The simplex algorithm using the random edge pivot-rule on any realization of a dual cyclic 4-polytope with n facets does not take more than O(n) pivot-steps. This even holds for general abstract objective functions (AOF) / acyclic unique sink orientations (AUSO). The methods can be used to show analogous results for products of two polygons. In contrast, we show that the random facet pivot-rule...

The ability to confront new questions, opportunities, and challenges is of fundamental importance human progress the resilience societies, yet capacity science meet demands remains poorly understood. Here we deploy a measurement framework investigate scientific response COVID-19 pandemic adaptability as whole. We find that rapidly shifted engage following advent virus, with scientists across al...

This presentation will show how one analyst uses the pivot table feature of Microsoft EXCEL to arrive at a quick performance analysis for DB2 and BATCH mainframe applications. At our enterprise, we use pivot tables and charts as monitoring tools, performance analysis, and management communication. An explanation of the basic concepts to create and manipulate pivot tables will be combined with a...

This paper discusses the pivot pattern of tongue movement. In this pattern, there is a point in the vocal tract where there is no motion, but there is motion at points of the vocal tract anterior and posterior to the pivot point. Based on tongue edge tracings of frames from ultrasound and x-ray dynamic imaging of the vocal tract, I will show that the pivot pattern is used in a variety of sequen...

We prove that every graph of rank-width k is a pivot-minor of a graph of tree-width at most 2k. We also prove that graphs of rank-width at most 1, equivalently distance-hereditary graphs, are exactly vertex-minors of trees, and graphs of linear rank-width at most 1 are precisely vertex-minors of paths. In addition, we show that bipartite graphs of rank-width at most 1 are exactly pivot-minors o...

We prove that every graph of rank-width k is a pivot-minor of a graph of tree-width at most 2k. We also prove that graphs of rank-width at most 1, equivalently distance-hereditary graphs, are exactly vertex-minors of trees, and graphs of linear rank-width at most 1 are precisely vertex-minors of paths. In addition, we show that bipartite graphs of rank-width at most 1 are exactly pivot-minors o...

This paper describes two algorithms for the compression of propositional resolution proofs. The first algorithm, RecyclePivotsWithIntersection, performs partial regularization, removing an inference η when it is redundant in the sense that its pivot literal already occurs as the pivot of another inference located below in the path from η to the root of the proof. The second algorithm, LowerUnit...