TY - JOUR
AB - Given a set of data points pi = (xi, yi ) for 1 ≤ i ≤ n, the least median of squares regression line is a line y = ax + b for which the median of the squared residuals is a minimum over all choices of a and b. An algorithm is described that computes such a line in O(n 2) time and O(n) memory space, thus improving previous upper bounds on the problem. This algorithm is an application of a general method built on top of the topological sweep of line arrangements.
AU - Herbert Edelsbrunner
AU - Souvaine, Diane L
ID - 4064
IS - 409
JF - Journal of the American Statistical Association
TI - Computing least median of squares regression lines and guided topological sweep
VL - 85
ER -
TY - JOUR
AB - We prove that given n⩾3 convex, compact, and pairwise disjoint sets in the plane, they may be covered with n non-overlapping convex polygons with a total of not more than 6n−9 sides, and with not more than 3n−6 distinct slopes. Furthermore, we construct sets that require 6n−9 sides and 3n−6 slopes for n⩾3. The upper bound on the number of slopes implies a new bound on a recently studied transversal problem.
AU - Herbert Edelsbrunner
AU - Robison, Arch D
AU - Shen, Xiao-Jun
ID - 4065
IS - 2
JF - Discrete Mathematics
TI - Covering convex sets with non-overlapping polygons
VL - 81
ER -
TY - JOUR
AB - We consider several problems involving points and planes in three dimensions. Our main results are: (i) The maximum number of faces boundingm distinct cells in an arrangement ofn planes isO(m 2/3 n logn +n 2); we can calculatem such cells specified by a point in each, in worst-case timeO(m 2/3 n log3 n+n 2 logn). (ii) The maximum number of incidences betweenn planes andm vertices of their arrangement isO(m 2/3 n logn+n 2), but this number is onlyO(m 3/5– n 4/5+2 +m+n logm), for any>0, for any collection of points no three of which are collinear. (iii) For an arbitrary collection ofm points, we can calculate the number of incidences between them andn planes by a randomized algorithm whose expected time complexity isO((m 3/4– n 3/4+3 +m) log2 n+n logn logm) for any>0. (iv) Givenm points andn planes, we can find the plane lying immediately below each point in randomized expected timeO([m 3/4– n 3/4+3 +m] log2 n+n logn logm) for any>0. (v) The maximum number of facets (i.e., (d–1)-dimensional faces) boundingm distinct cells in an arrangement ofn hyperplanes ind dimensions,d>3, isO(m 2/3 n d/3 logn+n d–1). This is also an upper bound for the number of incidences betweenn hyperplanes ind dimensions andm vertices of their arrangement. The combinatorial bounds in (i) and (v) and the general bound in (ii) are almost tight.
AU - Herbert Edelsbrunner
AU - Guibas, Leonidas
AU - Sharir, Micha
ID - 4066
IS - 1
JF - Discrete & Computational Geometry
TI - The complexity of many cells in arrangements of planes and related problems
VL - 5
ER -
TY - CONF
AB - This paper proves an O(m 2/3 n 2/3+m+n) upper bound on the number of incidences between m points and n hyperplanes in four dimensions, assuming all points lie on one side of each hyperplane and the points and hyperplanes satisfy certain natural general position conditions. This result has application to various three-dimensional combinatorial distance problems. For example, it implies the same upper bound for the number of bichromatic minimum distance pairs in a set of m blue and n red points in three-dimensional space. This improves the best previous bound for this problem.
AU - Herbert Edelsbrunner
AU - Sharir, Micha
ID - 4067
TI - A hyperplane Incidence problem with applications to counting distances
VL - 450
ER -
TY - JOUR
AB - LetS be a collection ofn convex, closed, and pairwise nonintersecting sets in the Euclidean plane labeled from 1 ton. A pair of permutations
(i1i2in−1in)(inin−1i2i1)
is called ageometric permutation of S if there is a line that intersects all sets ofS in this order. We prove thatS can realize at most 2n–2 geometric permutations. This upper bound is tight.
AU - Herbert Edelsbrunner
AU - Sharir, Micha
ID - 4068
IS - 1
JF - Discrete & Computational Geometry
TI - The maximum number of ways to stabn convex nonintersecting sets in the plane is 2n−2
VL - 5
ER -
TY - JOUR
AB - 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.
AU - Herbert Edelsbrunner
ID - 4069
IS - 3
JF - Combinatorica
TI - An acyclicity theorem for cell complexes in d dimension
VL - 10
ER -
TY - JOUR
AB - Let S be a set of n closed intervals on the x-axis. A ranking assigns to each interval, s, a distinct rank, p(s) [1, 2,…,n]. We say that s can see t if p(s)<p(t) and there is a point ps∩t so that pu for all u with p(s)<p(u)<p(t). It is shown that a ranking can be found in time O(n log n) such that each interval sees at most three other intervals. It is also shown that a ranking that minimizes the average number of endpoints visible from an interval can be computed in time O(n 5/2). The results have applications to intersection problems for intervals, as well as to channel routing problems which arise in layouts of VLSI circuits.
AU - Herbert Edelsbrunner
AU - Overmars, Mark H
AU - Welzl, Emo
AU - Hartman, Irith Ben-Arroyo
AU - Feldman,Jack A
ID - 4070
IS - 3-4
JF - International Journal of Computer Mathematics
TI - Ranking intervals under visibility constraints
VL - 34
ER -
TY - CONF
AB - We show that a triangulation of a set of n points in the plane that minimizes the maximum angle can be computed in time O(n2 log n) and space O(n). In the same amount of time and space we can also handle the constrained case where edges are prescribed. The algorithm iteratively improves an arbitrary initial triangulation and is fairly easy to implement.
AU - Herbert Edelsbrunner
AU - Tan, Tiow Seng
AU - Waupotitsch, Roman
ID - 4071
TI - An O(n^2log n) time algorithm for the MinMax angle triangulation
ER -
TY - JOUR
AB - We show that the total number of edges ofm faces of an arrangement ofn lines in the plane isO(m 2/3– n 2/3+2 +n) for any>0. The proof takes an algorithmic approach, that is, we describe an algorithm for the calculation of thesem faces and derive the upper bound from the analysis of the algorithm. The algorithm uses randomization and its expected time complexity isO(m 2/3– n 2/3+2 logn+n logn logm). If instead of lines we have an arrangement ofn line segments, then the maximum number of edges ofm faces isO(m 2/3– n 2/3+2 +n (n) logm) for any>0, where(n) is the functional inverse of Ackermann's function. We give a (randomized) algorithm that produces these faces and takes expected timeO(m 2/3– n 2/3+2 log+n(n) log2 n logm).
AU - Herbert Edelsbrunner
AU - Guibas, Leonidas J
AU - Sharir, Micha
ID - 4072
IS - 1
JF - Discrete & Computational Geometry
TI - The complexity and construction of many faces in arrangements of lines and of segments
VL - 5
ER -
TY - CONF
AB - A number of rendering algorithms in computer graphics sort three-dimensional objects by depth and assume that there is no cycle that makes the sorting impossible. One way to resolve the problem caused by cycles is to cut the objects into smaller pieces. The problem of estimating how many such cuts are always sufficient is addressed. A few related algorithmic and combinatorial geometry problems are considered
AU - Chazelle, Bernard
AU - Herbert Edelsbrunner
AU - Guibas, Leonidas J
AU - Pollack, Richard
AU - Seidel, Raimund
AU - Sharir, Micha
AU - Snoeyink, Jack
ID - 4073
TI - Counting and cutting cycles of lines and rods in space
ER -
TY - JOUR
AU - Clarkson, Kenneth L
AU - Herbert Edelsbrunner
AU - Guibas, Leonidas J
AU - Sharir, Micha
AU - Welzl, Emo
ID - 4074
IS - 1
JF - Discrete & Computational Geometry
TI - Combinatorial complexity bounds for arrangements of curves and spheres
VL - 5
ER -
TY - JOUR
AB - A key problem in computational geometry is the identification of subsets of a point set having particular properties. We study this problem for the properties of convexity and emptiness. We show that finding empty triangles is related to the problem of determining pairs of vertices that see each other in a star-shaped polygon. A linear-time algorithm for this problem which is of independent interest yields an optimal algorithm for finding all empty triangles. This result is then extended to an algorithm for finding empty convex r-gons (r> 3) and for determining a largest empty convex subset. Finally, extensions to higher dimensions are mentioned.
