Computational problems without computation

Problemen uit de discrete wiskunde lijken op het eerste gezicht vaak erg simpel. Ze kunnen meestal gemakkelijk en zonder gebruik te maken van wiskundige begrippen worden geformuleerd. Toch komt het vaak voor dat zo’n ogenschijnlijk eenvoudig probleem nog open is of dat er, zoals bij het handelsreizigersprobleem, wel een oplossing gegeven kan worden,maar alleen een die onbruikbaar is omdat de rekentijd bij grotere getallen te snel groeit. In dit artikel, gebaseerd op zijn voordracht op het NMC 2002, kijkt Gerhard Woeginger naar de tegenovergestelde situatie. Hij introduceert allerlei discrete\ud problemen die onoplosbaar lijken, maar waarvoor er een simpele oplossing bestaat

Minimal generators of toric ideals of graphs

Let $I_G$ be the toric ideal of a graph $G$. We characterize in graph theoretical terms the primitive, the minimal, the indispensable and the fundamental binomials of the toric ideal $I_G$

Field evidence of social influence in the expression of political preferences: the case of secessionist flags in Barcelona

Different models of social influence have explored the dynamics of social contagion, imitation, and diffusion of different types of traits, opinions, and conducts. However, few behavioral data indicating social influence dynamics have been obtained from direct observation in `natural' social contexts. The present research provides that kind of evidence in the case of the public expression of political preferences in the city of Barcelona, where thousands of citizens supporting the secession of Catalonia from Spain have placed a Catalan flag in their balconies. We present two different studies. 1) In July 2013 we registered the number of flags in 26% of the the city. We find that there is a large dispersion in the density of flags in districts with similar density of pro-independence voters. However, we find that the density of flags tends to be fostered in those electoral district where there is a clear majority of pro-independence vote, while it is inhibited in the opposite cases. 2) During 17 days around Catalonia's 2013 National Holiday we observed the position at balcony resolution of the flags displayed in the facades of 82 blocks. We compare the clustering of flags on the facades observed each day to equivalent random distributions and find that successive hangings of flags are not independent events but that a local influence mechanism is favoring their clustering. We also find that except for the National Holiday day the density of flags tends to be fostered in those facades where there is a clear majority of pro-independence vote.Comment: 27 pages, 13 figures, 2 table

Algorithms for detecting dependencies and rigid subsystems for CAD

Geometric constraint systems underly popular Computer Aided Design soft- ware. Automated approaches for detecting dependencies in a design are critical for developing robust solvers and providing informative user feedback, and we provide algorithms for two types of dependencies. First, we give a pebble game algorithm for detecting generic dependencies. Then, we focus on identifying the "special positions" of a design in which generically independent constraints become dependent. We present combinatorial algorithms for identifying subgraphs associated to factors of a particular polynomial, whose vanishing indicates a special position and resulting dependency. Further factoring in the Grassmann- Cayley algebra may allow a geometric interpretation giving conditions (e.g., "these two lines being parallel cause a dependency") determining the special position.Comment: 37 pages, 14 figures (v2 is an expanded version of an AGD'14 abstract based on v1

Historical sociology of the city

About the book: This Handbook consists of 26 chapters on historical sociology. It is divided into three parts. Part One is devoted to Foundations and covers Marx, Weber, evolutionary and functionalist approaches, the Annales School, Elias, Nelson and Eisenstadt. Part Two moves on to consider major approaches, such as modernization approaches, late Marxist approaches, historical geography, institutional approaches, cultural history, intellectual history, postcolonial and genealogical approaches. The third part is devoted to the major substantive themes in historical sociology ranging from state formation, nationalism, social movements, classes, patriarchy, architecture, religion and moral regulation to problems of periodization and East-West divisions. Each part includes an introduction that summarizes and contextualizes chapters. A general introduction to the volume outlines the current situation of historical sociology after the cultural turn in the social sciences. It argues that historical sociology is deeply divided between explanatory `sociological' approaches and more empirical and interpretative `historical' approaches