TY - JOUR
AB - This paper proves that for every n ≥ 4 there is a convex n-gon such that the vertices of 2n - 7 vertex pairs are one unit of distance apart. This improves the previously best lower bound of ⌊ (5n - 5) 3⌋ given by Erdo{combining double acute accent}s and Moser if n ≥ 17.
AU - Herbert Edelsbrunner
AU - Hajnal, Péter
ID - 4056
IS - 2
JF - Journal of Combinatorial Theory Series A
TI - A lower bound on the number of unit distances between the vertices of a convex polygon
VL - 56
ER -
TY - JOUR
AU - Herbert Edelsbrunner
ID - 4057
IS - 2
JF - Journal of Computer and System Sciences
TI - Corrigendum
VL - 42
ER -
TY - CONF
AB - We present a randomized incremental algorithm for computing a single face in an arrangement of n line segments in the plane that is fairly simple to implement. The expected running
time of the algorithm is O (nα(n) log n). The analysis of the algorithm uses a novel approach that generalizes and extends the Clarkson-Shor analysis technique.
AU - Chazelle, Bernard
AU - Herbert Edelsbrunner
AU - Guibas, Leonidas
AU - Sharir, Micha
AU - Snoeyink, Jack
ID - 4058
TI - Computing a face in an arrangement of line segments
ER -
TY - CONF
AB - Let P be a simple polygon with n vertices. We present a simple decomposition scheme that partitions the interior of P into O(n) so-called geodesic triangles, so that any line segment interior to P crosses at most 2 log n of these triangles. This decomposition can be used to preprocess P in time O(n log n) and storage O(n), so that any ray-shooting query can be answered in time O(log n).The algorithms are fairly simple and easy to implement. We also extend this technique to the case of ray-shooting amidst k polygonal obstacles with a total of n edges, so that a query can be answered in O(radicklog n) time.
AU - Chazelle, Bernard
AU - Herbert Edelsbrunner
AU - Grigni, Michelangelo
AU - Guibas, Leonidas
AU - Hershberger, John
AU - Sharir, Micha
AU - Snoeyink, Jack
ID - 4059
TI - Ray shooting in polygons using geodesic triangulations
VL - 510
ER -
TY - JOUR
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(Fd (N,N) logd N), where Fd (n,m) is the time required to compute a bichromatic closest pair among n red and m green points in Ed . If Fd (N,N)=Ω(N1+ε), for some fixed e{open}>0, then the running time improves to O(Fd (N,N)). Furthermore, we describe a randomized algorithm to compute a bichromatic closest pair in expected time O((nm log n log m)2/3+m log2 n+n log2 m) in E3, which yields an O(N4/3 log4/3 N) expected time, algorithm for computing a Euclidean minimum spanning tree of N points in E3. In d≥4 dimensions we obtain expected time O((nm)1-1/([d/2]+1)+ε+m log n+n log m) for the bichromatic closest pair problem and O(N2-2/([d/2]+1)ε) for the Euclidean minimum spanning tree problem, for any positive e{open}.
AU - Agarwal, Pankaj K
AU - Herbert Edelsbrunner
AU - Schwarzkopf, Otfried
AU - Welzl, Emo
ID - 4061
IS - 1
JF - Discrete & Computational Geometry
TI - Euclidean minimum spanning trees and bichromatic closest pairs
VL - 6
ER -
TY - JOUR
AB - We prove that for any set S of n points in the plane and n3-α triangles spanned by the points in S there exists a point (not necessarily in S) contained in at least n3-3α/(c log5 n) of the triangles. This implies that any set of n points in three-dimensional space defines at most {Mathematical expression} halving planes.
AU - Aronov, Boris
AU - Chazelle, Bernard
AU - Herbert Edelsbrunner
AU - Guibas, Leonidas J
AU - Sharir, Micha
AU - Wenger, Rephael
ID - 4062
IS - 1
JF - Discrete & Computational Geometry
TI - Points and triangles in the plane and halving planes in space
VL - 6
ER -
TY - CONF
AB - We extend the specification language of temporal logic, the corresponding verification framework, and the underlying computational model to deal with real-time properties of concurrent and reactive systems. A global, discrete, and asynchronous clock is incorporated into the 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 upperbound real-time requirements for transitions. We show how to model real-time systems that communicate either through shared variables or by message passing, and how to represent the important real-time constructs of priorities (interrupts), scheduling, and timeouts in this framework. Two styles for the specification of real-time properties are presented. The first style uses bounded versions of the temporal operators; the real-time requirements expressed in this style are classified ...
