Equitability Revisited: Why the “Equitable Threat Score” Is Not Equitable

Equitability Revisited: Why the ‘‘Equitable Threat Score’’ Is Not Equitable

In the forecasting of binary events, verification measures that are ‘‘equitable’’ were defined by Gandin and Murphy to satisfy two requirements: 1) they award all random forecasting systems, including those that always issue the same forecast, the same expected score (typically zero), and 2) they are expressible as the linear weighted sum of the elements of the contingency table, where the weig...

Equitable Revisited

The randomized k-paging algorithm Equitable given by Achlioptas et al. is Hk-competitive and uses O(k 2 log k) memory. This competitive ratio is best possible. The randomized algorithm RMark given by Fiat et al. is (2Hk − 1)-competitive, but only uses O(k) memory. Borodin and El Yaniv [6] list as an open question whether there exists an Hk-competitive randomized algorithm which requires O(k) me...

The equitable dispersion problem

Article history: Received 20 July 2007 Accepted 4 June 2008 Available online 13 June 2008

k-equitable mean labeling

Epidemic Outbreaks in Networks with Equitable or Almost-Equitable Partitions

We study the diffusion of epidemics on networks that are partitioned into local communities. The gross structure of hierarchical networks of this kind can be described by a quotient graph. The rationale of this approach is that individuals infect those belonging to the same community with higher probability than individuals in other communities. In community models the nodal infection probabili...