AU - Dobkin, David P
AU - Herbert Edelsbrunner
AU - Overmars, Mark H
ID - 4075
IS - 4
JF - Algorithmica
TI - Searching for empty convex polygons
VL - 5
ER -
TY - CONF
AB - We present an algorithm to compute a Euclidean minimum spanning tree of a given set S of n points in Ed in time O(Td(N, N) logd N), where Td(n, m) is the time required to compute a bichromatic closest pair among n red and m blue points in Ed. If Td(N, N) = Ω(N1+ε), for some fixed ε > 0, then the running time improves to O(Td(N, N)). Furthermore, we describe a randomized algorithm to compute a bichromatic closets pair in expected time O((nm log n log m)2/3+m log2 n + n log2 m) in E3, which yields an O(N4/3log4/3 N) expected time algorithm for computing a Euclidean minimum spanning tree of N points in E3.
AU - Agarwal, Pankaj K
AU - Herbert Edelsbrunner
AU - Schwarzkopf, Otfried
AU - Welzl, Emo
ID - 4076
TI - Euclidean minimum spanning trees and bichromatic closest pairs
ER -
TY - CONF
AB - We prove that for any set S of n points in the plane and n3-α triangles spanned by the points of S there exists a point (not necessarily of S) contained in at least n3-3α/(512 log25 n) of the triangles. This implies that any set of n points in three - dimensional space defines at most 6.4n8/3 log5/3 n halving planes.
AU - Aronov, Boris
AU - Chazelle, Bernard
AU - Herbert Edelsbrunner
AU - Guibas, Leonidas J
AU - Sharir, Micha
AU - Wenger, Rephael
ID - 4077
TI - Points and triangles in the plane and halving planes in space
ER -
TY - CONF
AB - In this paper we derived combinatorial point selection results for geometric objects defined by pairs of points. In a nutshell, the results say that if many pairs of a set of n points in some fixed dimension each define a geometric object of some type, then there is a point covered by many of these objects. Based on such a result for three-dimensional spheres we show that the combinatorial size of the Delaunay triangulation of a point set in space can be reduced by adding new points. We believe that from a practical point of view this is the most important result of this paper.
AU - Chazelle, Bernard
AU - Herbert Edelsbrunner
AU - Guibas, Leonidas J
AU - Hershberger, John E
AU - Seidel, Raimund
AU - Sharir, Micha
ID - 4078
TI - Slimming down by adding; selecting heavily covered points
ER -
TY - GEN
AU - Nicholas Barton
AU - Jones, Steve
ID - 4310
T2 - Nature
TI - The language of the genes
VL - 346
ER -
TY - CHAP
AU - Nicholas Barton
AU - Clark,A.
ED - Wöhrmann, Klaus
ED - Jain, Subodh K
ID - 4311
T2 - Population biology: ecological and evolutionary viewpoints
TI - Population structure
ER -
TY - CONF
AB - The interleaving model is both adequate and sufficiently abstract to allow for the practical specification and verification of many properties of concurrent systems. We incorporate real time into this model by defining the abstract notion of a real-time transition system as a conservative extension of traditional transition systems: qualitative fairness requirements are replaced (and superseded) by quantitative lower-bound and upper-bound real-time requirements for transitions.
We present proof rules to establish lower and upper real-time bounds for response properties of real-time transition systems. This proof system can be used to verify bounded-invariance and bounded-response properties, such as timely termination of shared-variables multi-process systems, whose semantics is defined in terms of real-time transition systems.
AU - Thomas Henzinger
AU - Manna, Zohar
AU - Pnueli,Amir
ID - 4510
TI - An interleaving model for real time
ER -
TY - CONF
AU - Thomas Henzinger
ID - 4522
TI - Half-order modal logic: How to prove real-time properties
ER -
TY - CONF
AB - A unifying framework for the study of real-time logics is developed. In analogy to the untimed case, the underlying classical theory of timed state sequences is identified, it is shown to be nonelementarily decidable, and its complexity and expressiveness are used as a point of reference. Two orthogonal extensions of PTL (timed propositional temporal logic and metric temporal logic) that inherit its appeal are defined: they capture elementary, yet expressively complete, fragments of the theory of timed state sequences, and thus are excellent candidates for practical real-time specification languages
AU - Alur, Rajeev
AU - Thomas Henzinger
ID - 4597
TI - Real-time logics: Complexity and expressiveness
ER -
TY - JOUR
AB - The effects of mast cell degranulating peptide (MCDP), a toxin from the honey bee, and of dendrotoxin (DTX), a toxin from the green mamba snake, were studied in voltage-clamped experiments with myelinated nerve fibres of Xenopus. MCDP and DTX blocked part of the K+ current. About 20% of the K+ current, however, was resistant to the toxins even in high concentrations. In Ringer solution half-maximal block was reached with concentrations of 33 nM MCDP and 11 nM DTX. In high-K+ solution the potency of both toxins was lower. β-Bungarotoxin (β-BuTX), another snake toxin, also blocked part of the K+ current, but was less potent than MCDP and DTX. Tail currents in high-K+ solution were analysed and three K+ current components were separated according to Dubois (1981b). Both MCDP and DTX selectively blocked a fast deactivating, slowly inactivating K+ current component which steeply activates between E = -60 mV and E = -40 mV (component f1). In concentrations around 100 nM, MCDP and DTX blocked neither the slow K+ current (component s) nor the fast deactivating, rapidly inactivating K+ current which activates between E = -40 mV and E = 20 mV (component f2). Similar results could be derived from K+ outward currents in Ringer solution. In high-K+, IC50 of MCDP for component f1 was 99 nM, whereas it was 7.6 μM for f2. Corresponding values for DTX are 68 nM and 1.8 μM. Binding studies with nerve fibre membranes of Xenopus reveal high-affinity binding sites for 125I-labelled DTX )K(D) = 22 pM in Ringer solution and 81 pM in high-K+ solution). 125I-labelled DTX can be displaced from its sites completely by unlabelled DTX, toxin I (black mamba toxin), MCDP, and partially by β-BuTX. Immunocytochemical staining demonstrates that binding sites for DTX are present in nodal and paranodal regions of the axonal membrane. The axonal membrane of motor and sensory nerve fibres is equipped with three types of well-characterized K+ channels and constitutes so far the best preparation to study MCDP- and DTX-sensitive K+ channels with electrophysiological and biochemical methods.
AU - Bräu, Michael E
AU - Dreyer, Florian W
AU - Peter Jonas
AU - Repp, Holger
AU - Vogel, Werner
ID - 3467
JF - Journal of Physiology
TI - A K+ channel in Xenopus nerve fibres selectively blocked by bee and snake toxins: binding and voltage-clamp experiments
VL - 420
ER -
TY - CHAP
AU - Dobkin, David P
AU - Herbert Edelsbrunner
AU - Yap, Chee K
ED - Cox, Ingemar J
ED - Wilfong, Gordon T
ID - 3565
T2 - Autonomous Robot Vehicles
TI - Probing convex polytopes
ER -
TY - JOUR
AB - Selection on polygenic characters is generally analyzed by statistical methods that assume a Gaussian (normal) distribution of breeding values. We present an alternative analysis based on multilocus population genetics. We use a general representation of selection, recombination, and drift to analyze an idealized polygenic system in which all genetic effects are additive (i.e., both dominance and epistasis are absent), but no assumptions are made about the distribution of breeding values or the numbers of loci or alleles. Our analysis produces three results. First, our equations reproduce the standard recursions for the mean and additive variance if breeding values are Gaussian; but they also reveal how non-Gaussian distributions of breeding values will alter these dynamics. Second, an approximation valid for weak selection shows that even if genetic variance is attributable to an effectively infinite number of loci with only additive effects, selection will generally drive the distribution of breeding values away from a Gaussian distribution by creating multilocus linkage disequilibria. Long-term dynamics of means can depart substantially from the predictions of the standard selection recursions, but the discrepancy may often be negligible for short-term selection. Third, by including mutation, we show that, for realistic parameter values, linkage disequilibrium has little effect on the amount of additive variance maintained at an equilibrium between stabilizing selection and mutation. Each of these analytical results is supported by numerical calculations.