AU - Thomas Henzinger
AU - Manna, Zohar
AU - Pnueli,Amir
ID - 4508
TI - Temporal proof methodologies for real-time systems
ER -
TY - THES
AU - Thomas Henzinger
ID - 4516
TI - The Temporal Specification and Verification of Real-time Systems
ER -
TY - JOUR
AU - Alur, Rajeev
AU - Thomas Henzinger
ID - 4592
IS - 3
JF - SIGACT News
TI - Time for logic
VL - 22
ER -
TY - JOUR
AB - Two types of metabolically regulated K channels have been identified for the first time in enzymatically demyelinated fibres of amphibian sciatic nerve using the patch-clamp technique. A maxi K channel with a single-channel conductance of 132 pS (105 mM K on both sides of the membrane, 15°C) is activated both by micromolar concentrations of internal Ca and by depolarization. A second type of K channel with a conductance of 44 pS is inhibited by intracellular adenosine 5'-triphosphate (ATP) with a half-maximal inhibitory concentration (IC50) of 35 μM. It is blocked by submicromolar concentrations of external glibenclamide. Both channels are sensitive to external tetraethylammonium chloride (IC50 = 0.2 mM for the maxi K channel and 4.2 mM for the ATP-sensitive channel). They may be part of a complex feedback system regulating axonal excitability under various metabolic conditions.
AU - Peter Jonas
AU - Koh, Duk S
AU - Kampe, Knut
AU - Hermsteiner, Markus
AU - Vogel, Werner
ID - 3468
IS - 1-2
JF - Pflugers Archiv : European Journal of Physiology
TI - ATP-sensitive and Ca-activated K channels in vertebrate axons: novel links between metabolism and excitability
VL - 418
ER -
TY - CHAP
AU - Herbert Edelsbrunner
AU - Sharir, Micha
ID - 3566
T2 - Applied Geometry and Discrete Mathematics: The Victor Klee Festschrift
TI - A hyperplane incidence problem with applications to counting distances
VL - 4
ER -
TY - CHAP
AU - Herbert Edelsbrunner
ID - 3567
T2 - Discrete & Computational Geometry
TI - Lines in space – A collection of results
VL - 6
ER -
TY - JOUR
AB - We compare the pattern of morphological and electrophoretic variation in the hybrid zone between Bombina bombina and B. variegata across two transects: one near Cracow and one 200 km away, near Przemysl in southeastern Poland. Morphological variation across the Przemysl transect had been surveyed more than 50 years ago; though we found a significant shift at one site, there is no evidence for gross movement over this period. Morphological and electrophoretic changes coincide, and the average shape of the clines is the same across both transects. At the center, most of the change in frequency of six diagnostic allozymes occurs within w = 6.05 km (2-unit support limits 5.56-6.54 km). These steep gradients are generated not by selection on the allozymes themselves, but by associations with other loci: though these markers are unlinked, they are in strong linkage disequilibrium with each other [R = D/ = 0.22 (0.15-0.29) at the center]. Disequilibria are broken up as alleles diffuse away from the zone and flow into the new genetic background. The net barrier to the flow of genes from bombina into variegata, which is generated by these disequilibria, is B = 51 (22-81) km. The fitness of hybrids must be substantially reduced to produce such a barrier [W̄H/W̄P = 0.58 (0.54-0.68)], and this selection must be spread over many loci [N = 55 (26-88)]. Alleles introgress significantly less far than would be expected from the age of the zone and the estimated dispersal rate [σ = 0.99 (0.82-1.14) km gen.-1/2]: this implies selection of se = 0.37 (0.15-0.58)% on the enzymes themselves. There is weak but significant linkage disequilibrium well away from the center of the zone; this, together with the presence of parental and F1 genotypes, suggests some long-range migration. However, such migration is not likely to cause significant introgression.
