Cross recurrence quantification for cover song identification

There is growing evidence that nonlinear time series analysis techniques can be used to successfully characterize, classify, or process signals derived from realworld dynamics even though these are not necessarily deterministic and stationary. In the present study we proceed in this direction by addressing an important problem our modern society is facing, the automatic classification of digital information. In particular, we address the automatic identification of cover songs, i.e. alternative renditions of a previously recorded musical piece. For this purpose we here propose a recurrence quantification analysis measure that allows tracking potentially curved and disrupted traces in cross recurrence plots. We apply this measure to cross recurrence plots constructed from the state space representation of musical descriptor time series extracted from the raw audio signal. We show that our method identifies cover songs with a higher accuracy as compared to previously published techniques. Beyond the particular application proposed here, we discuss how our approach can be useful for the characterization of a variety of signals from different scientific disciplines. We study coupled Rössler dynamics with stochastically modulated mean frequencies as one concrete example to illustrate this point.

Shifts in species and phylogenetic diversity between sapling and tree communities indicate negative density dependence in a lowland rain forest

1. As trees in a given cohort progress through ontogeny, many individuals die. This risk of mortality is unevenly distributed across species because of many processes such as habitat filtering, interspecific competition and negative density dependence. Here, we predict and test the patterns that such ecological processes should inscribe on both species and phylogenetic diversity as plants recruit from saplings to the canopy. 2. We compared species and phylogenetic diversity of sapling and tree communities at two sites in French Guiana. We surveyed 2084 adult trees in four 1-ha tree plots and 943 saplings in sixteen 16-m2 subplots nested within the tree plots. Species diversity was measured using Fisher's alpha (species richness) and Simpson's index (species evenness). Phylogenetic diversity was measured using Faith's phylogenetic diversity (phylogenetic richness) and Rao's quadratic entropy index (phylogenetic evenness). The phylogenetic diversity indices were inferred using four phylogenetic hypotheses: two based on rbcLa plastid DNA sequences obtained from the inventoried individuals with different branch lengths, a global phylogeny available from the Angiosperm Phylogeny Group, and a combination of both. 3. Taxonomic identification of the saplings was performed by combining morphological and DNA barcoding techniques using three plant DNA barcodes (psbA-trnH, rpoC1 and rbcLa). DNA barcoding enabled us to increase species assignment and to assign unidentified saplings to molecular operational taxonomic units. 4. Species richness was similar between saplings and trees, but in about half of our comparisons, species evenness was higher in trees than in saplings. This suggests that negative density dependence plays an important role during the sapling-to-tree transition. 5. Phylogenetic richness increased between saplings and trees in about half of the comparisons. Phylogenetic evenness increased significantly between saplings and trees in a few cases (4 out of 16) and only with the most resolved phylogeny. These results suggest that negative density dependence operates largely independently of the phylogenetic structure of communities. 6. Synthesis. By contrasting species richness and evenness across size classes, we suggest that negative density dependence drives shifts in composition during the sapling-to-tree transition. In addition, we found little evidence for a change in phylogenetic diversity across age classes, suggesting that the observed patterns are not phylogenetically constrained.

The Alps Vegetation Database - a geo-referenced community-level archive of all terrestrial plants occurring in the Alps.

Mountain ranges are biodiversity hotspots worldwide and provide refuge to many organisms under contemporary climate change. Gathering field information on mountain biodiversity over time is of primary importance to understand the response of biotic communities to climate changes. For plants, several long-term observation sites and networks of mountain biodiversity are emerging worldwide to gather field data and monitor altitudinal range shifts and community composition changes under contemporary climate change. Most of these monitoring sites, however, focus on alpine ecosystems and mountain summits, such as the global observation research initiative in alpine environments (GLORIA). Here we describe the Alps Vegetation Database, a comprehensive community level archive (GIVD ID EU-00-014) which aims at compiling all available geo-referenced vegetation plots from lowland forests to alpine grasslands across the greatest mountain range in Europe: the Alps. This research initiative was funded between 2008 and 2011 by the Danish Council for Independent Research and was part of a larger project to compare cross-scale plant community structure between the Alps and the Scandes. The Alps Vegetation Database currently harbours 35,731 geo-referenced vegetation plots and 5,023 valid taxa across Mediterranean, temperate and alpine environments. The data are mainly used by the main contributors of the Alps Vegetation Database in an ecoinformatics approach to test hypotheses related to plant macroecology and biogeography, but external proposals for joint collaborations are welcome.

