The great circle epidemic model

The Sis Great Circle Epidemic Model

We consider a stochastic SIS model for the spread of an epidemic amongst a population of n individuals that are equally spaced upon the circumference of a circle. Whilst infectious, an individual, i say, makes both local and global infectious contacts at the points of homogeneous Poisson point processes. Global contacts are made uniformly at randomwithmembers of the entire population, whilst lo...

Odd Graphs and the Great Circle Challenge

Edge (5, 3)-bicolorings of a (5, 3)-regular bipartite graph relating 5cycles and vertices of the Petersen graph lead to solutions of the Great Circle Challenge puzzle. This takes for odd n = 2k + 1 > 1 to a oneto-one correspondence from the family Cn of n-cycles of Kn onto the family Ok of n-cycles of the odd graph Ok+1. It also takes for odd l with 3 ≤ l ≤ ⌊n/2⌋ to a graph having Ok as vertex ...

Great Circle Challenge and Odd Graphs

Edge (5, 3)-colorings of a (5, 3)-regular bipartite graph relating 5cycles and vertices of the Petersen graph lead to solutions of the Great Circle Challenge. This takes, for odd n = 2k + 1 > 1, to a canonical 1-1 correspondence from the family of n-cycles of the complete graph Kn onto the family Ck of n-cycles of the odd graph Ok+1 and onto the family of their pullback 2n-cycles in the middle-...

Microlensing of tidal debris on the Magellanic great circle

Increasing evidences suggest that the Galactic halo is lumpy on kpc scales due to the accretion of at least a dozen small galaxies (LMC/SMC, Sgr, Fornax etc.). Faint stars in such lumpy structures can significant microlense a background star with an optical depth 10−7 − 10−6, which is comparable to the observed value to the LMC (Alcock et al. 1996c). The observed several microlensing events tow...

The Great Circle Camera: a New Drift Scanning Instrument