A collocation method for high frequency scattering by convex polygons

We consider the problem of scattering of a time-harmonic acoustic incident plane wave by a sound soft convex polygon. For standard boundary or finite element methods, with a piecewise polynomial approximation space, the computational cost required to achieve a prescribed level of accuracy grows linearly with respect to the frequency of the incident wave. Recently Chandler–Wilde and Langdon proposed a novel Galerkin boundary element method for this problem for which, by incorporating the products of plane wave basis functions with piecewise polynomials supported on a graded mesh into the approximation space, they were able to demonstrate that the number of degrees of freedom required to achieve a prescribed level of accuracy grows only logarithmically with respect to the frequency. Here we propose a related collocation method, using the same approximation space, for which we demonstrate via numerical experiments a convergence rate identical to that achieved with the Galerkin scheme, but with a substantially reduced computational cost.

A high frequency boundary element method for scattering by convex polygons with impedance boundary conditions

We consider scattering of a time harmonic incident plane wave by a convex polygon with piecewise constant impedance boundary conditions. Standard finite or boundary element methods require the number of degrees of freedom to grow at least linearly with respect to the frequency of the incident wave in order to maintain accuracy. Extending earlier work by Chandler-Wilde and Langdon for the sound soft problem, we propose a novel Galerkin boundary element method, with the approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh with smaller elements closer to the corners of the polygon. Theoretical analysis and numerical results suggest that the number of degrees of freedom required to achieve a prescribed level of accuracy grows only logarithmically with respect to the frequency of the incident wave.

Quadratic Time Computable Instances of MaxMin and MinMax Area Triangulations of Convex Polygons

We consider the problems of finding two optimal triangulations of a convex polygon: MaxMin area and MinMax area. These are the triangulations that maximize the area of the smallest area triangle in a triangulation, and respectively minimize the area of the largest area triangle in a triangulation, over all possible triangulations. The problem was originally solved by Klincsek by dynamic programming in cubic time [2]. Later, Keil and Vassilev devised an algorithm that runs in O(n^2 log n) time [1]. In this paper we describe new geometric findings on the structure of MaxMin and MinMax Area triangulations of convex polygons in two dimensions and their algorithmic implications. We improve the algorithm’s running time to quadratic for large classes of convex polygons. We also present experimental results on MaxMin area triangulation.

A Comparison of the Home Range Sizes of Mainland and Island Populations of Black-Faced Lion Tamarins (Leontopithecus caissara) Using Different Spatial Analysis

The critically endangered black-faced lion tamarin, Leontopithecus caissara, has a restricted geographical distribution consisting of small mainland and island populations, each with distinct habitats in coastal southeastern Brazil. Necessary conservation management actions require an assessment of whether differences in habitats are reflected in use of space by the species. We studied two tamarin groups on the mainland at Sao Paulo state between August 2005 and March 2007, and compared the results with data from Superagui Island. Three home range estimators were used: minimum convex polygon (MCP), Kernel, and the new technique presented dissolved monthly polygons (DMP). These resulted, respectively, in home ranges of 345, 297, and 282 ha for the 12-month duration of the study. Spatial overlap of mainland groups was extensive, whereas temporal overlap was not, a pattern that indicates resource partitioning is an important strategy to avoid intraspecific competition. L. caissara large home ranges seem to be dynamic, with constant incorporation of new areas and abandonment of others through time. The main difference between mainland and island groups is the amount and variety of sleeping sites. A better understanding of the home range sizes, day range lengths, and territorial behavior of this species will aid in developing better management strategies for its protection. Additionally, the presented DMP protocol is a useful improvement over the MCP method as it results in more realistic home range sizes for wildlife species. Am. J. Primatol. 73: 1114-1126, 2011. (C) 2011 Wiley Periodicals, Inc.

Activity patterns and foraging behaviour of Audouin's gulls at the Ebro Delta, NW Mediterranean.

Twenty Audouin´s gulls, Larus audouinii, breeding in the Ebro Delta (NW Mediterranean) were radio-tracked in 1998 to study their foraging behaviour and activity patterns. Some detrimental effects of tagging on the breeding success of the birds were detected, especially when both members of the pair were tagged. The results were actually constrained by the low number of locations due to natural breeding failure and failure in tag emission, as well as the adverse effect of tagging. However, through a combination of aircraft surveys at sea and a fixed station for automatic tracking of the presence of the birds at the colony, novel individual-based information of home ranges and activity patterns was obtained. Trawler fishing activity seemed to influence both the foraging range and habitat use: while trawlers operated, gulls overlapped their fishing grounds with vessels, probably to scavenge on discards. Very few locations were obtained during a trawling moratorium period, although they were all recorded in coastal bays and terrestrial habitats. During the trawling activity period, gulls ranged over a minimum convex polygon area of 2900 km2. Gulls were tracked up to 40 km from the colony, but some individuals were observed beyond 150 km while still breeding. Arrivals and departures from the colony were in accordance with the trawling timetable. However, most birds also showed some nocturnal foraging activity, probably linked to active fishing of clupeoids (following diel migrations) or to the exploitation of purse-seine fishing activity. Foraging trips lasted on average 15 hours: males performed significantly shorter trips than females, which spent more time outside the colony. The proportion of nocturnal time involved in the foraging trips was the same for males and females, but whilst all males initiated their trips both during the day and at night, some females only initiated their trips during the day. Hatching success was found to be related to foraging effort by males. Gulls spent on average ca. 38% of their time budget outside the nesting territory, representing the time devoted mainly to flying, foraging and other activities.