Problemas entomológicos na cultura do tomate em Cabo Verde. Estudo de caso na Ilha de Santiago

O tomate (Lycopersicon esculentum) é uma das principais hortícolas produzidas na Ilha de Santiago, Cabo Verde. Com o objectivo de se identificar as principais pragas associadas a esta cultura e de se acompanhar a evolução ao longo do ciclo fenológico, instalaram-se parcelas experimentais em São Jorge dos Órgãos, São Domingos e Tarrafal. No presente trabalho caracterizou-se a agricultura cabo-verdiana e ilustrou-se a importância do sector hortícola na agricultura. Descreveu-se sucintamente a cultura do tomate e as variedades utilizadas. Apresentou-se uma revisão bibliográfica para as pragas referenciadas neste país e para as potenciais, incidindo-se principalmente nos meios de protecção. Para a concretização dos objectivos propostos realizaram-se amostragens semanais nas parcelas instaladas. Identificaram-se algumas espécies anteriormente referenciadas como pragas e outras que foram observadas a infestar a cultura: Aphis sp., Brachycaudus sp., cicadelídeo, Megalurothrips sp. e Tuta absoluta. Acompanhou-se a evolução da incidência e da população de tripes, mosquinhas-brancas, lagartas, minas de larvas mineiras, afídeos e mirídeos no período de observação e analisou-se a sua distribuição vertical na planta. Identificou-se Tuta absoluta em campos de agricultores e avaliaram-se os estragos provocados por esta praga, através da realização de inquéritos por questionário aos agricultores afectados.

Flora das Culturas Agrícolas da Ilha de Santiago (cabo Verde)

Com o objectivo de caracterizar as comunidades vegetais que acompanham as culturas agrícolas de sequeiro e de regadio praticadas em Santiago e, particularmente, no vale da ribeira Seca, efectuaram-se 16 levantamentos titoecológicos ao longo deste curso de água e encostas sobranceiras. A inventaria@0 floristica revelou a presenta de 118 taro pertencenteas 3 3 familias. Analisaram-sea, inda,6 2 levantamentorse alizadose m diversosp ontosd a ilha, tendo sido identificados1 72t axa pertencenteas 42 familiasG. ramineae. Leguminosae e Compositue sao as famílias melhor representadasA. flora inventariadaC comparadac om a referida em trabalhos precedentesr,e alizadosp or outrosa utores,r evelandolao correnciad e, pelo menos,1 82t axa na flora infestante. Os levantamentos da ribeira Seca foram analisadosa travt5sd o programad e análise numérica TWINSPAN, que indicou a presentad e 4 agrupamentosv egetais distintos, cuja interpretacao,a tendendoà s característicase dáticas,c limáticase topográticasd os locais onde ocorrem,s ugeriua disponibilidadeh idrica comoo factorm aisd eterminantde as uac omposicáo. Palavras-chavefl:o ra, adventiciasd asc ulturasT, WINSPAN, ilhasd eC aboV erde, Santiago. In order to identify and to characterizeth e plant communitiesp resenat t the irrigated and dry cropso f ribeira Secav alley, it were established16 s amplep lots. The tloristic inventory has revealedt he presenteo f 118 tara belongingt o 33 families.I n addition,m ore 62 samplep lots,were establishedth roughoutt he island,w hich permittedt he identifkation of 172t ara from 42 families.G ramineae, CompQsitae &ndL eguminosae weret he mostr epresentativeosn es.T his flora is comparedw ith that referred in precedingw orksf rom othersa uthors,r evealingt he occurrence of, at least, 182 tma in the weed flora. The application of the TWINSPAN numerical analysis, to the plots in the ribeira Seca vallcy. has revealed the presente of 4 distinct plant communities, which were related with edaphic,c limatic and topographicf actors.T his analysiss uggestetdh at the water availability wa.s the mainf actor affecting the speciesc ompositionof the communities. Key-words:f lora weedsT, WINSPAN, CapeV erdei slandsS, antiago.

