Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca - contact me Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca on Twitter Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca - Lumondo Photography Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca - Pi Art Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca - Hilbertonians - Creatures on the Hilbert Curve
music + dance + projected visualsNosaj Thingmarvel at perfect timing

Bioinformatics and Genome Analysis Course. Izmir International Biomedicine and Genome Institute, Izmir, Turkey. May 2–14, 2016


visualization + design

Like paths? Got your lines twisted in a bunch?
Take a look at my 2014 Pi Day art that folds Pi.

Hilbert Curve Art, Hilbertonians and Monkeys

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.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca

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.

Hilbert curve art posters

There are wheels within wheels in this village and fires within fires!
— Arthur Miller (The Crucible)

Recursive art. Same line. A variety of styles. Font is Gotham Light.

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

All the art here is available for purchase at Fine Art America.

Here are some samples of the posters. They are classified into categories.


news + thoughts

Gene Volume Control

Thu 11-06-2015

I was commissioned by Scientific American to create an information graphic based on Figure 9 in the landmark Nature Integrative analysis of 111 reference human epigenomes paper.

The original figure details the relationships between more than 100 sequenced epigenomes and genetic traits, including disease like Crohn's and Alzheimer's. These relationships were shown as a heatmap in which the epigenome-trait cell depicted the P value associated with tissue-specific H3K4me1 epigenetic modification in regions of the genome associated with the trait.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Figure 9 from Integrative analysis of 111 reference human epigenomes (Nature (2015) 518 317–330). (details)

As much as I distrust network diagrams, in this case this was the right way to show the data. The network was meticulously laid out by hand to draw attention to the layered groups of diseases of traits.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Network diagram redesign of the heatmap for a select set of traits. Only relationships with –log P > 3.9 are displayed. Appears on Graphic Science page in June 2015 issue of Scientific American. (details)

This was my second information graphic for the Graphic Science page. Last year, I illustrated the extent of differences in the gene sequence of humans, Denisovans, chimps and gorillas.

Sampling distributions and the bootstrap

Thu 11-06-2015

The bootstrap is a computational method that simulates new sample from observed data. These simulated samples can be used to determine how estimates from replicate experiments might be distributed and answer questions about precision and bias.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Sampling distributions and the bootstrap. (read)

We discuss both parametric and non-parametric bootstrap. In the former, observed data are fit to a model and then new samples are drawn using the model. In the latter, no model assumption is made and simulated samples are drawn with replacement from the observed data.

Kulesa, A., Krzywinski, M., Blainey, P. & Altman, N (2015) Points of Significance: Sampling distributions and the bootstrap Nature Methods 12:477-478.

Background reading

Krzywinski, M. & Altman, N. (2013) Points of Significance: Importance of being uncertain. Nature Methods 10:809-810.

...more about the Points of Significance column

Bayesian statistics

Thu 30-04-2015

Building on last month's column about Bayes' Theorem, we introduce Bayesian inference and contrast it to frequentist inference.

Given a hypothesis and a model, the frequentist calculates the probability of different data generated by the model, P(data|model). When this probability to obtain the observed data from the model is small (e.g. `alpha` = 0.05), the frequentist rejects the hypothesis.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Bayesian Statistics. (read)

In contrast, the Bayesian makes direct probability statements about the model by calculating P(model|data). In other words, given the observed data, the probability that the model is correct. With this approach it is possible to relate the probability of different models to identify one that is most compatible with the data.

The Bayesian approach is actually more intuitive. From the frequentist point of view, the probability used to assess the veracity of a hypothesis, P(data|model), commonly referred to as the P value, does not help us determine the probability that the model is correct. In fact, the P value is commonly misinterpreted as the probability that the hypothesis is right. This is the so-called "prosecutor's fallacy", which confuses the two conditional probabilities P(data|model) for P(model|data). It is the latter quantity that is more directly useful and calculated by the Bayesian.

Puga, J.L, Krzywinski, M. & Altman, N. (2015) Points of Significance: Bayes' Theorem Nature Methods 12:277-278.

Background reading

Puga, J.L, Krzywinski, M. & Altman, N. (2015) Points of Significance: Bayes' Theorem Nature Methods 12:277-278.

...more about the Points of Significance column

Bayes' Theorem

Wed 22-04-2015

In our first column on Bayesian statistics, we introduce conditional probabilities and Bayes' theorem

P(B|A) = P(A|B) × P(B) / P(A)

This relationship between conditional probabilities P(B|A) and P(A|B) is central in Bayesian statistics. We illustrate how Bayes' theorem can be used to quickly calculate useful probabilities that are more difficult to conceptualize within a frequentist framework.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Bayes' Theorem. (read)

Using Bayes' theorem, we can incorporate our beliefs and prior experience about a system and update it when data are collected.

Puga, J.L, Krzywinski, M. & Altman, N. (2015) Points of Significance: Bayes' Theorem Nature Methods 12:277-278.

Background reading

Oldford, R.W. & Cherry, W.H. Picturing probability: the poverty of Venn diagrams, the richness of eikosograms. (University of Waterloo, 2006)

...more about the Points of Significance column

Happy 2015 Pi Day—can you see `pi` through the treemap?

Sat 14-03-2015

Celebrate `pi` Day (March 14th) with splitting its digit endlessly. This year I use a treemap approach to encode the digits in the style of Piet Mondrian.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Digits of `pi`, `phi` and `e`. (details)

The art has been featured in Ana Swanson's Wonkblog article at the Washington Post—10 Stunning Images Show The Beauty Hidden in `pi`.

I also have art from 2013 `pi` Day and 2014 `pi` Day.

Split Plot Design

Tue 03-03-2015

The split plot design originated in agriculture, where applying some factors on a small scale is more difficult than others. For example, it's harder to cost-effectively irrigate a small piece of land than a large one. These differences are also present in biological experiments. For example, temperature and housing conditions are easier to vary for groups of animals than for individuals.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Split plot design. (read)

The split plot design is an expansion on the concept of blocking—all split plot designs include at least one randomized complete block design. The split plot design is also useful for cases where one wants to increase the sensitivity in one factor (sub-plot) more than another (whole plot).

Altman, N. & Krzywinski, M. (2015) Points of Significance: Split Plot Design Nature Methods 12:165-166.

Background reading

1. Krzywinski, M. & Altman, N. (2014) Points of Significance: Designing Comparative Experiments Nature Methods 11:597-598.

2. Krzywinski, M. & Altman, N. (2014) Points of Significance: Analysis of variance (ANOVA) and blocking Nature Methods 11:699-700.

3. Blainey, P., Krzywinski, M. & Altman, N. (2014) Points of Significance: Replication Nature Methods 11:879-880.

...more about the Points of Significance column