AU - Turelli, Michael
AU - Nicholas Barton
ID - 3649
IS - 1
JF - Theoretical Population Biology
TI - Dynamics of polygenic characters under selection
VL - 38
ER -
TY - JOUR
AB - Hybrid zones can yield estimates of natural selection and gene flow. The width of a cline in gene frequency is approximately proportional to gene flow (σ) divided by the square root of per-locus selection ( &s). Gene flow also causes gametic correlations (linkage disequilibria) between genes that differ across hybrid zones. Correlations are stronger when the hybrid zone is narrow, and rise to a maximum roughly equal to s. Thus cline width and gametic correlations combine to give estimates of gene flow and selection. These indirect measures of σ and s are especially useful because they can be made from collections, and require no field experiments. The method was applied to hybrid zones between color pattern races in a pair of Peruvian Heliconius butterfly species. The species are Mullerian mimics of one another, and both show the same changes in warning color pattern across their respective hybrid zones. The expectations of cline width and gametic correlation were generated using simulations of clines stabilized by strong frequency-dependent selection. In the hybrid zone in Heliconius erato, clines at three major color pattern loci were between 8.5 and 10.2 km wide, and the pairwise gametic correlations peaked at R & 0.35. These measures suggest that s & 0.23 per locus, and that σ & 2.6 km. In erato, the shapes of the clines agreed with that expected on the basis of dominance. Heliconius melpomene has a nearly coincident hybrid zone. In this species, cline widths at four major color pattern loci varied between 11.7 and 13.4 km. Pairwise gametic correlations peaked near R & 1.00 for tightly linked genes, and at R & 0.40 for unlinked genes, giving s & 0.25 per locus and σ & 3.7 km. In melpomene, cline shapes did not perfectly fit theoretical shapes based on dominance; this deviation might be explained by long-distance migration and/or strong epistasis. Compared with erato, sample sizes in melpomene are lower and the genetics of its color patterns are less well understood. In spite of these problems, selection and gene flow are clearly of the same order of magnitude in the two species. The relatively high per locus selection coefficients agree with ``major gene'' theories for the evolution of Mullerian mimicry, but the genetic architecture of the color patterns does not. These results show that the genetics and evolution of mimicry are still only sketchily understood.
AU - Mallet, James L
AU - Nicholas Barton
AU - Lamas,Gerado M
AU - Santisteban, José C
AU - Muedas, Manuel M
AU - Eeley, Harriet
ID - 3650
IS - 4
JF - Genetics
TI - Estimates of selection and gene flow from measures of cline width and linkage disequilibrium in Heliconius hybrid zones
VL - 124
ER -
TY - JOUR
AB - It is widely held that each gene typically affects many characters, and that each character is affected by many genes. Moreover, strong stabilizing selection cannot act on an indefinitely large number of independent traits. This makes it likely that heritable variation in any one trait is maintained as a side effect of polymorphisms which have nothing to do with selection on that trait. This paper examines the idea that variation is maintained as the pleiotropic side effect of either deleterious mutation, or balancing selection. If mutation is responsible, it must produce alleles which are only mildly deleterious (s & 10(-3)), but nevertheless have significant effects on the trait. Balancing selection can readily maintain high heritabilities; however, selection must be spread over many weakly selected polymorphisms if large responses to artificial selection are to be possible. In both classes of pleiotropic model, extreme phenotypes are less fit, giving the appearance of stabilizing selection on the trait. However, it is shown that this effect is weak (of the same order as the selection on each gene): the strong stabilizing selection which is often observed is likely to be caused by correlations with a limited number of directly selected traits. Possible experiments for distinguishing the alternatives are discussed.
AU - Nicholas Barton
ID - 3651
IS - 3
JF - Genetics
TI - Pleiotropic models of quantitative variation
VL - 124
ER -
TY - JOUR
AB - Distribution of putative glutamatergic neurons in the lower brainstem and cerebellum of the rat was examined immunocytochemically by using a monoclonal antibody against phosphate-activated glutaminase, which has been proposed to be a major synthetic enzyme of transmitter glutamate and so may serve as a marker for glutamatergic neurons in the central nervous system. Intensely-immunolabeled neuronal cell bodies were densely distributed in the main precerebellar nuclei sending mossy fibers to the cerebellum; in the pontine nuclei, pontine tegmental reticular nucleus of Bechterew, external cuneate nucleus, and lateral reticular nucleus of the medulla oblongata. Phosphate-activated glutaminase-immunoreactive granular deposits were densely seen in the brachium pontis and restiform body, suggesting the immunolabeling of mossy fibers of passage. In the cerebellum, neuropil within the granule cell layer of the cerebellar cortex displayed intense phosphate-activated glutaminase-immunoreactivity, and that within the deep cerebellar nuclei showed moderate immunoreactivity. These results indicate that many mossy fiber terminals originate from phosphate-activated glutaminase-containing neurons and utilize phosphate-activated glutaminase for the synthesis of transmitter glutamate. Intensely-immunostained neuronal cell bodies were further observed in other regions which have been reported to contain neurons sending mossy fibers to the cerebellum; in the dorsal part of the principal sensory trigeminal nucleus, dorsomedial part of the oral subnucleus of the spinal trigeminal nucleus, interpolar subnucleus of the spinal trigeminal nucleus, paratrigeminal nucleus, supragenual nucleus, regions dorsal to the abducens nucleus and genu of the facial nerve, superior and medial vestibular nuclei, cell groups f, x and y, hypoglossal prepositus nucleus, intercalated nucleus, nucleus of Roller, reticular regions intercalated between the motor trigeminal and principal sensory trigeminal nuclei, linear nucleus, and gigantocellular and paramedian reticular formation. Neuronal cell bodies with intense phosphate-activated glutaminase-immunoreactivity were also found in other brainstem regions, such as the paracochlear glial substance, posterior ventral cochlear nucleus, and cell group e. Although it is still controversial whether all glutamatergic neurons use phosphate-activated glutaminase in a transmitter-related process and whether phosphate-activated glutaminase is involved in other metabolism-related processes, the neurons showing intense phosphate-activated glutaminase-immuno-reactivity in the present study were suggested to be putative glutamatergic neurons.
AU - Kaneko, Takeshi
AU - Itoh, Kazuo
AU - Ryuichi Shigemoto
AU - Mizuno, Noboru
ID - 2479
IS - 1
JF - Neuroscience
TI - Glutaminase-like immunoreactivity in the lower brainstem and cerebellum of the adult rat
VL - 32
ER -
TY - JOUR
AB - This paper describes the amino acid sequence of the rat substance P receptor and its comparison with that of the rat substance K receptor on the basis of molecular cloning and sequence analysis. From a rat brain cDNA library constructed with an RNA expression vector, we identified a cDNA mixture containing a functional substance P receptor cDNA by examining electrophysiologically a receptor expression following injection of the mRNAs synthesized in vitro into Xenopus oocytes. A receptor cDNA clone was then isolated by cross-hybridization with the bovine substance K receptor DNA. The clone was confirmed by selective binding of substance P to the cloned receptor expressed in mammalian COS cells. The deduced amino acid sequence (407 amino acid residues) possesses seven putative membrane spanning domains and shows a sequence similarity to the members of G-protein-coupled receptors. The rat substance P and substance K receptor are very similar in both size and amino acid sequences, particularly in the putative transmembrane similarity is in marked contrast to the sequence divergence in the amino- and carboxyl-terminal regions and the third cytoplasmic loop. The observed sequence similarytity and divergence would thus contribute to the expression of similar but pharmacological regions and the first and second cytoplasmic loops. This distinguishable activities of the two tachykinin receptors.
AU - Yokota, Yoshifumi
AU - Sasai, Yoshiki
AU - Tanaka, Kohichi
AU - Fujiwara, Tsutomu
AU - Tsuchida, Kunihiro
AU - Ryuichi Shigemoto
AU - Kakizuka, Akira
AU - Ohkubo, Hiroaki
AU - Nakanishi, Shigetada
ID - 2525
IS - 30
JF - Journal of Biological Chemistry
TI - Molecular characterization of a functional cDNA for rat substance P receptor
VL - 264
ER -
TY - JOUR
AB - When WGA-HRP (wheat germ agglutinin-horseradish peroxidase conjugate) or HRP was injected into the regions around the superior central and/or the dorsal raphe nuclei in the cat, cell bodies of a number of non-pyramidal neurons were labeled in Ammon's horn. Thus the existence of direct projections from non-pyramidal neurons in Ammon's horn to the rostral raphe regions in the brainstem was suggested in the cat.
