When it distributes it inverts the order of the matrix multiplication:
How to implement Nested set model in SQL:
- stackoverflow.com/questions/192220/what-is-the-most-efficient-elegant-way-to-parse-a-flat-table-into-a-tree/42781302#42781302 contains the correct left/size representation and update queries, which makes it much easier to maintain the tree without having to worry about the sizes of siblings which are constant
- stackoverflow.com/questions/192220/what-is-the-most-efficient-elegant-way-to-parse-a-flat-table-into-a-tree/194031#194031 amazing ASCII art representations of the structure. Unfortunately uses a wonky left/right representation, rather than the much more natural left/size representation from the other post
This is an example of the
qiskit.circuit.library.QFT implementation of the Quantum Fourier transform function which is documented at: docs.quantum.ibm.com/api/qiskit/0.44/qiskit.circuit.library.QFTOutput:So this also serves as a more interesting example of quantum compilation, mapping the
init: [1, 0, 0, 0, 0, 0, 0, 0]
qc
┌──────────────────────────────┐┌──────┐
q_0: ┤0 ├┤0 ├
│ ││ │
q_1: ┤1 Initialize(1,0,0,0,0,0,0,0) ├┤1 QFT ├
│ ││ │
q_2: ┤2 ├┤2 ├
└──────────────────────────────┘└──────┘
transpiled qc
┌──────────────────────────────┐ ┌───┐
q_0: ┤0 ├────────────────────■────────■───────┤ H ├─X─
│ │ ┌───┐ │ │P(π/2) └───┘ │
q_1: ┤1 Initialize(1,0,0,0,0,0,0,0) ├──────■───────┤ H ├─┼────────■─────────────┼─
│ │┌───┐ │P(π/2) └───┘ │P(π/4) │
q_2: ┤2 ├┤ H ├─■─────────────■──────────────────────X─
└──────────────────────────────┘└───┘
Statevector([0.35355339+0.j, 0.35355339+0.j, 0.35355339+0.j,
0.35355339+0.j, 0.35355339+0.j, 0.35355339+0.j,
0.35355339+0.j, 0.35355339+0.j],
dims=(2, 2, 2))
init: [0.0, 0.35355339059327373, 0.5, 0.3535533905932738, 6.123233995736766e-17, -0.35355339059327373, -0.5, -0.35355339059327384]
Statevector([ 7.71600526e-17+5.22650714e-17j,
1.86749130e-16+7.07106781e-01j,
-6.10667421e-18+6.10667421e-18j,
1.13711443e-16-1.11022302e-16j,
2.16489014e-17-8.96726857e-18j,
-5.68557215e-17-1.11022302e-16j,
-6.10667421e-18-4.94044770e-17j,
-3.30200457e-16-7.07106781e-01j],
dims=(2, 2, 2))QFT gate to Qiskit Aer primitives.If we don't
transpile in this example, then running blows up with:qiskit_aer.aererror.AerError: 'unknown instruction: QFT'The second input is:and the output of that approximately:which can be defined simply as the normalized DFT of the input quantum state vector.
[0, 1j/sqrt(2), 0, 0, 0, 0, 0, 1j/sqrt(2)]From this we see that the Quantum Fourier transform is equivalent to a direct discrete Fourier transform on the quantum state vector, related: physics.stackexchange.com/questions/110073/how-to-derive-quantum-fourier-transform-from-discrete-fourier-transform-dft
CIA 2010 covert communication websites 2013 DNS Census virtual host cleanup heuristic keyword searches by 
Ciro Santilli 37 Updated 2025-07-16
Ciro Santilli 37 Updated 2025-07-16There are two keywords that are killers: "news" and "world" and their translations or closely related words. Everything else is hard. So a good start is:
grep -e news -e noticias -e nouvelles -e world -e globaliran + football:
- iranfootballsource.com: the third hit for this area after the two given by Reuters! Epic.
