ON TRANSLATING ELLIPSES AMIDST ELLIPTIC OBSTACLES.

The problem of moving an elliptic object A, surrounded by a set of elliptic obstacles B//j , is considered. The initial and final positions of the object are known and the intention is to move A solely by performing translations in the plane. The motion must be performed in such a way that A does not collide with any of the obstacles. The following algorithms are presented: (i) An algorithm, of complexity O(N log N), where N is the number of obstacles, which yields the set of all directions along which the object is separable from the obstacles by a single translation: (ii) An algorithm, quadratic in the number of obstacles, which yields a path for A to be moved from its starting configuration to its final configuration. The proposed technique first transforms the ellipse A into a circle A prime . This same transformation changes each ellipse B//j into another figure B//j prime , which is also elliptic. The algorithms then compute the path of translation by processing the configuration obstacles of space of B//j prime with respect to the circle A prime

On the problem of translating an elliptic object through a workspace of elliptic obstacles

Two algorithms are presented which deal with translating an elliptic object, A, without collision amidst elliptic obstacles. These are: (i) An exact algorithm, of complexity O(N log N), where N is the number of obstacles, yielding all directions along which the object is separable from the obstacles by a single translation. (ii) An algorithm quadratic in N, which yields, with a degree of approximation determined by the user, a path of the object from its initial to its final position

Quadratic Assignment Problem. 1 Acknowledgments

When they introduced the Ant System paradigm, Dorigo, Maniezzo, and Colorni also suggested an improvement to the original algorithm. By making use of global information, a set of ‘elitist ’ ants could focus the search, potentially accelerating convergence on an optimal solution. In a later paper, White, Kaegi, and Oda proposed a refinement of elitism in which local information is used instead of global information. By focusing the search on the local best tours (LBT) rather than the global best tour, the ants could search a wider area and avoid becoming trapped in local optima. Test results using the symmetric Travelling Salesman Problem showed considerable promise. We will examine the effectiveness of this refinement when applied against the assymetrica

Community trait structure in phytoplankton: seasonal dynamics from a method for sparse trait data

The distribution of functional traits in communities, and how trait distributions shift over time and space, is critical information for understanding community structure, the maintenance of diversity, and community effects on ecosystem function. It is often the case that traits tightly linked to ecological performance, such as physiological capacities, are laborious to measure and largely unknown for speciose communities; however, these traits are particularly important for unraveling the mechanistic basis of community structure. Here I develop a method combining sparse trait data with a statistical niche model, to infer trait distributions for phytoplankton communities, and how these vary over ten years in the western English Channel. I find that community-average nitrate affinity, light-limited growth rate, and maximum growth rate all show major seasonal patterns, reflecting alternate limitation by light vs. nitrogen. Trait diversity exhibits a variety of patterns distinct from community trait means, suggesting complex regulation of functional diversity. Patterns such as these are important for predicting how ocean ecosystems will respond to global change, and for developing trait-based models of emergent community structure. The statistical approach used here could be applied to any kind of organism, if they exhibit strong relationships between traits and statistical niche estimates