AU - Ino, Tadashi
AU - Itoh, Kazuo
AU - Kamiya, Hiroto
AU - Kaneko, Takeshi
AU - Ryuichi Shigemoto
AU - Akiguchi, Ichiro
AU - Mizuno, Noboru
ID - 2526
IS - 1
JF - Brain Research
TI - Direct projections from Ammon's horn to the rostral raphe regions in the brainstem of the cat
VL - 479
ER -
TY - JOUR
AU - Akimoto, Masumi
AU - Ryuichi Shigemoto
AU - Kawamura, Makiko
AU - Yamagata, Hideharu
AU - Kurihara, Takeshi
AU - Takata, S
AU - Miwa, Yoko
AU - Akagami, N
AU - Katsu, Kenichi
AU - Yamauchi, D
ID - 2527
IS - 11
JF - Japanese Journal of Gastroenterology
TI - Effect of endothelin on gastric mucosal blood flow in rat
VL - 86
ER -
TY - JOUR
AU - Herbert Edelsbrunner
AU - Skiena, Steven Sol
ID - 4079
IS - 7
JF - American Mathematical Monthly
TI - On the number of furthest neighbor pairs in a point set
VL - 96
ER -
TY - JOUR
AB - 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.
AU - Herbert Edelsbrunner
AU - Hasan, Nany
AU - Seidel, Raimund
AU - Shen, Xiao-Jun
ID - 4080
IS - 1
JF - Geometriae Dedicata
TI - Circles through two points that always enclose many points
VL - 32
ER -
TY - JOUR
AB - 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.
AU - Herbert Edelsbrunner
AU - Guibas, Leonidas J
AU - Sharir, Micha
ID - 4081
IS - 1
JF - Discrete & Computational Geometry
TI - The upper envelope of piecewise linear functions: Algorithms and applications
VL - 4
ER -
TY - JOUR
AB - 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.
AU - Herbert Edelsbrunner
AU - Guibas, Leonidas J
ID - 4082
IS - 1
JF - Journal of Computer and System Sciences
TI - Topologically sweeping an arrangement
VL - 38
ER -
TY - JOUR
AB - 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.
AU - Yao, F. Frances
AU - Dobkin, David P
AU - Herbert Edelsbrunner
AU - Paterson,Michael S
ID - 4083
IS - 2
JF - SIAM Journal on Computing
TI - Partitioning space for range queries
VL - 18
ER -
TY - JOUR
AB - 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.
AU - Herbert Edelsbrunner
AU - Rote,Günter
AU - Welzl, Emo
ID - 4084
IS - 2
JF - Theoretical Computer Science
TI - Testing the necklace condition for shortest tours and optimal factors in the plane
VL - 66
ER -
TY - CONF
AB - 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.
AU - Herbert Edelsbrunner
ID - 4085
TI - An acyclicity theorem for cell complexes in d dimension
ER -
TY - JOUR
AB - 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.
AU - Herbert Edelsbrunner
ID - 4086
IS - 4
JF - Discrete & Computational Geometry
TI - The upper envelope of piecewise linear functions: Tight bounds on the number of faces
VL - 4
ER -
TY - CONF
AB - 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.
AU - Herbert Edelsbrunner
AU - Preparata, Franco P
AU - West, Douglas B
ID - 4087
TI - Tetrahedrizing point sets in three dimensions
VL - 358
ER -
TY - JOUR
AB - 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.
AU - Herbert Edelsbrunner
AU - Guibas, Leonidas
AU - Hershberger, John
AU - Seidel, Raimund
AU - Sharir, Micha
AU - Snoeyink, Jack
AU - Welzl, Emo
ID - 4088
IS - 1
JF - Discrete & Computational Geometry
TI - Implicitly representing arrangements of lines or segments
VL - 4
ER -
TY - JOUR
AB - 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.
AU - Herbert Edelsbrunner
AU - Guibas, Leonidas
AU - Hershberger, John
AU - Pach, János
AU - Pollack, Richard
AU - Seidel, Raimund
AU - Sharir, Micha
AU - Snoeyink, Jack
ID - 4089
IS - 1
JF - Discrete & Computational Geometry
TI - On arrangements of Jordan arcs with three intersections per pair
VL - 4
ER -
TY - CONF
AU - Chazelle, Bernard
AU - Herbert Edelsbrunner
AU - Guibas, Leonidas J
AU - Sharir, Micha
ID - 4092
TI - A singly exponential stratification scheme for real semi-algebraic varieties and its applications
VL - 372
ER -
TY - JOUR
AB - 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.
AU - Chazelle, Bernard
AU - Herbert Edelsbrunner
AU - Guibas, Leonidas J
ID - 4093
IS - 1
JF - Discrete & Computational Geometry
TI - The complexity of cutting complexes
VL - 4
ER -
TY - JOUR
AB - 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.
AU - Slatkin, Montgomery
AU - Nicholas Barton
ID - 4309
IS - 7
JF - Evolution; International Journal of Organic Evolution
TI - A comparison of three methods for estimating average levels of gene flow
VL - 43
ER -
TY - JOUR
AU - Nicholas Barton
AU - Turelli, Michael
ID - 4312
JF - Annual Review of Genetics
TI - Evolutionary quantitative genetics: how little do we know ?
VL - 23
ER -
TY - CHAP
AU - Nicholas Barton
ED - Otte, Daniel
ED - Endler, John A
ID - 4313
T2 - Speciation and its consequences
TI - Founder effect speciation
ER -
TY - JOUR
AB - 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.
AU - Nicholas Barton
ID - 4314
IS - 1
JF - Genetical Research
TI - The divergence of a polygenic system under stabilising selection, mutation and drift
VL - 54
ER -
TY - CONF
AB - A real-time temporal logic for the specification of reactive systems is introduced. The novel feature of the logic, TPTL, is the adoption of temporal operators as quantifiers over time variables; every modality binds a variable to the time(s) it refers to. TPTL is demonstrated to be both a natural specification language and a suitable formalism for verification and synthesis. A tableau-based decision procedure and model-checking algorithm for TPTL are presented. Several generalizations of TPTL are shown to be highly undecidable.
AU - Alur, Rajeev
AU - Thomas Henzinger
ID - 4596
TI - A really temporal logic
ER -
TY - JOUR
AB - 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.
AU - Peter Jonas
ID - 3465
IS - 3
JF - Journal of Membrane Biology
TI - Temperature dependence of gating current in myelinated nerve fibers
VL - 112
ER -
TY - JOUR
AB - Amphibian myelinated nerve fibers were treated with collagenase and protease. Axons with retraction of the myelin sheath were patch-clamped in the nodal and paranodal region. One type of Na channel was found. It has a single-channel conductance of 11 pS (15 degrees C) and is blocked by tetrodotoxin. Averaged events show the typical activation and inactivation kinetics of macroscopic Na current. Three potential-dependent K channels were identified (I, F, and S channel). The I channel, being the most frequent type, has a single-channel conductance of 23 pS (inward current, 105 mM K on both sides of the membrane), activates between -60 and -30 mV, deactivates with intermediate kinetics, and is sensitive to dendrotoxin. The F channel has a conductance of 30 pS, activates between -40 and 60 mV, and deactivates with fast kinetics. The former inactivates within tens of seconds; the latter inactivates within seconds. The third type, the S channel, has a conductance of 7 pS and deactivates slowly. All three channels can be blocked by external tetraethylammonium chloride. We suggest that these distinct K channel types form the basis for the different components of macroscopic K current described previously.
