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.
Caelum non animum mutant qui trans mare currunt.
This year: creatures that don't exist, but once did, in the skies.
And a poem Of Black Body.
This year's `\pi` day song is Exploration by Karminsky Experience Inc. Why? Because "you never know what you'll find on an exploration".
The `\pi` star chart has 80 constellations. Many of them have stories to tell—look up and listen.
I would love to have a complete mythology for each constellation. Please submit your stories!
Camptor — Veronica Falconeri
The symbols beside the constellation index indicate which hemisphere the constellation can be found (◓ north, ◒ south or ● both). The first 25 brightest stars in the constellation are also listed, along with their apparent magnitude, longitude and latitude.
Alaotra is frustrated that Tadorna seems to get all the attention. Often confused for a duck, Alaotra would love you to know that she's in fact a grebe. She's very proud of this fact, despite of being prone to falls due to some biomechanical issues having to do with foot placement.
Shape: 3/57 stars, 3 edges.
Shape: 4/42 stars, 4 edges.
Shape: 2/21 stars, 1 edges.
Araucaria is truly a marvel. She is so large, in fact, that the constellation only shows the canopy and does not include the tree trunk—which was known to reach a height of 100 m. Araucaria offers plenty of protection and has many flying friends all around, including Urania, Moho and WhĒkau. Just a little further are the ducks (and a grebe), Camptor, Mariana, Tadorna and Alaotra. They would love to visit Araucaria but worry that they are too heavy to perch on her branches.
Shape: 8/1232 stars, 8 edges.
Shape: 7/1838 stars, 7 edges.
Shape: 5/1019 stars, 4 edges.
Shape: 14/2287 stars, 14 edges.
Urged by Camelops, Ardea is trying to beat Aepyornis and be the first to see beyond the sky. It looks like she may be winning, but Camelops knows its a futile pursuit. Only he knows what is beyond the sky.
Shape: 9/1768 stars, 9 edges.
Argentavis is a big bird in the big sky. There are many stories of his feud with Pelagornis, who spreads his wings in the southern hemisphere — both insist that they have the biggest wing span.
Shape: 5/69 stars, 4 edges.
Runs in the vast plains of the north together with Mammuthus and Quagga.
Shape: 7/62 stars, 7 edges.
The king lizard dives into the depths of the sky at the very tip of the south hemisphere. Some say that he is chasing the South star, `\alpha` Basilosaurus.
Shape: 3/61 stars, 2 edges.
Shape: 5/602 stars, 5 edges.
It's hard to be bigger than Bron. He must always pay attention not to step on his frolicking friend Compsognathus, who seeks to find protection in Bron's shadow. Some believe that if Bron stretches his neck, he can look above the sky! But don't tell Ardea this—she's in a contest with Aepyornis to be the first!
Shape: 12/5230 stars, 11 edges.
Camelops played a cruel joke on Ardea and Aepyornis, asking them to try to look beyond the sky. Both think they have the longest neck, so they're still trying!
Shape: 6/1789 stars, 5 edges.
Camptor flew long and far to find a pond without ducks on Earth, but could find no such pond. So she chose longest journey, and flew to settle in the sky.
Shape: 3/570 stars, 3 edges.
Shape: 4/7 stars, 4 edges.
The last elk was shot in Pennsylvania. Oops.
Shape: 6/296 stars, 5 edges.
The tiniest of dinosaurs, Compsognathus hides in the protection of Bron's shadow.
Shape: 2/190 stars, 1 edges.
Shape: 5/364 stars, 5 edges.
Shape: 6/57 stars, 5 edges.
Shape: 3/82 stars, 2 edges.
Shape: 4/1164 stars, 3 edges.
Ever since meeting Pinta, they've been fast (and slow) friends.
Shape: 4/233 stars, 4 edges.
Shape: 5/47 stars, 5 edges.
It is thought that each night Desmodus flies up against the dome of the sky, looking for a way to escape.
Shape: 3/122 stars, 3 edges.
The last pidgeon, Martha, died in 1914 at the Cincinanati zoo. What a place to leave the earth from, eh?
Shape: 3/33 stars, 3 edges.
The Glyptodon is very slowly crossing from the south to the north hemisphere to play with Bron and Compsognathus. Will he make it?
Shape: 7/332 stars, 7 edges.
Shape: 7/437 stars, 7 edges.
Shape: 3/73 stars, 3 edges.
Shape: 3/53 stars, 3 edges.
Shape: 4/72 stars, 3 edges.
Shape: 6/817 stars, 6 edges.
Toads are studied by herpetologists. I'd love to be one just so that I can say that word at a party.
Shape: 4/106 stars, 4 edges.
Shape: 5/48 stars, 4 edges.
Shape: 8/2155 stars, 7 edges.
Shape: 5/714 stars, 5 edges.
Shape: 6/1028 stars, 6 edges.
Not much is known about when Malpaisomys became extinct. Some think it's when humans and dogs arrived on the Canary islands. Malpaisomys worries that because of his small size, nobody cares.
Shape: 3/38 stars, 3 edges.
Shape: 8/69 stars, 7 edges.
Shape: 3/17 stars, 3 edges.
One word: terrifying. More words: endlessly chasing Tecopa. The megalodon possesses the brightest star in the sky.