AU - Szymura, Jacek M
AU - Nicholas Barton
ID - 3646
IS - 2
JF - Evolution
TI - The genetic structure of the hybrid zone between the fire-bellied toads Bombina bombina and B. variegata: comparisons between transects and between loci
VL - 45
ER -
TY - JOUR
AB - A method is developed that describes the effects on an arbitrary number of autosomal loci of selection on haploid and diploid stages, of nonrandom mating between haploid individuals, and of recombination. We provide exact recursions for the dynamics of allele frequencies and linkage disequilibria (nonrandom associations of alleles across loci). When selection is weak relative to recombination, our recursions provide simple approximations for the linkage disequilibria among arbitrary combinations of loci. We show how previous models of sex-independent natural selection on diploids, assortative mating between haploids, and sexual selection on haploids can be analyzed in this framework. Using our weak-selection approximations, we derive new results concerning the coevolution of male traits and female preferences under natural and sexual selection. In particular, we provide general expressions for the intensity of linkage-disequilibrium induced selection experienced by loci that contribute to female preferences for specific male traits. Our general results support the previous observation that these indirect selection forces are so weak that they are unlikely to dominate the evolution of preference-producing loci.
AU - Nicholas Barton
AU - Turelli, Michael
ID - 3647
IS - 1
JF - Genetics
TI - Natural and sexual selection on many loci
VL - 127
ER -
TY - JOUR
AB - We investigate the probability of fixation of a chromosome rearrangement in a subdivided population, concentrating on the limit where migration is so large relative to selection (m ≫ s) that the population can be thought of as being continuously distributed. We study two demes, and one- and two-dimensional populations. For two demes, the probability of fixation in the limit of high migration approximates that of a population with twice the size of a single deme: migration therefore greatly reduces the fixation probability. However, this behavior does not extend to a large array of demes. Then, the fixation probability depends primarily on neighborhood size (Nb), and may be appreciable even with strong selection and free gene flow (≈exp(-B·Nb) in one dimension, ≈exp(-B\cdotNb) in two dimensions). Our results are close to those for the more tractable case of a polygenic character under disruptive selection.
AU - Nicholas Barton
AU - Rouhani, Shahin
ID - 3648
IS - 3
JF - Evolution
TI - The probability of fixation of a new karyotype in a continuous population
VL - 45
ER -
TY - JOUR
AB - Functional cDNA clones for rat neuromedin K receptor were isolated from a rat brain cDNA library by cross-hybridization with the bovine substance K recepor cDNA. Injection of the mRNA synthesized in vitro from the cloned cDNA into Xenopus oocytes elicited electrophysiological responses to tachykinins, with the most potent sensitivity being to neuromedin K. Ligand-binding displacement in membranes of mammalian COS cells transfected with the cDNA indicated the rank order of affinity of the receptor to tachykinins; neuromedin K > substance K > substance P. The hybridization analysis showed that the neuromedin K receptor mRNA is expressed in both the brain and the peripheral tissues at different levels. The rat neuromedin K receptor consists of 452 amino acid residues and belongs to the family of G protein-coupled receptors, which are thought to have seven transmembrane domains. The sequence comparison of the rat neuromedin K, substance P, and substance K receptors revealed that these receptors are highly conserved in the seven transmembrane domains and the cytoplasmic sides of the receptors. They also show some structural characteristics, including the common presence of histidine residues in transmembrane segments V and VI and the difference in the numbers and distributions of serine and threonine residues as possible phosphorylation sites in the cytoplasmic regions. This paper thus presents the first comprehensive analysis of the molecular nature of the multiple peptide receptors that exhibit similar but pharmacologically distinguishable activities.
AU - Ryuichi Shigemoto
AU - Yokota, Yoshifumi
AU - Tsuchida, Kunihiro
AU - Nakanishi, Shigetada
ID - 2480
IS - 2
JF - Journal of Biological Chemistry
TI - Cloning and expression of a rat neuromedin K receptor cDNA
VL - 265
ER -
TY - JOUR
AB - The family of mammalian tachykinin receptors consists of substance P receptor (SPR), neuromedin K receptor (NKR) and substance K receptor (SKR). In this investigation, tissue and regional distributions of the mRNAs for the three rat tachykinin receptors were investigated by blot-hybridization and RNase-protection analyses using the previously cloned receptor cDNAs. SPR mRNA is widely distributed in both the nervous system and peripheral tissues and is expressed abundantly in the hypothalamus and olfactory buld, as well as in the urinary bladder, salivary glands and small and large intestines. In contrast, NKR mRNA is predominantly expressed in the nervous system, particularly in the cortex, hypothalamus and cerebellum, whereas SKR mRNA expression is restricted to the peripheral tissues, being abundant in the urinary bladder, large intestine, stomach and adenal glands. Thus, the mRNAs for the three tachykinin receptors show distinct patterns of expression between the nervous system and peripheral tissues. Blot-hybridization analysis in combination with S1 nuclease protection and primer-extension analyses revealed that there are two large forms of SKR mRNA expressed commonly in the peripheral tissues, and two additional small forms of the mRNA expressed specifically in the adrenal gland and eye. These analyses also showed that the multiple forms of SKR mRNA differ in the lengths of the 5' mRNA portions, and that the two small forms of the mRNA, if translated, encode a truncated SKR polypeptide lacking the first two transmembrane domains. This investigation thus provides the comprehensive analysis of the distribution and mode of expression of the mRNAs for the multiple peptide receptors and offers a new basis on which to interpret the diverse functions of multiple tachykinin peptides in the CNS and peripheral tissues.
