To note for today- the slide on graphs, with Edge and Node list has a list of all edges, alongside o nthe right list of nodes - the list of nodes isn't meant to line up with the list on the left - its just a list for node i=1-5, what other nodes, in the directed graph, are adjacent (look at arrows on edges - note in 2 cases (1<->2 and 5<->4, they are bi-directional)....
fun references today:-
Ghost Maps
Collatz
Kirchoff
Erdos
Small Worlds...
DDOS visualised
Couple more corrigenda/errata
1. in the alpha/beta models of random graphs, there's k used for average degree of the net (e.g. pN in the alpha model), but also used for the toal number of edges (N*(N-1)/2) - so take care with k
2. there's an expression in the slides about max-flow in DAR (the "Sticky Random Routing" for the telephoen net) for using Erlang's call blocking probability for a given link, then work out what the toal capacity will be for 1 hop and 2-hop/tandem routes - this has n, which is number of calls you get through, then mentioned a technique called LP to solve the maximisation problem given in terms of sum of calls that get through (or are blocked) over all direct and tandem routes- we are'nt covering that technique this year, but LP stands for Linear Programming, and is fairly straightforward if you want to look it up - it is commonly used in optimisation and shows up in Operations research/Logistics (freight etc) and so on all the time.
fun references today:-
Ghost Maps
Collatz
Kirchoff
Erdos
Small Worlds...
DDOS visualised
Couple more corrigenda/errata
1. in the alpha/beta models of random graphs, there's k used for average degree of the net (e.g. pN in the alpha model), but also used for the toal number of edges (N*(N-1)/2) - so take care with k
2. there's an expression in the slides about max-flow in DAR (the "Sticky Random Routing" for the telephoen net) for using Erlang's call blocking probability for a given link, then work out what the toal capacity will be for 1 hop and 2-hop/tandem routes - this has n, which is number of calls you get through, then mentioned a technique called LP to solve the maximisation problem given in terms of sum of calls that get through (or are blocked) over all direct and tandem routes- we are'nt covering that technique this year, but LP stands for Linear Programming, and is fairly straightforward if you want to look it up - it is commonly used in optimisation and shows up in Operations research/Logistics (freight etc) and so on all the time.
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