latest news

Distractions and amusements, with a sandwich and coffee.

Poetry is just the evidence of life. If your life is burning well, poetry is just the ash
•
• burn something
• more quotes

visualization
**+** design

Here, I help you understand color blindness and describe a process by which you can make good color choices when designing for accessibility. You can also delve into the mathematics behind the color blindness simulations.

Different color blindness simulations don't all agree on the luminance of the simulated color. See methods for details.

In an audience of 8 men and 8 women, chances are 50% that at least one has some degree of color blindness^{1,2}. When encoding information or designing content, use colors that is color-blind safe.

^{1}About 8% of males and 0.5% of females are affected with some kind of color blindness in populations of European descent (wikipedia, Worldwide prevalence of red-green color deficiency, JOSAA). The rate for other races is lower Asians and Africans is lower (Caucasian Boys Show Highest Prevalence of Color Blindness Among Preschoolers, AAO).

^{2}The probability that among `N=8` men and `N=8` women at least one person is affected by color blindness is `P(men,women) = P(8,8) = 1 - (1-0.08)^8(1-0.005)^8 = 0.51`. For `N=34` (i.e., 68 people in total), this probability is `P(34,34)=0.95`. Because the rate of color blindness in women is so low, for most groups of mixed gender we can approximate the probability by only counting the men. For example, in a group of 17 women the probability that at least one of them is color blind is `P(0,17) = 0.082`, which is the same probability as for 1 man, `P(1,0)`.

The normal human eye is a 3-channel color detector^{3}. There are three types of photoreceptors, each sensitive to a different part of the spectrum. Their combined response to a given wavelength produces a unique response that is the basis of the perception of color.

^{3}Compared to hearing, the color vision is a primitive detector. While we can hear thousands of distinct frequencies and process them simultaneously, we have only three independent color inputs. While the ear can distinguish pure tones from complex sounds that have multiple frequencies the eye is relatively unsophisticated in separating a color sensation into its three constituent primary stimuli.

People with color blindness have one of the photo receptor groups either reduced in number or entirely missing. With only two groups of photoreceptors, the perception of hue is drastically altered.

For example, in *deuteranopia*, the most common type of color blindness, the medium (M) wavelength photoreceptors are reduced in number or missing. This results in the loss of perceived difference between reds and greens because only one group of photoreceptors (L) are sensitive to the wavelengths of these colors. The spectrum appears to be split into two hues along the blue-green boundary (see figure below), which is roughly where the photoreceptor sensitivities curves cross.

Visible light is in the range of 390–700 nm. The exact definition of the upper limit varies, with some sources giving as high as 760 nm. Shorter wavelengths are absorbed by the cornea (<295nm) and lens (315–390nm). Some near infrared light also reaches the retina (760–1,400nm).

The Ishihara test is a color perception test for protanopia and deuteranopia. Think of the Rorschach test, except with a different diagnosis if you can't see a pattern.

Traditionally, the Ishihara test is performed with digits but why not use Mr. Spock^{4}. He knows all the digits and is much more insteresting.

^{4}In tribute to Leonard Nimoy, 1931–2015

Color blindness comes in varying degrees and types. Let's consider total deuternanopia—where the M receptors are missing or completely dysfunctional. Because they only have two kinds of color receptors, someone with this condition will see only two dimensions of color.

To understand how to simulate color blindness we have to look briefly at how color can be represented. You're probaby familiar with the RGB color space—just one kind of many color spaces. The RGB coordinates of a color are a device-dependent output model—they tell a device, such as your monitor or TV how much of a pixel's red, green and blue to activate. Obviously, depending on which specific display panel we're talking about, the output color might actually look very different—it's a function of the actual phosphors and any calibration and adjustments.

It turns out that we can also specify color in terms of coordinates in a space based on the physiological response of the eye to the color. Since a normal eye has three photoreceptors whose sensitivity is centered on short (S), medium (M) and long (L) wavelengths, any given color (i.e. monochromatic light) creates a unique combination of S, M and L cone response.

Using a color's LMS coordinates we can simulate color blindness by modifying the coordinate that corresponds to the missing photoreceptor under the observations that (a) deuteranopes, for example, can distinguish white and greys from blues and greens and (b) colors for which the sensitivity of the missing photoreceptors is low should be perceived normally.