Do the Golden-winged Warbler and Blue-winged Warbler Exhibit Species-specific Differences in their Breeding Habitat Use?

We compared habitat features of Golden-winged Warbler (Vermivora chrysoptera) territories in the presence and absence of the Blue-winged Warbler (V. cyanoptera) on reclaimed coal mines in southeastern Kentucky, USA. Our objective was to determine whether there are species specific differences in habitat that can be manipulated to encourage population persistence of the Golden-winged Warbler. When compared with Blue-winged Warblers, Golden-winged Warblers established territories at higher elevations and with greater percentages of grass and canopy cover. Mean territory size (minimum convex polygon) was 1.3 ha (se = 0.1) for Golden-winged Warbler in absence of Blue-winged Warbler, 1.7 ha (se = 0.3) for Golden-winged Warbler coexisting with Blue-winged Warbler, and 2.1 ha (se = 0.3) for Blue-winged Warbler. Territory overlap occurred within and between species (18 of n = 73 territories, 24.7%). All Golden-winged and Blue-winged Warblers established territories that included an edge between reclaimed mine land and mature forest, as opposed to establishing territories in open grassland/shrubland habitat. The mean distance territories extended from a forest edge was 28.0 m (se = 3.8) for Golden-winged Warbler in absence of Blue-winged Warbler, 44.7 m (se = 5.7) for Golden-winged Warbler coexisting with Blue-winged Warbler, and 33.1 m (se = 6.1) for Blue-winged Warbler. Neither territory size nor distances to forest edges differed significantly between Golden-winged Warbler in presence or absence of Blue-winged Warbler. According to Monte Carlo analyses, orchardgrass (Dactylis glomerata), green ash (Fraxinus pennsylvanica) seedlings and saplings, and black locust (Robinia pseudoacacia) saplings were indicative of sites with only Golden-winged Warblers. Sericea lespedeza, goldenrod (Solidago spp.), clematis vine (Clematis spp.), and blackberry (Rubus spp.) were indicative of sites where both species occurred. Our findings complement recent genetic studies and add another factor for examining Golden-winged Warbler population decline. Further, information from our study will aid land managers in manipulating habitat for the Golden-winged Warbler.

Investigating the practicality of using radio tracking to determine home range and movements of Picathartidae

Radiotelemetry is an important tool used to aid the understanding and conservation of cryptic and rare birds. The two bird species of the family Picathartidae are little-known, secretive, forest-dwelling birds endemic to western and central Africa. In 2005, we conducted a radio-tracking trial of Grey-necked Picathartes Picathartes oreas in the Mbam Minkom Mountain Forest, southern Cameroon, using neck collar (two birds) and tail-mounted (four birds) transmitters to investigate the practicality of radio-tracking Picathartidae. Three birds with tail-mounted transmitters were successfully tracked with the fourth, though not relocated for radio tracking, resighted the following breeding season. Two of these were breeding birds that continued to provision young during radio tracking. One neck-collared bird was found dead three days after transmitter attachment and the other neither relocated nor resighted. As mortality in one bird was potentially caused by the neck collar transmitter we recommend tail-mounted transmitters in future radio-tracking studies of Picathartidae. Home ranges, shown using minimum convex polygon and kernel estimation methods, were generally small (<0.5 km(2)) and centred around breeding sites. A minimum of 60 fixes were found to be sufficient for home range estimation.

Collision prediction of a moving object within a virtual world

This paper provides a solution for predicting moving/moving and moving/static collisions of objects within a virtual environment. Feasible prediction in real-time virtual worlds can be obtained by encompassing moving objects within a sphere and static objects within a convex polygon. Fast solutions are then attainable by describing the movement of objects parametrically in time as a polynomial.

