@article{4079, author = {Edelsbrunner, Herbert and Skiena, Steven}, issn = {1930-0972}, journal = {American Mathematical Monthly}, number = {7}, pages = {614 -- 618}, publisher = {Mathematical Association of America}, title = {{On the number of furthest neighbor pairs in a point set}}, doi = {10.1080/00029890.1989.11972250}, volume = {96}, year = {1989}, } @article{4080, abstract = {This paper proves that any set of n points in the plane contains two points such that any circle through those two points encloses at least n12−112+O(1)n47 points of the set. The main ingredients used in the proof of this result are edge counting formulas for k-order Voronoi diagrams and a lower bound on the minimum number of semispaces of size at most k.}, author = {Edelsbrunner, Herbert and Hasan, Nany and Seidel, Raimund and Shen, Xiao}, issn = {1572-9168}, journal = {Geometriae Dedicata}, number = {1}, pages = {1 -- 12}, publisher = {Springer}, title = {{Circles through two points that always enclose many points}}, doi = {10.1007/BF00181432}, volume = {32}, year = {1989}, } @article{4081, abstract = {This paper studies applications of envelopes of piecewise linear functions to problems in computational geometry. Among these applications we find problems involving hidden line/surface elimination, motion planning, transversals of polytopes, and a new type of Voronoi diagram for clusters of points. All results are either combinatorial or computational in nature. They are based on the combinatorial analysis in two companion papers [PS] and [E2] and a divide-and-conquer algorithm for computing envelopes described in this paper.}, author = {Edelsbrunner, Herbert and Guibas, Leonidas and Sharir, Micha}, issn = {1432-0444}, journal = {Discrete & Computational Geometry}, number = {1}, pages = {311 -- 336}, publisher = {Springer}, title = {{The upper envelope of piecewise linear functions: Algorithms and applications}}, doi = {10.1007/BF02187733}, volume = {4}, year = {1989}, } @article{4082, abstract = {Sweeping a collection of figures in the Euclidean plane with a straight line is one of the novel algorithmic paradigms that have emerged in the field of computational geometry. In this paper we demonstrate the advantages of sweeping with a topological line that is not necessarily straight. We show how an arrangement of n lines in the plane can be swept over in O(n2) time and O(n) space by a such a line. In the process each element, i.e., vertex, edge, or region, is visited once in a consistent ordering. Our technique makes use of novel data structures which exhibit interesting amortized complexity behavior; the result is an algorithm that improves upon all its predecessors either in the space or the time bounds, as well as being eminently practical. Numerous applications of the technique to problems in computational geometry are given—many through the use of duality transforms. Examples include solving visibility problems, detecting degeneracies in configurations, computing the extremal shadows of convex polytopes, and others. Even though our basic technique solves a planar problem, its applications include several problems in higher dimensions.}, author = {Edelsbrunner, Herbert and Guibas, Leonidas}, issn = {1090-2724}, journal = {Journal of Computer and System Sciences}, number = {1}, pages = {165 -- 194}, publisher = {Elsevier}, title = {{Topologically sweeping an arrangement}}, doi = {10.1016/0022-0000(89)90038-X}, volume = {38}, year = {1989}, } @article{4083, abstract = {It is shown that, given a set S of n points in $R^3 $, one can always find three planes that form an eight-partition of S, that is, a partition where at most ${n / 8}$ points of S lie in each of the eight open regions. This theorem is used to define a data structure, called an octant tree, for representing any point set in $R^3 $. An octant tree for n points occupies $O(n)$ space and can be constructed in polynomial time. With this data structure and its refinements, efficient solutions to various range query problems in two and three dimensions can be obtained, including (1) half-space queries: find all points of S that lie to one side of any given plane; (2) polyhedron queries: find all points that lie inside (outside) any given polyhedron; and (3) circle queries in $R^2 $: for a planar set S, find all points that lie inside (outside) any given circle. The retrieval time for all these queries is $T(n) = O(n^\alpha + m)$, where $\alpha = 0.8988$ (or 0.8471 in case (3)), and m is the size of the output. This performance is the best currently known for linear-space data structures that can be deterministically constructed in polynomial time.