Roundup of recent Quanta popularizations and the research they come from:
Near-optimal expansion for 2d surfaces: https://www.quantamagazine.org/impossible-seeming-surfaces-confirmed-decades-after-conjecture-20220602/, https://arxiv.org/abs/2107.05292
Inequality between cohomology rank and number of Hamiltonian flow orbits, https://www.quantamagazine.org/mathematicians-transcend-geometric-theory-of-motion-20211209/, https://arxiv.org/abs/2103.01507
Among pairwise-coprime sequences, primes maximize \(\sum 1/n_i\log n_i\): https://www.quantamagazine.org/graduate-students-side-project-proves-prime-number-conjecture-20220606/, https://arxiv.org/abs/2202.02384
A while ago @davidphys1 asked why nobody had made animations of the shunting yard algorithm with cutesy trains.
There is no surer way to summon me!
I've spent some of my spare time over the bank holidays making exactly that: https://somethingorotherwhatever.com/shunting-yard-animation/
You can (sort of) verify your identity on Mastodon if you own a website.
1. Go to Edit Profile > Appearance > Profile Metadata, add your website address (including https://) to the metadata section.
2. Copy the verification code into your website's code. (The verification code is next to the Metadata section)
3. Click "Save Changes" after you have done all of the above.
Your website will then be listed on your profile with a green background and a tick next to it, proving you are the owner.
Let's have some fun with the Heisenberg group H! It is the group of upper triangular matrices of the form
/ 1 a c \
| 0 1 b |
\ 0 0 1 /
Muliplying two such matrices you can easily see it's a monoid, because the result is again an upper triangular matrix:
/ 1 a+A c+aB+C \
| 0 1 b+B |
\ 0 0 0 /
You can also read this thread on my blog:
Thread about Reversible Cellular Automata! #reversible_ca
RCA is CA that has exactly one previous and exactly one next state. For example, Conway's Game Of Life is not reversible, because you can have multiple states converge to emptiness. And GoL can have [0; inf) previous states, and exactly one next. Thus, non-reversible CA constantly lose information.
The GIF shows glider in a RCA called "Single rotate", it uses Margolus neighorhood with block of size 2. (Source http://dmishin.blogspot.com/2013/11/the-single-rotation-rule-remarkably.html)
@jt There are plenty of pretrained models for French! I think it's probably one of the most well-studied languages: https://huggingface.co/models?language=fr&sort=downloads
Thanks for the refs!
@jt I'm not very familiar with Bayesian models for NLP, do you have some pointers? For what it's worth, there are pretrained models that can be used with very few data now if you're interested. Of course understanding them deeply is another issue...
@roydanroy Yes! (in industry) Although I wish I could find where the ML people are on Mastodon. Back on Twitter, I follow maths and ML related people, and for now I mostly found maths people here.
People from Mathstodon: if you want to share your maths with people from other instances, keep in mind that LaTeX rendering is only available on a browser, and for people also on mathstodon.
If you still want to write formulas, mathstodon can be used to export LaTeX to unicode, like \sum to ∑, \prod to ∏, and so on.
Just click on the Tab key and if your equation can be rendered using unicode it will be transformed.
Example: ϕ(x)=∑ₖⁿ xᵏ
It's not perfect, but you can see it on a phone app!
Are you looking for people to follow on Mastodon and the Fediverse?
Click below for a directory of hundreds of recommended follows organised into 74 topics:
(If a category has several pages of follows, click "show older" at the bottom to see the next page.)
This is just a tiny fraction of accounts on here, but hopefully it will give people's timelines a good start.
Please do share this with anyone you think might benefit, for example people who are new here.
announcement (boosts appreciated)
We're delighted to announce the HoTTEST Summer School, which will take place online everywhere in the world during the months of July and August 2022.
The school will run both synchronously and asynchronously. The lectures will be delivered live (between 2:30-4pm UTC) and paired with various tutorial sessions run by teaching assistants. The course will also feature a discord-based all-hours Q&A and an online archive of all course materials so that participants can follow along on their own schedule.
This school is for everyone and anyone with some familiarity with abstract mathematics or theoretical computer science and an itching to learn about homotopy type theory. Our goal is to make homotopy type theory accessible to, and inclusive of, everyone who is interested, regardless of cultural background, age, ability, formal education, ethnicity, gender identity, or expression. We believe HoTT is for everyone, and are committed to fostering a kind, inclusive environment.
Read more: https://groups.google.com/g/homotopytypetheory/c/Ir2joc7imyI
Join the Discord: https://discord.gg/tkhJ9zCGs9
@JordiGH @ColinTheMathmo Indeed, that's an interesting thought. Maybe the federated aspect will incentivise users to interact more. On Twitter I have never felt the need to participate much in conversations (and many of them were not that interesting anyway), and I know many people with the same experience.
Great article by Christopher Manning, doing a complete historical tour of NLP: https://www.amacad.org/publication/human-language-understanding-reasoning
The last part in particular, about denotational vs distributional semantics, is one of the nicest explanations I have seen on this topic.
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