of the system.Comment: 5 pages, 7 figure

Metastable States in Spin Glasses and Disordered Ferromagnets

We study analytically M-spin-flip stable states in disordered short-ranged Ising models (spin glasses and ferromagnets) in all dimensions and for all M. Our approach is primarily dynamical and is based on the convergence of a zero-temperature dynamical process with flips of lattice animals up to size M and starting from a deep quench, to a metastable limit. The results (rigorous and nonrigorous, in infinite and finite volumes) concern many aspects of metastable states: their numbers, basins of attraction, energy densities, overlaps, remanent magnetizations and relations to thermodynamic states. For example, we show that their overlap distribution is a delta-function at zero. We also define a dynamics for M=infinity, which provides a potential tool for investigating ground state structure.Comment: 34 pages (LaTeX); to appear in Physical Review

EUPHRESCO – DeCLAIM: a decision support system, for control of alien invasive macrophytes

This report contains the result of a research programme on four invasive aquatic macrophytes, Cabomba caroliniana (Fanwort), Hydrocotyle ranunculoides (Floating pennywort) , Myriophyllum aquaticum (Parrott’s feather) and Ludwigia grandiflora (Water primrose). The collaborative project was intended to generate a prototype decision support system for optimising control measures for these species, considered to be the four most troublesome invasive alien aquatic weeds at present in the UK and NL. A further reason for selecting these species is that they are widely sold in the horticultural trade and are therefore the number of invaded sites is likely to increase in the short term. C. caroliniana, was selected as a representative of the Myriophyllids growth form, representing 35% of the import volume of aquarium plants in The Netherlands. In 2009 it is found at three sites in The Netherlands, posing serious problems at one. It has been present at two sites in the UK recent past and was collected from one site again in autumn 2011. H. ranunculoides, was selected as a representative of the Stratiotids s.l. growth form, is at present the most troublesome invasive alien aquatic weed in the United Kingdom and The Netherlands, and is showing increased distribution in neighbouring countries, including Belgium and Germany as well as in Australia, Uganda and Zimbabwe. A second representative of the Stratiotids s.l. growth form, L. grandiflora, has proven to have a severe detrimental ecological impact in France and is gaining importance in The Netherlands. In the UK promising management strategies have already been developed using and the infestation in the wild has responded well to rapid application fo control measures. The third representative of the Stratiotids s.l growth form is M. aquaticum. This species has been sold extensively by the aquatic nursery trade as an ornamental species for domestic ponds. It is now present in many natural lowland static water sites in the UK. The species is still very popular in The Netherlands, and the number of occurrences is increasing. The project was divided into several work packages in order to prioritise the order in which data were derived and used in the project. The first stage was to collect all published data on the individual species, in order to gain information on various physiological parameters of the species to put into the model CHARISMA, a model that predicts biomass of a species given both physiological and environmental data. We found that although the species were relatively common in the UK and the Netherlands, data on physiology were not widely available and we had to estimate some of the more important model parameters to get a realistic output. This is an area of possible experimental error and can only be corrected by actual field and laboratory measurements on net photosynthetic rate, light compensation point, biomass production related to nutrient availability and other indices, including shoot to root ratios, leaf area indices etc.. The literature survey also provided information on the native range of the species from which we were able to derive optimum environmental conditions for growth in Europe and the effect of any management techniques already in use. The literature survey also produced information on the main reproductive strategies, either by vegetative means such as fragmentation, or by seed production, or a combination of both. Most species have very effective reproductive strategies using vegetative fragmentation and seed production in both countries was considered to be relatively unimportant. Stage two of the project involved an assessment of the areas at risk of colonisation by the four species in both countries. For the Netherlands it was assumed that if the site of an occurrence shared both physical and chemical characteristics, then it should be classed as at risk. The low altitudes and low slopes of most watercourses in the Netherlands create a situation in which the whole country can be considered at risk. For the UK, we used the elevation data for known occurrence and plotted an area at risk based on this altitude plus 100m, to account for any unknown sites. This produced different maps for each species as some had been found at higher altitudes than others. We do not consider this to be as accurate as possible and the integration of temperature data, especially a day degree index could improve the prediction of at risk areas for each species in the UK. This is an important topic for inclusion in future work. The third area of work was to assess current methods of control and to develop or optimise new techniques. This was carried out in conjunction between all four project partners. Considerable improvements in the management of C. caroliniana were made during this project and have been implemented by water boards in the Netherlands. A consistent approach to management of H. ranunculoides has been adopted in this project and the approaches to management of the two other species have been shown to be effective in the current regulatory conditions. The spatially explicit model CHARISMA was developed for two native macrophytes species in the Netherlands and was used in this project to model growth and biomass accumulation of the four nonnative invasive macrophyte species. Some of the input parameters used in the original model were not valid for the new species, and estimates or adjustments had to be made. However, for three out of four of the new species, the predictions of biomass and dominance were quite accurate and the model could be developed for these species without excessive modification. The only species that did not comply well with the model was C. caroliniana, but only in the degree of overwintering biomass required for dominance in the following season. This is probably due to a lack of any data for physiological characteristics of this species in winter in Europe and this data gap should be addressed for this species and others in order to accurately model the behaviour of other species in European conditions. The main objective of this project was to produce a draft Decision Support System that could be used by field operatives and office based managers to identify the species accurately, and to enable a rapid risk assessment to be made in the field that could be reported in a consistent manner, enabling a rapid response to be made against the species with the aim of preventing further spread and eventually eradication the species from the affected watercourse. In order to make the response to aquatic non-native species consistent and proportionate a pictorial field and office guide has been produced that provides descriptive photographs of characteristic features, areas at risk, typical habitat types, and available management techniques. We have deliberately left out costs of management as these vary within each country and certainly between countries. In addition, each species chapter will be made available at www.declaim.eu . The DSS was submitted to the Non Native Species Secretariat in the UK for comment before being used by managers. In the Netherlands the DSS was submitted to representatives of various water boards that are actively involved in trials to control invasive macrophytes. The comments received were positive and helpful and led to developments in the current version

