The volume of a ball of radius r in n dimensions is
B(n,r) = π^{n/2}/Γ(n/2+1) r^n
If you look at the volumes of the balls (blue circles) inscribed inside hypercubes with edge length 1 and volume 1, they go to zero as n gets larger:
lim n→∞ B(n,½) = 0
If you look at the volumes of the balls (red circles) that circumscribe each hypercube (of diagonal √n), they go to infinity:
lim n→∞ B(n,½√n) = ∞
But what if you always choose the radius of an n-ball so that its volume is exactly 1 (green circles)?
r₁(n) = Γ(n/2+1)^{1/n} / √π
This gives us B(n,r₁(n)) = 1
It turns out that:
lim n→∞ (r₁(n) - √[n/(2eπ)]) = 0
In other words, r₁(n) is asymptotic to a multiple of √n, so it approaches a fixed ratio with the length of the diagonal of the hypercube with the same volume.
"Dimensionally cursed phenomena occur in domains such as numerical analysis, sampling, combinatorics, machine learning, data mining and databases. The common theme of these problems is that when the dimensionality increases, the volume of the space increases so fast that the available data become sparse. In order to obtain a reliable result, the amount of data needed often grows exponentially with the dimensionality. Also, organizing and searching data often relies on detecting areas where objects form groups with similar properties; in high dimensional data, however, all objects appear to be sparse and dissimilar in many ways, which prevents common data organization strategies from being efficient. "
I really like this script to get details for all followers of accounts on #Mastodon: https://blog.tomaszdunia.pl/mastodon-api-followers-following-eng/
But sadly it doesn’t work for really big accounts like @heiseonline. Is there somebody here interested in and capable of building something like that?
Not necessarily for a complete list, but rather a pie chart for the instances where all the followers are from. And maybe the 10 biggest followers.
Is that a stupid idea?
This is what it looks like as a tiny #youtube person if the almighty algorithm picks up a video of yours to actually serve to users.
That's why I like the #fediverse and #mastodon - I feel much more in control and like there is a real chance to be discovered and seen by people who might be interested in what you got to say/show/etc.
Mind that this particular video isn't any different from what I usually do.
You may think you’ve done a good job designing your app in a privacy minded way. You may have passed a security audit for some of your source code. But what toxic assets and data are you collecting, that you haven’t even thought of, that you are aggregating over time, building up toxicity, exposing your users to increased risk?! CONTACT US NOW FOR YOUR FREE TOXIC ASSET AUDIT! https://cleaninsights.org/toxic#privacy#cleaninsights#gdpr#data#analytics#tracking
AI can be used to create high-quality content, provide 24/7 customer service, generate leads, track and analyze data, and optimize your website and marketing campaigns.
AI for digital marketing: 5 ways to use it to improve your results (www.slideserve.com)
AI can be used to create high-quality content, provide 24/7 customer service, generate leads, track and analyze data, and optimize your website and marketing campaigns.