Simulated annealing applied to the irregular rotational placement of shapes over containers with fixed dimensions

This work deals with the problem of minimizing the waste of space that occurs on a rotational placement of a set of irregular two dimensional polygons inside a two dimensional container. This problem is approached with an heuristic based on simulated annealing. Traditional 14 external penalization"" techniques are avoided through the application of the no-fit polygon, that determinates the collision free area for each polygon before its placement. The simulated annealing controls: the rotation applied, the placement and the sequence of placement of the polygons. For each non placed polygon, a limited depth binary search is performed to find a scale factor that when applied to the polygon, would allow it to be fitted in the container. It is proposed a crystallization heuristic, in order to increase the number of accepted solutions. The bottom left and larger first deterministic heuristics were also studied. The proposed process is suited for non convex polygons and containers, the containers can have holes inside. (C) 2009 Elsevier Ltd. All rights reserved.

Placement over containers with fixed dimensions solved with adaptive neighborhood simulated annealing

This work deals with the problem of minimizing the waste of space that occurs on a rotational placement of a set of irregular bi-dimensional items inside a bi-dimensional container. This problem is approached with a heuristic based on Simulated Annealing (SA) with adaptive neighborhood. The objective function is evaluated in a constructive approach, where the items are placed sequentially. The placement is governed by three different types of parameters: sequence of placement, the rotation angle and the translation. The rotation applied and the translation of the polygon are cyclic continuous parameters, and the sequence of placement defines a combinatorial problem. This way, it is necessary to control cyclic continuous and discrete parameters. The approaches described in the literature deal with only type of parameter (sequence of placement or translation). In the proposed SA algorithm, the sensibility of each continuous parameter is evaluated at each iteration increasing the number of accepted solutions. The sensibility of each parameter is associated to its probability distribution in the definition of the next candidate.

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.

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.

Paper surfaces and dynamical limits

It is very common in mathematics to construct surfaces by identifying the sides of a polygon together in pairs: For example, identifying opposite sides of a square yields a torus. In this article the construction is considered in the case where infinitely many pairs of segments around the boundary of the polygon are identified. The topological, metric, and complex structures of the resulting surfaces are discussed: In particular, a condition is given under which the surface has a global complex structure (i.e., is a Riemann surface). In this case, a modulus of continuity for a uniformizing map is given. The motivation for considering this construction comes from dynamical systems theory: If the modulus of continuity is uniform across a family of such constructions, each with an iteration defined on it, then it is possible to take limits in the family and hence to complete it. Such an application is briefly discussed.