He apparently slid off the end of his unknotted rope and fell to his death.
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She then unknotted all of the buns, which revealed a "cool, almost dread-like texture," she says.
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Suddenly I too can see the point of having my questions answered, the teasing threads unknotted, cases closed.
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The dispersal of her things suggests that Plath's story, controlled so tightly for so long, has finally begun to come unknotted.
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One of Ochiai's unknots featuring 139 vertices, for example, was originally unknotted by computer in 108 hours, but this time has been reduced in more recent research to 10 minutes.
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Three linked golden rectangles in a regular icosahedron A realization of the Borromean rings by three mutually perpendicular golden rectangles can be found within a regular icosahedron by connecting three opposite pairs of its edges. Every three unknotted polygons in Euclidean space may be combined, after a suitable scaling transformation, to form the Borromean rings. If all three polygons are planar, then scaling is not needed. More generally, Matthew Cook has conjectured that any three unknotted simple closed curves in space, not all circles, can be combined without scaling to form the Borromean rings.
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The Lickorish–Wallace theorem states that any closed, orientable, connected 3-manifold may be obtained by performing Dehn surgery on a framed link in the 3-sphere with \pm 1 surgery coefficients. Furthermore, each component of the link can be assumed to be unknotted.
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This was the invitation to attend the completion ceremony:Invitation for the completion and grand opening of the Unweave the Weave project According to the White Bear Press,White Bear Press Home Page state and local employees unknotted a rope instead of cutting a ribbon to mark the project complete.
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The bowline is a quick, practical method of forming a loop in the end of a piece of rope. However, the bowline has an awkward tendency to shake undone when not loaded. The bowline also reduces the strength of the rope at the knot to ~45% of the original unknotted strength.
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In the mathematical theory of knots, the Fary–Milnor theorem, named after István Fáry and John Milnor, states that three-dimensional smooth curves with small total curvature must be unknotted. The theorem was proved independently by Fáry in 1949 and Milnor in 1950. It was later shown to follow from the existence of quadrisecants .
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Take a copy of S^3, the three-dimensional sphere. Now find a compact unknotted solid torus T_1 inside the sphere. (A solid torus is an ordinary three-dimensional doughnut, i.e., a filled-in torus, which is topologically a circle times a disk.) The closed complement of the solid torus inside S^3 is another solid torus.
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Before she drowned, she unknotted her boddice to allow Kate to crawl away and escape. He asked Gladys how Kate could have escaped unbeknownst to anybody, but he no longer sensed Gladys. Thereafter, Grainier lived in his cabin, even through the winters. To pay for lodging for his horses during the winter, he worked in the Washington woods one summer, his last time doing so.
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42, No. 2, 2001, pp. 301–306. Similarly a stuck open chain is an open polygonal chain such that the segments may not be aligned by moving rigidly its segments. Topologically such a chain can be unknotted, but the limitation of using only rigid motions of the segments can create nontrivial knots in such a chain. Consideration of such "stuck" configurations arises in the study of molecular chains in biochemistry.
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In mathematics, a stuck unknot is a closed polygonal chain that is topologically equal to the unknot but cannot be deformed to a simple polygon by rigid motions of the segments.G. Aloupis, G. Ewald, and G. T. Toussaint, "More classes of stuck unknotted hexagons," Contributions to Algebra and Geometry, Vol. 45, No. 2, 2004, pp. 429–434.G. T. Toussaint, "A new class of stuck unknots in Pol-6," Contributions to Algebra and Geometry, Vol.
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To remove knots from highly crowded chromatin, one would need an active process that should not only provide the energy to move the system from the state of topological equilibrium but also guide topoisomerase-mediated passages in such a way that knots would be efficiently unknotted instead of making the knots even more complex. It has been shown that the process of chromatin-loop extrusion is ideally suited to actively unknot chromatin fibres in interphase chromosomes.
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Let M be a Mazur manifold that is constructed as S^1 \times D^3 union a 2-handle. Here is a sketch of Mazur's argument that the double of such a Mazur manifold is S^4. M \times [0,1] is a contractible 5-manifold constructed as S^1 \times D^4 union a 2-handle. The 2-handle can be unknotted since the attaching map is a framed knot in the 4-manifold S^1 \times S^3.
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The craftsmanship of Elves displayed their subtle, instinctive control of magic. Lembas, a food given to the Fellowship by the Elves of Lothlórien, was capable of keeping a "traveller on his feet for a day of long labour".The Fellowship of the Ring, book 2, ch. 8 "Farewell to Lórien" Their hithlain rope had properties ranging from being an excellent material to frankly magical: it was strong, tough, light, long, soft to the hand, packed close and unknotted itself at spoken command.
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Example 1: A connect-sum of a trefoil and figure-8 knot. A satellite knot K can be picturesquely described as follows: start by taking a nontrivial knot K' lying inside an unknotted solid torus V. Here "nontrivial" means that the knot K' is not allowed to sit inside of a 3-ball in V and K' is not allowed to be isotopic to the central core curve of the solid torus. Then tie up the solid torus into a nontrivial knot. Example 2: The Whitehead double of the figure-8.
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Essential ingredients of the proof are their joint work with Marc Culler and Peter Shalen on the cyclic surgery theorem, combinatorial techniques in the style of Litherland, thin position, and Scharlemann cycles. For link complements, it is not in fact true that links are determined by their complements. For example, JHC Whitehead proved that there are infinitely many links whose complements are all homeomorphic to the Whitehead link. His construction is to twist along a disc spanning an unknotted component (as is the case for either component of the Whitehead link).
