One of my goals in life, which I can now say has been accomplished, is to make biology look like astrophysics. Call it my love for the Torino Impact Hazard Scale.
Recently, I was given an opportunity to attend to this (admittedly vague) goal when Linda Chang from Aly Karsan's group approached me with some microscopy photos of mouse veins. I was asked to do "something" with these images for a cover submission to accompany the manuscript.
When people see my covers, sometimes they ask "How did you do that?" Ok, actually they never ask this. But being a scientist, I'm trained me to produce answers in anticipation of such questions. So, below, I show you how the image was constructed.
The image was published on the cover of PNAS (PNAS 1 May 2012; 109 (18))
Below are a few of the images I had the option to work with. These are mouse embryonic blood vessels, with a carotid artery shown in the foreground with endothelial cells in green, vascular smooth muscle cells in red and the nuclei in blue.
Of course, as soon as I saw the images, I realized that there was very little that I needed to do to trigger the viewer's imagination. These photos were great!
Immediately I thought of two episodes of Star Trek (original series): Doomsday Machine and the Immunity Syndrome, as well as of images from the Hubble Telescope.
I though it would be pretty easy to make the artery images look all-outer-spacey. They already looked it.
And then I saw the image below.
The background was created from the two images shown here. The second image was sampled three times, at different rotations.
The channel mixer was used to remove the green channel and leave only red and blue.
The next layer was composed of what looked like ribbons of blue gas. This was created by sampling the oval shapes from the source images. Here the red channel was a great source for cloud shapes, and this was the only channel that was kept. The hue was shifted to blue and a curve adjustment was applied to increase the contrast.
When the foreground and middle ground elements were combined, the result was already 40 parsecs away.
The foreground was created from the spectacular comet-like image of a mouse artery. Very little had to be done to make this element look good. It already looked good.
I applied a little blur using Alien Skin's Bokeh 2 to narrow the apparent depth of field, masked out elements at the bottom of the image and removed some of the green channel. The entire blue channel was removed altogether (this gave the tail of the comet a mottled, flame-like appearance).
And here we have the final image.
Today is the day and it's hardly an approximation. In fact, `22/7` is 20% more accurate of a representation of `\pi` than `3.14`!
Time to celebrate, graphically. This year I do so with perfect packing of circles that embody the approximation.
By warping the circle by 8% along one axis, we can create a shape whose ratio of circumference to diameter, taken as twice the average radius, is 22/7.
Regression can be used on categorical responses to estimate probabilities and to classify.
The next column in our series on regression deals with how to classify categorical data.
We show how linear regression can be used for classification and demonstrate that it can be unreliable in the presence of outliers. Using a logistic regression, which fits a linear model to the log odds ratio, improves robustness.
Logistic regression is solved numerically and in most cases, the maximum-likelihood estimates are unique and optimal. However, when the classes are perfectly separable, the numerical approach fails because there is an infinite number of solutions.
Altman, N. & Krzywinski, M. (2016) Points of Significance: Logistic regression. Nature Methods 13:541-542.
Altman, N. & Krzywinski, M. (2016) Points of Significance: Regression diagnostics? Nature Methods 13:385-386.
Altman, N. & Krzywinski, M. (2015) Points of Significance: Multiple Linear Regression Nature Methods 12:1103-1104.
Altman, N. & Krzywinski, M. (2015) Points of significance: Simple Linear Regression Nature Methods 12:999-1000.
Genomic instability is one of the defining characteristics of cancer and within a tumor, which is an ever-evolving population of cells, there are many genomes. Mutations accumulate and propagate to create subpopulations and these groups of cells, called clones, may respond differently to treatment.
It is now possible to sequence individual cells within a tumor to create a profile of genomes. This profile changes with time, both in the kinds of mutation that are found and in their proportion in the overall population.
Clone evolution diagrams visualize these data. These diagrams can be qualitative, showing only trends, or quantitative, showing temporal and population changes to scale. In this Molecular Cell forum article I provide guidelines for drawing these diagrams, focusing with how to use color and navigational elements, such as grids, to clarify the relationships between clones.
Krzywinski, M. (2016) Visualizing Clonal Evolution in Cancer. Mol Cell 62:652-656.
Limitations in print resolution and visual acuity impose limits on data density and detail.
Your printer can print at 1,200 or 2,400 dots per inch. At reading distance, your reader can resolve about 200–300 lines per inch. This large gap—how finely we can print and how well we can see—can create problems when we don't take visual acuity into account.
The column provides some guidelines—particularly relevant when showing whole-genome data, where the scale of elements of interest such as genes is below the visual acuity limit—for binning data so that they are represented by elements that can be comfortably discerned.
Krzywinski, M. (2016) Points of view: Binning high-resolution data. Nature Methods 13:463.