}, author = {Yao, F. and Dobkin, David and Edelsbrunner, Herbert and Paterson, Michael}, issn = {1095-7111}, journal = {SIAM Journal on Computing}, number = {2}, pages = {371 -- 384}, publisher = {SIAM}, title = {{Partitioning space for range queries}}, doi = {10.1137/0218025}, volume = {18}, year = {1989}, } @article{4084, abstract = {A tour of a finite set P of points is a necklace-tour if there are disks with the points in P as centers such that two disks intersect if and only if their centers are adjacent in . It has been observed by Sanders that a necklace-tour is an optimal traveling salesman tour. In this paper, we present an algorithm that either reports that no necklace-tour exists or outputs a necklace-tour of a given set of n points in O(n2 log n) time. If a tour is given, then we can test in O(n2) time whether or not this tour is a necklace-tour. Both algorithms can be generalized to ƒ-factors of point sets in the plane. The complexity results rely on a combinatorial analysis of certain intersection graphs of disks defined for finite sets of points in the plane.}, author = {Edelsbrunner, Herbert and Rote, Günter and Welzl, Emo}, issn = {1879-2294}, journal = {Theoretical Computer Science}, number = {2}, pages = {157 -- 180}, publisher = {Elsevier}, title = {{Testing the necklace condition for shortest tours and optimal factors in the plane}}, doi = {10.1016/0304-3975(89)90133-3}, volume = {66}, year = {1989}, } @inproceedings{4085, abstract = {Let C be a cell complex in d-dimensional Euclidean space whose faces are obtained by orthogonal projection of the faces of a convex polytope in d + 1 dimensions. For example, the Delaunay triangulation of a finite point set is such a cell complex. This paper shows that the in_front/behind relation defined for the faces of C with respect to any fixed viewpoint x is acyclic. This result has applications to hidden line/surface removal and other problems in computational geometry.}, author = {Edelsbrunner, Herbert}, booktitle = {Proceedings of the 5th annual symposium on Computational geometry}, isbn = {978-0-89791-318-8}, location = {Saarbruchen, Germany}, pages = {145 -- 151}, publisher = {ACM}, title = {{An acyclicity theorem for cell complexes in d dimension}}, doi = {10.1145/73833.73850}, year = {1989}, } @article{4086, abstract = {This note proves that the maximum number of faces (of any dimension) of the upper envelope of a set ofn possibly intersectingd-simplices ind+1 dimensions is (n d (n)). This is an extension of a result of Pach and Sharir [PS] who prove the same bound for the number ofd-dimensional faces of the upper envelope.}, author = {Edelsbrunner, Herbert}, issn = {1432-0444}, journal = {Discrete & Computational Geometry}, number = {4}, pages = {337 -- 343}, publisher = {Springer}, title = {{The upper envelope of piecewise linear functions: Tight bounds on the number of faces }}, doi = {10.1007/BF02187734}, volume = {4}, year = {1989}, } @inproceedings{4087, abstract = {This paper offers combinatorial results on extremum problems concerning the number of tetrahedra in a tetrahedrization of n points in general position in three dimensions, i.e. such that no four points are coplanar. It also presents an algorithm that in O(nlog n) time constructs a tetrahedrization of a set of n points consisting of at most 3n–11 tetrahedra.}, author = {Edelsbrunner, Herbert and Preparata, Franco and West, Douglas}, booktitle = { International Symposium on Symbolic and Algebraic Computation}, location = {Rome, Italy}, pages = {315 -- 331}, publisher = {Springer}, title = {{Tetrahedrizing point sets in three dimensions}}, doi = {10.1007/3-540-51084-2_31}, volume = {358}, year = {1989}, } @article{4088, abstract = {Anarrangement ofn lines (or line segments) in the plane is the partition of the plane defined by these objects. Such an arrangement consists ofO(n 2) regions, calledfaces. In this paper we study the problem of calculating and storing arrangementsimplicitly, using subquadratic space and preprocessing, so that, given any query pointp, we can calculate efficiently the face containingp. First, we consider the case of lines and show that with (n) space1 and (n 3/2) preprocessing time, we can answer face queries in (n)+O(K) time, whereK is the output size. (The query time is achieved with high probability.) In the process, we solve three interesting subproblems: (1) given a set ofn points, find a straight-edge spanning tree of these points such that any line intersects only a few edges of the tree, (2) given a simple polygonal path , form a data structure from which we can find the convex hull of any subpath of quickly, and (3) given a set of points, organize them so that the convex hull of their subset lying above a query line can be found quickly. Second, using random sampling, we give a tradeoff between increasing space and decreasing query time. Third, we extend our structure to report faces in an arrangement of line segments in (n 1/3)+O(K) time, given(n 4/3) space and (n 5/3) preprocessing time. Lastly, we note that our techniques allow us to computem faces in an arrangement ofn lines in time (m 2/3 n 2/3+n), which is nearly optimal.