Spatial pattern of floral morphology: a possible insight into the effects of pollinators on plant distribution

Pollination syndromes involve convergent evolution towards phenotypes composed of specific scents, colours or floral morphologies that attract or restrict pollinator access to reward. How these traits might influence the distributions of plant species in interaction with pollinators has rarely been investigated. We sampled 870 vegetation plots in the western Swiss Alps and classified the plant species into seven blossom types according to their floral morphology (wind, disk, funnel, tube, bilabiate, head or brush). We investigated the environmental features of plots with functional diversity (FD) lower than expected by chance alone to detect potential pollination filtering and related the proportions of the seven blossom types to a combination of environmental descriptors. From these results, we inferred the potential effect of the pollinator on the spatial distribution of plant species. The vegetation plots with significantly lower FD of blossom types than expected by chance were found at higher altitudes, and the proportions of blossom types were strongly patterned along the same gradient. These results support a biotic filtering effect on plant species assemblages through pollination: disk blossoms became dominant at higher altitudes, resulting in a lower FD. In harsh conditions at high altitudes, pollinators usually decrease in activity, and the openness of the disk blossom grants access to any available pollinator. Inversely, bilabiate blossoms, which are mostly pollinated by bees, were more abundant at lower elevations, which are characterised by greater abundance and diversity of bees. Generalisation through openness of the blossom could be advantageous at high elevations, while specialisation could be a successful alternative strategy at lower elevations. The approach used in this study is purely correlative, and further investigations should be conducted to infer the nature of the causal relationship between plant and pollinator distributions.

Density and distribution of nests of Mycetophylax simplex (Emery) (Hymenoptera, Formicidae) in areas with mobile dunes on the northern coast of Rio Grande do Sul, Brazil

Studies on lower attines are scarce, especially on nesting and foraging ecology and behavior. This study aimed to contribute to the knowledge of an Attini in dunes ecosystems through the description of density and spatial distribution of Mycetophylax simplex (Emery, 1887) nests in a strip of mobile dunes in the Praia Grande beach, Torres, northern coast of Rio Grande do Sul, Brazil. The density and spatial distribution of nests were estimated in four plots of 2,500 m² each, in which were found 20, 209, 284 and 324 nests, with average densities of 0.01 nests/m², 0.09, 0.11 and 0.13 nests/m², respectively. The nests were found near to the vegetation and showed clumped distribution. The density and distribution pattern of the nests seem to be related to the availability of nesting places and foraging resources.

Improving rainwater-use in Cabo Verde drylands by reducing runoff

Dryland agriculture in Cabo Verde copes with steep slopes, inadequate practices, irregular intense rain, recurrent droughts, high runoff rates, severe soil erosion and declining fertility, leading to the inefficient use of rainwater. Maize and beans occupy N80% of the arable land in low-input, low-yielding subsistence farming. Three collaborative field trialswere conducted in different agroecological zones to evaluate the effects ofwater-conservation techniques (mulching of crop residue, a soil surfactant and pigeon-pea hedges) combinedwith organic amendments (compost and animal or green manure) on runoff and soil loss. During the 2011 and 2012 rainy seasons, three treatments and one control (traditional practice) were applied to 44- and 24-m2 field plots. A local maize variety and two types of beanswere planted. Runoff and suspended sedimentswere collected and quantified after each daily erosive rainfall. Runoff occurred for rainfalls≥50mm(slope b10%, loamy Kastanozem),≥60mm(slope≤23%, silt–clay–loam Regosol) and≥40mm(slope≤37%, sandy loam Cambisol). Runoffwas significantly reduced only with themulch treatment on the slope N10% and in the treatment of surfactant with organic amendment on the slope b10%. Soil loss reached 16.6, 5.1, 6.6 and 0.4 Mg ha−1 on the Regosol (≤23% slope) for the control, surfactant, pigeon-pea and mulch/pigeon-pea (with organic amendment) treatments, respectively; 3.2, 0.9, 1.3 and 0.1 Mg ha−1 on the Cambisol (≤37% slope) and b0. 2Mg ha−1 for all treatments and control on the Kastanozem(b10% slope). Erosion was highly positively correlated with runoff. Mulch with pigeon-pea combinedwith an organic amendment significantly reduced runoff and erosion fromagricultural fields on steep slopes, contributing to improved use of rainwater at the plot level. Sustainable land management techniques, such as mulching with pigeon-pea hedges and an organic amendment, should be advocated and promoted for the semiarid hillsides of Cabo Verde prone to erosion to increase rainwater-use and to prevent further soil degradation.

