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Packing And Covering Triangles In Tripartite Graphs
"... . It is shown that if G is a tripartite graph such that the maximum size of a set of pairwise edgedisjoint triangles is (G), then there is a set C of edges of G of size at most (2 ")(G) such that E(T ) \ C 6= ; for every triangle T of G, where " > 0:044. This improves the previous bo ..."
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Cited by 4 (2 self)
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bound of (7=3)(G) due to Tuza [6]. x0. Introduction In this note we are concerned with a packing and covering problem for triangles in graphs. Let a graph G be given. We say that a family F of triangles in G is independent if the elements of F are pairwise edgedisjoint. Moreover, we say that a set C
Observation of BoseEinstein condensation in a dilute atomic vapor
 Science
, 1995
"... A BoseEinstein condensate was produced in a vapor of rubidium87 atoms that was confined by magnetic fields and evaporatively cooled. The condensate fraction first appeared near a temperature of 170 nanokelvin and a number density of 2.5 x 1012 per cubic centimeter and could be preserved for more t ..."
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Cited by 352 (8 self)
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A BoseEinstein condensate was produced in a vapor of rubidium87 atoms that was confined by magnetic fields and evaporatively cooled. The condensate fraction first appeared near a temperature of 170 nanokelvin and a number density of 2.5 x 1012 per cubic centimeter and could be preserved for more than 15 seconds. Three primary signatures of BoseEinstein condensation were seen. (i) On top of a broad thermal velocity distribution, a narrow peak appeared that was centered at zero velocity. (ii) The fraction of the atoms that were in this lowvelocity peak increased abruptly as the sample temperature was lowered. (iii) The peak exhibited a nonthermal, anisotropic velocity distribution expected of the minimumenergy quantum state of the magnetic trap in contrast to the isotropic, thermal velocity distribution observed in the broad uncondensed fraction. On the microscopic quantum level, there are profound differences between fermions (particles with half integer spin) and bosons (particles with integer spin). Every statistical mechanics text discusses how these differences
FPT algorithms for pathtransversals and cycletransversals problems in graphs
"... Abstract. In this article, we consider problems on graphs of the following form: given a graph, remove p edges/vertices to achieve some property. The first kind of problems are separation problems on graphs, where we aim at separating distinguished vertices in a graph. The second kind of problems ar ..."
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Cited by 23 (2 self)
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Abstract. In this article, we consider problems on graphs of the following form: given a graph, remove p edges/vertices to achieve some property. The first kind of problems are separation problems on graphs, where we aim at separating distinguished vertices in a graph. The second kind of problems
Packing Odd Circuits in Eulerian Graphs
 Journal of Combinatorial Theory, Series B
"... Let C be the clutter of odd circuits of a signed graph (G; ). For nonnegative integral edge{weights w, we are interested in the linear program min(w t x : x(C) 1; for C 2 C; and x 0), which we denote by (P ). Solving the related integer program is clearly equivalent to the maximum cut problem, ..."
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Cited by 10 (3 self)
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Let C be the clutter of odd circuits of a signed graph (G; ). For nonnegative integral edge{weights w, we are interested in the linear program min(w t x : x(C) 1; for C 2 C; and x 0), which we denote by (P ). Solving the related integer program is clearly equivalent to the maximum cut problem
Finding Odd Cycle Transversals
, 2003
"... We present an O(mn) algorithm to determine whether a graph G with m edges and n vertices has an odd cycle cover of order at most k, for any fixed k. We also obtain an algorithm that determines, in the same time, whether a graph has a half integral packing of odd cycles of weight k. ..."
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Cited by 97 (2 self)
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We present an O(mn) algorithm to determine whether a graph G with m edges and n vertices has an odd cycle cover of order at most k, for any fixed k. We also obtain an algorithm that determines, in the same time, whether a graph has a half integral packing of odd cycles of weight k.
Conformal Uniformization And Packings
"... . A new short proof is given for Brandt and Harrington's theorem about conformal uniformizations of planar finitely connected domains as domains with boundary components of specified shapes. This method of proof generalizes to periodic domains. Letting the uniformized domains degenerate in a co ..."
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Cited by 8 (3 self)
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controlled manner, we deduce the existence of packings of specified shapes and with specified combinatorics. The shapes can be arbitrary smooth disks specified up to homothety, for example. The combinatorics of the packing is described by the contacts graph, which can be specified to be any finite planar
Automated 3D Extraction of Inner and Outer Surfaces of Cerebral Cortex from MRI
 NEUROIMAGE
, 2000
"... Automatic computer processing of large multidimensional images such as those produced by magnetic resonance imaging (MRI) is greatly aided by deformable models, which are used to extract, identify, and quantify specific neuroanatomic structures. A general method of deforming polyhedra is presented h ..."
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Cited by 179 (17 self)
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Automatic computer processing of large multidimensional images such as those produced by magnetic resonance imaging (MRI) is greatly aided by deformable models, which are used to extract, identify, and quantify specific neuroanatomic structures. A general method of deforming polyhedra is presented here, with two novel features. First, explicit prevention of selfintersecting surface geometries is provided, unlike conventional deformable models, which use regularization constraints to discourage but not necessarily prevent such behavior. Second, deformation of multiple surfaces with intersurface proximity constraints allows each surface to help guide other surfaces into place using modelbased constraints such as expected thickness of an anatomic surface. These two features are used advantageously to identify automatically the total surface of the outer and inner boundaries of cerebral cortical gray matter from normal human MR images, accurately locating the depths of the sulci, even where noise and partial volume artifacts in the image obscure the visibility of sulci. The extracted surfaces are enforced to be simple twodimensional manifolds (having the topology of a sphere), even though the data may have topological holes. This automatic 3D cortex segmentation technique has been applied to 150 normal subjects, simultaneously extracting both the gray/white and gray/cerebrospinal fluid interface from each individual. The collection of surfaces has been used to create a spatial map of the mean and standard deviation for the location and the thickness of cortical gray matter. Three alternative criteria for defining cortical thickness at each cortical location were developed and compared. These results are shown to corroborate published postmortem and in vivo measurements of cortical thickness.
Constructions for Difference Triangle Sets
"... Abstractâ€”Difference triangle sets are useful in many practical problems of information transmission. This correspondence studies combinatorial and computational constructions for difference triangle sets having small scopes. Our algorithms have been used to produce difference triangle sets whose sco ..."
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scopes are the best currently known. Index Termsâ€”Algorithms, difference packings, difference triangle sets. I.
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