Relative Convex Hull Determination from Convex Hulls in the Plane

A new algorithm for the determination of the relative convex hull in the plane of a simple polygon A with respect to another simple polygon B which contains A, is proposed. The relative convex hull is also known as geodesic convex hull, and the problem of its determination in the plane is equivalent to find the shortest curve among all Jordan curves lying in the difference set of B and A and encircling A. Algorithms solving this problem known from Computational Geometry are based on the triangulation or similar decomposition of that difference set. The algorithm presented here does not use such decomposition, but it supposes that A and B are given as ordered sequences of vertices. The algorithm is based on convex hull calculations of A and B and of smaller polygons and polylines, it produces the output list of vertices of the relative convex hull from the sequence of vertices of the convex hull of A.Comment: 15 pages, 4 figures, Conference paper published. We corrected two typing errors in Definition 2: $I_S$ has to be defined based on $O_S$, and $I_E$ has to be defined based on $O_E$ (not just using $O$). These errors appeared in the text of the original conference paper, which also contained the pseudocode of an algorithm where $I_S$ and $I_E$ appeared as correctly define

Signature of effective mass in crackling noise asymmetry

Crackling noise is a common feature in many dynamic systems [1-9], the most familiar instance of which is the sound made by a sheet of paper when crumpled into a ball. Although seemingly random, this noise contains fundamental information about the properties of the system in which it occurs. One potential source of such information lies in the asymmetric shape of noise pulses emitted by a diverse range of noisy systems [8-12], but the cause of this asymmetry has lacked explanation [1]. Here we show that the leftward asymmetry observed in the Barkhausen effect [2] - the noise generated by the jerky motion of domain walls as they interact with impurities in a soft magnet - is a direct consequence of a magnetic domain wall's negative effective mass. As well as providing a means of determining domain wall effective mass from a magnet's Barkhausen noise our work suggests an inertial explanation for the origin of avalanche asymmetries in crackling noise phenomena more generally.Comment: 13 pages, 4 figures, to appear in Nature Physic

The entropy of black holes: a primer

After recalling the definition of black holes, and reviewing their energetics and their classical thermodynamics, one expounds the conjecture of Bekenstein, attributing an entropy to black holes, and the calculation by Hawking of the semi-classical radiation spectrum of a black hole, involving a thermal (Planckian) factor. One then discusses the attempts to interpret the black-hole entropy as the logarithm of the number of quantum micro-states of a macroscopic black hole, with particular emphasis on results obtained within string theory. After mentioning the (technically cleaner, but conceptually more intricate) case of supersymmetric (BPS) black holes and the corresponding counting of the degeneracy of Dirichlet-brane systems, one discusses in some detail the ``correspondence'' between massive string states and non-supersymmetric Schwarzschild black holes.Comment: 51 pages, 4 figures, talk given at the "Poincare seminar" (Paris, 6 December 2003), to appear in Poincare Seminar 2003 (Birkhauser

Quantifying the effect of testate amoeba decomposition on peat-based water-table reconstructions

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.Testate amoebae are a widely-used tool for palaeohydrological reconstruction from peatlands. However, it has been observed that weak idiosomic siliceous tests (WISTs) are common in uppermost peats, but very rarely found as subfossils deeper in the peat profile. This taphonomic problem has been noted widely and it has been established that WISTs disaggregate and/or dissolve in the low pH condition of ombrotrophic peatlands. Here we investigate the effect of this taphonomic problem on water-table reconstructions from thirty European peatlands through the comparison of reconstructions based on all taxa and those with WISTs removed. In almost all cases the decomposition of WISTs does not introduce discernible bias to peatland water-table reconstructions. However, some discrepancy is apparent when large abundances of Corythion-Trinema type are present (9−12 cm deviation with 50–60% abundance of this particular taxon). We recommend that WISTs should be removed before carrying out water-table reconstructions, and that the minimum count of testate amoebae per sample should exclude WISTs to ensure the development of robust reconstructions

Vertical zonation of testate amoebae in the Elatia Mires, northern Greece : palaeoecological evidence for a wetland response to recent climate change or autogenic processes?

The Elatia Mires of northern Greece are unique ecosystems of high conservation value. The mires are climatically marginal and may be sensitive to changing hydroclimate, while northern Greece has experienced a significant increase in aridity since the late twentieth century. To investigate the impact of recent climatic change on the hydrology of the mires, the palaeoecological record was investigated from three near-surface monoliths extracted from two sites. Testate amoebae were analysed as sensitive indicators of hydrology. Results were interpreted using transfer function models to provide quantitative reconstructions of changing water table depth and pH. AMS radiocarbon dates and 210Pb suggest the peats were deposited within the last c. 50 years, but do not allow a secure chronology to be established. Results from all three profiles show a distinct shift towards a more xerophilic community particularly noted by increases in Euglypha species. Transfer function results infer a distinct lowering of water tables in this period. A hydrological response to recent climate change is a tenable hypothesis to explain this change; however other possible explanations include selective test decay, vertical zonation of living amoebae, ombrotrophication and local hydrological change. It is suggested that a peatland response to climatic change is the most probable hypothesis, showing the sensitivity of marginal peatlands to recent climatic change

