Author Keywords: Graph drawing; Voronoi diagrams; Graph characterization; Geometric graphs 相似文献
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991.
Let G be a 4-regular plane graph and suppose that G has a cycle decomposition S (i.e., each edge of G is in exactly one cycle of the decomposition) with every pair of adjacent edges on a face always in different cycles of S. Such a graph G arises as a superposition of simple closed curves in the plane with tangencies disallowed. Two 4-chromatic edge critical graphs of order 48 generated by four curves are presented. 相似文献
992.
We study the problem of characterizing sets of points whose Voronoi diagrams are trees and if so, what are the combinatorial properties of these trees. The second part of the problem can be naturally turned into the following graph drawing question: Given a tree T, can one represent T so that the resulting drawing is a Voronoi diagram of some set of points? We investigate the problem both in the Euclidean and in the Manhattan metric. The major contributions of this paper are as follows.
• We characterize those trees that can be drawn as Voronoi diagrams in the Euclidean metric.
• We characterize those sets of points whose Voronoi diagrams are trees in the Manhattan metric.
• We show that the maximum vertex degree of any tree that can be drawn as a Manhattan Voronoi diagram is at most five and prove that this bound is tight.
• We characterize those binary trees that can be drawn as Manhattan Voronoi diagrams.
993.
994.
Biomembranes consist of a lipid bi-layer into which proteins are embedded to fulfill numerous tasks in localized regions of
the membrane. Often, the proteins have to reach these regions by simple diffusion. Motivated by the observation that IP3 receptor channels (IP3R) form clusters on the surface of the endoplasmic reticulum (ER) during ATP-induced calcium release, the reaction rate of
small diffusing molecules on a cylindrical membrane is calculated based on the Smoluchowski approach. In this way, the cylindrical
topology of the tubular ER is explicitly taken into account. The problem can be reduced to the solution of the diffusion equation
on a finite cylindrical surface containing a small absorbing hole. The solution is constructed by matching appropriate ‘inner’
and ‘outer’ asymptotic expansions. The asymptotic results are compared with those from numerical simulations and excellent
agreement is obtained. For realistic parameter sets, we find reaction rates in the range of experimentally measured clustering
rates of IP3R. This supports the idea that clusters are formed by a purely diffusion limited process. 相似文献
995.
In our earlier paper [9], generalizing the well known notion of graceful graphs, a (p, m, n)-signed graph S of order p, with m positive edges and n negative edges, is called graceful if there exists an injective function f that assigns to its p vertices integers 0, 1,...,q = m + n such that when to each edge uv of S one assigns the absolute difference |f(u)-f(v)| the set of integers received by the positive edges of S is {1,2,...,m} and the set of integers received by the negative edges of S is {1,2,...,n}. Considering the conjecture therein that all signed cycles Zk, of admissible length k 3 and signed structures, are graceful, we establish in this paper its truth for all possible signed cycles of lengths 0, 2 or 3 (mod 4) in which the set of negative edges forms a connected subsigraph. 相似文献
996.
In this paper, we make estimates for the radius of balls contained in some component of the complementary of a complete hypersurface
into a space form, generalizing and improving analogous radius estimates for embedded compact hypersurfaces obtained by Blaschke,
Koutroufiotis and the authors. The results are obtained using an algebraic lemma and a tangency principle related with the
length of the second fundamental form. The algebraic lemma also is used to improve a result for graphs due to Hasanis–Vlachos.
The first author dedicates this work to his parents José (in memoriam) and Herondina 相似文献
997.
Let D=(V,E) be a minimally k-edge-connected simple directed graph. We prove that there is a function f(k) such that |V|f(k) implies |E|2k(|V|–k). We also determine the extremal graphs whose size attains this upper bound.Basic Research in Computer Science, funded by the Danish National Research Foundation.Supported by the MTA-ELTE Egerváry Research Group on Combinatorial Optimization, and the Hungarian Scientific Research Fund grant No. F034930, T037547, and FKFP grant No. 0143/2001. Part of this research was done when the second author visited BRICS, University of Aarhus, Denmark. 相似文献
998.
A directed acyclic graph (DAG) representation of optimization problems represents each variable, each operation, and each
constraint in the problem formulation by a node of the DAG, with edges representing the flow of the computation. Using bounds
on ranges of intermediate results, represented as weights on the nodes and a suitable mix of forward and backward evaluation,
it is possible to give efficient implementations of interval evaluation and automatic differentiation. It is shown how to
combine this with constraint propagation techniques to produce narrower interval derivatives and slopes than those provided
by using only interval automatic differentiation preceded by constraint propagation. The implementation is based on earlier
work by L.V. Kolev, (1997), Reliable Comput., 3, 83–93 on optimal slopes and by C. Bliek, (1992), Computer Methods for Design Automation, PhD Thesis, Department of Ocean Engineering, Massachusetts Institute of Technology on backward slope evaluation. Care is
taken to ensure that rounding errors are treated correctly. Interval techniques are presented for computing from the DAG useful
redundant constraints, in particular linear underestimators for the objective function, a constraint, or a Lagrangian. The
linear underestimators can be found either by slope computations, or by recursive backward underestimation. For sufficiently
sparse problems the work is proportional to the number of operations in the calculation of the objective function (resp. the
Lagrangian).
Mathematics Subject Classification (2000). primary 65G40, secondary 90C26 相似文献
999.
Isaac Pesenson 《Proceedings of the American Mathematical Society》2005,133(12):3647-3655
The notion of band limited functions is introduced on a quantum graph. The main results of the paper are a uniqueness theorem and a reconstruction algorithm of such functions from discrete sets of values. It turns out that some of our band limited functions can have compact supports and their frequencies can be localized on the ``time" side. It opens an opportunity to consider signals of a variable band width and to develop a sampling theory with variable rate of sampling.
1000.
Gérard?Ben ArousEmail author Leonid V.?Bogachev Stanislav A.?Molchanov 《Probability Theory and Related Fields》2005,132(4):579-612
We study limiting distributions of exponential sums as t→∞, N→∞, where (Xi) are i.i.d. random variables. Two cases are considered: (A) ess sup Xi = 0 and (B) ess sup Xi = ∞. We assume that the function h(x)= -log P{Xi>x} (case B) or h(x) = -log P {Xi>-1/x} (case A) is regularly varying at ∞ with index 1 < ϱ <∞ (case B) or 0 < ϱ < ∞ (case A). The appropriate growth scale of N relative to t is of the form , where the rate function H0(t) is a certain asymptotic version of the function (case B) or (case A). We have found two critical points, λ1<λ2, below which the Law of Large Numbers and the Central Limit Theorem, respectively, break down. For 0 < λ < λ2, under the slightly stronger condition of normalized regular variation of h we prove that the limit laws are stable, with characteristic exponent α = α (ϱ, λ) ∈ (0,2) and skewness parameter β ≡ 1.Research supported in part by the DFG grants 436 RUS 113/534 and 436 RUS 113/722.Mathematics Subject Classification (2000): 60G50, 60F05, 60E07 相似文献