Because color blindess reduces the number of color dimensions, a large number of colors distinguishable to people with normal vision appear the same to someone with color blidness. The ramps below show these families of equivalent colors.

The opposite condition to color blindness exists too—tetrachromacy. In this case, an individual has an extra type of color receptor which improves discrimination in the red part of the spectrum. While the anatomy of their retina can be described, how true tetrachromats subjectively perceive color is unknown. And, perhaps, even unknowable.

Tetrachromacy is common in other animals, such as fish (e.g. goldfish, zebrafish) and birds (e.g. finch, starling). The dimensionality of the perceived color space isn't necessarily proportional to the number of different receptors. If the signal from 3 color receptors are combined by the brain and each processor has a weighted response to a broad range of wavelengths, then a color can be modeled by a point in 3-dimensional space, in which the receptors are the axes. This system can perceive a large number of colors.

In the extreme case where the receptors respond to a very narrow range, of which none overlap with the other, a color is one of three points in a 1-dimensional space. This sytem can perceive only 3 colors.

For example, although the mantis shrimp has 12 different color receptors, the receptors work independently, their color discrimination is poorer than ours.

We are celebrating the publication of our 50th column!

To all our coauthors — thank you and see you in the next column!

*When modelling epidemics, some uncertainties matter more than others.*

Public health policy is always hampered by uncertainty. During a novel outbreak, nearly everything will be uncertain: the mode of transmission, the duration and population variability of latency, infection and protective immunity and, critically, whether the outbreak will fade out or turn into a major epidemic.

The uncertainty may be structural (which model?), parametric (what is `R_0`?), and/or operational (how well do masks work?).

This month, we continue our exploration of epidemiological models and look at how uncertainty affects forecasts of disease dynamics and optimization of intervention strategies.

We show how the impact of the uncertainty on any choice in strategy can be expressed using the Expected Value of Perfect Information (EVPI), which is the potential improvement in outcomes that could be obtained if the uncertainty is resolved before making a decision on the intervention strategy. In other words, by how much could we potentially increase effectiveness of our choice (e.g. lowering total disease burden) if we knew which model best reflects reality?

This column has an interactive supplemental component (download code) that allows you to explore the impact of uncertainty in `R_0` and immunity duration on timing and size of epidemic waves and the total burden of the outbreak and calculate EVPI for various outbreak models and scenarios.

Bjørnstad, O.N., Shea, K., Krzywinski, M. & Altman, N. (2020) Points of significance: Uncertainty and the management of epidemics. *Nature Methods* **17**.

Bjørnstad, O.N., Shea, K., Krzywinski, M. & Altman, N. (2020) Points of significance: Modeling infectious epidemics. *Nature Methods* **17**:455–456.

Bjørnstad, O.N., Shea, K., Krzywinski, M. & Altman, N. (2020) Points of significance: The SEIRS model for infectious disease dynamics. *Nature Methods* **17**:557–558.

Our design on the cover of Nature Genetics's August 2020 issue is “Dichotomy of Chromatin in Color” . Thanks to Dr. Andy Mungall for suggesting this terrific title.

The cover design accompanies our report in the issue Gagliardi, A., Porter, V.L., Zong, Z. *et al.* (2020) Analysis of Ugandan cervical carcinomas identifies human papillomavirus clade–specific epigenome and transcriptome landscapes. *Nature Genetics* **52**:800–810.

*Clear, concise, legible and compelling.*

The PDF template is a poster about making posters. It provides design, typography and data visualiation tips with minimum fuss. Follow its advice until you have developed enough design sobriety and experience to know when to go your own way.

*Realistic models of epidemics account for latency, loss of immunity, births and deaths.*

We continue with our discussion about epidemic models and show how births, deaths and loss of immunity can create epidemic waves—a periodic fluctuation in the fraction of population that is infected.

This column has an interactive supplemental component (download code) that allows you to explore epidemic waves and introduces the idea of the phase plane, a compact way to understand the evolution of an epidemic over its entire course.

Bjørnstad, O.N., Shea, K., Krzywinski, M. & Altman, N. (2020) Points of significance: The SEIRS model for infectious disease dynamics. *Nature Methods* **17**:557–558.

Bjørnstad, O.N., Shea, K., Krzywinski, M. & Altman, N. (2020) Points of significance: Modeling infectious epidemics. *Nature Methods* **17**:455–456.