AU - Peter Jonas
AU - Bräu, Michael E
AU - Hermsteiner, Markus
AU - Vogel, Werner
ID - 3466
IS - 18
JF - PNAS
TI - Single-channel recording in myelinated nerve fibers reveals one type of Na channel but different K channels
VL - 86
ER -
TY - CONF
AU - Herbert Edelsbrunner
ID - 3549
TI - Spatial triangulations with dihedral angle conditions
ER -
TY - JOUR
AB - Frequency-dependent selection against rare forms can maintain clines. For weak selection, s, in simple linear models of frequency-dependence, single locus clines are stabilized with a maximum slope of between {complex}s/{complex}8 {sigma} and {complex}s/{complex}12 {delta}, where {sigma} is the dispersal distance. These clines are similar to those maintained by heterozygote disadvantage. Using computer simulations, the weak-selection analytical results are extended to higher selection pressures with up to three unlinked genes. Graphs are used to display the effect of selection, migration, dominance, and number of loci on cline widths, speeds of cline movements, two-way gametic correlations (``linkage disequilibria''), and heterozygote deficits. The effects of changing the order of reproduction, migration, and selection, are also briefly explored. Epistasis can also maintain tension zones. We show that epistatic selection is similar in its effects to frequency-dependent selection, except that the disequilibria produced in the zone will be higher for a given level of selection. If selection consists of a mixture of frequency-dependence and epistasis, as is likely in nature, the error made in estimating selection is usually less than twofold. From the graphs, selection and migration can be estimated using knowledge of the dominance and number of genes, of gene frequences and of gametic correlations from a hybrid zone.
AU - Mallet, James L
AU - Nicholas Barton
ID - 3652
IS - 4
JF - Genetics
TI - Inference from clines stabilized by frequency-dependent selection
VL - 122
ER -
TY - JOUR
AB - Frequency-dependent selection on warning color can maintain narrow hybrid zones between unpalatable prey taxa. To measure such selection, we transferred marked Heliconius erato (Lepidoptera: Nymphalidae) in both directions across a 10-km-wide hybrid zone between Peruvian races differing in color pattern. These experimental H. erato were released at four sites, along with control H. erato of the phenotype native to each site. Survival of experimental butterflies was significantly lower than that of controls at two sites and overall. Most selection, measured as differences in survival, occurred soon after release. Selection against foreign morphs was 52% (confidence limits: 25-71%) and was probably due to bird attacks on unusual warning-color morphs (more than 10% of the recaptures had beak marks). Since only three major loci determine the color-pattern differences, this suggests an average selection coefficient of 0.17 per locus, sufficient to maintain the narrow clines in H. erato.
AU - Mallet, James L
AU - Nicholas Barton
ID - 3653
JF - Evolution
TI - Strong natural selection in a warning color hybrid zone
VL - 43
ER -
TY - JOUR
AB - Many species are divided into a mosaic of genetically distinct populations, separated by narrow zones of hybridization. Studies of hybrid zones allow us to quantify the genetic differences responsible for speciation, to measure the diffusion of genes between diverging taxa, and to understand the spread of alternative adaptations.
AU - Nicholas Barton
AU - Hewitt, Godfrey M
ID - 3654
JF - Nature
TI - Adaptation, speciation and hybrid zones
VL - 341
ER -
TY - JOUR
AB - 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.
AU - Ino, Tadashi
AU - Itoh, Kazuo
AU - Kamiya, Hiroto
AU - Ryuichi Shigemoto
AU - Akiguchi, Ichiro
AU - Mizuno, Noboru
ID - 2522
IS - 1
JF - Brain Research
TI - Direct projections of non-pyramidal neurons of Ammon's horn to the supramammillary region in the cat
VL - 460
ER -
TY - JOUR
AB - 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.
AU - Mizuno, Noboru
AU - Ueyama, Teizo
AU - Itoh, Kazuo
AU - Satoda, Takahiro
AU - Tashiro, Takashi
AU - Ryuichi Shigemoto
ID - 2523
IS - 1
JF - Neuroscience Letters
TI - Direct projections from the subthalamic nucleus of Luys to the spinal cord in the Japanese monkey
VL - 89
ER -
TY - JOUR
AB - Alpha-ketoglutamate (α-KG) reductive amination activity in rat brain was found to be mostly absorbed with an antibody against liver glutamate dehydrogenase. With this and anti-glutamine synthetase antibodies, α-KG reductive amination activity was immunocytochemically shown to coexist with glutamine synthetase activity in astrocytes. The results suggest that astrocytes de novo synthesize glutamate from α-KG and ammonia, and metabolize it to glutamine.
AU - Kaneko, Takeshi
AU - Ryuichi Shigemoto
AU - Mizuno, Noboru
ID - 2524
IS - 1
JF - Brain Research
TI - Metabolism of glutamate and ammonia in astrocyte an immunocytochemical study
VL - 457
ER -
TY - JOUR
AU - Leonid Sazanov
AU - Karavaev, V A
AU - Kukushkin, A K
ID - 1941
JF - J. Phys. Chem-Russia
TI - Mathematical model of photosynthesis regulation accounts for the effects of changes in external conditions and observed oscillations
VL - 52
ER -
TY - JOUR
AB - In this paper we study the problem of polygonal separation in the plane, i.e., finding a convex polygon with minimum number k of sides separating two given finite point sets (k-separator), if it exists. We show that for k = Θ(n), is a lower bound to the running time of any algorithm for this problem, and exhibit two algorithms of distinctly different flavors. The first relies on an O(n log n)-time preprocessing task, which constructs the convex hull of the internal set and a nested star-shaped polygon determined by the external set; the k-separator is contained in the annulus between the boundaries of these two polygons and is constructed in additional linear time. The second algorithm adapts the prune-and-search approach, and constructs, in each iteration, one side of the separator; its running time is O(kn), but the separator may have one more side than the minimum.
AU - Herbert Edelsbrunner
AU - Preparata, Franco P
ID - 4090
IS - 3
JF - Information and Computation
TI - Minimum polygonal separation
VL - 77
ER -
TY - JOUR
AB - 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.
AU - Herbert Edelsbrunner
AU - Skiena,Steven S
ID - 4091
IS - 5
JF - SIAM Journal on Computing
TI - Probing convex polygons with X-Rays
VL - 17
ER -
TY - CONF
AU - Herbert Edelsbrunner
ID - 4096
TI - Geometric structures in computational geometry
VL - 317
ER -
TY - CONF
AB - Arrangements of curves in the plane are of fundamental significance in many problems of computational and combinatorial geometry (e.g. motion planning, algebraic cell decomposition, etc.). In this paper we study various topological and combinatorial properties of such arrangements under some mild assumptions on the shape of the curves, and develop basic tools for the construction, manipulation, and analysis of these arrangements. Our main results include a generalization of the zone theorem of [EOS], [CGL] to arrangements of curves (in which we show that the combinatorial complexity of the zone of a curve is nearly linear in the number of curves), and an application of (some weaker variant of) that theorem to obtain a nearly quadratic incremental algorithm for the construction of such arrangements.
AU - Herbert Edelsbrunner
AU - Guibas, Leonidas
AU - Pach, János
AU - Pollack, Richard
AU - Seidel, Raimund
AU - Sharir, Micha
ID - 4097
TI - Arrangements of curves in the plane - topology, combinatorics, and algorithms
VL - 317
ER -
TY - GEN
AU - Coyne, Jerry A
AU - Nicholas Barton
ID - 4315
T2 - Nature
TI - What do we know about speciation ?
VL - 331
ER -
TY - GEN
AU - Nicholas Barton
AU - Jones, Steve
ID - 4316
T2 - Nature
TI - Molecular evolutionary genetics
VL - 332
ER -
TY - CHAP
AU - Nicholas Barton
ED - Myers, Alan A
ED - Giller, Paul S
ID - 4317
T2 - Analytical biogeography
TI - Speciation
ER -
TY - GEN
AU - Nicholas Barton
AU - Jones, Steve
AU - Mallet, James L
ID - 4318
T2 - Nature
TI - No barriers to speciation
VL - 336
ER -
TY - JOUR
AU - Dallas, John F
AU - Nicholas Barton
AU - Dover, Gabriel A.