Continuum theory of vacancy-mediated diffusion

We present and solve a continuum theory of vacancy-mediated diffusion (as evidenced, for example, in the vacancy driven motion of tracers in crystals). Results are obtained for all spatial dimensions, and reveal the strongly non-gaussian nature of the tracer fluctuations. In integer dimensions, our results are in complete agreement with those from previous exact lattice calculations. We also extend our model to describe the vacancy-driven fluctuations of a slaved flux line.Comment: 25 Latex pages, subm. to Physical Review

Tracking Black Holes in Numerical Relativity

This work addresses and solves the problem of generically tracking black hole event horizons in computational simulation of black hole interactions. Solutions of the hyperbolic eikonal equation, solved on a curved spacetime manifold containing black hole sources, are employed in development of a robust tracking method capable of continuously monitoring arbitrary changes of topology in the event horizon, as well as arbitrary numbers of gravitational sources. The method makes use of continuous families of level set viscosity solutions of the eikonal equation with identification of the black hole event horizon obtained by the signature feature of discontinuity formation in the eikonal's solution. The method is employed in the analysis of the event horizon for the asymmetric merger in a binary black hole system. In this first such three dimensional analysis, we establish both qualitative and quantitative physics for the asymmetric collision; including: 1. Bounds on the topology of the throat connecting the holes following merger, 2. Time of merger, and 3. Continuous accounting for the surface of section areas of the black hole sources.Comment: 14 pages, 16 figure

Instream and riparian implications of weed cutting in a chalk river

Macrophyte growth is extensive in the iconic chalk streams that are concentrated in southern and eastern England. Widespread and frequent weed cutting is undertaken to maintain their key functions (e.g. flood water conveyance and maintenance of viable fisheries). In this study, a multidisciplinary approach was adopted to quantify coincident physico-chemical responses (instream and riparian) that result from weed cutting and to discuss their potential implications. Three weed cuts were monitored at a site on the River Lambourn (The CEH River Lambourn Observatory) and major instream and riparian impacts were observed. Measurements clearly demonstrated how weed cutting enhanced flood flow conveyance, reduced water levels (river and wetland), increased river velocities, and mobilised suspended sediment (with associated chemicals) and reduced the capacity for its retention within the river channel. Potential implications in relation to flood risk, water resources, downstream water quality, instream and riparian ecology, amenity value of the river, and wetland greenhouse gas emissions were considered. Provided the major influence of macrophytes on instream and riparian environments is fully understood then the manipulation of macrophytes represents an effective management tool that demonstrates the great potential of working with nature

Proof of the Hyperplane Zeros Conjecture of Lagarias and Wang

We prove that a real analytic subset of a torus group that is contained in its image under an expanding endomorphism is a finite union of translates of closed subgroups. This confirms the hyperplane zeros conjecture of Lagarias and Wang for real analytic varieties. Our proof uses real analytic geometry, topological dynamics and Fourier analysis.Comment: 25 page