latest news

Distractions and amusements, with a sandwich and coffee.

Here we are now at the middle of the fourth large part of this talk.
•
• get nowhere
• more quotes

I collaborated with Scientific American to create a data graphic for the September 2014 issue. The graphic compared the genomes of the Denisovan, bonobo, chimp and gorilla, showing how our own genomes are almost identical to the Denisovan and closer to that of the bonobo and chimp than the gorilla.

Here you'll find Hilbert curve art, a introduction to Hilbertonians, the creatures that live on the curve, an explanation of the Scientific American graphic and downloadable SVG/EPS Hilbert curve files.

There are wheels within wheels in this village and fires within fires!

— Arthur Miller (The Crucible)

The Hilbert curve is one of many space-filling curves. It is a mapping between one dimension (e.g. a line) and multiple dimensions (e.g. a square, a cube, etc). It's useful because it preserves locality—points that are nearby on the line are usually mapped onto nearby points on the curve.

The Hilbert curve is a line that gives itself a hug.

It's a pretty strange mapping, to be sure. Although a point on a line maps uniquely onto the curve this is not the case in reverse. At infinite order the curve intersects itself infinitely many times! This shouldn't be a surprise if you consider that the unit square has the same number of points as the unit line. Now that's the real surprise! So surprising in fact that it apparently destabilized Cantor's mind, who made the initial discovery.

Bryan Hayes has a great introduction (Crinkly Curves) to the Hilbert curve at American Scientist.

If manipulated so that its ends are adjacent, the Hilbert curve becomes the Moore curve.

The order 1 curve is generated by dividing a square into quadrants and connecting the centers of the quadrants with three lines. Which three connections are made is arbitrary—different choices result in rotations of the curve.

The order 6 curve is the highest order whose structure can be discerned at this figure resolution. Though just barely. The length of this curve is about 64 times the width of the square, so about 9,216 pixels! That's tight packing.

By order 7 the structure in the 620 pixel wide image (each square is 144 px wide) cannot be discerned. By order 8 the curve has 65,536 points, which exceeds the number of pixels its square in the figure. A square of 256 x 256 would be required to show all the points without downsampling.

Two order 10 curves have 1,048,576 points each and would approximately map onto all the pixels on an average monitor (1920 x 1200 pixels).

A curve of order 33 has `7.38 * 10^19` points and if drawn as a square of average body height would have points that are an atom's distance from one another (`10^{-10}` m).

By mapping the familiar rainbow onto the curve you can see how higher order curves "crinkle" (to borrow Bryan's term) around the square.

order | points | segments | length |

`n` | `4^n` | `4^{n-1}` | `2^n-2^{-n}` |

1 | 4 | 3 | 1.5 |

2 | 16 | 15 | 3.75 |

3 | 64 | 63 | 7.875 |

4 | 256 | 255 | 15.9375 |

5 | 1,024 | 1,023 | 31.96875 |

6 | 4,096 | 4,095 | 63.984375 |

7 | 16,384 | 16,383 | 127.9921875 |

8 | 65,536 | 65,535 | 255.99609375 |

9 | 262,144 | 262,143 | 511.998046875 |

10 | 1,048,576 | 1,048,575 | 1023.9990234375 |

11 | 4,194,304 | 4,194,303 | 2047.99951171875 |

12 | 16,777,216 | 16,777,215 | 4095.99975585938 |

13 | 67,108,864 | 67,108,863 | 8191.99987792969 |

14 | 268,435,456 | 268,435,455 | 16383.9999389648 |

15 | 1,073,741,824 | 1,073,741,823 | 32767.9999694824 |

16 | 4,294,967,296 | 4,294,967,295 | 65535.9999847412 |

17 | 17,179,869,184 | 17,179,869,183 | 131071.999992371 |

18 | 68,719,476,736 | 68,719,476,735 | 262143.999996185 |

19 | 274,877,906,944 | 274,877,906,943 | 524287.999998093 |

20 | 1,099,511,627,776 | 1,099,511,627,775 | 1048575.99999905 |

21 | 4,398,046,511,104 | 4,398,046,511,103 | 2097151.99999952 |

22 | 17,592,186,044,416 | 17,592,186,044,415 | 4194303.99999976 |

23 | 70,368,744,177,664 | 70,368,744,177,663 | 8388607.99999988 |

24 | 281,474,976,710,656 | 281,474,976,710,655 | 16777215.9999999 |

You can download the basic curve shapes for orders 1 to 10 and experiment yourself. Both square and circular forms are available.

*Genetic sequences of the coronavirus tell story of when the virus arrived in each country and where it came from.*

Our graphic in Scientific American's Graphic Science section in the June 2020 issue shows a phylogenetic tree based on a snapshot of the data model from Nextstrain as of 31 March 2020.

Our design on the cover of Nature Cancer's April 2020 issue shows mutation spectra of patients from the POG570 cohort of 570 individuals with advanced metastatic cancer.

The cover design accompanies our report in the issue Pleasance, E., Titmuss, E., Williamson, L. et al. (2020) Pan-cancer analysis of advanced patient tumors reveals interactions between therapy and genomic landscapes. *Nat Cancer* **1**:452–468.

*Every day sadder and sadder news of its increase. In the City died this week 7496; and of them, 6102 of the plague. But it is feared that the true number of the dead this week is near 10,000 ....*

—Samuel Pepys, 1665

This month, we begin a series of columns on epidemiological models. We start with the basic SIR model, which models the spread of an infection between three groups in a population: susceptible, infected and recovered.

We discuss conditions under which an outbreak occurs, estimates of spread characteristics and the effects that mitigation can play on disease trajectories. We show the trends that arise when "flattenting the curve" by decreasing `R_0`.

This column has an interactive supplemental component that allows you to explore how the model curves change with parameters such as infectious period, basic reproduction number and vaccination level.

Bjørnstad, O.N., Shea, K., Krzywinski, M. & Altman, N. (2020) Points of significance: Modeling infectious epidemics. *Nature Methods* **17**:455–456.

I'm writing poetry daily to put my feelings into words more often during the COVID-19 outbreak.

Small hours of the world and me.

A poster full of epidemiological worry and statistics. Now updated with the genome of SARS-CoV-2 and COVID-19 case statistics as of 3 March 2020.

Bacterial and viral genomes of various diseases are drawn as paths with color encoding local GC content and curvature encoding local repeat content. Position of the genome encodes prevalence and mortality rate.

The deadly genomes collection has been updated with a posters of the genomes of SARS-CoV-2, the novel coronavirus that causes COVID-19.

A workshop in using the Circos Galaxy wrapper by Hiltemann and Rasche. Event organized by Australian Biocommons.

Galaxy wrapper training materials, Saskia Hiltemann, Helena Rasche, 2020 Visualisation with Circos (Galaxy Training Materials).