Continuum sea ice rheology determined from subcontinuum mechanics

[1] A method is presented to calculate the continuum-scale sea ice stress as an imposed, continuum-scale strain-rate is varied. The continuum-scale stress is calculated as the area-average of the stresses within the floes and leads in a region (the continuum element). The continuum-scale stress depends upon: the imposed strain rate; the subcontinuum scale, material rheology of sea ice; the chosen configuration of sea ice floes and leads; and a prescribed rule for determining the motion of the floes in response to the continuum-scale strain-rate. We calculated plastic yield curves and flow rules associated with subcontinuum scale, material sea ice rheologies with elliptic, linear and modified Coulombic elliptic plastic yield curves, and with square, diamond and irregular, convex polygon-shaped floes. For the case of a tiling of square floes, only for particular orientations of the leads have the principal axes of strain rate and calculated continuum-scale sea ice stress aligned, and these have been investigated analytically. The ensemble average of calculated sea ice stress for square floes with uniform orientation with respect to the principal axes of strain rate yielded alignment of average stress and strain-rate principal axes and an isotropic, continuum-scale sea ice rheology. We present a lemon-shaped yield curve with normal flow rule, derived from ensemble averages of sea ice stress, suitable for direct inclusion into the current generation of sea ice models. This continuum-scale sea ice rheology directly relates the size (strength) of the continuum-scale yield curve to the material compressive strength.

Home range and habitat use by the roadside hawk, Rupornis magnirostris (Gmelin, 1788) (Aves: Falcaniformes) in southeastern Brazil

Although most raptor species are found mainly in the tropics, information on their home range and spatial requirements in the Neotropics is still scarce. In this study, we used radio telemetry to evaluate the home range and the habitat use and selection of five Roadside hawks, Rupornis magnirostris (Gmelin, 1788) in a heterogeneous landscape in southeastern Brazil. The average home range size calculated using the adaptive kernel method (95% isopleth) was 126.1ha (47.4-266.7ha), but using the minimum convex polygon method (95% isopleth) it was 143.54ha (32.6-382.3ha). The roadside hawk explored a wide variety of habitats, most of them opportunistically, as suggested in the literature. Despite this, habitat quality could influence home range size and promote habitat selection. The observation of habitat use as expected, as well as the relatively small home range size, could be related to the generalist/opportunistic behaviour of the roadside hawk.

Home range and habitat use by the roadside hawk, Rupornis magnirostris (Gmelin, 1788) (Aves: Falcaniformes) in southeastern Brazil

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Habitat use and home range of brown-nosed coati, Nasua nasua (Carnivora: Procyonidae) in the Brazilian Cerrado biome

The brown-nosed coati (Nasua nasua) is a carnivorous species found in all the Brazilian biomes, some of which are endangered areas. The aim of this work was to determine the habitat use and selection, home range and core area of N. nasua in the Cerrado biome, central region of Tocantins, Brazil. The study was carried out in an area of approximately 20 000ha from May 2000 to July 2002. A total of seven box traps were placed in the area for 13 months, three of 11 captured animals were followed and monitored by radio-tracking during 13 months. The monitoring was conducted once a day, three times a week using a car and walking through the study area (radio-tracking and visual contact). The results demonstrate that these three males used more frequently the gallery forest formation, followed by cerrado and wetlands. The use of gallery forest by these animals indicated an habitat selection (Proportion test, z=12.98, p< 0.01). Besides, adult males used the gallery forest more frequently (Fisher's exact test, p<0.01) and wetlands less frequently (Fisher's exact test, p<0.01) than juvenile males, without significant differences between animal ages for cerrado percentage of habitat use. Besides, results also showed a gallery forest selection by adult (Proportion test z= 13.62, p<0.01) and juvenile (Proportion test z=2.68, p<0.01) males, and a wetland selection by the juvenile male (Proportion test z=3.90, p<0.01). The home ranges varied from 2.20 to 7.55km2 for the Minimum Convex Polygon 100% (MCP 100%) and from 4.38 to 13.32km2 for the Harmonic Mean 95% (HM 95%). The smallest home range overlap occurred between the adult males (Nm1 and Nm3), and the greatest between the juvenile Njm2 and the adult Nm1. The average of the core area (HM 75%) for the three monitored animals represented 21.29% of the home range calculated with HM 95%. No overlap between core areas was observed for adult males, but, it was an overlap between the core area of the juvenile male and its band with that of the two adult males. The present study provides new data on core area size and frequency habitat use by adult and juvenile males of N. nasua in the Brazilian Cerrado, that may support conservation efforts. Rev. Biol. Trop. 58 (3): 1069-1077. Epub 2010 September 01.

Growth and home range size of the gracile mouse opossum Gracilinanus microtarsus (Marsupialia: Didelphidae) in Brazilian cerrado

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Identificação e análise das áreas domicilares do boto-cinza, Sotalia guianensis (Van Bénéden, 1864), no estuário de Cananéia, São Paulo

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Área de vida da choca-do-planalto Thamnophilus pelzelni Hellmayr, 1924 (Passeriformes: Thamnophilidae) na estação ecológica de Jataí, Luiz Antônio, SP

Pós-graduação em Ciências Biológicas (Zoologia) - IBRC