@article{3465, abstract = {Asymmetrical displacement currents and Na currents of single myelinated nerve fibers of Xenopus laevis were studied in the temperature range from 5 to 24 degrees C. The time constant of the on-response at E = 4 mV, tau on, was strongly temperature dependent, whereas the amount of displaced charge at E = 39 mV, Qon, was only slightly temperature dependent. The mean Q10 for tau on-1 was 2.54, the mean Q10 for Qon was 1.07. The time constant of charge immobilization, tau i, at E = 4 mV varied significantly (alpha = 0.001) with temperature. The mean Q10 for tau i-1 was 2.71 +/- 0.38. The time constants of immobilization of gating charge and of fast inactivation of Na permeability were similar in the temperature range from 6 to 22 degrees C. The Qoff/Qon ratio for E = 4 mV pulses of 0.5 msec duration decreased with increasing temperature. The temperature dependence of the time constant of the off-response could not be described by a single Q10 value, since the Q10 depended on the duration of the test pulse. Increasing temperature shifted Qon (E) curves to more negative potentials by 0.51 mV K-1, but shifted PNa (E) curves and h infinity (E) curves to more positive potentials by 0.43 and 0.57 mV K-1, respectively. h infinity (E = -70 mV) increased monotonously with increasing temperature. The present data indicate that considerable entropy changes may occur when the Na channel molecule passes from closed through open to inactivated states.}, author = {Jonas, Peter M}, issn = {1432-1424}, journal = {Journal of Membrane Biology}, number = {3}, pages = {277 -- 289}, publisher = {Springer}, title = {{Temperature dependence of gating current in myelinated nerve fibers}}, doi = {10.1007/BF01870958}, volume = {112}, year = {1989}, } @article{4091, abstract = {An X-ray probe through a polygon measures the length of intersection between a line and the polygon. This paper considers the properties of various classes of X-ray probes, and shows how they interact to give finite strategies for completely describing convex n-gons. It is shown that (3n/2)+6 probes are sufficient to verify a specified n-gon, while for determining convex polygons (3n-1)/2 X-ray probes are necesssary and 5n+O(1) sufficient, with 3n+O(1) sufficient given that a lower bound on the size of the smallest edge of P is known.}, author = {Edelsbrunner, Herbert and Skiena, Steven}, issn = {1095-7111}, journal = {SIAM Journal on Computing}, number = {5}, pages = {870 -- 882}, publisher = {SIAM}, title = {{Probing convex polygons with X-Rays}}, doi = {10.1137/0217054 }, volume = {17}, year = {1988}, } @inbook{4317, author = {Barton, Nicholas H}, booktitle = {Analytical biogeography: An integrated approach to the study of animal and plant distributions}, editor = {Myers, Alan and Giller, Paul}, isbn = {978-0-412-40050-6}, issn = {978-94-009-0435-4}, keywords = {biogeography, biology, complexity, distribution, evolution, geology}, pages = {185 -- 218}, publisher = {Springer}, title = {{Speciation}}, doi = {10.1007/978-94-009-0435-4}, year = {1988}, } @article{4098, abstract = {To points p and q of a finite set S in d-dimensional Euclidean space Ed are extreme if {p, q} = S ∩ h, for some open halfspace h. Let e2(d)(n) be the maximum number of extreme pairs realized by any n points in Ed. We give geometric proofs of , if n⩾4, and e2(3)(n) = 3n−6, if n⩾6. These results settle the question since all other cases are trivial.}, author = {Edelsbrunner, Herbert and Stöckl, Gerd}, issn = {1096-0899}, journal = {Journal of Combinatorial Theory Series A}, number = {2}, pages = {344 -- 349}, publisher = {Elsevier}, title = {{The number of extreme pairs of finite point-sets in Euclidean spaces}}, doi = {10.1016/0097-3165(86)90075-0}, volume = {43}, year = {1986}, } @article{4103, abstract = {Let A be an arrangement of n lines in the plane. Suppose F1,…, Fk are faces in the dissection induced by A and that Fi is a t(Fi)-gon. We give asymptotic bounds on the maximal sum ∑i=1kt(Fi) which can be realized by k different faces in an arrangement of n lines. The results improve known bounds for k of higher order than n(1/2).}, author = {Edelsbrunner, Herbert and Welzl, Emo}, issn = {1096-0899}, journal = {Journal of Combinatorial Theory Series A}, number = {2}, pages = {159 -- 166}, publisher = {Elsevier}, title = {{On the maximal number of edges of many faces in an arrangement}}, doi = {10.1016/0097-3165(86)90078-6}, volume = {41}, year = {1986}, } @article{4104, abstract = {Point location, often known in graphics as “hit detection,” is one of the fundamental problems of computational geometry. In a point location query we want to identify which of a given collection of geometric objects contains a particular point. Let $\mathcal{S}$ denote a subdivision of the Euclidean plane into monotone regions by a straight-line graph of $m$ edges. In this paper we exhibit a substantial refinement of the technique of Lee and Preparata [SIAM J. Comput., 6 (1977), pp. 594–606] for locating a point in $\mathcal{S}$ based on separating chains. The new data structure, called a layered dag, can be built in $O(m)$ time, uses $O(m)$ storage, and makes possible point location