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This love loves love. It's a strange love, strange love.Liz Fraserfind a way to love

pi: beautiful

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

visualization + design

Typography geek? If you like the geometry and mathematics of these posters, you may enjoy something more lettered. Visions of type: Type Peep Show: The Private Curves of Letters posters.

`pi` Approximation Day 2014 Art Posters

Martin Krzywinski @MKrzywinski
Support Ellie Balk's Kickstarter community math mural project in which Brooklyn students learn math and art to visualize `pi`.

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski
2013 `pi` day

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski
2014 `pi` day

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski
2015 `pi` day

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski
2014 `pi` approx day

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski
Circular `pi` art

The never-repeating digits of `pi` can be approximated by 22/7 = 3.142857 to within 0.04%. These pages artistically and mathematically explore rational approximations to `pi`. This 22/7 ratio is celebrated each year on July 22nd. If you like hand waving or back-of-envelope mathematics, this day is for you: `pi` approximation day!

Want more math + art? Discover the Accidental Similarity Number. Find humor in my poster of the first 2,000 4s of `pi`.

getting it mostly right

Curiously, the 22/7 rational approximation of `pi` is more accurate (0.04%) than using the first three digits 3.14, which are accurate to 0.05%.

It seems that `pi` Approximation Day is 20% more accurate! And therefore worth celebrating.

art of `pi` rational approximation

The poster shows the accuracy of 10,000 rational approximations of `pi` for each m/n and m=1..10,000. Read about the details of the method.

Pi Approximation Day Art Poster / Martin Krzywinski @MKrzywinski buy artwork
Pi Approximation Day Art Poster | July 22nd is Pi Approximation Day. Celebrate with this post-modern poster. (PNG, BUY ARTWORK)

news + thoughts

Association, correlation and causation

Thu 01-10-2015

Correlation implies association, but not causation. Conversely, causation implies association, but not correlation.

This month, we distinguish between association, correlation and causation.

Association, also called dependence, is a very general relationship: one variable provides information about the other. Correlation, on the other hand, is a specific kind of association: an increasing or decreasing trend. Not all associations are correlations. Moreover, causality can be connected only to association.

Martin Krzywinski @MKrzywinski
Nature Methods Points of Significance column: Association, correlation and causation. (read)

We discuss how correlation can be quantified using correlation coefficients (Pearson, Spearman) and show how spurious corrlations can arise in random data as well as very large independent data sets. For example, per capita cheese consumption is correlated with the number of people who died by becoming tangled in bedsheets.

...more about the Points of Significance column

Bayesian networks

Thu 01-10-2015

For making probabilistic inferences, a graph is worth a thousand words.

This month we continue with the theme of Bayesian statistics and look at Bayesian networks, which combine network analysis with Bayesian statistics.

In a Bayesian network, nodes represent entities, such as genes, and the influence that one gene has over another is represented by a edge and probability table (or function). Bayes' Theorem is used to calculate the probability of a state for any entity.

Martin Krzywinski @MKrzywinski
Nature Methods Points of Significance column: Bayesian networks. (read)

In our previous columns about Bayesian statistics, we saw how new information (likelihood) can be incorporated into the probability model (prior) to update our belief of the state of the system (posterior). In the context of a Bayesian network, relationships called conditional dependencies can arise between nodes when information is added to the network. Using a small gene regulation network we show how these dependencies may connect nodes along different paths.

Background reading

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

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

Unentangling complex plots

Fri 10-07-2015

The Points of Significance column is on vacation this month.

Meanwhile, we're showing you how to manage small multiple plots in the Points of View column Unentangling Complex Plots.

Martin Krzywinski @MKrzywinski
Nature Methods Points of View column: Unentangling complex plots. (download, more about Points of View)

Data in small multiples can vary in range, noise level and trend. Gregor McInerny and myself show you how you can deal with this by cropped and scaling the multiples to a different range to emphasize relative changes while preserving the context of the full data range to show absolute changes.

McInerny, G. & Krzywinski, M. (2015) Points of View: Unentangling complex plots. Nature Methods 12:591.

...more about the Points of View column

Fixing Jurassic World science visualizations

Fri 10-07-2015

The Jurassic World Creation Lab webpage shows you how one might create a dinosaur from a sample of DNA. First extract, sequence, assemble and fill in the gaps in the DNA and then incubate in an egg and wait.

Martin Krzywinski @MKrzywinski
We can't get dinosaur genomics right, but we can get it less wrong. (a) Corn genome used in Jurassic World Creation Lab website. Image is from the Science publication B73 Maize Genome: Complexity, Diversity, and Dynamics. Photo and composite by Universal Studios and Amblin Entertainment. (b) Random data on 8 chromosomes from chicken genome resized to triceratops genome size (3.2 Gb). Image by Martin Krzywinski. (c) Actual genome data for lizard genome, UCSC anoCar2.0, May 2010. Image by Martin Krzywinski. Triceratops outline in (b,c) from wikipedia.

With enough time, you'll grow your own brand new dinosaur. Or a stalk of corn ... with more teeth.

What went wrong? Let me explain.

Martin Krzywinski @MKrzywinski
Corn World: Teeth on the Cob.

Printing Genomes

Tue 07-07-2015

You've seen bound volumes of printouts of the human reference genome. But what if at the Genome Sciences Center we wanted to print everything we sequence today?

Martin Krzywinski @MKrzywinski
Curiously, printing is 44 times as expensive as sequencing. (details)

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
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
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.