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Ultimate explanation: math.stackexchange.com/questions/776039/intuition-behind-normal-subgroups/3732426#3732426
Only normal subgroups can be used to form quotient groups: their key definition is that they plus their cosets form a group.
Intuition:
One key intuition is that "a normal subgroup is the kernel" of a group homomorphism, and the normal subgroup plus cosets are isomorphic to the image of the isomorphism, which is what the fundamental theorem on homomorphisms says.
Therefore "there aren't that many group homomorphism", and a normal subgroup it is a concrete and natural way to uniquely represent that homomorphism.
The best way to think about the, is to always think first: what is the homomorphism? And then work out everything else from there.
dnshistory.org contains historical domain -> mappings.
We have not managed to extract much from this source, they don't have as much data on the range of interest.
But they do have some unique data at least, perhaps we should try them a bit more often, e.g. they were the only source we've seen so far that made the association: headlines2day.com -> 212.209.74.126 which places it in the more plausible globalbaseballnews.com IP range.
TODO can it do IP to domain? Or just domain to IP? Asked on their Discord: discord.com/channels/698151879166918727/968586102493552731/1124254204257632377. Their banner suggests that yes:
With our new look website you can now find other domains hosted on the same IP address, your website neighbours and more even quicker than before.
Owner replied, you can't:
At the moment you can only do this for current not historical records
This is a shame, reverse IP here could be quite valuable.
In principle, we could obtain this data from search engines, but Google doesn't track that entire website well, e.g. no hits for
site:dnshistory.org "62.22.60.48" presumably due to heavy IP throttling.Homepage dnshistory.org/ gives date starting in 2009:and it is true that they do have some hits from that useful era.
Here at DNS History we have been crawling DNS records since 2009, our database currently contains over 1 billion domains and over 12 billion DNS records.
Any data that we have the patience of extracting from this we will dump under github.com/cirosantilli/media/blob/master/cia-2010-covert-communication-websites/hits.json.
Strictly speaking, only defined for decision problems: cs.stackexchange.com/questions/9664/is-it-necessary-for-np-problems-to-be-decision-problems/128702#128702
Number of synapses in the human brain by 
Ciro Santilli 35 Updated 2024-12-23 +Created 1970-01-01
Ciro Santilli 35 Updated 2024-12-23 +Created 1970-01-01- 1,000 trillion arxiv.org/abs/1906.01703
Why would physicists use a letter such that:Why? Why?????????
On the Law of Distribution of Energy in the Normal Spectrum by Ciro Santilli 35 Updated 2024-12-23 +Created 1970-01-01
Ciro Santilli 35 Updated 2024-12-23 +Created 1970-01-01The Planck's law paper.
hermes.ffn.ub.es/luisnavarro/nuevo_maletin/Planck%20(1900),%20Distribution%20Law.pdf contains a replica of the translation present in The Old Quantum Theory by Dirk ter Haar (1967).
Projects:
Open source analog-to-digital converter by Ciro Santilli 35 Updated 2024-12-23 +Created 1970-01-01
Ciro Santilli 35 Updated 2024-12-23 +Created 1970-01-01Open Source 8.5 Digit Voltmeter from CERN by Marco Reps (2021)
Source. - www.quora.com/Will-Google-open-source-AlphaGo Will Google open source AlphaGo?
- www.nature.com/articles/nature16961 Mastering the game of Go with deep neural networks and tree search by Silver et al. (2016), published without source code
Consider the E. Coli K-12 MG1655 operon thrLABC.
That single operon can produce two different mRNA transcription units:
- thrL only, the transcription unit is also called thrL: biocyc.org/ECOLI/NEW-IMAGE?object=TU0-42486
- thrL + thrA + thrB + thrC all together, the transcription unit is called thrLABC: biocyc.org/ECOLI/NEW-IMAGE?type=OPERON&object=TU00178
The reason for this appears to be that there is a rho-independent termination region after thrL. But then under certain conditions, that must get innactivated, and then the thrLABC is produced instead.
Open source software that is not-FOSS by Ciro Santilli 35 Updated 2024-12-23 +Created 1970-01-01
Ciro Santilli 35 Updated 2024-12-23 +Created 1970-01-01- 2022: $15 million www.orcacomputing.com/blog/orca-computing-completes-15-million-series-a-funding-round
- 2021: $14.5 million for an Innovate UK project
has order
Don't like this very much, but if it's the only way...
Maybe focus on job ads like Stack Overflow.
Then:
- like YouTube, pay creators proportionally to views/metrics
- paid subscription to remove ads from site
Computer Aided Simulation & Design in Chemical Engineering by Chemical Engineering Guy (2016)
Source. Interesting overview of the different types of modelling software used in chemical process design.How to Design a Total Synthesis by Mike Christiansen (2013)
Source. Just a ultra quick hello world with some very basic ideas, but worth watching. How to use an Oxford Nanopore MinION to extract DNA from river water and determine which bacteria live in it by Ciro Santilli 35 Updated 2024-12-23 +Created 1970-01-01
Ciro Santilli 35 Updated 2024-12-23 +Created 1970-01-01This article gives an idea of how this kind of biological experiment feels like to a software engineer who has never done any biology like Ciro Santilli.
Pinned article: ourbigbook/introduction-to-the-ourbigbook-project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivative - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.
Figure 3. Visual Studio Code extension installation.
Figure 4. Visual Studio Code extension tree navigation.
Figure 5. . You can also edit articles on the Web editor without installing anything locally. Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.Video 4. OurBigBook Visual Studio Code extension editing and navigation demo. Source. - Internal cross file references done right:
- Infinitely deep tables of contents:
Figure 6. Dynamic article tree with infinitely deep table of contents.Live URL: ourbigbook.com/cirosantilli/chordateDescendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact