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25
Finding the Best Viewpoints for ThreeDimensional Graph Drawings
 Proc. 5th International Symp. on Graph Drawing (GD ’97
, 1997
"... In this paper we address the problem of finding the best viewpoints for threedimensional straightline graph drawings. We define goodness in terms of preserving the relational structure of the graph, and develop two continuous measures of goodness under orthographic parallel projection. We develop ..."
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Cited by 19 (0 self)
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In this paper we address the problem of finding the best viewpoints for threedimensional straightline graph drawings. We define goodness in terms of preserving the relational structure of the graph, and develop two continuous measures of goodness under orthographic parallel projection. We develop Voronoi variants to find the best viewpoints under these measures, and present results on the complexity of these diagrams.
Nonconstructible complexes and the bridge index
, 1999
"... We show that if a 3dimensional polytopal complex has a knot in its 1skeleton, where the bridge index of the knot is larger than the number of edges of the knot, then the complex is not constructible, and hence, not shellable. As an application we settle a conjecture of Hetyei concerning the shella ..."
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Cited by 11 (2 self)
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We show that if a 3dimensional polytopal complex has a knot in its 1skeleton, where the bridge index of the knot is larger than the number of edges of the knot, then the complex is not constructible, and hence, not shellable. As an application we settle a conjecture of Hetyei concerning the shellability of cubical barycentric subdivisions of 3spheres. We also obtain similar bounds concluding that a 3sphere or 3ball is nonshellable or not vertex decomposable. These two last bounds are sharp.
An obstruction to embedding 4tangles in links
 J. Knot Theory Ramifications
, 1999
"... Abstract. We consider the ways in which a 4tangle T inside a unit cube can be extended outside the cube into a knot or link L. We present two links n(T) and d(T) such that the greatest common divisor of the determinants of these two links always divides the determinant of the link L. In order to pr ..."
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Cited by 6 (0 self)
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Abstract. We consider the ways in which a 4tangle T inside a unit cube can be extended outside the cube into a knot or link L. We present two links n(T) and d(T) such that the greatest common divisor of the determinants of these two links always divides the determinant of the link L. In order to prove this result we give a twointeger invariant of 4tangles. Calculations are facilitated by viewing the determinant as the Kauffman bracket at a fourth root of1, which sets the loop factor to zero. For rational tangles, our invariant coincides with the value of the associated continued fraction. 1.
A Stevedore’s Protein Knot
, 2010
"... Protein knots, mostly regarded as intriguing oddities, are gradually being recognized as significant structural motifs. Seven distinctly knotted folds have already been identified. It is by and large unclear how these exceptional structures actually fold, and only recently, experiments and simulatio ..."
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Protein knots, mostly regarded as intriguing oddities, are gradually being recognized as significant structural motifs. Seven distinctly knotted folds have already been identified. It is by and large unclear how these exceptional structures actually fold, and only recently, experiments and simulations have begun to shed some light on this issue. In checking the new protein structures submitted to the Protein Data Bank, we encountered the most complex and the smallest knots to date: A recently uncovered ahaloacid dehalogenase structure contains a knot with six crossings, a socalled Stevedore knot, in a projection onto a plane. The smallest protein knot is present in an as yet unclassified protein fragment that consists of only 92 amino acids. The topological complexity of the Stevedore knot presents a puzzle as to how it could possibly fold. To unravel this enigma, we performed folding simulations with a structurebased coarsegrained model and uncovered a possible mechanism by which the knot forms in a single loop flip.
A SymbolicNumeric Algorithm for Computing the Alexander polynomial of . . .
"... We report on a symbolicnumeric algorithm for computing the Alexander polynomial of each singularity of a plane complex algebraic curve defined by a polynomial with coefficients of limited accuracy, i.e. the coefficients are both exact and inexact data. We base the algorithm on combinatorial methods ..."
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Cited by 3 (3 self)
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We report on a symbolicnumeric algorithm for computing the Alexander polynomial of each singularity of a plane complex algebraic curve defined by a polynomial with coefficients of limited accuracy, i.e. the coefficients are both exact and inexact data. We base the algorithm on combinatorial methods from knot theory which we combine with computational geometry algorithms in order to compute efficient and accurate results. Nonetheless the problem we are dealing with is illposed, in the sense that tiny perturbations in the coefficients of the defining polynomial cause huge errors in the computed results.
Tie knots, random walks and topology
 PHYSICA A
, 2000
"... Necktie knots are inherently topological structures; what makes them tractable is the particular manner in which they are constructed. This observation motivates a map between tie knots and persistent walks on a triangular lattice. The topological structure embedded in a tie knot may be determined b ..."
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Necktie knots are inherently topological structures; what makes them tractable is the particular manner in which they are constructed. This observation motivates a map between tie knots and persistent walks on a triangular lattice. The topological structure embedded in a tie knot may be determined by appropriately manipulating its projection; we derive corresponding rules for tie knot sequences. We classify knots according to their size and shape and quantify the number of knots in a class. Aesthetic knots are characterised by the conditions of symmetry and balance. Of the 85 knots which may be tied with conventional tie, we recover the four traditional knots and introduce nine new aesthetic ones. For large (though impractical) halfwinding number, we
Some Examples of TemperleyLieb Algebras
"... TemperleyLieb algebras appear in exactly solvable statistical mechanics models as well as in the knot theory in mathematics. We have found many new solutions of TemperleyLieb algebra in addition to some old known ones. We also discuss their rel evance with respect to knot invariant. We have also ..."
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TemperleyLieb algebras appear in exactly solvable statistical mechanics models as well as in the knot theory in mathematics. We have found many new solutions of TemperleyLieb algebra in addition to some old known ones. We also discuss their rel evance with respect to knot invariant. We have also found a class of solutions of the YangBaxter equation without the spectral parameter which satisfy a quadratic equation. PACS: 02.90.+p, 05.90+m 1.
BMC Bioinformatics BioMed Central Methodology article Coloring the Mu transpososome
, 2006
"... © 2006 Darcy et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License ..."
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© 2006 Darcy et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License