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@c_drosten Hi, ich habe kurz mal aus Interesse den Welch-Test, bezüglich Figure 2 durchgezogen (ich habe eine solche Rechnung bisher nicht gemacht) und komme für den p-value auf einen Wert von 0.006. Die Unterschrift sagt dies aber für den Mann-Whitney rank test aus, oder? 
@c_drosten Ich kann mich da durchaus irren! Kann das jemand validieren?
@c_drosten I implemented the Welch test by hand writing my own function.#Mathematica complains that the data sets are not normally distributed. Hence, I visualized in Mathematica QQ-Plots against the normal distribution. Especially,the healthy data set seems to be off.#CoronaDaten #Drosten
composing circular motion of different frequencies (columns) with harmonic motion of different frequencies (rows). All patterns are centered on zero except the ones on the diagonal.
this is a demonstration that sine waves with integer frequencies are orthogonal (∫ f.g = 0) - a fact that Fourier analysis hinges on
#mathematica code to produce this animation pastebin.com/Jbiwetnh
draw a random polygon, and connect the midpoints of its edges to make a new polygon. Repeat this and it converges to an ellipse
inspired by @jasondavies jasondavies.com/random-polygon…
#mathematica code to create this animation pastebin.com/WHKWsMeY
draw a line, and extend it deflected by a fixed angle. Continue, adding the angle again each time. The result is a Euler spiral
with the right angle, it's even possible to create an Euler spiral of Euler spirals
#mathematica code
\[Theta]inc = 0.05;
n = 50000;
pts = Accumulate[
Table[With[{\[Theta] = \[Theta]inc i (i - 1)/2}, {Cos[\[Theta]],
Sin[\[Theta]]}], {i, n}]];
Graphics[
{White, Opacity[0.8], Thickness[0.003], Line[pts]},
Background -> Black
]
\[Theta]inc = 0.05;
n = 50000;
pts = Accumulate[
Table[With[{\[Theta] = \[Theta]inc i (i - 1)/2}, {Cos[\[Theta]],
Sin[\[Theta]]}], {i, n}]];
Graphics[
{White, Opacity[0.8], Thickness[0.003], Line[pts]},
Background -> Black
]
the centre of a logarithmic spiral traces a straight line as it is rolled. this means a pair can be used as unconventional gears
There is no slipping between the two gears, and the point of contact moves at a constant speed from the centre of one gear to the other (with a discontinuity at each turn).
The slope of the straight line traced by the centre is called the spiral's pitch. A golden spiral is a logarithmic spiral with pitch 17.032°
#mathematica challenge - how many ways can you find to plot a circle?
a few to get started:
Graphics[Circle[]]
PolarPlot[1, {th, 0, 2 Pi}]
ParametricPlot[{Sin[th], Cos[th]}, {th, 0, 2 Pi}]
ContourPlot[x^2 + y^2 == 1, {x, -1, 1}, {y, -1, 1}]
a few to get started:
Graphics[Circle[]]
PolarPlot[1, {th, 0, 2 Pi}]
ParametricPlot[{Sin[th], Cos[th]}, {th, 0, 2 Pi}]
ContourPlot[x^2 + y^2 == 1, {x, -1, 1}, {y, -1, 1}]
Plot[{-1, 1} Sqrt[1 - x^2], {x, -1, 1}]
RegionPlot[x^2 + y^2 < 1, {x, -1, 1}, {y, -1, 1}, PlotStyle -> None]
there are 627 ways to partition the number 20 into whole-number pieces (such as 15 + 4 + 1). each partition is shown here as a spiral (walk 15, turn xº left, walk 4, turn xº left, walk 1). this animation shows all 627 as paths for varying x.
#math
#math
higher res for 1/8th turns, showing all partitions of 20
fractal built using recursive replacement rules that vary smoothly with their input
Another, based on the Sierpinski carpet
