A distributed task is local if its time complexity is (nearly) constant, otherwise it is global. Unfortunately, local tasks are relatively scarce, and most distributed tasks require time at least logarithmic in the network size (and often higher than that). In a dynamic setting, i.e., when the network undergoes repeated and frequent topological changes, such as vertex and edge insertions and de...

In the Firefighter Problem, a fire breaks out at a vertex of a graph G, then f firefighters protect f vertices. At each subsequent time step, the fire spreads from each “burned” vertex to all of its unprotected neighbours, then f firefighters “protect” f unburned vertices. Once a vertex is protected or burned, it remains so from then onward. A common objective is to determine the minimum number...

A SIC consists of N equiangular unit vectors in an N dimensional Hilbert space. The frame potential is a function of N unit vectors. It has a unique global minimum if the vectors form a SIC, and this property has been made use of in numerical searches for SICs. When the vectors form an orbit of the Heisenberg group the frame potential becomes a function of a single fiducial vector. We analytica...

Considering a control system with fast and slow variations, the purpose of this note is to propose a notion of “average control system” that does not depend on how fast or slow the controls will be. This differs from the more usual use of averaging in control where the fast or slow variations of the control have to be specified before performing averaging. We also present an application to low ...

Due to the nature of the geological and mining activities, different input parameters in the grade estimation and mineral resource evaluation are always tainted with uncertainties. It is possible to investigate the uncertainties related to the measurements and parameters of the variogram model using the fuzzy kriging method instead of the kriging method. The fuzzy kriging theory has already bee...