On March 14th celebrate `\pi` Day. Hug `\pi`—find a way to do it.
For those who favour `\tau=2\pi` will have to postpone celebrations until July 26th. That's what you get for thinking that `\pi` is wrong.
If you're not into details, you may opt to party on July 22nd, which is `\pi` approximation day (`\pi` ≈ 22/7). It's 20% more accurate that the official `\pi` day!
Finally, if you believe that `\pi = 3`, you should read why `\pi` is not equal to 3.
The folded paths show `\pi` on a path that maximizes adjacent prime digits and were created using a protein-folding algorithm.
The frequency circles colourfully depict the ratio of digits in groupings of 3 or 6. Oh, look, there's the Feynman Point!
Download the HP lattice simulation binary. You'll need one of the three 2D methods — I used
rem2dm, which does local and pull moves. If you'd like to learn more about the algorithm, read the publication.
A replica exchange Monte Carlo algorithm for protein folding in the HP model. Chris Thachuk, Alena Shmygelska and Holger H Hoos, BMC Bioinformatics 2007, 8:342 (17 Sep 2007).
Download the batch file for 64- or 768-digit folding.
When you run the 64-digit simulation, you're likely to find a path with
E=-23, which is the lowest energy I've been able to sample. On my Intel Xeon E5540 (2.53 GHz) it takes anywhere from 1-30 seconds to find a
E=-23 path (there are many possible paths at this energy), depending on the random seed. Here's the output of a typical run of the 64-digit folding simulation
> rem2dm -seq=hppphphphhhpphphhhppphpphhphhhphphppppphppphpphhhpphphpphpppphph -maxT=220 -numLocalSteps=500 -eng=100 -maxRunTime=60 -traceFile=pi.64 -minT=160 -expID=pi.64 -numReps=10 REMC-HP2D-M Begin Simulation 0.01: Current Best Solution: -8 0.01: Current Best Solution: -10 0.01: Current Best Solution: -13 0.02: Current Best Solution: -15 0.03: Current Best Solution: -16 0.03: Current Best Solution: -17 0.04: Current Best Solution: -18 0.04: Current Best Solution: -19 0.16: Current Best Solution: -20 0.27: Current Best Solution: -21 0.69: Current Best Solution: -22 36.23: Current Best Solution: -23 Real time: 120 ggslrrsrllssrrlrrllsrrlrrlslslrrsrlssrrsllrslrrlrsllsrsrrlsrssrs p--h--p | | h--h h--p--p--p | | p--p h H h--p--p | | | | | p--h h--h--p p p--p | | | p--p--h h--p p--p p | | | | | h--h h h--p--h h--p | | | p--h h h--p--H h--p | | | | p--p p p--h--h | | p p--h--p | | p--p--h h | | p--p End Simulation
If you want to apply this to different number (e.g.
), you'll need to replace the digits with either
h. Remember, the simulation will try to group the
h's together. You can download 1,000,000 of
The best path I could find for 768 digits is one with
E=-223. In 1000s of simulations this solution came up only once. I also saw one path at
E=-222. After that, there were many solutions at each of the less optimal energy levels.
If you manage to find a better one, let me know right away!
If you obtain a segmentation fault,
> ./rem2dlm REMC-HP2D-LM Begin Simulation Real time: 0 Segmentation fault
don't panic just yet. The folding binaries don't do a lot of error checking, so you have to get the input parameters correct.
For example, if you do not include the
-eng parameter, the code will segfault.
> bin/rem2dm -seq=hhpppphhhhpppphh -maxRunTime=5 -eng 10 REMC-HP2D-M Begin Simulation 3.13877e-17: Current Best Solution: -2 5.49284e-17: Current Best Solution: -3 1.0201e-16: Current Best Solution: -4 1.33398e-16: Current Best Solution: -5 Real time: 5 ggrllslsssrllsls p--p--p | | h h--p | | H h | H h | | p--h h | | p--p--p
If this segfaults, then you'll need to recompile the code (see below).
If these don't work on your system, you need to recompile them. Download the the protein folding code and see INSTALL.txt for compilation instructions.
Data visualization should be informative and, where possible, tasty.
Stefan Reuscher from Bioscience and Biotechnology Center at Nagoya University celebrates a publication with a Circos cake.
The cake shows an overview of a de-novo assembled genome of a wild rice species Oryza longistaminata.
The presence of constraints in experiments, such as sample size restrictions, awkward blocking or disallowed treatment combinations may make using classical designs very difficult or impossible.
Optimal design is a powerful, general purpose alternative for high quality, statistically grounded designs under nonstandard conditions.
We discuss two types of optimal designs (D-optimal and I-optimal) and show how it can be applied to a scenario with sample size and blocking constraints.
Smucker, B., Krzywinski, M. & Altman, N. (2018) Points of significance: Optimal experimental design Nature Methods 15:599–600.
Krzywinski, M., Altman, N. (2014) Points of significance: Two factor designs. Nature Methods 11:1187–1188.
Krzywinski, M. & Altman, N. (2014) Points of significance: Analysis of variance (ANOVA) and blocking. Nature Methods 11:699–700.
Krzywinski, M. & Altman, N. (2014) Points of significance: Designing comparative experiments. Nature Methods 11:597–598.
An illustration of the Tree of Life, showing some of the key branches.
The tree is drawn as a DNA double helix, with bases colored to encode ribosomal RNA genes from various organisms on the tree.
All living things on earth descended from a single organism called LUCA (last universal common ancestor) and inherited LUCA’s genetic code for basic biological functions, such as translating DNA and creating proteins. Constant genetic mutations shuffled and altered this inheritance and added new genetic material—a process that created the diversity of life we see today. The “tree of life” organizes all organisms based on the extent of shuffling and alteration between them. The full tree has millions of branches and every living organism has its own place at one of the leaves in the tree. The simplified tree shown here depicts all three kingdoms of life: bacteria, archaebacteria and eukaryota. For some organisms a grey bar shows when they first appeared in the tree in millions of years (Ma). The double helix winding around the tree encodes highly conserved ribosomal RNA genes from various organisms.
Johnson, H.L. (2018) The Whole Earth Cataloguer, Sactown, Jun/Jul, p. 89
An article about keyboard layouts and the history and persistence of QWERTY.
McDonald, T. (2018) Why we can't give up this odd way of typing, BBC, 25 May 2018.
I've previously taken a more fine-art approach to cover design, such for those of Nature, Genome Research and Trends in Genetics. I've used microscopy images to create a cover for PNAS—the one that made biology look like astrophysics—and thought that this is kind of material I'd start with for the MCS cover.