Topics Top articles New articles Updated articles Top users New users New discussions Top discussions New comments+ New article
A Ring can be seen as a generalization of a field where:
- multiplication is not necessarily commutative. If this is satisfied, we can call it a commutative ring.
- multiplication may not have inverse elements. If this is satisfied, we can call it a division ring.
Addition however has to be commutative and have inverses, i.e. it is an Abelian group.
The simplest example of a ring which is not a full fledged field and with commutative multiplication are the integers. Notably, no inverses exist except for the identity itself and -1. E.g. the inverse of 2 would be 1/2 which is not in the set. More specifically, the integers are a commutative ring.
A polynomial ring is another example with the same properties as the integers.
The simplest non-commutative, non-division is is the set of all 2x2 matrices of real numbers:Note that is not a ring because you can by addition reach the zero matrix.
- we know that 2x2 matrix multiplication is non-commutative in general
- some 2x2 matrices have a multiplicative inverse, but others don't
Two ways to see it:
- a ring that is commutative
- a field where inverses might not exist
An algebra over a field where division exists.
Continuous problems are simpler than discrete ones by 
Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01This is a general philosophy that Ciro Santilli, and likely others, observes over and over.
Basically, continuity, or higher order conditions like differentiability seem to impose greater constraints on problems, which make them more solvable.
Some good examples of that:
- complex discrete problems:
- simple continuous problems:
- characterization of Lie groups
They are the finite projective special linear groups.
This was the first infinite family of simple groups discovered after the simple cyclic groups and alternating groups. The first case discovered was by Galois. You should understand that one first.
Birch and Swinnerton-Dyer conjecture by Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01The BSD conjecture states that if your name is long enough, it will always count as two letters on a famous conjecture.
Maybe also insert a joke about BSD Operating Systems if you're into that kind of stuff.
The conjecture states that Equation 1. "BSD conjecture" holds for every elliptic curve over the rational numbers (which is defined by its constants and )
Equation 1. . Where the following numbers are defined for the elliptic curve we are currently considering, defined by its constants and :
- : number of elements of the elliptic curve over the finite field, where the finite field comes from the reduction of an elliptic curve from to . can be calculated algorithmically with Schoof's algorithm in polynomial time
- : rank of the elliptic curve over the rational numbers. We don't really have a good general way to calculate this besides this conjecture (?).
- : a constant
The conjecture, if true, provides a (possibly inefficient) way to calculate the rank of an elliptic curve over the rational numbers, since we can calculate the number of elements of an elliptic curve over a finite field by Schoof's algorithm in polynomial time. So it is just a matter of calculating like that up to some point at which we are quite certain about .
The Wikipedia page of the this conecture is the perfect example of why it is not possible to teach natural sciences on Wikipedia. A million dollar problem, and the page is thoroughly incomprehensible unless you already know everything!
Birch and Swinnerton-Dyer conjecture by Kinertia (2020)
Source. The $1,000,000 Birch and Swinnerton-Dyer conjecture by Absolutely Uniformly Confused (2022)
Source. A respectable 1 minute attempt. But will be too fast for most people. The sweet spot is likely 2 minutes.A fancy name for calculus, with the "more advanced" connotation.
E. Coli Whole Cell Model by Covert Lab by Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01github.com/CovertLab/WholeCellEcoliRelease is a whole cell simulation model created by Covert Lab and other collaborators.
The project is written in Python, hurray!
But according to te README, it seems to be the use a code drop model with on-request access to master. Ciro Santilli asked at rationale on GitHub discussion, and they confirmed as expected that it is to:
- to prevent their publication ideas from being stolen. Who would steal publication ideas with public proof in an issue tracker without crediting original authors? Academia is broken. Academia should be the most open form of knowledge sharing. But instead we get this silly competition for publication points.
- to prevent noise from non-collaborators. But they only get like 2 issues as year on such a meganiche subject... Did you know that you can ignore people, and even block them if they are particularly annoying? Much more likely is that no one will every hear about your project and that it will die with its last graduate student slave.
The project is a followup to the earlier M. genitalium whole cell model by Covert lab which modelled Mycoplasma genitalium. E. Coli has 8x more genes (500 vs 4k), but it the undisputed bacterial model organism and as such has been studied much more thoroughly. It also reproduces faster than Mycoplasma (20 minutes vs a few hours), which is a huge advantages for validation/exploratory experiments.
The project has a partial dependency on the proprietary optimization software CPLEX which is freeware, for students, not sure what it is used for exactly, from the comment in the
requirements.txt the dependency is only partial.This project makes Ciro Santilli think of the E. Coli as an optimization problem. Given such external nutrient/temperature condition, which DNA sequence makes the cell grow the fastest? Balancing metabolites feels like designing a Factorio speedrun.
There is one major thing missing thing in the current model: promoters/transcription factor interactions are not modelled due to lack/low quality of experimental data: github.com/CovertLab/WholeCellEcoliRelease/issues/21. They just have a magic direct "transcription factor to gene" relationship, encoded at reconstruction/ecoli/flat/foldChanges.tsv in terms of type "if this is present, such protein is expressed 10x more". Transcription units are not implemented at all it appears.