Colonic movements in healthy subjects as monitored by a Magnet Tracking System.

The Magnet Tracking System (MTS) is a minimally-invasive technique of continuous evaluation of gastrointestinal motility. In this study, MTS was used to analyse colonic propulsive dynamics and compare the transit of a magnetic pill with that of standard radio-opaque markers. MTS monitors the progress in real time of a magnetic pill through the gut. Ten men and 10 women with regular daily bowel movements swallowed this pill and 10 radio-opaque markers at 8 pm. Five hours of recordings were conducted during 2 following mornings. Origin, direction, amplitude and velocity of movements were analysed relative to space-time plots of the pill trajectory. Abdominal radiographs were taken to compare the progress of both pill and markers. The magnetic pill lay idle for 90% of its sojourn in the colon; its total retrograde displacement accounted for only 20% of its overall movement. Analysis of these movements showed a bimodal distribution of velocities: around 1.5 and 50 cm min(-1), the latter being responsible for 2/3 of distance traversed. There were more movements overall and more mass movements in males. Net hourly forward progress was greater in the left than right colon, and greater in males. The position of the magnetic pill correlated well with the advancement of markers. MTS showed patterns and propulsion dynamics of colonic segments with as yet unmet precision. Detailed analysis of slow and fast patterns of colonic progress makes it possible to specify the motility of colonic segments, and any variability in gender. Such analysis opens up promising avenues in studies of motility disorders.

Manual de uso del software Ocean Data View (ODV)

El presente manual de uso del software de visualización de datos “Ocean Data View” (ODV) describe la exploración, análisis y visualización de datos oceanográficos según el formato de la colección mundial de base de datos del océano “World Ocean Database” (WOD). El manual comprende 6 ejercicios prácticos donde se describe paso a paso la creación de las metavariables, la importación de los datos y su visualización mediante mapas de latitud, longitud y gráficos de dispersión, secciones verticales y series de tiempo. Se sugiere el uso extensivo del ODV para la visualización de datos oceanográficos por el personal científico del IMARPE.

Influence of tree species on the herbaceous understory and soil chemical characteristics in a silvopastoral system in semi-arid northeastern Brazil

Studies from some semi-arid regions of the world have shown the beneficial effect of trees in silvopastoral systems, by promoting the formation of resource islands and increasing the sustainability of the system. No data are available in this respect for tree species of common occurrence in semi-arid Northeastern Brazil. In the present study, conducted in the summer of 1996, three tree species (Zyziphus joazeiro, Spondias tuberosa and Prosopis juliflora: ) found within Cenchrus ciliaris pastures were selected to evaluate differences on herbaceous understory and soil chemical characteristics between samples taken under the tree canopy and in open grass areas. Transects extending from the tree trunk to open grass areas were established, and soil (0-15 cm) and herbaceous understory (standing live biomass in 1 m² plots) samples were taken at 0, 25, 50, 100, 150 and 200% of the average canopy radius (average radius was 6.6 ± 0.5, 4.5 ± 0.5, and 5.3 ± 0.8 m for Z. joazeiro, P. juliflora, and S. tuberosa , respectively). Higher levels of soil C, N, P, Ca, Mg, K, and Na were found under the canopies of Z. joazeiro and P. juliflora: trees, as compared to open grass areas. Only soil Mg organic P were higher under the canopies of S. tuberosa trees, as compared to open grass areas. Herbaceous understory biomass was significantly lower under the canopy of S. tuberosa and P. juliflora trees (107 and 96 g m-2, respectively) relatively to open grass areas (145 and 194 g m-2). No herbaceous biomass differences were found between Z. joazeiro canopies and open grass areas (107 and 87 g m-2, respectively). Among the three tree species studied, Z. joazeiro was the one that presented the greatest potential for use in a silvopastoral system at the study site, since it had a larger nutrient stock in the soil without negatively affecting herbaceous understory biomass, relatively to open grass areas.