Testate amoeba response to acid deposition in a Scottish peatland

Peatlands around the world are exposed to anthropogenic or volcanogenic sulphur pollution. Impacts on peatland microbial communities have been inferred from changes in gas flux but have rarely been directly studied. In this study, the impacts of sulphuric acid deposition on peatland testate amoebae were investigated by analysis of experimental plots on a Scottish peatland almost 7 years after acid treatment. Results showed reduced concentration of live amoebae and changes in community structure which remained significant even when differences in pH were accounted for. Several possible explanations for the impacts can be proposed including taphonomic processes and changes in plant communities. Previous studies have inferred a shift from methanogenic archaea to sulphate-reducing bacteria in sulphate-treated peats; it is possible that the impacts detected here might relate to this change, perhaps through testate amoeba predation on methanotrophs

The regulatory role of long-term depression in juvenile and adult mouse ocular dominance plasticity

The study of experience-dependent ocular dominance (OD) plasticity has greatly contributed to the understanding of visual development. During the critical period, preventing input from one eye results in a significant impairment of vision, and loss of cortical responsivity via the deprived eye. Residual ocular dominance plasticity has recently been observed in adulthood. Accumulating evidence suggests that OD plasticity involves N-methyl-D-aspartate receptor (NMDAR)-dependent long-term depression (LTD). Here we report that the administration of a selective LTD antagonist prevented the ocular dominance shift during the critical period. The NMDAR co-agonist D-serine facilitated adult visual cortical LTD and the OD shift in short-term monocularly deprived (MD) adult mice. When combined with reverse suture, D-serine proved effective in restoring a contralaterally-dominated visual input pattern in long-term MD mice. This work suggests LTD as a key mechanism in both juvenile and adult ocular dominance plasticity, and D-serine as a potential therapeutic in human amblyopic subjects

How many is enough? Determining optimal count totals for ecological and palaeoecological studies of testate amoebae

Testate amoebae are increasingly used in ecological and palaeoecological studies of wetlands. To characterise the amoeba community a certain number of individuals need to be counted under the microscope. To date, most studies have aimed for 150 individuals, but that sample size is not based on adequate evidence. When testate amoeba concentrations are low, it can be difficult or impossible to reach this total. The impacts of lower count totals have never been seriously scrutinised. We investigated the impact of count size on number of taxa identified, quantitative inferences of environmental variables and the strength of the links between amoebae and environmental data in the context of predicting depth to water table. Low counts were simulated by random selection of individuals from four existing datasets. Results show progressively diminishing returns by all criteria as count size increases from low numbers to counts of 150. A higher count is required to identify all taxa than to adequately characterise the community for transfer function inference. We suggest that in most cases, it will be a more efficient use of time to count a greater number of samples to a lower count. While a count of 50 individuals may be sufficient for some samples from some sites we recommend that counts of 100 individuals should be sufficient for most samples. Counts need only be increased to 150 or more where the aim is to identify relatively minor, but still potentially ecologically relevant community changes. This approach will help reduce lack of replication and low resolution, which are common limitations in testate amoeba-based palaeoecological and ecological studies

Potential implications of differential preservation of testate amoeba shells for paleoenvironmental reconstruction in peatlands

Testate amoebae are now commonly used in paleoenvironmental studies but little is known of their taphonomy. There is some experimental evidence for differential preservation of some testate amoeba shell types over others, but it is unclear what, if any impact this has on palaeoenvironmental reconstruction. To investigate this issue we looked at palaeoecological evidence for the preservation of different shell types. We then investigated the possible impact of selective preservation on quantitative palaeoenvironmental inference. We first used existing palaeoecological data sets to assess the vertical patterns of relative abundance in four testate amoeba shell types: (1) shells made of secreted biosilica plates (idiosomes, e.g. Euglypha), (2) idiosomes with thick organic coating (Assulina), (3) proteinaceous shells (e.g. Hyalosphenia), (4) shells built from recycled organic or mineral particles (xenosomes) (e.g. Difflugia, Centropyxis). In three diagrams a clear pattern of decay was only observed for the idiosome type. In order to assess the implications of differential preservation of testate amoeba taxa for paleoenvironmental reconstruction we then carried out simulations using three existing transfer functions and a wide range of scenarios, downweighting different test categories to represent the impact of selective test decomposition. Simulation results showed that downweighting generally reduced overall model performance. However downweighting a shell type only produced a consistent directional bias in inferred water table depth where that shell type is both dominant and shows a clear preference along the ecological gradient. Applying a scenario derived from previous experimental work did not lead to significant difference in inferred water table. Our results show that differential shell preservation has little impact on paleohydrological reconstruction from Sphagnum-dominated peatlands. By contrast, for the minerotrophic peatlands data-set loss of idiosome tests leads to consistent underestimation of water table depth. However there are few studies from fens and it is possible that idiosome tests are not always dominant, and/or that differential decomposition is less marked than in Sphagnum peatlands. Further work is clearly needed to assess the potential of testate amoebae for paleoecological studies of minerotrophic peatlands