It was like unknotting scar tissue and re-finding my inner confident self.
|
|
The book is, blessedly, not about offering a diagnosis or unknotting the riddle of how Kate understands time; rather it is about illuminating the riddle itself.
|
|
The slow, unglamorous work of unknotting ourselves from fear is something we all have to work towards: through electoral politics, of course, and involvement in the great civic project of this nation.
|
|
He especially liked the "accelerometer system as a proxy to determine the role of the inertia of the loop and free end of the shoelace in the unknotting," he told Gizmodo in an email.
|
|
But better yet is the genius with which he appropriates spiraling configurations of the classical dancer's arms and transforms them into B-Boy moves, knotting and unknotting his limbs with miraculous fluidity and speed.
|
|
Zellner's tactics may be flashy—she tweets openly about the case, and still does—but they come from a place of distrust for institutions, an instinct that has guided her work unknotting so many false convictions.
|
|
First steps toward determining the computational complexity were undertaken in proving that the problem is in larger complexity classes, which contain the class P. By using normal surfaces to describe the Seifert surfaces of a given knot, showed that the unknotting problem is in the complexity class NP. claimed the weaker result that unknotting is in AM ∩ co- AM; however, later they retracted this claim.Mentioned as a "personal communication" in reference [15] of . In 2011, Greg Kuperberg proved that (assuming the generalized Riemann hypothesis) the unknotting problem is in co- NP, and in 2016, Marc Lackenby provided an unconditional proof of co-NP membership. The unknotting problem has the same computational complexity as testing whether an embedding of an undirected graph in Euclidean space is linkless.
|
|
Two simple diagrams of the unknot A tricky unknot diagram by Morwen Thistlethwaite In mathematics, the unknotting problem is the problem of algorithmically recognizing the unknot, given some representation of a knot, e.g., a knot diagram. There are several types of unknotting algorithms. A major unresolved challenge is to determine if the problem admits a polynomial time algorithm; that is, whether the problem lies in the complexity class P.
|
|
Hass is known for proving the equal-volume special case of the double bubble conjecture, for proving that the unknotting problem is in NP, and for giving an exponential bound on the number of Reidemeister moves needed to reduce the unknot to a circle.
|
|
There are related concepts of average crossing number and asymptotic crossing number. Both of these quantities bound the standard crossing number. Asymptotic crossing number is conjectured to be equal to crossing number. Other numerical knot invariants include the bridge number, linking number, stick number, and unknotting number.
|
|
Type IA also requires an exposed single-stranded region within the DNA substrate. The linking number of DNA changes with relaxation. Type IA topoisomerase can catalyze catenation, decatenation, knotting and unknotting of the DNA. There are three classes within the subfamily of type IB topoisomerase: topoisomerase I in eukaryotes, topoisomerase V in prokaryotes, and the poxvirus topoisomerase.
|
|
The four half-twist stevedore knot is created by passing the one end of an unknot with four half-twists through the other. All twist knots have unknotting number one, since the knot can be untied by unlinking the two ends. Every twist knot is also a 2-bridge knot. Of the twist knots, only the unknot and the stevedore knot are slice knots.
|
|
The link group is not the fundamental group of the link complement, since the components of the link are allowed to move through themselves, though not each other, but thus is a quotient group of the link complement's fundamental group, since one can start with elements of the fundamental group, and then by knotting or unknotting components, some of these elements may become equivalent to each other.
|
|
Simultaneous, but different, approaches by other mathematicians resulted in the Witten–Reshetikhin–Turaev invariants and various so-called "quantum invariants", which appear to be the mathematically rigorous version of Witten's invariants . In the 1980s John Horton Conway discovered a procedure for unknotting knots gradually known as Conway notation. In 1992, the Journal of Knot Theory and Its Ramifications was founded, establishing a journal devoted purely to knot theory. In the early 1990s, knot invariants which encompass the Jones polynomial and its generalizations, called the finite type invariants, were discovered by Vassiliev and Goussarov.
|
|
Lackenby in 1997 Marc Lackenby is a professor of mathematics at the University of Oxford whose research concerns knot theory, low-dimensional topology, and group theory. Lackenby studied mathematics at the University of Cambridge beginning in 1990, and earned his Ph.D. in 1997, with a dissertation on Dehn Surgery and Unknotting Operations supervised by W. B. R. Lickorish. After positions as Miller Research Fellow at the University of California, Berkeley and as Research Fellow at Cambridge, he joined Oxford as a Lecturer and Fellow of St Catherine's in 1999. He was promoted to Professor at Oxford in 2006.
|
|
Force spectroscopy measures the behavior of a molecule under stretching or torsional mechanical force. In this way a great deal has been learned in recent years about the mechanochemical coupling in the enzymes responsible for muscle contraction, transport in the cell, energy generation (F1-ATPase), DNA replication and transcription (polymerases), DNA unknotting and unwinding (topoisomerases and helicases). As a single-molecule technique, as opposed to typical ensemble spectroscopies, it allows a researcher to determine properties of the particular molecule under study. In particular, rare events such as conformational change, which are masked in an ensemble, may be observed.
|
|
In 2011, Vázquez received a National Science Foundation CAREER Award to research topological mechanisms of DNA unlinking. In 2012, she was the first San Francisco State University faculty member to receive the Presidential Early Career Award for Scientists and Engineers. She received a grant for computer analysis of DNA unknotting from the National Institutes of Health in 2013. In 2016, she was chosen for the Blackwell-Tapia prize, which is awarded every other year to a mathematician who has made significant research contributions in their field, and who has worked to address the problem of under-representation of minority groups in mathematics.
|
|
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..
|
|
The Whitehead link is link homotopic to the unlink, but not isotopic to the unlink. The link group of an n-component link is essentially the set of (n + 1)-component links extending this link, up to link homotopy. In other words, each component of the extended link is allowed to move through regular homotopy (homotopy through immersions), knotting or unknotting itself, but is not allowed to move through other component. This is a weaker condition than isotopy: for example, the Whitehead link has linking number 0, and thus is link homotopic to the unlink, but it is not isotopic to the unlink.
|
|
The double-helical configuration of DNA strands makes them difficult to separate, which is required by helicase enzymes if other enzymes are to transcribe the sequences that encode proteins, or if chromosomes are to be replicated. In circular DNA, in which double- helical DNA is bent around and joined in a circle, the two strands are topologically linked, or knotted. Otherwise identical loops of DNA, having different numbers of twists, are topoisomers, and cannot be interconverted without the breaking of DNA strands. Topoisomerases catalyze and guide the unknotting or unlinking of DNA by creating transient breaks in the DNA using a conserved tyrosine as the catalytic residue.
|
|
Wimpel painted on linen, Jewish Museum (New York) When the child comes of age to begin learning Torah (age 3), he and his family bring the wimpel to the synagogue for Shabbat morning services. After the Torah reading, the child performs the ritual of gelila, perhaps with the help of his father, by wrapping the wimpel many times around the Torah scroll and tucking the end of the cloth into the folds. In this way, the child's individual responsibilities to God and His commandments are literally wrapped around his communal responsibilities, a figurative lesson for the child and his family. Rabbi Shimon Schwab, Rav of Khal Adath Yeshurun synagogue in Washington Heights, New York, which revived the custom among the younger generation of Yekke congregants, suggested that perhaps the source of the wimpel custom was to avoid knotting and unknotting a tie around the Torah on Shabbat (see the 39 categories of activity prohibited on the Sabbath).
|
|