The Forward-Backward Algorithm is a fundamental technique used in the field of Hidden Markov Models (HMMs) for performing inference, particularly for computing the probabilities of sequences of observations given a model. This algorithm is particularly useful in various applications such as speech recognition, natural language processing, bioinformatics, and more. ### Key Concepts 1. **Hidden Markov Model (HMM)**: An HMM is characterized by: - A set of hidden states.
Locally decodable codes (LDCs) are a type of error-correcting code that allows for the recovery of specific bits of information from a coded message with a small number of queries to the encoded data. They are designed to efficiently decode parts of the original message even if the encoded message is partially corrupted, and without needing to access the entire codeword.
Message authentication is a process used to verify the integrity and authenticity of a message. It ensures that a message has not been altered in transit and confirms the identity of the sender. This is crucial in various communication systems to prevent unauthorized access, tampering, and impersonation. Key concepts in message authentication include: 1. **Integrity**: Ensuring the message has not been modified during transmission. If any part of the message is altered, the integrity check will fail.
Zemor's decoding algorithm is a decoding method primarily used for certain types of error-correcting codes known as low-density parity-check (LDPC) codes, as well as for specific algebraic and combinatorial codes. Named after J. Zemor, the algorithm is designed to efficiently recover the original information from a received codeword that may contain errors due to noise in communication channels.
Coroglen is a small rural locality located in the Waikato region of New Zealand, specifically in the Thames-Coromandel District. It is situated near the Coromandel Peninsula and is known for its scenic landscapes, which include forests and farmland. This area serves as a gateway to various outdoor activities, such as hiking, fishing, and exploring nearby beaches. Coroglen is also notable for its community aspects, including local businesses and events that reflect the rural lifestyle.
Rank error-correcting codes are a class of codes used in error detection and correction, particularly for structured data such as matrices or tensors. These codes are designed to correct errors that can occur during the transmission or storage of data, ensuring that the original information can be retrieved even in the presence of errors. ### Key Concepts: 1. **Rank**: In the context of matrices, the rank of a matrix is the dimension of the vector space generated by its rows or columns.
Here is a vendor showcasing their device. They claim in that video that a single photon is produced and detected:
Concrete device described at: Video "How to use an SiPM - Experiment Video by SensLTech (2018)".
Can be achieved in two ways it seems:
- macroscopic beam splitter and optical table
- photolithography
Animation of Hong-Ou-Mandel Effect on a silicon like structure by Quantum Light University of Sheffield (2014): www.youtube.com/watch?v=ld2r2IMt4vg No maths, but gives the result clear: the photons are always on the same side.
- quantum dot source. TODO how do you produce identical photons from two separate quantum dots? See also: quantum dot single photon source.
- superconducting nanowire detector. So the device has to be cooled then? Video "Jeremy O'Brien: "Quantum Technologies" by GoogleTechTalks (2014)" youtube.com/watch?v=7wCBkAQYBZA&t=2497 however says that semiconducting devices can also be used
This section discusses the pre-photon understanding of the polarization of light. For the photon one see: photon polarization.
People were a bit confused when experiments started to show that light might be polarized. How could a wave that propages through a 3D homgenous material like luminiferous aether have polarization?? Light would presumably be understood to be analogous to a sound wave in 3D medium, which cannot have polarization. This was before Maxwell's equations, in the early 19th century, so there was no way to know.
A device that modifies photon polarization.
As mentioned at Video "Quantum Mechanics 9b - Photon Spin and Schrodinger's Cat II by ViaScience (2013)", it can be modelled as a bra.
Good overgrown section in the middle of Fresnel's biography: en.wikipedia.org/w/index.php?title=Augustin-Jean_Fresnel&oldid=1064236740#Historical_context:_From_Newton_to_Biot.
Particularly cool is to see how Fresnel fully understood that light is somehow polarized, even though he did not know that it was made out of electromagnetism, clear indication of which only came with the Faraday effect in 1845.
spie.org/publications/fg05_p03_maluss_law:
At the beginning of the nineteenth century the only known way to generate polarized light was with a calcite crystal. In 1808, using a calcite crystal, Malus discovered that natural incident light became polarized when it was reflected by a glass surface, and that the light reflected close to an angle of incidence of 57° could be extinguished when viewed through the crystal. He then proposed that natural light consisted of the s- and p-polarizations, which were perpendicular to each other.
Matches the quantum superposition probability proportional to the square law. Poor Étienne-Louis Malus, who died so much before this was found.
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. 
- 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