CelticGraph: Drawing Graphs as Celtic Knots and Links

Celtic knots are an ancient art form often attributed to Celtic cultures, used to decorate monuments and manuscripts, and to symbolise eternity and interconnectedness. This paper describes the framework CelticGraph to draw graphs as Celtic knots and links. The drawing process raises interesting combinatorial concepts in the theory of circuits in planar graphs. Further, CelticGraph uses a novel algorithm to represent edges as B\'ezier curves, aiming to show each link as a smooth curve with limited curvature.Comment: Appears in the Proceedings of the 31st International Symposium on Graph Drawing and Network Visualization (GD 2023

Angles of Arc-Polygons and Lombardi Drawings of Cacti

We characterize the triples of interior angles that are possible in non-self-crossing triangles with circular-arc sides, and we prove that a given cyclic sequence of angles can be realized by a non-self-crossing polygon with circular-arc sides whenever all angles are at most pi. As a consequence of these results, we prove that every cactus has a planar Lombardi drawing (a drawing with edges depicted as circular arcs, meeting at equal angles at each vertex) for its natural embedding in which every cycle of the cactus is a face of the drawing. However, there exist planar embeddings of cacti that do not have planar Lombardi drawings.Comment: 12 pages, 8 figures. To be published in Proc. 33rd Canadian Conference on Computational Geometry, 202

The Scattered Global Financial Safety Net and the Role of Regional Financial Arrangements

The global financial safety net provides backstop during times of financial crises. Its elements underwent fundamental changes since the global financial crisis. The International Monetary Fund (IMF) introduced new facilities on the global level, new regional financial arrangements (RFAs) were created, and bilateral swap agreements emerged as a new element. In this paper, we ask how these changes influence the use of the different safety net options, and what role RFAs have in the safety net today. We created a database with all the cases in which a RFA member drew on one of the elements of the global safety net. This allows us to analyze which other options the country had at hand, and to examine their use along the institutional design in terms of timeliness, volume, and policy conditionality. We find today’s global financial safety net to be not a global, but a geographically and structurally scattered net. RFAs make the safety net safer only for small member countries. Just few countries can count on a bilateral swap line, their selection being subject to the discretion of the swap partner. Thus, a large number of countries fall through important knots of the safety net and have the IMF as their only option

Safety for whom? The scattered global financial safety net and the role of regional financial arrangements

The global financial safety net provides backstop during times of financial crises. Its elements underwent fundamental changes since the global financial crisis. The International Monetary Fund (IMF) introduced new facilities on the global level, new regional financial arrangements (RFAs) were created, and bilateral swap agreements emerged as a new element. In this paper, we ask how these changes influence the use of the different safety net options, and what role RFAs have in the safety net today. We created a database with all the cases in which a RFA member drew on one of the elements of the global safety net. This allows us to analyze which other options the country had at hand, and to examine their use along the institutional design in terms of timeliness, volume, and policy conditionality. We find today's global financial safety net to be not a global, but a geographically and structurally scattered net. RFAs make the safety net safer only for small member countries. Just few countries can count on a bilateral swap line, their selection being subject to the discretion of the swap partner. Thus, a large number of countries fall through important knots of the safety net and have the IMF as their only option

Classroom facilities : a body of creative work exploring representations of knowledge through schematic means

Bibliography: leaves 78-83.I had just turned thirteen and it was the summer before high school started. My mother and I went over to the Roberts' house. Ruby had just matriculated from the same school and was handing down her faded old checked uniforms. To my amazement, there in the lounge bathed in afternoon January sunlight, was her father Billy, kneeling, deeply absorbed in a large strange chart that had been laid out on the floor. It was a school timetable and it was his task, as vice principle, to organise the day-to-day workings of the year ahead. The timetable was scattered with various coloured shapes that he shuffled back and forth across the gridded surface, trying to make a coherent system. This anecdote is important to my body of work for three reasons. The first is that Mr. Roberts' challenging activity that day is not unlike the process of sorting and reordering that is central to my work. The appearance of the chart is mimicked in the schemata-like quality of many of my pieces, as is its conceptual framework - an urge to order a set of already existing pieces into a new, meaningful and functional relationship. Ruby's uniforms are also important. I cherished these second-hand dresses precisely because of the qualities they acquired through having been worn already. These dresses were softer to touch, had a better fit and more beauty in colour --soft pink checks as opposed to harsh maroon-- than other girls' crisp new sacks

Knowledge of knots: shapes in action

Logic is to natural language what knot theory is to natural knots. Logic is concerned with some cognitive performances; in particular, some natural language inferences are captured by various types of calculi (propositional, predicate, modal, deontic, quantum, probabilistic, etc.), which in turn may generate inferences that are arguably beyond natural logic abilities, or non-well synchronized therewith (eg. ex falso quodlibet, material implication). Mathematical knot theory accounts for some abilities - such as recognizing sameness or differences of some knots, and in turn generates a formalism for distinctions that common sense is blind to. Logic has proven useful in linguistics and in accounting for some aspects of reasoning, but which knotting performaces are there, over and beyond some intuitive discriminating abilities, that may require extensions or restrictions of the normative calculus of knots? Are they amenable to mathematical treatment? And what role is played in the game by mental representations? I shall draw from a corpus of techniques and practices to show to what extent compositionality, lexical and normative elements are present in natural knots, with the prospect of formally exploring an area of human competence that interfaces thought, perception and action in a complex fabric

Leonardo, la politica e le allegorie

International audienceCatalogue of the exhibition (Milan, Biblioteca Ambrosiana, june-september 2010

Why knot?

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Architecture, 1991.Includes bibliographical references (p. 535-551).Carol Strohecker.Ph.D