3 easy hits with "noticias" (news in Portuguese or Spanish"), uncovering two brand new ip ranges:
- 66.45.179.205 noticiasporjanua.com
- 66.237.236.247 comunidaddenoticias.com
- 204.176.38.143 noticiassofisticadas.com
Let's see some French "nouvelles/actualites" for those tumultuous Maghrebis:
- 216.97.231.56 nouvelles-d-aujourdhuis.com
news + global:
- 204.176.39.115 globalprovincesnews.com
- 212.209.74.105 globalbaseballnews.com
- 212.209.79.40: hydradraco.com
OK, I've decided to do a complete Wayback Machine CDX scanning of
news... Searching for .JAR or https.*cgi-bin.*\.cgi are killers, particularly the .jar hits, here's what came out:- 62.22.60.49 telecom-headlines.com
- 62.22.61.206 worldnewsnetworking.com
- 64.16.204.55 holein1news.com
- 66.104.169.184 bcenews.com
- 69.84.156.90 stickshiftnews.com
- 74.116.72.236 techtopnews.com
- 74.254.12.168 non-stop-news.net
- 193.203.49.212 inews-today.com
- 199.85.212.118 just-kidding-news.com
- 207.210.250.132 aeronet-news.com
- 212.4.18.129 sightseeingnews.com
- 212.209.90.84 thenewseditor.com
- 216.105.98.152 modernarabicnews.com
"headline": only 140 matches in 2013-dns-census-a-novirt.csv and 3 hits out of 269 hits. Full inspection without CDX led to no new hits.
Take the element and apply it to itself. Then again. And so on.
In the case of a finite group, you have to eventually reach the identity element again sooner or later, giving you the order of an element of a group.
The continuous analogue for the cycle of a group are the one parameter subgroups. In the continuous case, you sometimes reach identity again and to around infinitely many times (which always happens in the finite case), but sometimes you don't.
An example where
SELECT FOR UPDATE is a good solution to an use case can be seen at: nodejs/sequelize/raw/parallel_select_and_update.js.SELECT FOR UPDATE vs/together with the SQL transaction isolation level is commented at: stackoverflow.com/questions/10935850/when-to-use-select-for-update.It is good to see that top-universities is still keeping up with it's main purpose: spontaneous eugenics:
This is a bit "formal hocus pocus first, action later". But withing that category, it is just barely basic enough that 2021 Ciro can understand something.
By: Tobias J. Osborne.
Lecture notes transcribed by a student: github.com/avstjohn/qft
18 1h30 lectures.
Followup course: Advanced quantum field theory lecture by Tobias Osborne (2017).
Ciro Santilli intends to move his beauty list here little by little: github.com/cirosantilli/mathematics/blob/master/beauty.md
The most beautiful things in mathematics are results that are:
- simple to state but hard to prove:
- Fermat's Last Theorem
- number of unknown rationality, e.g. is rational?
- transcendental number conjectures, e.g. is transcendental?
- basically any conjecture involving prime numbers:
- many combinatorial game questions, e.g.:
- surprising results: we had intuitive reasons to believe something as possible or not, but a theorem shatters that conviction and brings us on our knees, sometimes via pathological counter-examples. General surprise themes include:Lists:
- classification of potentially infinite sets like: compact manifolds, etc.
- problems that are more complicated in low dimensions than high like:
- generalized Poincaré conjectures. It is also fun to see how in many cases complexity peaks out at 4 dimensions.
- classification of regular polytopes
- unpredictable magic constants:
- why is the lowest dimension for an exotic sphere 7?
- why is 4 the largest degree of an equation with explicit solution? Abel-Ruffini theorem
- undecidable problems, especially simple to state ones:
- mortal matrix problem
- sharp frontiers between solvable and unsolvable are also cool:
- attempts at determining specific values of the Busy beaver function for Turing machines with a given number of states and symbols
- related to Diophantine equations:
- applications: make life easier and/or modeling some phenomena well, e.g. in physics. See also: explain how to make money with the lesson
Good lists of such problems Lists of mathematical problems.
Whenever Ciro Santilli learns a bit of mathematics, he always wonders to himself:Unfortunately, due to how man books are written, it is not really possible to reach insight without first doing a bit of memorization. The better the book, the more insight is spread out, and less you have to learn before reaching each insight.
Am I achieving insight, or am I just memorizing definitions?
Some notable ones:
Ciro Santilli's birthplace!
Pinned article: 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!
Intro to OurBigBook
. Source. 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/derivativeVideo 2. OurBigBook Web topics demo. Source. - 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 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. 
- Infinitely deep tables of contents:
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