The Cayley plane, often denoted as \( \mathbb{OP}^2 \), is a projective variety that arises in the context of octonions, which are an extension of the complex numbers and quaternions. The Cayley plane can be thought of as a geometric realization of the properties of octonions, particularly as it relates to their structure as a non-associative algebra.

In ring theory, a branch of abstract algebra, the **center** of a ring is a fundamental concept that helps to analyze the structure of the ring. The center of a ring \( R \), denoted as \( Z(R) \), is defined as the set of all elements in the ring that commute with every other element of the ring.

A Chevalley basis is a particular kind of basis for the root system associated with a semisimple Lie algebra. It provides a way to represent elements of the Lie algebra that are closely related to the algebra's structure and the geometry of its representation theory.

Chiral Lie algebras are algebraic structures that arise in the context of conformal field theory and string theory, particularly in the study of two-dimensional conformal symmetries. They can be thought of as a special type of Lie algebra that captures the "chiral" aspects of symmetry in these theoretical frameworks. ### Key Features: 1. **Chirality**: The term "chiral" refers to the property of being distinguishable from its mirror image.

Chiral algebras are mathematical structures that arise primarily in the context of conformal field theory (CFT) and represent a type of algebra that captures some symmetries and properties of two-dimensional quantum field theories. They are particularly significant in the study of two-dimensional conformal field theories, string theory, and related topics in mathematical physics.

The character tables for chemically important 3D point groups provide crucial information about the symmetry properties of molecules and their corresponding vibrational modes. Below is a list of the most common point groups along with their character tables: ### Character Tables for 3D Point Groups 1.

"The New Crystal Silence" is a collaborative album by jazz pianist Chick Corea and vibraphonist Gary Burton, released in 2007. It serves as a sequel to their earlier work, "Crystal Silence," which was released in 1973. This album features the two musicians performing in a duo format, showcasing their intricate interplay, improvisation, and unique musical chemistry.

"Simply Red Farewell – Live in Concert at Sydney Opera House" refers to a special concert event featuring the British band Simply Red, known for their soulful music and pop hits. This concert was part of the band's farewell tour, which celebrated their enduring legacy, and it took place at the iconic Sydney Opera House—a renowned venue famous for its unique architecture and cultural significance. The event showcased the band performing some of their most popular songs, highlighting their distinctive blend of jazz, soul, and pop.

"Live at the Sydney Opera House" is a live album by Australian singer-songwriter Josh Pyke, released in 2014. The album captures Pyke's performance at the iconic Sydney Opera House, showcasing his distinctive acoustic sound and storytelling ability. The recording features a mix of his popular songs along with a few anecdotes and interactions with the audience, creating an intimate concert experience.

"Live at the Sydney Opera House" is an album by Australian composer and oud player Joseph Tawadros. Released in 2017, the album features live recordings from a performance at the iconic Sydney Opera House. It showcases Tawadros's virtuosity on the oud, a traditional Middle Eastern stringed instrument, and highlights his ability to blend different musical styles, including jazz and classical influences.

"Live at Sydney Opera House" is a term that typically refers to a concert or performance that takes place at the iconic Sydney Opera House in Sydney, Australia. The venue is renowned for hosting a wide range of performances, including music concerts, opera, theater, and dance.

Some of the software-based artificial life simulators can be used as AI training game.

Ciro Santilli just always feels that what can be classified as "artificial life" simulators have too much focus on beating more continuous population mechanics, and lack the discrete elements which he feels could be important to AGI: Section "The missing link between continuous and discrete AI".

There is great interest in this direction of research however quite clearly.

Fairport Live Convention is a music festival held annually in the UK, organized by Fairport Convention, one of the pioneering bands in British folk rock. The festival usually features performances from various artists across the folk and rock genres, showcasing both established acts and emerging talent. Fairport Convention itself often performs at the event, celebrating its legacy and contributions to the music scene.

"Compassion" is an album featuring the compositions of Australian composer Nigel Westlake, performed by the Australian vocalist Lior and the Sydney Symphony Orchestra. Released in 2018, the album is known for its poignant and emotive music that seeks to explore themes of empathy and human connection. The project combines orchestral arrangements with Lior's distinctive voice, creating a powerful and moving listening experience.

The term "Russian relativity theorists" generally refers to a group of physicists and mathematicians from Russia who have contributed to the field of relativity, particularly the theories put forth by Albert Einstein—special relativity and general relativity—as well as their applications and implications.

"Amanda Palmer Goes Down Under" is a live album and documentary by the musician Amanda Palmer, released in 2012. It captures her performances and experiences during her tour in Australia and New Zealand. The project showcases not only her music but also her interactions with local fans and the unique cultural aspects of the regions she visited. The album includes a mix of live performances, interviews, and behind-the-scenes footage, providing an intimate look at Palmer's artistic process and her connection with her audience.

Giulia Bartrum is a scholar and academic known for her work in the field of art history, particularly focusing on the ancient and early medieval periods. Her research often explores themes related to the cultural and artistic exchanges of those times.

The Dürerbund, also known as the Dürer Society, was a cultural and artistic organization founded in Munich in 1908. Its primary focus was to promote and preserve the artistic heritage associated with the German artist Albrecht Dürer, who lived during the Renaissance. The organization was dedicated to fostering a deeper understanding of Dürer’s work and its significance in art history, as well as encouraging collaboration among artists and craftsmen.

This technique has managed to determine protein 3D structures for proteins that people were not able to crystallize for X-ray crystallography.

It is said however that cryoEM is even fiddlier than X-ray crystallography, so it is mostly attempted if crystallization attempts fail.

By looking at Figure 1. "A cryoEM image", you can easily understand the basics of cryoEM.

We just put a gazillion copies of our molecule of interest in a solution, and then image all of them in the frozen water.

Each one of them appears in the image in a random rotated view, so given enough of those point of view images, we can deduce the entire 3D structure of the molecule.

Ciro Santilli once watched a talk by Richard Henderson about cryoEM circa 2020, where he mentioned that he witnessed some students in the 1980's going to Germany, and coming into contact with early cryoEM. And when they came back, they just told their principal investigator: "I'm going to drop my PhD theme and focus exclusively on cryoEM". That's how hot the cryo thing was! So cool.