The alkaline intraplate volcanism of the Antalya nappes (Turkey): a Late Triassic remnant of the Neotethys

Late Triassic submarine alkali basalts and hawaiites were collected from two superimposed tectonic slices belonging to the Kara Dere - Sayrun unit of the Middle Antalya nappes, southwestern Turkey. New determinations on conodont faunas allow to date this sequence to the Lower Carnian (Julian). The volcanic rocks show rather homogeneous compositions, with high TiO2 and relatively low MgO and Ni contents which suggest olivine fractionation. Their primitive mantle-normalised multi-elements plots show Nb and Ta enrichments relative to La, Pb negative anomalies and heavy rare earth element and Y depletions typical of intraplate ocean island basalts. These characteristics are consistent with the major and trace element compositions of their primary clinopyroxene phenocrysts, which do not show any feature ascribable to crustal contamination. The studied lavas display a restricted range of epsilon Nd (+4.6 to +5.2) which falls within the range of ocean island basalts. Their initial (Nd-143/Nd-144)i ratios are too low to be explained by a simple mixing line between depleted MORB mantle (DMM) and HIMU components. Their Pb and Nd isotopic compositions plot along a mixing line between HIMU component and an enriched mantle, the composition of which could be the result of the addition of about 5 to 8% of an EM2 component (recycled marine sediments) to DMM. The lack of evidence for any continental crustal component. in their genesis could be consistent with their emplacement in an intra-oceanic setting.

Reliable tidal volume estimates at the airway opening with an infant monitor during high-frequency oscillatory ventilation.

OBJECTIVE: To assess the suitability of a hot-wire anemometer infant monitoring system (Florian, Acutronic Medical Systems AG, Hirzel, Switzerland) for measuring flow and tidal volume (Vt) proximal to the endotracheal tube during high-frequency oscillatory ventilation. DESIGN: In vitro model study. SETTING: Respiratory research laboratory. SUBJECT: In vitro lung model simulating moderate to severe respiratory distress. INTERVENTION: The lung model was ventilated with a SensorMedics 3100A ventilator. Vt was recorded from the monitor display (Vt-disp) and compared with the gold standard (Vt-adiab), which was calculated using the adiabatic gas equation from pressure changes inside the model. MEASUREMENTS AND MAIN RESULTS: A range of Vt (1-10 mL), frequencies (5-15 Hz), pressure amplitudes (10-90 cm H2O), inspiratory times (30% to 50%), and Fio2 (0.21-1.0) was used. Accuracy was determined by using modified Bland-Altman plots (95% limits of agreement). An exponential decrease in Vt was observed with increasing oscillatory frequency. Mean DeltaVt-disp was 0.6 mL (limits of agreement, -1.0 to 2.1) with a linear frequency dependence. Mean DeltaVt-disp was -0.2 mL (limits of agreement, -0.5 to 0.1) with increasing pressure amplitude and -0.2 mL (limits of agreement, -0.3 to -0.1) with increasing inspiratory time. Humidity and heating did not affect error, whereas increasing Fio2 from 0.21 to 1.0 increased mean error by 6.3% (+/-2.5%). CONCLUSIONS: The Florian infant hot-wire flowmeter and monitoring system provides reliable measurements of Vt at the airway opening during high-frequency oscillatory ventilation when employed at frequencies of 8-13 Hz. The bedside application could improve monitoring of patients receiving high-frequency oscillatory ventilation, favor a better understanding of the physiologic consequences of different high-frequency oscillatory ventilation strategies, and therefore optimize treatment.

Reconsolidation of the soil surface after tillage discontinuity, with and without cultivation, related to erosion and its prediction with RUSLE

