We introduce monotone Boolean functions through two quite different examples from biology. The first is in metabolic networks, where they enumerate both the elementary modes and the minimal knock out strategies in a network. The second is in ancestral genome reconstruction, where they generate minimal obstacles (Conflicting Sets) to the consecutive-ones property for binary matrices. Generating these functions is an interesting computational challenge. We use the package , which implements an algorithm of Fredman and Khachiyan.
Tamon Stephen is an Associate Professor of Mathematics at Simon Fraser University in British Columbia, Canada, specializing in Operations Research. He completed his Ph.D. at the University of Michigan under the supervision of Alexander Barvinok, and was a postdoctoral fellow at the Institute for Mathematics and its Applications (IMA) in Minnesota, McMaster University in Canada and the University of Magdeburg in Germany. His recent research themes include high-dimensional computational geometry problems, such as colourful linear programming and the polynomial Hirsch conjecture, and using monotone Boolean functions to understand complex systems in biology. External collaborations include Vancouver Coastal Health, the City of Surrey Fire Services, Wesgar Inc. and 1QB Information Technologies.