The quantum NOT gate swaps the state of and , i.e. it maps:As a result, this gate also inverts the probability of measuring 0 or 1, e.g.
- if the old probability of 0 was 0, then it becomes 1
- if the old probability of 0 was 0.2, then it becomes 0.8
When Ciro Santilli was studying electronics at the University of São Paulo, the courses, which were heavily inspired from the USA 50's were obsessed by this one! Thinking about it, it is kind of a cool thing though.
That Wikipedia page is the epitome of Wikipedia failure to explain things in a way that is of any interest to any learner. Video 1. "Tutorial on LC resonant circuits by w2aew (2012)" is the opposite.
Tutorial on LC resonant circuits by w2aew (2012)
Source. - youtu.be/hqhV50852jA?t=239 series LC circuit on a breadboard driven by an AC source. Shows behaviour on oscilloscope as source frequency is modified. We clearly see voltage going to zero at resonance. This is why thie circuit can be seen as a filter.
- youtu.be/hqhV50852jA?t=489 shows the parallel LC circuit. We clearly see current reaching a maximum on resonance.
Introduction to LC Oscillators by USAF (1974)
Source. - youtu.be/W31CCN_ZF34?t=740 mentions that LC circuit formation is the root cause for Audio feedback with a quick demo. Not very scientific, but cool.
LC circuit by Eugene Khutoryansky (2016)
Source. Exactly what you would expect from an Eugene Khutoryansky video. The key insight is that the inductor resists to changes in current. So when current is zero, it slows down the current. And when current is high, it tries to keep it going, which recharges the other side of the capacitor.Super-resolution means resolution beyond the diffraction limit.
They you can observe fluorophores firing one by one. Their exact position is a bit stochastic and beyond the diffraction limit, but so long as there aren't to many in close proximity, you can wait for it to fire a bunch of times, and the center of the Gaussian is the actual location.
From this we see that super-resolution microscopy is basically a space-time tradeoff: the more time we wait, the better spacial resolution we get. But we can't do it if things are moving too fast in the sample.
Tradeoff with cryoEM: you get to see things moving in live cell. Electron microscopy fully kills cells, so you have no chance of seeing anything that moves ever.
Caveats:
- initial illumination to saturate most fluorophores I think can still kill cells, things get harder the less light you put in. So it's not like you don't kill things at all necessarily, you just get a chance not to
- the presence fluorophore disturbs the system slightly, and is not at the same Exact location of the protein of interest
Not to be confused with the Michigan State University. Not confusing at all right!
Functional Analysis I course of the University of Oxford 2023-2024 by 
Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16Open access with solutions: courses.maths.ox.ac.uk/course/view.php?id=4988
Lecturer: Luc Nguyen
Research group of the Department of physics of the University of Oxford by Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16 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 3. Visual Studio Code extension installation.
Figure 4. Visual Studio Code extension tree navigation.
Figure 5. Web editor. 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. 
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