latest news

Distractions and amusements, with a sandwich and coffee.

And she looks like the moon. So close and yet, so far.
•
• aim high
• more quotes

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`.

There are two kinds of `\pi` Approximation Day posters.

The first uses the Archimedean spiral for its design, which I've used before for other numerical art. The second packs warped circles, whose ratio of circumference to average diameter is `22/7` into what I call `\pi`-approximate circular packing.

In the Approximation Day poster, all `m/n` rational approximations to `\pi` are shown as circles on a spiral. The circle at the start of the spiral (top) corresponds to `m=1`. The circle at the center of the spiral corresponds to `m=10000`.

Each circle is colored by the accuracy of the best possible approximation `m/n` according to the color scheme below, which is the legend inset. For example, for `m=22` the best approximation has `n=7`.

The accuracy cutoffs were selected to assign roughly the same number of points to each category.

The location of the best approximations within each accuracy window is shown below.

Decision trees classify data by splitting it along the predictor axes into partitions with homogeneous values of the dependent variable. Unlike logistic or linear regression, CART does not develop a prediction equation. Instead, data are predicted by a series of binary decisions based on the boundaries of the splits. Decision trees are very effective and the resulting rules are readily interpreted.

Trees can be built using different metrics that measure how well the splits divide up the data classes: Gini index, entropy or misclassification error.

When the predictor variable is quantitative and not categorical, regression trees are used. Here, the data are still split but now the predictor variable is estimated by the average within the split boundaries. Tree growth can be controlled using the complexity parameter, a measure of the relative improvement of each new split.

Individual trees can be very sensitive to minor changes in the data and even better prediction can be achieved by exploiting this variability. Using ensemble methods, we can grow multiple trees from the same data.

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

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Logistic regression. *Nature Methods* **13**:541-542.

Altman, N. & Krzywinski, M. (2015) Points of Significance: Multiple Linear Regression *Nature Methods* **12**:1103-1104.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Classifier evaluation. *Nature Methods* **13**:603-604.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Model Selection and Overfitting. *Nature Methods* **13**:703-704.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Regularization. *Nature Methods* **13**:803-804.

The artwork was created in collaboration with my colleagues at the Genome Sciences Center to celebrate the 5 year anniversary of the Personalized Oncogenomics Program (POG).

The Personal Oncogenomics Program (POG) is a collaborative research study including many BC Cancer Agency oncologists, pathologists and other clinicians along with Canada's Michael Smith Genome Sciences Centre with support from BC Cancer Foundation.

The aim of the program is to sequence, analyze and compare the genome of each patient's cancer—the entire DNA and RNA inside tumor cells— in order to understand what is enabling it to identify less toxic and more effective treatment options.

Principal component analysis (PCA) simplifies the complexity in high-dimensional data by reducing its number of dimensions.

To retain trend and patterns in the reduced representation, PCA finds linear combinations of canonical dimensions that maximize the variance of the projection of the data.

PCA is helpful in visualizing high-dimensional data and scatter plots based on 2-dimensional PCA can reveal clusters.

Altman, N. & Krzywinski, M. (2017) Points of Significance: Principal component analysis. *Nature Methods* **14**:641–642.

Altman, N. & Krzywinski, M. (2017) Points of Significance: Clustering. *Nature Methods* **14**:545–546.

Similar to the `h` index in publishing, the `k` index is a measure of fitness performance.

To achieve a `k` index for a movement you must perform `k` unbroken reps at `k`% 1RM.

The expected value for the `k` index is probably somewhere in the range of `k = 26` to `k=35`, with higher values progressively more difficult to achieve.

In my `k` index introduction article I provide detailed explanation, rep scheme table and WOD example.

I've applied the char-rnn recurrent neural network to generate new words, names of drugs and countries.

The effect is intriguing and facetious—yes, those are real words.

But these are not: *necronology*, *abobionalism*, *gabdologist*, and *nonerify*.

These places only exist in the mind: *Conchar and Pobacia*, *Hzuuland*, *New Kain*, *Rabibus and Megee Islands*, *Sentip and Sitina*, *Sinistan* and Urzenia.

And these are the imaginary afflictions of the imagination: *ictophobia*, *myconomascophobia*, and *talmatomania*.

And these, of the body: *ophalosis*, *icabulosis*, *mediatopathy* and *bellotalgia*.

Want to name your baby? Or someone else's baby? Try *Ginavietta Xilly Anganelel* or *Ferandulde Hommanloco Kictortick*.

When taking new therapeutics, never mix *salivac* and *labromine*. And don't forget that *abadarone* is best taken on an empty stomach.

And nothing increases the chance of getting that grant funded than proposing the study of a new –ome! We really need someone to looking into the *femome* and *manome*.

An exploration of things that are missing in the human genome. The nullomers.

Julia Herold, Stefan Kurtz and Robert Giegerich. Efficient computation of absent words in genomic sequences. *BMC Bioinformatics* (2008) **9**:167