ID - 3655
IS - 6
JF - Molecular Biology and Evolution
TI - Interracial rDNA variation in the grasshopper Podisma pedestris
VL - 5
ER -
TY - JOUR
AU - Nishimura, Masaki
AU - Ryuichi Shigemoto
AU - Matsubayashi, K
AU - Mimori, Y
AU - Kameyama, Masakuni
ID - 2521
IS - 11
JF - Clinical Neurology
TI - Meningoencephalitis during the pre-icteric phase of hepatitis A - a case report
VL - 27
ER -
TY - BOOK
AB - Computational geometry as an area of research in its own right emerged in the early seventies of this century. Right from the beginning, it was obvious that strong connections of various kinds exist to questions studied in the considerably older field of combinatorial geometry. For example, the combinatorial structure of a geometric problem usually decides which algorithmic method solves the problem most efficiently. Furthermore, the analysis of an algorithm often requires a great deal of combinatorial knowledge. As it turns out, however, the connection between the two research areas commonly referred to as computa tional geometry and combinatorial geometry is not as lop-sided as it appears. Indeed, the interest in computational issues in geometry gives a new and con structive direction to the combinatorial study of geometry. It is the intention of this book to demonstrate that computational and com binatorial investigations in geometry are doomed to profit from each other. To reach this goal, I designed this book to consist of three parts, acorn binatorial part, a computational part, and one that presents applications of the results of the first two parts. The choice of the topics covered in this book was guided by my attempt to describe the most fundamental algorithms in computational geometry that have an interesting combinatorial structure. In this early stage geometric transforms played an important role as they reveal connections between seemingly unrelated problems and thus help to structure the field.
AU - Edelsbrunner, Herbert
ID - 3900
SN - 9783540137221
TI - Algorithms in Combinatorial Geometry
VL - 10
ER -
TY - JOUR
AB - The visibility graph of a finite set of line segments in the plane connects two endpoints u and v if and only if the straight line connection between u and v does not cross any line segment of the set. This article proves that 5n - 4 is a lower bound on the number of edges in the visibility graph of n nonintersecting line segments in the plane. This bound is tight.
AU - Herbert Edelsbrunner
AU - Shen, Xiaojun
ID - 4094
IS - 2
JF - Information Processing Letters
TI - A tight lower bound on the size of visibility graphs
VL - 26
ER -
TY - JOUR
AB - he kth-order Voronoi diagram of a finite set of sites in the Euclidean plane E2 subdivides E2 into maximal regions such that all points within a given region have the same k nearest sites. Two versions of an algorithm are developed for constructing the kth-order Voronoi diagram of a set of n sites in O(n2 log n + k(n - k) log2 n) time, O(k(n - k)) storage, and in O(n2 + k(n - k) log2 n) time, O(n2) storage, respectively.
AU - Chazelle, Bernard
AU - Herbert Edelsbrunner
ID - 4095
IS - 11
JF - IEEE Transactions on Computers
TI - An improved algorithm for constructing kth-order Voronoi diagrams
VL - 36
ER -
TY - JOUR
AB - This paper investigates the existence of linear space data structures for range searching. We examine thehomothetic range search problem, where a setS ofn points in the plane is to be preprocessed so that for any triangleT with sides parallel to three fixed directions the points ofS that lie inT can be computed efficiently. We also look atdomination searching in three dimensions. In this problem,S is a set ofn points inE 3 and the question is to retrieve all points ofS that are dominated by some query point. We describe linear space data structures for both problems. The query time is optimal in the first case and nearly optimal in the second.
AU - Chazelle, Bernard
AU - Herbert Edelsbrunner
ID - 4100
IS - 1
JF - Discrete & Computational Geometry
TI - Linear space data structures for two types of range search
VL - 2
ER -
TY - JOUR
AB - In a number of recent papers, techniques from computational geometry (the field of algorithm design that deals with objects in multi-dimensional space) have been applied to some problems in the area of computer graphics. In this way, efficient solutions were obtained for the windowing problem that asks for those line segments in a planar set that lie in given window (range) and the moving problem that asks for the first line segment that comes into the window when moving the window in some direction. In this paper we show that also the zooming problem, which asks for the first line segment that comes into the window when we enlarge it, can be solved efficiently. This is done by repeatedly performing range queries with ranges of varying sizes. The obtained structure is dynamic and yields a query time of O(log2n) and an insertion and deletion time of O(log2n), where n is the number of line segments in the set. The amount of storage required is O(n log n). It is also shown that the technique of repeated range search can be used to solve several other problems efficiently.
AU - Herbert Edelsbrunner
AU - Overmars, Mark H
ID - 4101
IS - 6
JF - Information Processing Letters
TI - Zooming by repeated range detection
VL - 24
ER -
TY - JOUR
AB - Determining or counting geometric objects that intersect another geometric query object is at the core of algorithmic problems in a number of applied areas of computer science. This article presents a family of space-efficient data structures that realize sublinear query time for points, line segments, lines and polygons in the plane, and points, line segments, planes, and polyhedra in three dimensions.
AU - Dobkin, David P
AU - Herbert Edelsbrunner
ID - 4102
IS - 3
JF - Journal of Algorithms
TI - Space searching for intersecting objects
VL - 8
ER -
TY - JOUR
AB - The grasshopper Podisma pedestris contains two chromosomal races, which differ by a Robertsonian fusion between the sex chromosome and an autosome, and which meet in a narrow hybrid zone in the Alpes Maritimes. DNA content variation across this hybrid zone was investigated by optical densitometry of Feulgen stained spermatids. Spermatids from males with the unfused sex chromosome stain more strongly than those from males with the fused chromosome. The difference between the karyotypes is greater in the centre of the hybrid zone, suggesting that it is not a pleiotropic effect of the fusion itself, but is due instead to differences at closely linked loci.
AU - Westerman, Michael
AU - Nicholas Barton
AU - Hewitt, Godfrey M
ID - 4319
JF - Heredity
TI - Differences in DNA content between two chromosomal races of the grasshopper Podisma pedestris
VL - 58
ER -
TY - JOUR
AB - Bosonic field theories may be formulated in terms of stochastic differential equations. The characteristic long term behaviour of these systems is a decay into the global minimum of their Hamiltonian. If local minima exist, the rate of this decay is determined by instanton effects. We calculate the decay rate and perform computer simulations on a 1 + 1 dimensional model to test the instanton approximation. We find the instanton approximations to be in very good agreement with the simulation results.
Copyright © 1987 Published by Elsevier B.V.
AU - Rouhani, Shahin
AU - Nicholas Barton
ID - 4320
IS - 1-2
JF - Physica A
TI - Instantons and stochastic quantization
VL - 143
ER -
TY - JOUR
AB - A method is developed for calculating the probability of establishment of an allele which is favoured in some places, but not others, in a large subdivided population. This method is quite general, and could be used to calculate the chance that any system which is linear near an absorbing boundary will move away from that boundary. The results are applied to a population distributed along one dimension. Only mutants which arise within a distance σ/ √2s of the region in which they are favoured stand an appreciable chance of establishment. The net chance of establishment of mutations distributed randomly across the habitat will be decreased by gene flow if selection against them is sufficiently strong. However, if the mutations are only weakly deleterious outside some limited region, gene flow may increase the net chance of establishment.
AU - Nicholas Barton
ID - 4322
IS - 1
JF - Genetical Research
TI - The probability of establishment of an advantageous mutation in a subdivided population
VL - 50
ER -
TY - CONF
AB - We consider the problem of obtaining sharp (nearly quadratic) bounds for the combinatorial complexity of the lower envelope (i.e. pointwise minimum) of a collection of n bivariate (or generally multi-variate) continuous and "simple" functions, and of designing efficient algorithms for the calculation of this envelope. This problem generalizes the well-studied univariate case (whose analysis is based on the theory of Davenport-Schinzel sequences), but appears to be much more difficult and still largely unsolved. It is a central problem that arises in many areas in computational and combinatorial geometry, and has numerous applications including generalized planar Voronoi diagrams, hidden surface elimination for intersecting surfaces, purely translational motion planning, finding common transversals of polyhedra, and more. In this abstract we provide several partial solutions and generalizations of this problem, and apply them to the problems mentioned above. The most significant of our results is that the lower envelope of n triangles in three dimensions has combinatorial complexity at most O(n2α(n)) (where α(n) is the extremely slowly growing inverse of Ackermann's function), that this bound is tight in the worst case, and that this envelope can be calculated in time O(n2α(n)).
