latest news

Distractions and amusements, with a sandwich and coffee.

I'm not real and I deny I won't heal unless I cry.
•
• let it go
• more quotes

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.

For the 2014 `\pi` day, two styles of posters are available: folded paths and frequency circles.

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.
φ
or
e
), you'll need to replace the digits with either `p`

or `h`

. Remember, the simulation will try to group the `h`

's together. You can download 1,000,000 of
π
,
φ
and
e
.

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.

Try one of the batch files above (64 digit batch file, 768 digit batch file) or the following simple job

> 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).

Precompiled binaries are available for download directly: rem2dm, rem2dlm, rem2dpm, rem3dm, rem3dlm, rem3dpm.

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.

We examine two very common supervised machine learning methods: linear support vector machines (SVM) and k-nearest neighbors (kNN).

SVM is often less computationally demanding than kNN and is easier to interpret, but it can identify only a limited set of patterns. On the other hand, kNN can find very complex patterns, but its output is more challenging to interpret.

We illustrate SVM using a data set in which points fall into two categories, which are separated in SVM by a straight line "margin". SVM can be tuned using a parameter that influences the width and location of the margin, permitting points to fall within the margin or on the wrong side of the margin. We then show how kNN relaxes explicit boundary definitions, such as the straight line in SVM, and how kNN too can be tuned to create more robust classification.

Bzdok, D., Krzywinski, M. & Altman, N. (2018) Points of Significance: Machine learning: a primer. Nature Methods 15:5–6.

Bzdok, D., Krzywinski, M. & Altman, N. (2017) Points of Significance: Machine learning: a primer. Nature Methods 14:1119–1120.

In a Nature graphics blog article, I present my process behind designing the stark black-and-white Nature 10 cover.

Nature 10, 18 December 2017

In this primer, we focus on essential ML principles— a modeling strategy to let the data speak for themselves, to the extent possible.

The benefits of ML arise from its use of a large number of tuning parameters or weights, which control the algorithmâ€™s complexity and are estimated from the data using numerical optimization. Often ML algorithms are motivated by heuristics such as models of interacting neurons or natural evolutionâ€”even if the underlying mechanism of the biological system being studied is substantially different. The utility of ML algorithms is typically assessed empirically by how well extracted patterns generalize to new observations.

We present a data scenario in which we fit to a model with 5 predictors using polynomials and show what to expect from ML when noise and sample size vary. We also demonstrate the consequences of excluding an important predictor or including a spurious one.

Bzdok, D., Krzywinski, M. & Altman, N. (2017) Points of Significance: Machine learning: a primer. Nature Methods 14:1119–1120.

Just in time for the season, I've simulated a snow-pile of snowflakes based on the Gravner-Griffeath model.

The work is described as a wintertime tale in In Silico Flurries: Computing a world of snow and co-authored with Jake Lever in the Scientific American SA Blog.

Gravner, J. & Griffeath, D. (2007) Modeling Snow Crystal Growth II: A mesoscopic lattice map with plausible dynamics.

My illustration of the location of genes in the human genome that are implicated in disease appears in The Objects that Power the Global Economy, a book by Quartz.

We introduce two common ensemble methods: bagging and random forests. Both of these methods repeat a statistical analysis on a bootstrap sample to improve the accuracy of the predictor. Our column shows these methods as applied to Classification and Regression Trees.

For example, we can sample the space of values more finely when using bagging with regression trees because each sample has potentially different boundaries at which the tree splits.

Random forests generate a large number of trees by not only generating bootstrap samples but also randomly choosing which predictor variables are considered at each split in the tree.

Krzywinski, M. & Altman, N. (2017) Points of Significance: Ensemble methods: bagging and random forests. *Nature Methods* **14**:933–934.

Krzywinski, M. & Altman, N. (2017) Points of Significance: Classification and regression trees. *Nature Methods* **14**:757–758.