Duality properties of indicatrices of knots

The bridge index and superbridge index of a knot are important invariants in knot theory. We define the bridge map of a knot conformation, which is closely related to these two invariants, and interpret it in terms of the tangent indicatrix of the knot conformation. Using the concepts of dual and derivative curves of spherical curves as introduced by Arnold, we show that the graph of the bridge map is the union of the binormal indicatrix, its antipodal curve, and some number of great circles. Similarly, we define the inflection map of a knot conformation, interpret it in terms of the binormal indicatrix, and express its graph in terms of the tangent indicatrix. This duality relationship is also studied for another dual pair of curves, the normal and Darboux indicatrices of a knot conformation. The analogous concepts are defined and results are derived for stick knots.Comment: 22 pages, 9 figure

Quantum mechanics: Myths and facts

A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of "myths", that is, widely accepted claims on which there is not really a general consensus among experts in foundations of QM. These myths include wave-particle duality, time-energy uncertainty relation, fundamental randomness, the absence of measurement-independent reality, locality of QM, nonlocality of QM, the existence of well-defined relativistic QM, the claims that quantum field theory (QFT) solves the problems of relativistic QM or that QFT is a theory of particles, as well as myths on black-hole entropy. The fact is that the existence of various theoretical and interpretational ambiguities underlying these myths does not yet allow us to accept them as proven facts. I review the main arguments and counterarguments lying behind these myths and conclude that QM is still a not-yet-completely-understood theory open to further fundamental research.Comment: 51 pages, pedagogic review, revised, new references, to appear in Found. Phy

Collaborative International Research in Clinical and Longitudinal Experience Study in NMOSD

OBJECTIVE: To develop a resource of systematically collected, longitudinal clinical data and biospecimens for assisting in the investigation into neuromyelitis optica spectrum disorder (NMOSD) epidemiology, pathogenesis, and treatment. METHODS: To illustrate its research-enabling purpose, epidemiologic patterns and disease phenotypes were assessed among enrolled subjects, including age at disease onset, annualized relapse rate (ARR), and time between the first and second attacks. RESULTS: As of December 2017, the Collaborative International Research in Clinical and Longitudinal Experience Study (CIRCLES) had enrolled more than 1,000 participants, of whom 77.5% of the NMOSD cases and 71.7% of the controls continue in active follow-up. Consanguineous relatives of patients with NMOSD represented 43.6% of the control cohort. Of the 599 active cases with complete data, 84% were female, and 76% were anti-AQP4 seropositive. The majority were white/Caucasian (52.6%), whereas blacks/African Americans accounted for 23.5%, Hispanics/Latinos 12.4%, and Asians accounted for 9.0%. The median age at disease onset was 38.4 years, with a median ARR of 0.5. Seropositive cases were older at disease onset, more likely to be black/African American or Hispanic/Latino, and more likely to be female. CONCLUSION: Collectively, the CIRCLES experience to date demonstrates this study to be a useful and readily accessible resource to facilitate accelerating solutions for patients with NMOSD

Buffalo law review

Abstract. We present a SAT-based algorithm for assisting users of Symbolic Trajectory Evaluation (STE) in manual abstraction refinement. As a case study, we demonstrate the usefulness of the algorithm by showing how to refine and verify an STE specification of a CAM.