Unknotting operations on knots and links

2021 ◽  
Vol 30 (02) ◽  
pp. 2171001
Author(s):  
Ayaka Shimizu
Keyword(s):  
Social Sciences ◽  
Mathematical Theory ◽  
Knot Theory ◽  
American Mathematical Society ◽  
Mathematical Society ◽  
The Social ◽  
Knots And Links

By considering unknotting operations, we obtain ways of measuring how knotted a knot is. Unknotting phenomena can be seen not only in knot theory, but also in various settings such as DNA knots, mind knots and so on ([C. C. Adams, The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots (American Mathematical Society, Providence, RI, 2004); A. Kawauchi, K. Kishimoto and A. Shimizu, Knot theory and game (in Japanese) (Asakura Publishing, Tokyo, 2013); L. Rudolph, Qualitative Mathematics for the Social Sciences (Routledge, London, 2013); K. Murasugi, Knot Theory and Its Applications, Translated from the 1993 Japanese original by Bohdan Kupita (Birkhauser, Boston, MA, 1996)], etc.). In this paper, we see how knots can be unknotted (and therefore how they are knotted) by considering various unknotting operations and their associated unknotting numbers.

scholarly journals Comparing demographics of signatories to public letters on diversity in the mathematical sciences

2019 ◽  
Author(s):  
Chad Topaz ◽  
James Cart ◽  
Carrie Diaz Eaton ◽  
Anelise Hanson Shrout ◽  
Jude A. Higdon ◽  
...  
Keyword(s):  
Social Sciences ◽  
Social Justice ◽  
Ethnic Groups ◽  
American Mathematical Society ◽  
White Men ◽  
Mathematical Achievement ◽  
Mathematical Society ◽  
Empirical Results ◽  
The Social ◽  
Mathematical Sciences

In its December 2019 edition, the Notices of the American Mathematical Society published an essay critical of the use of diversity statements in academic hiring. The publication of this essay prompted many responses, including three public letters circulated within the mathematical sciences community. Each letter was signed by hundreds of people and was published online, also by the American Mathematical Society. We report on a study of the signatories' demographics, which we infer using a crowdsourcing approach. Letter A highlights diversity and social justice. The pool of signatories contains relatively more individuals inferred to be women and/or members of underrepresented ethnic groups. Moreover, this pool is diverse with respect to the levels of professional security and types of academic institutions represented. Letter B does not comment on diversity, but rather, asks for discussion and debate. This letter was signed by a strong majority of individuals inferred to be white men in professionally secure positions at highly research intensive universities. Letter C speaks out specifically against diversity statements, calling them "a mistake," and claiming that their usage during early stages of faculty hiring "diminishes mathematical achievement." Individuals who signed both Letters B and C, that is, signatories who both privilege debate and oppose diversity statements, are overwhelmingly inferred to be tenured white men at highly research intensive universities. Our empirical results are consistent with theories of power drawn from the social sciences.

New biologically motivated knot table

2013 ◽  
Vol 41 (2) ◽  
pp. 606-611 ◽  
Author(s):  
Reuben Brasher ◽  
Rob G. Scharein ◽  
Mariel Vazquez
Keyword(s):  
Present Article ◽  
American Mathematical Society ◽  
Mathematical Society ◽  
Large Ensemble ◽  
Numerical Evidence ◽  
Type K ◽  
The Mean ◽  
Knots And Links

The knot nomenclature in common use, summarized in Rolfsen's knot table [Rolfsen (1990) Knots and Links, American Mathematical Society], was not originally designed to distinguish between mirror images. This ambiguity is particularly inconvenient when studying knotted biopolymers such as DNA and proteins, since their chirality is often significant. In the present article, we propose a biologically meaningful knot table where a representative of a chiral pair is chosen on the basis of its mean writhe. There is numerical evidence that the sign of the mean writhe is invariant for each knot in a chiral pair. We review numerical evidence where, for each knot type K, the mean writhe is taken over a large ensemble of randomly chosen realizations of K. It has also been proposed that a chiral pair can be distinguished by assessing the writhe of a minimal or ideal conformation of the knot. In all cases examined to date, the two methods produce the same results.

What Can We Learn From Factorial Surveys About Human Behavior?

Methodology ◽  
2019 ◽  
Vol 15 (1) ◽  
pp. 19-30 ◽  
Author(s):  
Knut Petzold ◽  
Tobias Wolbring
Keyword(s):  
Social Sciences ◽  
Behavioral Intentions ◽  
Actual Behavior ◽  
Full Time ◽  
Factorial Survey ◽  
Survey Experiment ◽  
Intended Behavior ◽  
The Social ◽  
Survey Experiments ◽  
High Level

Abstract. Factorial survey experiments are increasingly used in the social sciences to investigate behavioral intentions. The measurement of self-reported behavioral intentions with factorial survey experiments frequently assumes that the determinants of intended behavior affect actual behavior in a similar way. We critically investigate this fundamental assumption using the misdirected email technique. Student participants of a survey were randomly assigned to a field experiment or a survey experiment. The email informs the recipient about the reception of a scholarship with varying stakes (full-time vs. book) and recipient’s names (German vs. Arabic). In the survey experiment, respondents saw an image of the same email. This validation design ensured a high level of correspondence between units, settings, and treatments across both studies. Results reveal that while the frequencies of self-reported intentions and actual behavior deviate, treatments show similar relative effects. Hence, although further research on this topic is needed, this study suggests that determinants of behavior might be inferred from behavioral intentions measured with survey experiments.

Sign in / Sign up

Export Citation Format

Share Document