}, author = {Edelsbrunner, Herbert and Guibas, Leonidas and Hershberger, John and Seidel, Raimund and Sharir, Micha and Snoeyink, Jack and Welzl, Emo}, issn = {1432-0444}, journal = {Discrete & Computational Geometry}, number = {1}, pages = {433 -- 466}, publisher = {Springer}, title = {{Implicitly representing arrangements of lines or segments}}, doi = {10.1007/BF02187742}, volume = {4}, year = {1989}, } @article{4089, abstract = {Motivated by a number of motion-planning questions, we investigate in this paper some general topological and combinatorial properties of the boundary of the union ofn regions bounded by Jordan curves in the plane. We show that, under some fairly weak conditions, a simply connected surface can be constructed that exactly covers this union and whose boundary has combinatorial complexity that is nearly linear, even though the covered region can have quadratic complexity. In the case where our regions are delimited by Jordan acrs in the upper halfplane starting and ending on thex-axis such that any pair of arcs intersect in at most three points, we prove that the total number of subarcs that appear on the boundary of the union is only (n(n)), where(n) is the extremely slowly growing functional inverse of Ackermann's function.}, author = {Edelsbrunner, Herbert and Guibas, Leonidas and Hershberger, John and Pach, János and Pollack, Richard and Seidel, Raimund and Sharir, Micha and Snoeyink, Jack}, issn = {1432-0444}, journal = {Discrete & Computational Geometry}, number = {1}, pages = {523 -- 539}, publisher = {Springer}, title = {{On arrangements of Jordan arcs with three intersections per pair}}, doi = {10.1007/BF02187745}, volume = {4}, year = {1989}, } @inproceedings{4092, author = {Chazelle, Bernard and Edelsbrunner, Herbert and Guibas, Leonidas and Sharir, Micha}, booktitle = {16th International Colloquium on Automata, Languages, and Programming}, location = {Stresa, Italy}, pages = {179 -- 193}, publisher = {Springer}, title = {{A singly exponential stratification scheme for real semi-algebraic varieties and its applications}}, doi = {10.1007/BFb0035760}, volume = {372}, year = {1989}, } @article{4093, abstract = {This paper investigates the combinatorial and computational aspects of certain extremal geometric problems in two and three dimensions. Specifically, we examine the problem of intersecting a convex subdivision with a line in order to maximize the number of intersections. A similar problem is to maximize the number of intersected facets in a cross-section of a three-dimensional convex polytope. Related problems concern maximum chains in certain families of posets defined over the regions of a convex subdivision. In most cases we are able to prove sharp bounds on the asymptotic behavior of the corresponding extremal functions. We also describe polynomial algorithms for all the problems discussed.}, author = {Chazelle, Bernard and Edelsbrunner, Herbert and Guibas, Leonidas}, issn = {1432-0444}, journal = {Discrete & Computational Geometry}, number = {1}, pages = {139 -- 181}, publisher = {Springer}, title = {{The complexity of cutting complexes}}, doi = {10.1007/BF02187720}, volume = {4}, year = {1989}, } @article{4309, abstract = {Three methods for estimating the average level of gene flow in natural population are discussed and compared. The three methods are FST, rare alleles, and maximum likelihood. All three methods yield estimates of the combination of parameters (the number of migrants [Nm] in a demic model or the neighborhood size [4πDσ2] in a continuum model) that determines the relative importance of gene flow and genetic drift. We review the theory underlying these methods and derive new analytic results for the expectation of FST in stepping-stone and continuum models when small sets of samples are taken. We also compare the effectiveness of the different methods using a variety of simulated data. We found that the FST and rare-alleles methods yield comparable estimates under a wide variety of conditions when the population being sampled is demographically stable. They are roughly equally sensitive to selection and to variation in population structure, and they approach their equilibrium values at approximately the same rate. We found that two different maximum-likelihood methods tend to yield biased estimates when relatively small numbers of locations are sampled but more accurate estimates when larger numbers are sampled. Our conclusion is that, although FST and rare-alleles methods are expected to be equally effective in analyzing ideal data, practical problems in estimating the frequencies of rare alleles in electrophoretic studies suggest that FST is likely to be more useful under realistic conditions.