Complementary series representation is a concept in mathematics and physics, especially in the context of wave functions and solutions to differential equations. The term is often associated with Legendre functions, spherical harmonics, and other orthogonal function systems where two series representations can complement each other to form a complete solution. Here's a more detailed explanation: ### 1. **In Mathematics**: - In certain contexts, functions can be expressed in terms of two series that together provide a full representation of the function.
The Bond Collection is a curated assemblage of items, artifacts, and memorabilia associated with the James Bond franchise, which includes films, books, and various media related to the iconic British secret agent created by author Ian Fleming. This collection typically features a range of items such as costumes, props, artwork, photographs, and more that highlight the history and impact of the Bond series on popular culture.
The Covers Record is an album by American indie rock musician Cat Power, released in 2000. The album features a collection of cover songs, showcasing Cat Power's unique interpretation of tracks originally by other artists. It includes covers of songs by notable musicians and bands such as The Rolling Stones, Bob Dylan, and Frank Sinatra, among others. The Covers Record is celebrated for its stripped-down, intimate sound, highlighting Cat Power's vocal style and emotive delivery.
"The Hit List" is a compilation album by rock musician Joan Jett, released in 1990. The album features a collection of cover songs, showcasing Jett's interpretations of tracks by various artists. Notable covers on the album include songs originally by Gary Glitter, The Beach Boys, and The Ramones, among others. The album highlights Jett's signature rock style and often pays tribute to the influences that shaped her music career.
"The Gospel Album" is a musical project by the American rapper and singer Lil' Wayne, released on October 30, 2020. The album features a blend of gospel music elements, hip-hop, and R&B, showcasing Lil' Wayne's versatility as an artist. It includes themes of faith, redemption, and personal struggles, and features collaborations with various artists and producers.
The hard part then is how to make any predictions from it:
- 2024 www.nature.com/articles/d41586-024-02935-z Fly-brain connectome helps to make predictions about neural activity. Summary of "Connectome-constrained networks predict neural activity across the fly visual system" by J. K. Lappalainen et. al.
2024: www.nature.com/articles/d41586-024-03190-y Largest brain map ever reveals fruit fly's neurons in exquisite detail
As of 2022, it had been almost fully decoded by post mortem connectome extraction with microtome!!! 135k neurons.
- 2021 www.nytimes.com/2021/10/26/science/drosophila-fly-brain-connectome.html Why Scientists Have Spent Years Mapping This Creature’s Brain by New York Times
That article mentions the humongous paper elifesciences.org/articles/66039 elifesciences.org/articles/66039 "A connectome of the Drosophila central complex reveals network motifs suitable for flexible navigation and context-dependent action selection" by a group from Janelia Research Campus. THe paper is so large that it makes eLife hang.
The Neurokernel Project aims to build an open software platform for the emulation of the entire brain of the fruit fly Drosophila melanogaster on multiple Graphics Processing Units (GPUs).
Bibliography:
- www.nature.com/articles/d41586-023-02559-9 The quest to map the mouse brain by Diana Kwon (2023)
Grouping their mouse brain projcts here.
Tutorial: Allen Developing Mouse Brain by Allen Institute (2014)
Source. 
Ciro Santilli feels it is not for his generation though, and that is one of the philosophical things that saddens him the most in this world.
On the other hand, Ciro's playing with the Linux kernel and other complex software which no single human can every fully understand cheer him up a bit. But still, the high level view, that we can have...
For now, Ciro's 2D reinforcement learning games.
By cranks:
- www.thehighestofthemountains.com/ has some diagrams. It is unclear how they were obtained, except that they were made over the course of 5 years by a "Space Shuttle Engineer", classic crank appeal to authority. The author belives that brain function is evidence of intelligent design.
External 3D view of the Brodmann areas
. Source. Adaptive music refers to a dynamic form of music that changes and responds in real-time based on various inputs or interactions from users or the environment. This concept is often used in video games, virtual reality, and interactive media to enhance the user experience by creating a more immersive atmosphere. Key features of adaptive music include: 1. **Dynamic Response**: The music changes based on the actions of the player or the progression of the narrative.
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