Site-specific regression coefficient values are essential for erosion prediction with empirical models. With the objective to investigate the surface-soilconsolidation factor, Cf, linked to the RUSLE's prior-land-use subfactor, PLU, an erosion experiment using simulated rainfall on a 0.075 m m-1 slope, sandy loam Paleudult soil, was conducted at the Agriculture Experimental Station of the Federal University of Rio Grande do Sul (EEA/UFRGS), in Eldorado do Sul, State of Rio Grande do Sul, Brazil. Firstly, a row-cropped area was excluded from cultivation (March 1995), the existing crop residue removed from the field, and the soil kept clean-tilled the rest of the year (to get a degraded soil condition for the intended purpose of this research). The soil was then conventional-tilled for the last time (except for a standard plot which was kept continuously cleantilled for comparison purposes), in January 1996, and the following treatments were established and evaluated for soil reconsolidation and soil erosion until May 1998, on duplicated 3.5 x 11.0 m erosion plots: (a) fresh-tilled soil, continuously in clean-tilled fallow (unit plot); (b) reconsolidating soil without cultivation; and (c) reconsolidating soil with cultivation (a crop sequence of three corn- and two black oats cycles, continuously in no-till, removing the crop residues after each harvest for rainfall application and redistributing them on the site after that). Simulated rainfall was applied with a Swanson's type, rotating-boom rainfall simulator, at 63.5 mm h-1 intensity and 90 min duration, six times during the two-and-half years of experimental period (at the beginning of the study and after each crop harvest, with the soil in the unit plot being retilled before each rainfall test). The soil-surface-consolidation factor, Cf, was calculated by dividing soil loss values from the reconsolidating soil treatments by the average value from the fresh-tilled soil treatment (unit plot). Non-linear regression was used to fit the Cf = e b.t model through the calculated Cf-data, where t is time in days since last tillage. Values for b were -0.0020 for the reconsolidating soil without cultivation and -0.0031 for the one with cultivation, yielding Cf-values equal to 0.16 and 0.06, respectively, after two-and-half years of tillage discontinuation, compared to 1.0 for fresh-tilled soil. These estimated Cf-values correspond, respectively, to soil loss reductions of 84 and 94 %, in relation to soil loss from the fresh-tilled soil, showing that the soil surface reconsolidated intenser with cultivation than without it. Two distinct treatmentinherent soil surface conditions probably influenced the rapid decay-rate of Cf values in this study, but, as a matter of a fact, they were part of the real environmental field conditions. Cf-factor curves presented in this paper are therefore useful for predicting erosion with RUSLE, but their application is restricted to situations where both soil type and particular soil surface condition are similar to the ones investigate in this study.

Surface and subsurface decomposition of a desiccated grass pasture biomass related to erosion and its prediction with RUSLE

Erosion is deleterious because it reduces the soil's productivity capacity for growing crops and causes sedimentation and water pollution problems. Surface and buried crop residue, as well as live and dead plant roots, play an important role in erosion control. An efficient way to assess the effectiveness of such materials in erosion reduction is by means of decomposition constants as used within the Revised Universal Soil Loss Equation - RUSLE's prior-land-use subfactor - PLU. This was investigated using simulated rainfall on a 0.12 m m-1 slope, sandy loam Paleudult soil, at the Agriculture Experimental Station of the Federal University of Rio Grande do Sul, in Eldorado do Sul, State of Rio Grande do Sul, Brazil. The study area had been covered by native grass pasture for about fifteen years. By the middle of March 1996, the sod was mechanically mowed and the crop residue removed from the field. Late in April 1996, the sod was chemically desiccated with herbicide and, about one month later, the following treatments were established and evaluated for sod biomass decomposition and soil erosion, from June 1996 to May 1998, on duplicated 3.5 x 11.0 m erosion plots: (a) and (b) soil without tillage, with surface residue and dead roots; (c) soil without tillage, with dead roots only; (d) soil tilled conventionally every two-and-half months, with dead roots plus incorporated residue; and (e) soil tilled conventionally every six months, with dead roots plus incorporated residue. Simulated rainfall was applied with a rotating-boom rainfall simulator, at an intensity of 63.5 mm h-1 for 90 min, eight to nine times during the experimental period (about every two-and-half months). Surface and subsurface sod biomass amounts were measured before each rainfall test along with the erosion measurements of runoff rate, sediment concentration in runoff, soil loss rate, and total soil loss. Non-linear regression analysis was performed using an exponential and a power model. Surface sod biomass decomposition was better depicted by the exponential model, while subsurface sod biomass was by the power model. Subsurface sod biomass decomposed faster and more than surface sod biomass, with dead roots in untilled soil without residue on the surface decomposing more than dead roots in untilled soil with surface residue. Tillage type and frequency did not appreciably influence subsurface sod biomass decomposition. Soil loss rates increased greatly with both surface sod biomass decomposition and decomposition of subsurface sod biomass in the conventionally tilled soil, but they were minimally affected by subsurface sod biomass decomposition in the untilled soil. Runoff rates were little affected by the studied treatments. Dead roots plus incorporated residues were effective in reducing erosion in the conventionally tilled soil, while consolidation of the soil surface was important in no-till. The residual effect of the turned soil on erosion diminished gradually with time and ceased after two years.