AU - Tsuchida, Kunihiro
AU - Ryuichi Shigemoto
AU - Yokota, Yoshifumi
AU - Nakanishi, Shigetada
ID - 2481
IS - 3
JF - European Journal of Biochemistry
TI - Tissue distribution and quantitation of the mRNAs for three rat tachykinin receptors
VL - 193
ER -
TY - JOUR
AB - We previously reported a novel rat membrane protein that exhibits a voltage-dependent potassium channel activity on the basis of molecular cloning combined with an electrophysiological assay. This protein, termed I(sK) protein, is small and different from the conventional potassium channel proteins but induces selective permeation of potassium ions on its expression in Xenopus oocytes. In this investigation, we examined cellular localization of rat I(sK) protein by preparing three different types of antibody that specifically reacts with a distinct part of rat I(sK) protein. Immunohistochemical analysis using these antibody preparations demonstrated that rat I(sK) protein is confined to the apical membrane portion of epithelial cells in the proximal tubule of the kidney, the submandibular duct and the uterine endometrium. The observed tissue distribution of rat I(sK) protein was consistent with that of the I(sK) protein mRNA determined by blot hybridization analysis. In epithelial cells, the sodium, potassium-ATPase pump in the basolateral membrane generates a sodium gradient across the epithelial cell and allows sodium ions to enter the cell through the apical membrane. Thus, taking into account the cellular localization of the I(sK) protein, together with its electrophysiological properties, we discussed a possible function of the I(sK) protein, namely that this protein is involved in potassium permeation in the apical membrane of epithelial cells through the depolarizing effect of sodium entry.
AU - Sugimoto, Tetsuo
AU - Tanabe, Yasuto
AU - Ryuichi Shigemoto
AU - Iwai, Masazumi
AU - Takumi, Toru
AU - Ohkubo, Hiroaki
AU - Nakanishi, Shigetada
ID - 2528
IS - 1
JF - Journal of Membrane Biology
TI - Immunohistochemical study of a rat membrane protein which induces a selective potassium permeation: Its localization in the apical membrane portion of epithelial cells
VL - 113
ER -
TY - JOUR
AB - We consider a multidimensional system consisting of a particle of mass M and radius r (molecule), surrounded by an infinite ideal gas of point particles of mass m (atoms). The molecule is confined to the unit ball and interacts with its boundary (barrier) via elastic collision, while the atoms are not affected by the boundary. We obtain convergence to equilibrium for the molecule from almost every initial distribution on its position and velocity. Furthermore, we prove that the infinite composite system of the molecule and the atoms is Bernoulli.
AU - László Erdös
AU - Tuyen, Dao Quang
ID - 2721
IS - 5-6
JF - Journal of Statistical Physics
TI - Ergodic properties of the multidimensional rayleigh gas with a semipermeable barrier
VL - 59
ER -
TY - JOUR
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 co-planar, It also presents an algorithm that in O(n log 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 - 4060
IS - 3-4
JF - Journal of Symbolic Computation
TI - Tetrahedrizing point sets in three dimensions
VL - 10
ER -
TY - JOUR
AB - This paper describes a general-purpose programming technique, called Simulation of Simplicity, that can be used to cope with degenerate input data for geometric algorithms. It relieves the programmer from the task of providing a consistent treatment for every single special case that can occur. The programs that use the technique tend to be considerably smaller and more robust than those that do not use it. We believe that this technique will become a standard tool in writing geometric software.
AU - Herbert Edelsbrunner
AU - Mücke, Ernst P
ID - 4063
IS - 1
JF - ACM Transactions on Graphics
TI - Simulation of simplicity: A technique to cope with degenerate cases in geometric algorithms
VL - 9
ER -
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 -