}, author = {Slatkin, Montgomery and Barton, Nicholas H}, issn = {1558-5646}, journal = {Evolution; International Journal of Organic Evolution}, number = {7}, pages = {1349 -- 1368}, publisher = {Wiley-Blackwell}, title = {{A comparison of three methods for estimating average levels of gene flow}}, doi = {10.1111/j.1558-5646.1989.tb02587.x }, volume = {43}, year = {1989}, } @article{4312, author = {Barton, Nicholas H and Turelli, Michael}, issn = {1545-2948}, journal = {Annual Review of Genetics}, pages = {337 -- 370}, publisher = {Annual Reviews}, title = {{Evolutionary quantitative genetics: how little do we know?}}, doi = {10.1146/annurev.ge.23.120189.002005}, volume = {23}, year = {1989}, } @inbook{4313, author = {Barton, Nicholas H}, booktitle = {Speciation and its consequences}, editor = {Otte, Daniel and Endler, John}, isbn = {‎ 978-0878936571}, publisher = {Sinauer Press}, title = {{Founder effect speciation}}, year = {1989}, } @article{4314, abstract = {Polygenic variation can be maintained by a balance between mutation and stabilizing selection. When the alleles responsible for variation are rare, many classes of equilibria may be stable. The rate at which drift causes shifts between equilibria is investigated by integrating the gene frequency distribution W2N II (pq)4N mu-1. This integral can be found exactly, by numerical integration, or can be approximated by assuming that the full distribution of allele frequencies is approximately Gaussian. These methods are checked against simulations. Over a wide range of population sizes, drift will keep the population near an equilibrium which minimizes the genetic variance and the deviation from the selective optimum. Shifts between equilibria in this class occur at an appreciable rate if the product of population size and selection on each locus is small (Ns alpha 2 less than 10). The Gaussian approximation is accurate even when the underlying distribution is strongly skewed. Reproductive isolation evolves as populations shift to new combinations of alleles: however, this process is slow, approaching the neutral rate (approximately mu) in small populations.}, author = {Barton, Nicholas H}, issn = {1469-5073}, journal = {Genetical Research}, number = {1}, pages = {59 -- 78}, publisher = {Cambridge University Press}, title = {{The divergence of a polygenic system under stabilising selection, mutation and drift}}, doi = {10.1017/S0016672300028378}, volume = {54}, year = {1989}, } @article{1941, author = {Sazanov, Leonid A and Karavaev, V A and Kukushkin, A K}, issn = {1990-7923}, journal = {Russian Journal of Physical Chemistry B}, pages = {3351 -- 3354}, publisher = {Elsevier}, title = {{Mathematical model of photosynthesis regulation accounts for the effects of changes in external conditions and observed oscillations}}, volume = {52}, year = {1988}, } @article{2522, abstract = {Non-pyramidal neurons in cat Ammon's horn were shown to send their axons to the supramammillary regions (SMR), i.e. the supramammillary nucleus and its vicinities including the supramammillary nucleus and the lateral, posterior and dorsal hypothalamic areas: wheat germ agglutinin-horseradish peroxidase (WGA-HRP) injection into Ammon's horn resulted in labeling of presumed axon terminals in the SMR; and after injecting HRP into the SMR, retrogradely labeled non-pyramidal neurons were seen in Ammon's horn.}, author = {Ino, Tadashi and Itoh, Kazuo and Kamiya, Hiroto and Shigemoto, Ryuichi and Akiguchi, Ichiro and Mizuno, Noboru}, issn = {1872-6240}, journal = {Brain Research}, number = {1}, pages = {173 -- 177}, publisher = {Elsevier}, title = {{Direct projections of non-pyramidal neurons of Ammon's horn to the supramammillary region in the cat}}, doi = {10.1016/0006-8993(88)91219-X}, volume = {460}, year = {1988}, } @article{2523, abstract = {Injection of large amounts of a mixture of horseradish peroxidase and wheat germ agglutinin-horseradish peroxidase conjugate into the upper cervical segments of the spinal cord in the Japanese monkey (Macaca fuscata) led to the retrograde labeling of a small number of neuronal cell bodies within the rostral part of the subthalamic nucleus of Luys. Direct projection from the subthalamic nucleus to the spinal cord appeared to be much less prominent in the Japanese monkey than in the cat and rat.}, author = {Mizuno, Noboru and Ueyama, Teizo and Itoh, Kazuo and Satoda, Takahiro and Tashiro, Takashi and Shigemoto, Ryuichi}, issn = {1872-7972}, journal = {Neuroscience Letters}, number = {1}, pages = {13 -- 18}, publisher = {Elsevier}, title = {{Direct projections from the subthalamic nucleus of Luys to the spinal cord in the Japanese monkey}}, doi = {10.1016/0304-3940(88)90473-9}, volume = {89}, year = {1988}, }