In the classification of finite simple groups, groups of Lie type are a set of infinite families of simple lie groups. These are the other infinite families besides te cyclic groups and alternating groups.
A decent list at: en.wikipedia.org/wiki/List_of_finite_simple_groups, en.wikipedia.org/wiki/Group_of_Lie_type is just too unclear. The groups of Lie type can be subdivided into:
- Chevalley groups
- TODO the rest
The first in this family discovered were a subset of the Chevalley groups by Galois: , so it might be a good first one to try and understand what it looks like.
TODO understand intuitively why they are called of Lie type. Their names , seem to correspond to the members of the classification of simple Lie groups which are also named like that.
But they are of course related to Lie groups, and as suggested at Video "Yang-Mills 1 by David Metzler (2011)" part 2, the continuity actually simplifies things.
Mathematics course of the University of Oxford structure Updated 2025-04-18 +Created 1970-01-01
Not a quantum computing pure-play, they also do sensing.
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',6,6,0The first time Ciro Santilli went to one was when an Indian friend of his took him to the one in the North of Paris when they were living there in the first half of the 2010's, the Gurdwara Singh Sabha France.
Much like Islam's Ramadan, Ciro Santilli appreciates this a lot due to due to Ciro Santilli's self perceived compassionate personality and Ciro Santilli's cheapness.
The half-life of radioactive decay, which as discovered a few years before quantum mechanics was discovered and matured, was a major mystery. Why do some nuclei fission in apparently random fashion, while others don't? How is the state of different nuclei different from one another? This is mentioned in Inward Bound by Abraham Pais (1988) Chapter 6.e Why a half-life?
The term also sees use in other areas, notably biology, where e.g. RNAs spontaneously decay as part of the cell's control system, see e.g. mentions in E. Coli Whole Cell Model by Covert Lab.
Hall effect experimental diagram
. Source. The Hall effect refers to the produced voltage , AKA on this setup.
An intuitive video is:
The key formula for it is:where:
- : current on x direction, which we can control by changing the voltage
- : strength of transversal magnetic field applied
- : charge carrier density, a property of the material used
- : height of the plate
- : electron charge
Applications:
- the direction of the effect proves that electric currents in common electrical conductors are made up of negative charged particles
- measure magnetic fields, TODO vs other methods
Other more precise non-classical versions:
is a hyperparameter, and are common choices when doing dataset exploration, as they can be easily visualized on a planar plot.
The mapping is done by projecting all points to a dimensional hyperplane. PCA is an algorithm for choosing this hyperplane and the coordinate system within this hyperplane.
The hyperplane choice is done as follows:
- the hyperplane will have origin at the mean point
- the first axis is picked along the direction of greatest variance, i.e. where points are the most spread out.Intuitively, if we pick an axis of small variation, that would be bad, because all the points are very close to one another on that axis, so it doesn't contain as much information that helps us differentiate the points.
- then we pick a second axis, orthogonal to the first one, and on the direction of second largest variance
- and so on until orthogonal axes are taken
www.sartorius.com/en/knowledge/science-snippets/what-is-principal-component-analysis-pca-and-how-it-is-used-507186 provides an OK-ish example with a concrete context. In there, each point is a country, and the input data is the consumption of different kinds of foods per year, e.g.:so in this example, we would have input points in 4D.
- flour
- dry codfish
- olive oil
- sausage
Suppose that every country consumes the same amount of flour every year. Then, that number doesn't tell us much about which country each point represents (has the least variance), and the first PCA axes would basically never point anywhere near that direction.
Another cool thing is that PCA seems to automatically account for linear dependencies in the data, so it skips selecting highly correlated axes multiple times. For example, suppose that dry codfish and olive oil consumption are very high in Portugal and Spain, but very low in Germany and Poland. Therefore, the variation is very high in those two parameters, and contains a lot of information.
However, suppose that dry codfish consumption is also directly proportional to olive oil consumption. Because of this, it would be kind of wasteful if we selected:since the information about codfish already tells us the olive oil. PCA apparently recognizes this, and instead picks the first axis at a 45 degree angle to both dry codfish and olive oil, and then moves on to something else for the second axis.
This game is quite detailed: www.youtube.com/watch?v=w4Jmqp8a_bU
Richard Feynman was working under him there, and was promoted to team lead by him because Richard impressed Hans.
He was also the person under which Freeman Dyson was originally under when he moved from the United Kingdom to the United States.
And Hans also impressed Feynman, both were problem solvers, and liked solving mental arithmetic and numerical analysis.
This relationship is what brought Feynman to Cornell University after World War II, Hans' institution, which is where Feynman did the main part of his Nobel prize winning work on quantum electrodynamics.
Applications:
- hash map which is a O(1) amortized implementation of a map
- creating unbreakable chains of data, e.g. for Git commits or Bitcoin.
- storing passwords on a server in a way that if the password database is stolen, attackers can't reuse them on other websites where the user used the same password: security.blogoverflow.com/2013/09/about-secure-password-hashing/
The prototypical example of it is the complex dot product.
Note that this form is neither strictly symmetric, it satisfies:where the over bar indicates the complex conjugate, nor is it linear for complex scalar multiplication on the second argument.
Bibliography:
Movies that are very expensive to make tend to be bad, because they have to make returns and thus appeal to a large amorphous population without any specialization, i.e. the lowest common denominator but in TV Tropes terminology rather than mathematics: tvtropes.org/pmwiki/pmwiki.php/Main/LowestCommonDenominator.
Looking down the largest flops of all time list didn't help much, only Heaven's gate appears reasonable from the top 20.
As of 2020, basically means "liquid nitrogen temperature", which is much cheaper than liquid helium.
The dream of course being room temperature and pressure superconductor.
Timeline of superconductivity from 1900 to 2015
. Source. 
There are unlisted articles, also show them or only show them.