Shape: 4/20 stars, 4 edges.
Shape: 5/122 stars, 5 edges.
The Minmi is actually much larger than his name suggests. He really wants you to know that.
Shape: 5/749 stars, 4 edges.
Shape: 5/60 stars, 5 edges.
The ʻōʻō has all its letters with diacriticals. This makes the whēkau jealous. They haven't talked since.
Shape: 6/70 stars, 6 edges.
I frankly hate olives and there's no end to my pleasure in throwing olives at the sky.
Shape: 4/784 stars, 4 edges.
Like Pipilo, the O'ahu 'akepa is the only other multi-part constellation. Here, a pair of akepas are chatting and spreading rumors about Tadorna.
Shape: 4/30 stars, 2 edges.
Rumor has it Palaeoaldrovanda was related to the carnivorous plant genus Aldrovanda! Xerces is seen flying nearby. He must be careful.
Shape: 3/121 stars, 3 edges.
The mayfly loves to pester Raphus, the Dodo bird. He is too worried about guarding his eggs to pay attention to Pecatonica, though.
Shape: 4/58 stars, 3 edges.
He can barely fit in the southern skies. With a wingspan of over 5 meters, he is certain that he is the biggest bird in the sky. However, Argentavis of the northern hemisphere disagrees.
Shape: 6/192 stars, 5 edges.
The Phelsuma was described as unafraid of humans and said to be tame and happy to eat fruit from your hand. Lessons to be learned here?
Shape: 10/131 stars, 10 edges.
Shape: 3/88 stars, 2 edges.
The last of its kind, a male named Lonesome George, died in 2012.
Shape: 5/402 stars, 5 edges.
A rare flocking constellation. Thef towhees cross hemispheres and keep the Glyptodon company.
Shape: 44/261 stars, 22 edges.
Shape: 5/406 stars, 5 edges.
Shape: 4/652 stars, 4 edges.
The last sighting of a pair of po'ouli was in 2004 and now again, in the sky of pi.
Shape: 4/145 stars, 4 edges.
Tiny guys in the corner.
Shape: 2/7 stars, 1 edges.
Shape: 9/1676 stars, 8 edges.
Comical and uncertain of its stripes, Quagga is often seen asking Aurochs for his advice.
Shape: 6/139 stars, 6 edges.
Raphus is guarding his eggs—the clusters of stars just south of β Raphus (the second brightest star in the constellation) while pestered by Pecatonica.
Shape: 5/358 stars, 5 edges.
Shape: 3/12 stars, 3 edges.
Fleeing from the giant Megalodon, Rodhocetus was an early whale that possessed land mammal characteristics. Some say that he managed to escape from Megalodon and lived out his life on the land, never returning to the sea.
Shape: 6/44 stars, 5 edges.
The last known stalk was given to Emperor Nero. As stories, some have said that he used Silphium as kindle to a larger fire.
Shape: 3/8 stars, 3 edges.
Shape: 5/577 stars, 4 edges.
Shape: 6/202 stars, 6 edges.
Swamphen is delighted to have a diacritical mark in its name, a characteristic shared only by the whēkau, who resides in the northern hemisphere and the ʻōʻō (Moho braccatus) who lives just to the north.
Shape: 3/19 stars, 2 edges.
Rumor has it Tadorna may have snuck into the sky without permission—while not seen since the 1960’s, some say the duck isn’t extinct.
Shape: 3/31 stars, 3 edges.
Tecopa can tolerate heat, which allows him to escape from Megalodon, who will not chase Tecopa through the hot springs.
Shape: 4/100 stars, 3 edges.
The last of its kind was shot by Willem Dafoe in the movie The Hunter. To this day, the Thylacine can be seen screaming in the sky.
Shape: 10/2205 stars, 9 edges.
Shape: 3/481 stars, 3 edges.
Trex is unhappy because he's such a tiny constellation -- he's barely eaten!
Shape: 5/40 stars, 4 edges.
Shape: 6/71 stars, 5 edges.
Shape: 6/751 stars, 5 edges.
Shape: 7/462 stars, 7 edges.
Some members of the genus are not extinct and enjoy being called "corn salad" even though they have never seen a salad.
Shape: 4/1313 stars, 3 edges.
Some say that whēkau can still be heard. Perhaps the joke is on us?
Shape: 3/57 stars, 2 edges.
Brilliant blue butterfly in the dark blue sky. Xerces is the only thing that is bluer than the sky itself. Some say that butterflies are flying flowers and Xerces is never far from Palaeoaldrovanda. He must be careful though. Rumor has it Palaeoaldrovanda was related to the carnivorous plant genus Aldrovanda! Nobody wants to take that chance.
Shape: 8/1299 stars, 8 edges.
Don't let Yersinia's small size fool you. The Black Death may be the smallest creature in the sky, but she'll liquify your insides before you can memorize the 80 constellations. Perhaps out of all the creatures in the sky, this is the one we're happy to see go. But, because it's small, you can never be quite sure Yersinia isn't extinct but merely hiding. Or waiting.
Shape: 3/418 stars, 3 edges.
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 algorithm’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 evolution—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.
Gravner, J. & Griffeath, D. (2007) Modeling Snow Crystal Growth II: A mesoscopic lattice map with plausible dynamics.
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.
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.