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Retrieved on 2017-04-26. though similar structures can be seen in Roman mosaics c. 200–250 AD. An example of a Möbius strip can be created by taking a paper strip, giving one end a half-twist, and then joining the ends to form a loop; its boundary is a simple closed curve which can be traced by single unknotted string. Any topological space homeomorphic to this example is also called a Möbius strip, allowing for a very wide variety of geometric realizations as surfaces with a definite size and shape.
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Since V is an unknotted solid torus, S^3 \setminus V is a tubular neighbourhood of an unknot J. The 2-component link K' \cup J together with the embedding f is called the pattern associated to the satellite operation. A convention: people usually demand that the embedding f \colon V \to S^3 is untwisted in the sense that f must send the standard longitude of V to the standard longitude of f(V). Said another way, given any two disjoint curves c_1,c_2 \subset V, f preserves their linking numbers i.e.: lk(f(c_1),f(c_2))=lk(c_1,c_2).
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By repeatedly simplifying the graph whenever such a subgraph is found, they reduce the problem to one in which the remaining graph has bounded treewidth, at which point it can be solved by dynamic programming. The problem of efficiently testing whether a given embedding is flat or linkless was posed by . It remains unsolved, and is equivalent in complexity to unknotting problem, the problem of testing whether a single curve in space is unknotted. Testing unknottedness (and therefore, also, testing linklessness of an embedding) is known to be in NP but is not known to be NP-complete..
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Also in 2000 was William Taylor's creation of an alternative computational method to analyze protein knotting that set the termini at a fixed point far enough away from the knotted component of the molecule that the knot type could be well-defined. In this study, Taylor discovered a deep 4_1 knot in a protein. With this study, Taylor confirmed the existence of deeply knotted proteins. In 2007, Eric Yeates reported the identification of a molecular slipknot, which is when the molecule contains knotted subchains even though their backbone chain as a whole is unknotted and does not contain completely knotted structures that are easily detectable by computational models.
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It has been a puzzle how decondensed interphase chromosomes remain essentially unknotted. The natural expectation is that in the presence of type II DNA topoisomerases that permit passages of double-stranded DNA regions through each other, all chromosomes should reach the state of topological equilibrium. The topological equilibrium in highly crowded interphase chromosomes forming chromosome territories would result in formation of highly knotted chromatin fibres. However, Chromosome Conformation Capture (3C) methods revealed that the decay of contacts with the genomic distance in interphase chromosomes is practically the same as in the crumpled globule state that is formed when long polymers condense without formation of any knots.
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Causal dynamical triangulation does not assume any pre-existing arena (dimensional space), but rather attempts to show how the spacetime fabric itself evolves. Christoph Schiller's Strand Model attempts to account for the gauge symmetry of the Standard Model of particle physics, U(1)×SU(2)×SU(3), with the three Reidemeister moves of knot theory by equating each elementary particle to a different tangle of one, two, or three strands (selectively a long prime knot or unknotted curve, a rational tangle, or a braided tangle respectively). Another attempt may be related to ER=EPR, a conjecture in physics stating that entangled particles are connected by a wormhole (or Einstein–Rosen bridge).
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A linkless embedding is an embedding of the graph with the property that any two cycles are unlinked; a knotless embedding is an embedding of the graph with the property that any single cycle is unknotted. The graphs that have linkless embeddings have a forbidden graph characterization involving the Petersen family, a set of seven graphs that are intrinsically linked: no matter how they are embedded, some two cycles will be linked with each other.. A full characterization of the graphs with knotless embeddings is not known, but the complete graph is one of the minimal forbidden graphs for knotless embedding: no matter how is embedded, it will contain a cycle that forms a trefoil knot..
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Different presentations of "Kirby calculus" have a different set of moves and these are sometimes called Kirby moves. Kirby's original formulation involved two kinds of move, the "blow-up" and the "handle slide"; Roger Fenn and Colin Rourke exhibited an equivalent construction in terms of a single move, the Fenn–Rourke move, that appears in many expositions and extensions of the Kirby calculus. Dale Rolfsen's book, Knots and Links, from which many topologists have learned the Kirby calculus, describes a set of two moves: 1) delete or add a component with surgery coefficient infinity 2) twist along an unknotted component and modify surgery coefficients appropriately (this is called the Rolfsen twist). This allows an extension of the Kirby calculus to rational surgeries.
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The music here feels loose and unknotted, broken open in the way you can only be after a tragedy." Pitchfork later named "Daydreaming" and "True Love Waits" among the best songs of 2016. Eric Renner Brown of Entertainment Weekly praised the variety and scale: "By nature, Radiohead albums will always be somewhat epic, but this one is more consistently grandiose than any of the band's releases since 2000's masterpiece Kid A." Jon Pareles, writing for The New York Times, wrote that A Moon Shaped Pool was perhaps "[Radiohead's] darkest statement – though the one with the band's most pastoral surface". He praised Yorke's vocals and Greenwood's string arrangements, writing: "Both Mr. Yorke and Mr. Greenwood are relentlessly inquisitive listeners, lovers of melody and explorers of idioms, makers of puzzles who don't shy away from emotion.
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