AU - Herbert Edelsbrunner
AU - Pach, János
AU - Schwartz, Jacob T
AU - Sharir, Micha
ID - 3514
TI - On the lower envelope of bivariate functions and its applications
ER -
TY - JOUR
AB - We have analysed the role of sampling drift in inducing shifts between alternative adaptive peaks, in small and rapidly growing populations. Using a simple model of disruptive selection on a polygenic character, we calculate the net probabilityofapeakshift. If the growth rate is high, theprobabilityofashiftina growing population is insensitive to selection on the character. Assuming that the character is effectively neutral during the brief initial increase, we find that theprobabilityofapeakshift is given by theprobabilityof finding a standard normal variate greater than √2ΔV where ΔV is the reduction in additive genetic variance during the growth period. This result holds for arbitrary pattern of increase in size, provided that the rate of increase is high enough for selection to be negligible, and the character depends on a large number of loci. Comparing theprobabilityofpeakshiftsin founding populations with the rate ofshiftsin static and allopatric populations it appears that although strongly selected shifts are only likely to occur ina growing population, a static population is a more congenial setting for adaptive shifts.
AU - Rouhani, Shahin
AU - Nicholas Barton
ID - 3656
IS - 1
JF - Journal of Theoretical Biology
TI - The probability of peak shifts in a founder population
VL - 126
ER -
TY - JOUR
AB - Shifts between adaptive peaks, caused by sampling drift, are involved in both speciation and adaptation via Wright's “shiftingbalance.” We use techniques from statistical mechanics to calculate the rate of such transitions for apopulation in a single panmictic deme and for apopulation which is continuously distributed over one- and two-dimensional regions. This calculation applies in the limit where transitions are rare. Our results indicate that stochastic divergence is feasible despite free gene flow, provided that neighbourhood size is low enough. In two dimensions, the rate of transition depends primarily on neighbourhood size N and only weakly on selection pressure (≈sk exp(− cN)), where k is a number determined by the local population structure, in contrast with the exponential dependence on selection pressure in one dimension (≈exp(− cN √s)) or in a single deme (≈exp(− cNs)). Our calculations agree with simulations of a single deme and a one-dimensional population.
AU - Rouhani, Shahin
AU - Nicholas Barton
ID - 3657
IS - 3
JF - Theoretical Population Biology
TI - Speciation and the "shifting balance" in a continuous population
VL - 31
ER -
TY - JOUR
AB - Females of the grasshopper Podisima pedestris were collected from the middle of a hybrid zone between two chromosomal races in the Alpes Maritimes. They had already mated in the field, and could therefore lay fertilised eggs in the laboratory. The embryos were karyotyped, and found to contain an excess of chromosomal homozygotes. No evidence of assortative mating was found from copulating pairs taken in the field. The excess appears to have been caused by a combination of multiple insemination and assortative fertilisation. The genetics of the assortment, and the implications for the evolution of reproductive isolation are discussed.
AU - Hewitt, Godfrey M
AU - Nichols, R. A.
AU - Nicholas Barton
ID - 3658
IS - 3
JF - Heredity
TI - Homogamy in a hybrid zone in the alpine grasshopper Podisma pedestris
VL - 59
ER -
TY - JOUR
AU - Charlesworth, Brian
AU - Coyne, Jerry A
AU - Nicholas Barton
ID - 3659
IS - 1
JF - American Naturalist
TI - The relative rates of evolution of sex chromosomes and autosomes.
VL - 130
ER -
TY - JOUR
AB - The maintenance of polygenic variability by a balance between mutation and stabilizing selection has been analysed using two approximations: the ‘Gaussian’ and the ‘house of cards’. These lead to qualitatively different relationships between the equilibrium genetic variance and the parameters describing selection and mutation. Here we generalize these approximations to describe the dynamics of genetic means and variances under arbitrary patterns of selection and mutation. We incorporate genetic drift into the same mathematical framework.
The effects of frequency-independent selection and genetic drift can be determined from the gradient of log mean fitness and a covariance matrix that depends on genotype frequencies. These equations describe an ‘adaptive landscape’, with a natural metric of genetic distance set by the covariance matrix. From this representation we can change coordinates to derive equations describing the dynamics of an additive polygenic character in terms of the moments (means, variances, …) of allelic effects at individual loci. Only under certain simplifying conditions, such as those derived from the Gaussian and house-of-cards approximations, do these general recursions lead to tractable equations for the first few phenotypic moments. The alternative approximations differ in the constraints they impose on the distributions of allelic effects at individual loci. The Gaussian-based prediction that evolution of the phenotypic mean does not change the genetic variance is shown to be a consequence of the assumption that the allelic distributions are never skewed. We present both analytical and numerical results delimiting the parameter values consistent with our approximations.
AU - Nicholas Barton
AU - Turelli, Michael
ID - 3660
IS - 2
JF - Genetical Research
TI - Adaptive landscapes, genetic distance, and the evolution of quantitative characters
VL - 49
ER -
TY - JOUR
AB - We derive a formula giving thefrequency with which random drift shifts a population betweenalternativeequilibria. This formula is valid when such shifts are rare (Ns >> 1), and applies over a wide range of mutation rates. When the number of mutations entering the population is low (4Nμ << 1), the rate of stochastic shifts reduces to the product ofthe mutation rate and the probability of fixation of a single mutation. However, when many mutations enter the population in each generation (4Nμ >> 1), the rate is higher than would be expected if mutations were established independently, and converges to that given by a gaussian approximation. We apply recent results on bistable systems to extend this formula to the general multidimensional case. This gives an explicit expression for thefrequencyof stochastic shifts, which depends only on theequilibrium probability distribution near the saddle point separating thealternative stable states. The plausibility of theories of speciation through random drift are discussed in the light of these results.
AU - Nicholas Barton
AU - Rouhani, Shahin
ID - 3661
IS - 4
JF - Journal of Theoretical Biology
TI - The frequency of shifts between alternative equilibria
VL - 125
ER -
TY - JOUR
AB - 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.
AU - Herbert Edelsbrunner
AU - Stöckl, Gerd
ID - 4098
IS - 2
JF - Journal of Combinatorial Theory Series A
TI - The number of extreme pairs of finite point-sets in Euclidean spaces
VL - 43
ER -
TY - JOUR
AB - Let S denote a set of n points in the Euclidean plane. A halfplanar range query specifies a halfplane h and requires the determination of the number of points in S which are contained in h. A new data structure is described which stores S in O(n) space and allows us to answer a halfplanar range query in O(nlog2(1+√5)−1) time in the worst case, thus improving the best result known before. The structure can be built in O(n log n) time.
AU - Herbert Edelsbrunner
AU - Welzl, Emo
ID - 4099
IS - 5
JF - Information Processing Letters
TI - Halfplanar range search in linear space and O(n0.695) query time
VL - 23
ER -
TY - JOUR
AB - 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).
AU - Herbert Edelsbrunner
AU - Welzl, Emo
ID - 4103
IS - 2
JF - Journal of Combinatorial Theory Series A
TI - On the maximal number of edges of many faces in an arrangement
VL - 41
ER -
TY - JOUR
AB - 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
AU - Herbert Edelsbrunner
AU - Guibas, Leonidas J
AU - Stolfi, Jorge
ID - 4104
IS - 2
JF - SIAM Journal on Computing
TI - Optimal point location in a monotone subdivision
VL - 15
ER -
TY - JOUR
AB - A finite set of lines partitions the Euclidean plane into a cell complex. Similarly, a finite set of $(d - 1)$-dimensional hyperplanes partitions $d$-dimensional Euclidean space. An algorithm is presented that constructs a representation for the cell complex defined by $n$ hyperplanes in optimal $O(n^d )$ time in $d$ dimensions. It relies on a combinatorial result that is of interest in its own right. The algorithm is shown to lead to new methods for computing $\lambda $-matrices, constructing all higher-order Voronoi diagrams, halfspatial range estimation, degeneracy testing, and finding minimum measure simplices. In all five applications, the new algorithms are asymptotically faster than previous results, and in several cases are the only known methods that generalize to arbitrary dimensions. The algorithm also implies an upper bound of $2^{cn^d } $, $c$ a positive constant, for the number of combinatorially distinct arrangements of $n$ hyperplanes in $E^d $.
