On reproducible research

• Sage and the future of mathematics, David Joyner
• Reproducible research and computational biology, Grant Jacobs
• WaveLab and Reproducible Research, J. B. Buckheit and D. L. Donoho
• Reproducible Research Planet!
• Call For Scientific Research Code To Be Released, on Slashdot
• Victoria Stodden
• Keeping computers from ending science’s reproducibility, on Ars Technica

Random oriented graphs

This one is from a recent sage-support thread.

Problem

Let be a digraph and let be vertices of . Then is said to be oriented if at most one of is an edge of . This means that might not contain any of the edges . However, if , then and vice versa. The problem now is to generate a random oriented graph.

Solution

A quick-and-dirty solution is as follows:

1. Generate a random graph with RanomGNP, i.e. is undirected.
2. Let be the digraph version of , i.e. if is an edge of , then is also an edge.
3. Let be the edge removal probability.
4. For each edge , generate a cutoff probability . If , remove from the digraph . Otherwise , so we remove from .

Here is sample code using Sage 4.4.1 illustrating the above procedure:

sage: G = graphs.RandomGNP(10, random())
sage: G.edges(labels=False)
[(0, 2), (0, 3), (0, 4), (0, 5), (0, 6), (0, 8), (1, 2), (1, 3), (1, 5), (1, 7), (1, 8), (2, 4), (2, 6), (2, 8), (2, 9), (3, 4), (3, 6), (3, 7), (3, 8), (3, 9), (4, 5), (4, 9), (5, 6), (5, 8), (5, 9), (6, 9), (7, 8), (8, 9)]
sage: D = G.to_directed()
sage: D.edges(labels=False)
[(0, 2), (0, 3), (0, 4), (0, 5), (0, 6), (0, 8), (1, 2), (1, 3), (1, 5), (1, 7), (1, 8), (2, 0), (2, 1), (2, 4), (2, 6), (2, 8), (2, 9), (3, 0), (3, 1), (3, 4), (3, 6), (3, 7), (3, 8), (3, 9), (4, 0), (4, 2), (4, 3), (4, 5), (4, 9), (5, 0), (5, 1), (5, 4), (5, 6), (5, 8), (5, 9), (6, 0), (6, 2), (6, 3), (6, 5), (6, 9), (7, 1), (7, 3), (7, 8), (8, 0), (8, 1), (8, 2), (8, 3), (8, 5), (8, 7), (8, 9), (9, 2), (9, 3), (9, 4), (9, 5), (9, 6), (9, 8)]
sage: D.size()
56
sage: P = random(); P
0.55638632541078259
sage: for u, v in G.edge_iterator(labels=False):
....:     p = random()
....:     if p <= P:
....:         D.delete_edge(u, v)
....:     else:
....:         D.delete_edge(v, u)
....: 
sage: D.edges(labels=False)
[(0, 2), (0, 3), (0, 6), (1, 2), (1, 5), (2, 8), (3, 1), (3, 6), (3, 8), (3, 9), (4, 0), (4, 2), (4, 3), (4, 5), (5, 0), (6, 2), (6, 5), (6, 9), (7, 1), (7, 3), (8, 0), (8, 1), (8, 5), (8, 7), (9, 2), (9, 4), (9, 5), (9, 8)]
sage: D.size()
28

Sage 4.4.2 release schedule

Sage 4.4.2 is intended to be a little release on the way to Sage 5.0. I’m devoting a week or so to managing the release of Sage 4.4.2. Here’s a proposed release schedule I posted to sage-release:

• Sage 4.4.2.alpha0 — release 10th May 2010
• Sage 4.4.2.rc0 — feature freeze; release 15th May 2010
• Anything critical to get Sage 4.4.2.final to stabilize
• Sage 4.4.2.final — release 18th May 2010

I’m being too optimistic here with the above schedule. But we’ll see how things go.