Andrew M. Webb

@AndrewM_Webb

Machine learning R&D | I make maths/science animations | 𝗧𝗼𝗽 𝘁𝘄𝗲𝗲𝘁𝘀:

Manchester, England
awebb.info
Vrijeme pridruživanja: svibanj 2015.
167 fotografija ili videozapisa Fotografije i videozapisi

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  1. Prikvačeni tweet
    2. sij

    To count an animal population if you can't catch them all: capture some, mark them, release, and capture again. The ratio of new vs already seen tells you something about the total number. Shown here is iterated mark-and-recapture with a Bayesian updates to belief about pop size

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  2. 22. sij

    Not sure how interesting that is, but it occurred to me today and I found it slightly surprising. That average error factor is for two numbers with mantissas uniform over [0, 10). In the worst case, the factor is ~1.74

    6 korisnika označava da im se sviđa
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  3. 22. sij

    To compute a geometric mean in normalized scientific notation, take the arithmetic mean of exponents and the geometric mean of mantissas. But for a quick mental approximation, take the arithmetic mean of *both*. The result is an overestimate, on average by a factor of only ~1.09

    22 proslijeđena tweeta 132 korisnika označavaju da im se sviđa
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  4. proslijedio/la je Tweet
    23. ožu 2018.

    No individual colour making up this wave travels faster than the grid lines, but the sum of all components appears to outrace the grid. This is how “group velocities” can exceed the speed of light without carrying information.

    14 replies 331 proslijeđeni tweet 871 korisnik označava da mu se sviđa
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  5. 13. sij

    A different version of the video comparing the speed of a hummingbird and the rotation rate of the fastest known pulsar. (I added a marker to the equator so you can see when it completes a full rotation, and the animation starts much faster.)

    12 replies 252 proslijeđena tweeta 1.106 korisnika označava da im se sviđa
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  6. 11. sij

    There is a neutron star that rotates 716 times per second. How fast is that? In this illustration, it rotates 9 times while a hummingbird executes half a flap of its wings. (h/t ) (Hummingbird footage from the Slow Mo Guys: )

    540 proslijeđenih tweetova 1.934 korisnika označavaju da im se sviđa
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  7. proslijedio/la je Tweet
    9. sij

    Because there is nothing more useful than a mathematical trick, and thanks to your feedback, find the updated ML trick slide -:) Please RT, add even more to the list !!!

    59 proslijeđenih tweetova 229 korisnika označava da im se sviđa
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  8. proslijedio/la je Tweet
    5. sij

    Sharing an interesting (and famous!) population sampling problem with kids thanks to and

    1 reply 3 proslijeđena tweeta 13 korisnika označava da im se sviđa
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  9. 5. sij

    Apologies for tweeting/deleting this a couple of times, there were a couple of mistakes in there.

    1 reply 5 korisnika označava da im se sviđa
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  10. 5. sij

    2^86 is conjectured to be the greatest power of two whose decimal does not contain the digit zero. Here's an informal argument showing that if you can treat the digits as random then the conjecture is probably true.

    6 replies 18 proslijeđenih tweetova 168 korisnika označava da im se sviđa
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  11. proslijedio/la je Tweet
    30. ruj 2019.

    Small differences are magnified in chaotic systems. This also makes it hard to reverse numerical simulations. In the forward sim, 2 pendulums are close until t=15. At t=22, velocities are reversed. In reverse simulation, they come together from t=15 to t=10, then diverge again

    6 replies 28 proslijeđenih tweetova 183 korisnika označavaju da im se sviđa
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  12. 2. sij

    Enough people asked for details that I wrote something about Bayesian iterated mark-and-recapture here: .
    4 proslijeđena tweeta 43 korisnika označavaju da im se sviđa
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  13. 2. sij

    Enough people asked for details that I wrote something about Bayesian iterated mark-and-recapture here: .

    0:24
    To count an animal population if you can't catch them all: capture some, mark them, release, and capture again. The ratio of new vs already seen tells you something about the total number. Shown here is iterated mark-and-recapture with a Bayesian updates to belief about pop size
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    6 replies 82 proslijeđena tweeta 330 korisnika označava da im se sviđa
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  14. 2. sij

    Assumption made here: the animals move around enough between measurements that you can treat each capture event as a random selection from the population, independent of the previous capture

    20 replies 10 proslijeđenih tweetova 255 korisnika označava da im se sviđa
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  15. 2. sij

    It's funny that the first 'measurement' is much less informative than subsequent ones: it just tells you that the population is at least as large as the number of animals you've captured.

    5 replies 7 proslijeđenih tweetova 166 korisnika označava da im se sviđa
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  16. 2. sij

    The left side shows a crude simulation of animals moving around, which are periodically captured. Colour indicates number of times captured. Right side is a distribution describing belief over the population size.

    8 proslijeđenih tweetova 141 korisnik označava da mu se sviđa
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  17. 30. pro 2019.

    Based on the 28 countries that appear in these two:

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  18. 30. pro 2019.

    I know I probably shouldn't even engage, but: here's some boring brutal actual data. There's actually a weak negative correlation for both men and women (coefficients -0.02 and -0.08) between welfare spending as a percentage of GDP and mean BMI.

    10 replies 8 proslijeđenih tweetova 69 korisnika označava da im se sviđa
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  19. 12. pro 2019.

    (Pre-empting replies, I'm sure the extent of maths education in CS programmes varies greatly!)

    1 reply 18 korisnika označava da im se sviđa
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  20. 12. pro 2019.

    Skills that need to be taught in undergraduate computer science curricula: - maths

    Skills that need to be taught in undergraduate physics curricula: - how to use git - proper code documentation - good mathematical writing for psets and papers - LaTeX - a computer algebra system (e.g. Mathematica) we can skip the 300th Ylm(θ,φ) problem to make room for these..
    7 replies 26 proslijeđenih tweetova 256 korisnika označava da im se sviđa
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