@inproceedings{2424,
abstract = {We introduce the adaptive neighborhood graph as a data structure for modeling a smooth manifold M embedded in some (potentially very high-dimensional) Euclidean space ℝd. We assume that M is known to us only through a finite sample P ⊂ M, as it is often the case in applications. The adaptive neighborhood graph is a geometric graph on P. Its complexity is at most min{2O(k)(n, n2}, where n = |P| and k = dim M, as opposed to the n⌈d/2⌉ complexity of the Delaunay triangulation, which is often used to model manifolds. We show that we can provably correctly infer the connectivity of M and the dimension of M from the adaptive neighborhood graph provided a certain standard sampling condition is fulfilled. The running time of the dimension detection algorithm is d2O(k7 log k) for each connected component of M. If the dimension is considered constant, this is a constant-time operation, and the adaptive neighborhood graph is of linear size. Moreover, the exponential dependence of the constants is only on the intrinsic dimension k, not on the ambient dimension d. This is of particular interest if the co-dimension is high, i.e., if k is much smaller than d, as is the case in many applications. The adaptive neighborhood graph also allows us to approximate the geodesic distances between the points in P.},
author = {Giesen, Joachim and Uli Wagner},
pages = {329 -- 337},
publisher = {ACM},
title = {{Shape dimension and intrinsic metric from samples of manifolds with high co-dimension}},
doi = {10.1145/777792.777841},
year = {2003},
}
@article{3917,
abstract = {Male dimorphism is not genetically determined, but is induced by environmental conditions particularly decreasing temperature and density.},
author = {Cremer, Sylvia and Heinze, Jürgen},
journal = {Blick in die Wissenschaft},
number = {15},
pages = {32 -- 36},
publisher = {Schnell und Steiner},
title = {{Zwischen Hochzeitsflug und Brudermord: reproduktive Taktiken bei Ameisenmännchen}},
volume = {12},
year = {2003},
}
@article{3921,
abstract = {Unlike most social insects, many Cardiocondyla ant species have two male morphs: wingless (ergatoid) males, who remain in the natal nest, and winged males who disperse but, strangely, before leaving may also mate within the nest. Whereas ergatoid males are highly intolerant of each other and fight among themselves, they tend to tolerate their winged counterparts. This is despite the fact that these winged males, like ergatoid males, represent mating competition. Why should ergatoid males tolerate their winged rivals? We developed a mathematical model to address this question. Our model focuses on a number of factors likely toinfluence whether ergatoid males are tolerant of winged males: ergatoid male–winged male relatedness, number of virgin queens, number of winged males, and the number of ejaculates a winged male has (winged males are sperm limited, whereas ergatoid males have lifelong spermatogenesis). Surprisingly, we found that increasing the number of virgin queens favors a kill strategy, whereas an increase in the other factors favors a let-live strategy; these predictions appear true for C. obscurior and for a number of other Cardiocondyla species. Two further aspects, unequal insemination success and multiple mating in queens, were also incorporated into the model and predictions made about their effects on toleration of winged males. The model is applicable more generally in species that have dimorphic males, such as some other ants, bees, and fig wasps.},
author = {Anderson, Carl and Cremer, Sylvia and Heinze, Jürgen},
journal = {Behavioral Ecology},
number = {1},
pages = {54 -- 62},
publisher = {Oxford University Press},
title = {{Live and let die: Why fighter males of the ant Cardiocondyla kill each other but tolerate their winged rivals}},
doi = {10.1093/beheco/14.1.54},
volume = {14},
year = {2003},
}
@article{3922,
abstract = {Dispersal is advantageous, but, at the same time, it implies high costs and risks. Due to these counteracting selection pressures, many species evolved dispersal polymorphisms, which, in ants, are typically restricted to the female sex (queens). Male polymorphism is presently only known from a few genera, such as Cardiocondyla, in which winged dispersing males coexist with wingless fighter males that mate exclusively inside their maternal nests. We studied the developmental mechanisms underlying these alternative male morphs and found that, first, male dimorphism is not genetically determined, but is induced by environmental conditions (decreasing temperature and density). Second, male morph is not yet fixed at the egg stage, but it differentiates during larval development. This flexible developmental pattern of male morphs allows Cardiocondyla ant colonies to react quickly to changes in their environment. Under good conditions, they invest exclusively in philopatric wingless males. But, when environmental conditions turn bad, colonies start to produce winged dispersal males, even though these males require a many times higher investment by the colony than their much smaller wingless counterparts. Cardiocondyla ants share this potential of optimal resource allocation with other colonial animals and some seed dimorphic plants.},
author = {Cremer, Sylvia and Heinze, Jürgen},
journal = {Current Biology},
number = {3},
pages = {219 -- 223},
publisher = {Cell Press},
title = {{Stress grows wings: Environmental induction of winged dispersal males in Cardiocondyla ants}},
doi = {10.1016/S0960-9822(03)00012-5},
volume = {13},
year = {2003},
}
@inbook{3991,
abstract = {We give analytic inclusion-exclusion formulas for the area and perimeter derivatives of a union of finitely many disks in the plane.},
author = {Cheng, Ho-Lun and Herbert Edelsbrunner},
booktitle = {Computer Science in Perspective: Essays Dedicated to Thomas Ottmann},
pages = {88 -- 97},
publisher = {Springer},
title = {{Area and perimeter derivatives of a union of disks}},
doi = {10.1007/3-540-36477-3_7},
volume = {2598},
year = {2003},
}