© 1986 Society for Industrial and Applied Mathematics
AU - Herbert Edelsbrunner
AU - O'Rourke, Joseph
AU - Seidel, Raimund
ID - 4105
IS - 2
JF - SIAM Journal on Computing
TI - Constructing arrangements of lines and hyperplanes with applications
VL - 15
ER -
TY - JOUR
AB - Let B be a set of nb black points and W a set of nw, white points in the Euclidean plane. A line h is said to bisect B (or W) if, at most, half of the points of B (or W) lie on any one side of h. A line that bisects both B and W is called a ham-sandwich cut of B and W. We give an algorithm that computes a ham-sandwich cut of B and W in 0((nh+nw) log (min {nb, nw}+ 1)) time. The algorithm is considerably simpler than the previous most efficient one which takes 0((nb + nw) log (nb + nw)) time.
AU - Herbert Edelsbrunner
AU - Waupotitsch, Roman
ID - 4106
IS - 2
JF - Journal of Symbolic Computation
TI - Computing a ham-sandwich cut in two dimensions
VL - 2
ER -
TY - JOUR
AB - A set of m planes dissects E3 into cells, facets, edges and vertices. Letting deg(c) be the number of facets that bound a cellc, we give exact and asymptotic bounds on the maximum of ∈cinCdeg(c), if C is a family of cells of the arrangement with fixed cardinality.
AU - Herbert Edelsbrunner
AU - Haussler, David H
ID - 4107
IS - C
JF - Discrete Mathematics
TI - The complexity of cells in 3-dimensional arrangements
VL - 60
ER -
TY - JOUR
AB - We propose a uniform and general framework for defining and dealing with Voronoi diagrams. In this framework a Voronoi diagram is a partition of a domainD induced by a finite number of real valued functions onD. Valuable insight can be gained when one considers how these real valued functions partitionD ×R. With this view it turns out that the standard Euclidean Voronoi diagram of point sets inR d along with its order-k generalizations are intimately related to certain arrangements of hyperplanes. This fact can be used to obtain new Voronoi diagram algorithms. We also discuss how the formalism of arrangements can be used to solve certain intersection and union problems.
AU - Herbert Edelsbrunner
AU - Seidel, Raimund
ID - 4108
IS - 1
JF - Discrete & Computational Geometry
TI - Voronoi diagrams and arrangements
VL - 1
ER -
TY - JOUR
AB - Rectangle location search in d dimensions is finding the d-dimensional axis-parallel box of a non-overlapping collection C that contains a query point. A new data structure is proposed that requires optimal space and 0(logd|C|) time for a search. The significance of this data structure in practical applications is substantiated by empirical examinations of its behaviour.
AU - Herbert Edelsbrunner
AU - Haring, Günter
AU - Hilbert, D
ID - 4109
IS - 1
JF - Computer Journal
TI - Rectangular point location in d-dimensions with applications
VL - 29
ER -
TY - JOUR
AB - For $H$ a set of lines in the Euclidean plane, $A(H)$ denotes the induced dissection, called the arrangement of $H$. We define the notion of a belt in $A(H)$, which is bounded by a subset of the edges in $A(H)$, and describe two algorithms for constructing belts. All this is motivated by applications to a host of seemingly unrelated problems including a type of range search and finding the minimum area triangle with the vertices taken from some finite set of points.
© 1986 © Society for Industrial and Applied Mathematics
AU - Herbert Edelsbrunner
AU - Welzl, Emo
ID - 4110
IS - 1
JF - SIAM Journal on Computing
TI - Constructing belts in two-dimensional arrangements with applications
VL - 15
ER -
TY - JOUR
AU - Szymura, Jacek M
AU - Nicholas Barton
ID - 4321
JF - Evolution; International Journal of Organic Evolution
TI - Genetic analysis of a hybrid zone between the fire-bellied toads Bombina bombina and B. variegata, near Cracow in Southern Poland
VL - 40
ER -
TY - JOUR
AB - It is noted that the sibling competition model for the evolution of sex and recombination, as it has been developed so far, involves truncation selection. After briefly reviewing aspects of the development and behaviour of such models an analytical treatment is presented which involves additive selection. Additive selection, as compared with truncation selection, decreases the advantage of sex to such an extent that it is unlikely that sibling competition could overcome its intrinsic two-fold cost, although it could still be important in promoting family variability produced by other mechanisms, such as polyandry.
AU - Nicholas Barton
AU - POST,R. J
ID - 4323
IS - 4
JF - Journal of Theoretical Biology
TI - Sibling competition and the advantage of mixed families
VL - 120
ER -
TY - JOUR
AB - The maintenance of polygenic variation through a balance between mutation and stabilizing selection can be approximated in two ways. In the ‘Gaussian’ approximation, a normal distribution of allelic effects is assumed at each locus. In the ‘House of Cards’ approximation, the effect of new mutations is assumed to be large compared with the spread of the existing distribution. These approximations were developed to describe models where alleles may have a continuous range of effects. However, previous analyses of models with only two alleles have predicted an equilibrium variance equal to that given by the ‘House of Cards’ approximation. These analyses of biallelic models have assumed that, at equilibrium, the population mean is at the optimum. Here, it is shown that many stable equilibria may coexist, each giving a slight deviation from the optimum. Though the variance is given by the ‘House of Cards’ approximation when the mean is at the optimum, it increases towards a value of the same order as that given by the ‘Gaussian’ approximation when the mean deviates from the optimum. Thus, the equilibrium variance cannot be predicted by any simple model, but depends on the previous history of the population.
AU - Nicholas Barton
ID - 4324
IS - 3
JF - Genetical Research
TI - The maintenance of polygenic variation through a balance between mutation and stabilising selection
VL - 47
ER -
TY - JOUR
AB - The effects of the major neurotoxic fraction isolated from scorpion venom of Tityus serrulatus, TiTx gamma, on peripheral nerve membrane of Xenopus laevis were studied under current- and voltage-clamp conditions. 700 nmol/l TiTx gamma depolarized the membrane and induced spontaneous activity (150 s-1, maximum value), which ceased within a few minutes. It reduced the amplitude of the action potentials from 109 mV to 52 mV and increased their duration from 1.25 ms to 4.5 ms. 440 nmol/l TiTx gamma induced inward Na current flow at resting potential. The descending branch of the Na current-voltage curve was flattened and shifted approximately 10 mV to more negative potentials. Maximum Na permeability was reduced to about 20%. Both development of and recovery from inactivation of Na permeability were slowed. The steepness of the steady-state inactivation curve was decreased, but the mid-potential changed only insignificantly. No prepulse was necessary to elicit either a shift of activation or an inward current at resting potential. Expressing the toxin effect either in terms of the decrease of Na peak current or of the slowing of inactivation, half-maximum effects were found with 0.3 +/- 0.1 and 3.7 +/- 0.7 mumol/l TiTx gamma, respectively.
AU - Peter Jonas
AU - Vogel, Werner
AU - Arantes, Eliane C
AU - Giglio, Jose R
ID - 3464
IS - 1
JF - Pflugers Archiv : European Journal of Physiology
TI - Toxin γ of the scorpion Tityus serrulatus modifies both activation and inactivation of sodium permeability of nerve membrane
VL - 407
ER -
TY - JOUR
AU - Herbert Edelsbrunner
AU - Jaromczyk, Jerzy W
ID - 3579
JF - Congressus Numerantium
TI - How often can you see yourself in a convex configuration of mirrors?
VL - 53
ER -
TY - JOUR
AB - An edge-skeleton in an arrangementA(H) of a finite set of planes inE 3 is a connected collection of edges inA(H). We give a method that constructs a skeleton inO(√n logn) time per edge. This method implies new and more efficient algorithms for a number of structures in computational geometry including order-k power diagrams inE 2 and space cutting trees inE 3.
We also give a novel method for handling special cases which has the potential to substantially decrease the amount of effort needed to implement geometric algorithms.
AU - Herbert Edelsbrunner
ID - 3580
IS - 1-4
JF - Algorithmica
TI - Edge-skeletons in arrangements with applications
VL - 1
ER -
TY - CONF
AU - Curtis,C. F
AU - Curtis,J.
AU - Nicholas Barton
ID - 3602
TI - Methodology for testing the hypothesis of single locus control of host resistance to infection and malignancy
ER -