Knot Theory: from Fox 3-colorings of links to Yang-Baxter homology and Khovanov homology

This paper is an extended account of my "Introductory Plenary talk at Knots in Hellas 2016" conference We start from the short introduction to Knot Theory from the historical perspective, starting from Heraclas text (the first century AD), mentioning R.Llull (1232-1315), A.Kircher (1602-1680), Leibniz idea of Geometria Situs (1679), and J.B.Listing (student of Gauss) work of 1847. We spend some space on Ralph H. Fox (1913-1973) elementary introduction to diagram colorings (1956). In the second section we describe how Fox work was generalized to distributive colorings (racks and quandles) and eventually in the work of Jones and Turaev to link invariants via Yang-Baxter operators, here the importance of statistical mechanics to topology will be mentioned. Finally we describe recent developments which started with Mikhail Khovanov work on categorification of the Jones polynomial. By analogy to Khovanov homology we build homology of distributive structures (including homology of Fox colorings) and generalize it to homology of Yang-Baxter operators. We speculate, with supporting evidence, on co-cycle invariants of knots coming from Yang-Baxter homology. Here the work of Fenn-Rourke-Sanderson (geometric realization of pre-cubic sets of link diagrams) and Carter-Kamada-Saito (co-cycle invariants of links) will be discussed and expanded. Dedicated to Lou Kauffman for his 70th birthday.Comment: 35 pages, 31 figures, for Knots in Hellas II Proceedings, Springer, part of the series Proceedings in Mathematics & Statistics (PROMS

Cyber security fear appeals:unexpectedly complicated

Cyber security researchers are starting to experiment with fear appeals, with a wide variety of designs and reported efficaciousness. This makes it hard to derive recommendations for designing and deploying these interventions. We thus reviewed the wider fear appeal literature to arrive at a set of guidelines to assist cyber security researchers. Our review revealed a degree of dissent about whether or not fear appeals are indeed helpful and advisable. Our review also revealed a wide range of fear appeal experimental designs, in both cyber and other domains, which confirms the need for some standardized guidelines to inform practice in this respect. We propose a protocol for carrying out fear appeal experiments, and we review a sample of cyber security fear appeal studies, via this lens, to provide a snapshot of the current state of play. We hope the proposed experimental protocol will prove helpful to those who wish to engage in future cyber security fear appeal research