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Distractions and amusements, with a sandwich and coffee.

This love's a nameless dream.
•
• try to figure it out
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They serve as the form for The Outbreak Poems.

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. I sympathize with this position and have `\tau` day art too!

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.

This year's `\pi` day art collection celebrates not only the digit but also one of the fundamental forces in nature: gravity.

In February of 2016, for the first time, gravitational waves were detected at the Laser Interferometer Gravitational-Wave Observatory (LIGO).

The signal in the detector was sonified—a process by which any data can be encoded into sound to provide hints at patterns and structure that we might otherwise miss—and we finally heard what two black holes sound like. A buzz and chirp.

The art is featured in the Gravity of Pi article on the Scientific American SA Visual blog.

All the art was processed while listening to Roses by Coeur de Pirate, a brilliant female French-Canadian songwriter, who sounds like a mix of Patricia Kaas and Lhasa. The lyrics Oublie-moi (Forget me) are fitting with this year's theme of gravity.

Mais laisse-moi tomber, laisse-nous tomber

Laisse la nuit trembler en moi

Laisse-moi tomber, laisse nous tomber

Cette fois

But let me fall, let us fall

Let the night tremble in me

Let me fall, let us fall

This time

The gravitational force between two masses `m_1` located at `(x_1,y_1)` and `m_2` located at `(x_2,y_2)` is given by

$$F = \frac{G m_1 m_2}{r^2} \tag{1} $$

where `r` is the distance between the masses given by

$$r = \sqrt{ \Delta x ^2 + \Delta y ^2 } = \sqrt{ (x_2-x_1)^2 + (y_2-y_1)^2 } \tag{2} $$

The force is directed along the vector formed by `r` and can be decomposed into `x` and `y` components using \begin{align} F_x &= F \frac{ \Delta x}{r} = F \frac{x_2-x_1}{r} \tag{3} \\ F_y &= F \frac{ \Delta y}{r} =F \frac{y_2-y_1}{r} \tag{4} \end{align}

The acceleration of each mass can be obtained using `F = ma` and similarly decomposed into `x` and `y` components \begin{align} a_{1x} &= \frac { F_{1x} }{ m_1} = \frac{G m_2 \Delta x}{r^3} \tag{5} \\ a_{1y} &= \frac { F_{1y} }{ m_1} = \frac{G m_2 \Delta y}{r^3} \tag{6} \\ a_{2x} &= \frac { F_{2x} }{ m_2} = -\frac{G m_1 \Delta x}{r^3} \tag{7} \\ a_{2y} &= \frac { F_{2y} }{ m_2} = -\frac{G m_1 \Delta y}{r^3} \tag{8} \end{align}

When there are `n` masses in the system, the acceleration of mass `i` is the sum of the accelerations due to all other masses \begin{align} a_{ix} &= \sum_{i \ne j} \frac{G m_j \Delta x_{ij}}{r_{ij}^3} \tag{9} \\ a_{iy} &= \sum_{i \ne j} \frac{G m_j \Delta y_{ij}}{r_{ij}^3} \tag{10} \end{align}

The equations of motion for the masses over a period of time `\Delta t` are

\begin{align} \Delta v_x &= \Delta t a_x \tag{11} \\ \Delta v_y &= \Delta t a_y \tag{12} \\ \Delta x &= \Delta t \left( v_x + a_x \frac{\Delta t}{2} \right) \tag{13} \\ \Delta y &= \Delta t \left( v_y + a_y \frac{\Delta t}{2} \right) \tag{14} \end{align}

There are various ways in which the numerical simulation can be performed. The Euler, Verlet, Runge-Kutta methods are perhaps the most common. I use the Verlet approach.

Using the equations of motions above, the Verlet simulation goes as follows

- calculate acceleration, `a_1` (eq 9,10)
- update position (eq 13,14)
- calculate new acceleration, `a_2` (eq 9,10)
- update velocity using `(a_1+a_2)/2` (eq 7,8)

The masses are initially uniformly distributed on a circle and given a zero initial velocity or a normally distributed random velocity.

I ran about 10,000 individual simulations with different values of `n` and `k` and collected ones that stood out as pretty.

The size of a mass is taken to be `s = m^{1/3}`. When two masses, `m_1` and `m_2` come within a distance of `\left( s_1 + s_2 \right)(1-z)` of each other, they collide. Here `z` is a collision margin parameter that I set to either `z=0` or `z=0.25`.

During the collision, a new body is created with mass `M = m_1 + m_2` given a speed that conserves momentum in the collision. \begin{align} v_x &= \frac{m_1 v_{1x} + m_2 v_{2x} }{M} \\ v_y &= \frac{m_1 v_{1y} + m_2 v_{2y} }{M} \end{align}

For my simulation, the following values are used

- `G = 100`
- mass for each digit, `d` is `(1+d)^k`
- masses placed on circle with radius `216`
- when randomized, `(v_x,v_y) \sim N(0,1)`
- `\Delta t = 0.01`
- simulation runs for up to 100,000 steps
- canvas size is `1440 \times 1440`

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.