in $O(\log m)$ time. Unlike previous structures that attain these optimal bounds, the layered dag can be implemented in a simple and practical way, and is extensible to subdivisions with edges more general than straight-line segments. © 1986 Society for Industrial and Applied Mathematics}, author = {Edelsbrunner, Herbert and Guibas, Leonidas and Stolfi, Jorge}, issn = {1095-7111}, journal = {SIAM Journal on Computing}, number = {2}, pages = {317 -- 340}, publisher = {SIAM}, title = {{Optimal point location in a monotone subdivision}}, doi = {10.1137/0215023}, volume = {15}, year = {1986}, } @article{4112, abstract = {The batched static version of a searching problem asks for performing a given set of queries on a given set of objects. All queries are known in advance. The batched dynamic version of a searching problem is the following: given a sequence of insertions, deletions, and queries, perform them on an initially empty set. We will develop methods for solving batched static and batched dynamic versions of searching problems which are in particular applicable to decomposable searching problems. The techniques show that batched static (dynamic) versions of searching problems can often be solved more efficiently than by using known static (dynamic) data structures. In particular, a technique called “streaming” is described that reduces the space requirements considerably. The methods have also a number of applications on set problems. E.g., the k intersecting pairs in a set of n axis-parallel hyper-rectangles in d dimensions can be reported in O (nlogd−1n + k) time using only O(n) space.}, author = {Edelsbrunner, Herbert and Overmars, Mark}, issn = {1090-2678}, journal = {Journal of Algorithms}, number = {4}, pages = {515 -- 542}, publisher = {Elsevier}, title = {{Batched dynamic solutions to decomposable searching problems}}, doi = {10.1016/0196-6774(85)90030-6}, volume = {6}, year = {1985}, } @article{4120, abstract = {Let P be a set of n points in the Euclidean plane and let C be a convex figure. We study the problem of preprocessing P so that for any query point q, the points of P in C+q can be retrieved efficiently. If constant time sumces for deciding the inclusion of a point in C, we then demonstrate the existence of an optimal solution: the algorithm requires O(n) space and O(k + log n) time for a query with output size k. If C is a disk, the problem becomes the wellknown fixed-radius neighbour problem, to which we thus provide the first known optimal solution.}, author = {Chazelle, Bernard and Edelsbrunner, Herbert}, issn = {1095-855X}, journal = {Journal of Symbolic Computation}, number = {1}, pages = {47 -- 56}, publisher = {Elsevier}, title = {{Optimal solutions for a class of point retrieval problems}}, doi = {10.1016/S0747-7171(85)80028-6}, volume = {1}, year = {1985}, } @inproceedings{3513, author = {Dobkin, David and Edelsbrunner, Herbert}, booktitle = {9th International Workshop on Graph Theoretic Concepts in Computer Science}, isbn = {3-853-20311-6}, location = {Haus Ohrbeck, Germany}, pages = {88 -- 99}, publisher = {Teubner}, title = {{Ham-sandwich theorems applied to intersection problems}}, year = {1984}, } @inbook{3563, abstract = {Usually in computer graphics, a two-dimensional view of a set of three-dimensional objects is considered. In this article we reduce the dimensionality by one in each case. In other words we study what, for obvious reasons, we call Flatland graphics. This forms the beginning of a mathematical investigation of computer graphics and, at the same time, provides uniform solutions for a number of computational geometry problems. In particular we study the maintenance of a view during insertion and deletion of objects and the "frame-to-frame" coherence while walking around a set of objects. Both parallel and perspective projections are considered. Our major concern is convex objects that are simple—in a sense, made precise in this article. However, we will close this article by discussing some possible extensions to nonconvex objects and/or to higher dimensions. The investigation also serves to demonstrate a number of tools that have been developed recently in the context of computational geometry. For example. dynamization and searching. }, author = {Edelsbrunner, Herbert and Overmars, Mark and Wood, Derick}, booktitle = {Computational Geometry: Theory and Applications}, editor = {Preparata, Franco}, isbn = {0-89232-356-6}, pages = {35 -- 59}, publisher = {Elsevier}, title = {{Graphics in Flatland: a case study}}, volume = {1}, year = {1983}, } @misc{4329, author = {Barton, Nicholas H}, booktitle = {Animal Behaviour}, issn = {1095-8282}, number = {2}, pages = {626 -- 627}, publisher = {Elsevier}, title = {{The extended phenotype: the gene as the unit of selection (review of Dawkins R 1982)}}, doi = {10.1016/S0003-3472(83)80100-6}, volume = {31}, year = {1983}, } @inbook{4332, author = {Barton, Nicholas H and Hewitt, Godfrey}, booktitle = {Evolution and Speciation}, editor = {Atchley, William and Woodruff, David}, isbn = {9-780-5212-3823-6}, pages = {109 -- 145}, publisher = {Cambridge University Press}, title = {{Hybrid zones and speciation}}, year = {1981}, }