Everything in this section refers to version 7e4cc9e57de76752df0f4e32eca95fb653ea64e4, the code drop from November 2020, and was tested on Ubuntu 21.04 with a docker install of
docker.pkg.github.com/covertlab/wholecellecolirelease/wcm-full with image id 502c3e604265, unless otherwise noted. Classification of 4-transitive groups by Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01en.wikipedia.org/w/index.php?title=Mathieu_group&oldid=1034060469#Multiply_transitive_groups is a nice characterization of 4 of the Mathieu groups.
dumps.wikimedia.org/enwiki/latest/enwiki-latest-category.sql.gz contains a list of categories. It only contains the categories and some counts, but it doesn't contain the subcategories and pages under each category, so it is a bit pointless.
The schema is listed at: www.mediawiki.org/wiki/Manual:Category_table
The SQL first defines the table:followed by a few humongous inserts:which we can see at: en.wikipedia.org/wiki/Category:Computer_storage_devices
CREATE TABLE `category` (
`cat_id` int(10) unsigned NOT NULL AUTO_INCREMENT,
`cat_title` varbinary(255) NOT NULL DEFAULT '',
`cat_pages` int(11) NOT NULL DEFAULT 0,
`cat_subcats` int(11) NOT NULL DEFAULT 0,
`cat_files` int(11) NOT NULL DEFAULT 0,
PRIMARY KEY (`cat_id`),
UNIQUE KEY `cat_title` (`cat_title`),
KEY `cat_pages` (`cat_pages`)
) ENGINE=InnoDB AUTO_INCREMENT=249228235 DEFAULT CHARSET=binary ROW_FORMAT=COMPRESSED;INSERT INTO `category` VALUES (2,'Unprintworthy_redirects',1597224,20,0),(3,'Computer_storage_devices',88,11,0)Se see that en.wikipedia.org/wiki/Category:Computer_storage_devices_by_companyso it contains only categories.
- en.wikipedia.org/wiki/Category:Computer_storage_devices is a subcategory of that category and it appears in that file.
- en.wikipedia.org/wiki/Acronis_Secure_Zone is a page of the category, and it does not appear
We can check this with:and it shows:There doesn't seem to be any interlink between the categories, only page and subcategory counts therefore.
sed -s 's/),/\n/g' enwiki-latest-category.sql | grep Computer_storage_devices(3,'Computer_storage_devices',88,11,0
(521773,'Computer_storage_devices_by_company',6,6,0 Download titles of all Wikipedia articles by Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01dumps.wikimedia.org/enwiki/latest/enwiki-latest-all-titles-in-ns0.gz Characterization:
- contains redirects, e.g. en.wikipedia.org/wiki/"Ampere_North" redirects to en.wikipedia.org/wiki/Ampere_North,_New_Jersey and both are present. Noted in this comment: stackoverflow.com/questions/24474288/how-to-obtain-a-list-of-titles-of-all-wikipedia-articles#comment136016773_24474476
To avoid duplication when citing multiple pages: Section "How to use a single source multiple times in a Wikipedia article?"
A good big sample definition:There is also
<ref name="googleStory">{{cite book |last1=Vise |first1=David |author-link1=David A. Vise |last2=Malseed |first2=Mark |author-link2=Mark Malseed |title=The Google Story |date=2008 |publisher=Delacorte Press |url=https://archive.org/details/isbn_9780385342728}}</ref>title-link to link to a wiki page. But it is incompatible with url= for Internet Archive Open Library links which is a shame.Riesz-Fischer theorem is a norm version of it, and Carleson's theorem is stronger pointwise almost everywhere version.
Note that the Riesz-Fischer theorem is weaker because the pointwise limit could not exist just according to it: norm sequence convergence does not imply pointwise convergence.
Login without password: askubuntu.com/questions/915585/how-to-login-mysql-shell-when-mysql-have-no-passwordworks on Ubuntu 20.10.
sudo mysqlCreate user for further logins without
sudo askubuntu.com/questions/915585/how-to-login-mysql-shell-when-mysql-have-no-password/1325689#1325689:sudo mysql -e "CREATE USER $USER"Run command from CLI stackoverflow.com/questions/1602904/how-do-you-run-a-single-query-through-mysql-from-the-command-line
mysql -e 'SHOW DATABASES'Create test user with password:and login as that user:Login with password given on the command line:The
sudo mysql -e 'CREATE USER user0 IDENTIFIED WITH mysql_native_password BY "a"'
sudo mysql -e 'GRANT ALL PRIVILEGES ON database_name.* TO "user0"'mysql -u user0 -pmysql -u user0 -pmypasswordIDENTIFIED WITH mysql_native_password part is to overcome "Client does not support authentication protocol requested by server" when connecting from Node.js.List users:
sudo mysql -e 'SELECT * FROM mysql.user'View permissions for each user on each DB: serverfault.com/questions/263868/how-to-know-all-the-users-that-can-access-a-database-mysql
sudo mysql -e 'SELECT * FROM mysql.db'List databases:
sudo mysql -e 'SHOW DATABASES'Create database:
sudo mysql -e 'CREATE DATABASE mydb0'Destroy database:
sudo mysql -e 'DROP DATABASE mydb0'Show tables in database:or:
sudo mysql -e 'SHOW TABLES' mydb0sudo mysql -e 'SHOW TABLES FROM mydb0'General Embryology review in 20 minutes by Medical Animations (2020)
Source. Completely devoid of passion, but once you already have the I should have loved biology by James Somers mindset, it's OK. 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