The accidental similarity number (ASN) is a kind of overlap between numbers. I came up with this concept after creating typographical art about the `i`-ness of `\pi`.
The poster shows the accidental similarity number for `\pi`, `\phi` and `e`.
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.