We consider a variant of the game of Cops and Robbers, called Lazy Cops and Robbers, where at most one cop can move in any round. The lazy cop number is the analogue of the usual cop number for this game. Lazy Cops and Robbers was recently introduced by Offner and Ojakian, who provided asymptotic upper and lower bounds on the analogue of the cop number of the hypercube. By investigating expansi...

AbstrAct Organizations have the potential to achieve advantage through communities of practice (COPs) initiatives. However, establishing and sustaining COPs is a challenging task. Facilitation is needed to help COPs BLOCKINovercome BLOCKINdifficulties BLOCKINthroughout BLOCKINtheir BLOCKINlife BLOCKINstages. BLOCKINFacilitators BLOCKINtake BLOCKINon BLOCKINleadership BLOCKINroles BLOCKINwithin ...

A dynamic covalent approach towards rigid aryleneethynylene covalent organic polyhedrons (COPs) was explored. Our study on the relationship of the COP structures and the geometry of their building blocks reveals that the topology of aryleneethynylene COPs strongly depends on the size of the building blocks. A tetramer (D2h symmetric), dimer, or interlocked complex can be formed from monomers wi...

2 Background 2 2.1 NP-hard Combinatorial (Optimization) Problems . . . . . . . . . . . . . . . 2 2.2 Algorithms for Attacking COPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2.1 Exact Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2.2 Non-Exact Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2.3 Comparison of the Tw...

This article is an introduction to Cluster Optimized Proximity Scaling (COPS) aimed at practitioners, as well a tutorial on the usage of corresponding R package cops. COPS variant multidimensional scaling (MDS) that aims providing clustered configuration while still representing multivariate dissimilarities faithfully. It subsumes most popular MDS versions special cases. We illustrate ideas, us...