Homological stability is a concept in algebraic topology and representation theory that deals with the behavior of homological groups of topological spaces or algebraic structures as their dimensions or parameters vary. The basic idea is that for a sequence of spaces \(X_n\) (or groups, schemes, etc.), as \(n\) increases, the homological properties of these spaces become stable in a certain sense.
Article likely written by him: www.theguardian.com/commentisfree/2010/feb/22/home-schooling-register-families
“Especially my father. He was doing most of it and he is a savoury, strong character. He has strong beliefs about the world and in himself, and he was helping me a lot, even when I was at university as an undergraduate.”An only child, Arran was born in 1995 in Glasgow, where his parents were studying at the time. His father has Spanish lineage, having a great grandfather who was a sailor who moved from Spain to St Vincent in the Carribean. A son later left the islands for the UK where he married an English woman. Arran’s mother is Norwegian.
One of the articles says his father has a PhD. TODO where did he work? What's his PhD on? Photo: www.topfoto.co.uk/asset/1357880/
www.thetimes.co.uk/article/the-everyday-genius-pxsq5c50kt9:
TODO where to find it: www.kaggle.com/general/50987
Subset generators:
- github.com/mf1024/ImageNet-datasets-downloader generates on download, very good. As per github.com/mf1024/ImageNet-Datasets-Downloader/issues/14 counts go over the limit due to bad multithreading. Also unfortunately it does not start with a subset of 1k.
- github.com/BenediktAlkin/ImageNetSubsetGenerator
Unfortunately, since ImageNet is a closed standard no one can upload such pre-made subsets, forcing everybody to download the full dataset, in ImageNet1k, which is huge!
This section is about companies that primarily specialize in machine learning.
The term "machine learning company" is perhaps not great as it could be argued that any of the Big tech are leaders and sometimes, especially in the case of Google, has a main product that is arguably a form of machine learning.
A locally constant sheaf is a concept from the field of sheaf theory, which is a branch of mathematics primarily used in algebraic topology, differential geometry, and algebraic geometry. To understand what a locally constant sheaf is, let's break it down into a few components. ### Sheaves 1. **Sheaf**: A sheaf on a topological space assigns data (like sets, groups, or rings) to open sets in a way that is "local".
Metaplectic structures are concepts arising in the context of symplectic geometry and representation theory. They are particularly associated with the study of the metaplectic group, which is a double cover of the symplectic group.
In algebraic geometry and related fields, an **orientation sheaf** is a concept that arises in the context of differentiable manifolds and schemes. It provides a way to systematically keep track of the "orientation" of a geometrical object, which is vital in various mathematical and physical applications, such as integration, intersection theory, and the study of moduli spaces.
In topology, a space is said to be **semi-locally simply connected** if, for every point in the space, there exists a neighborhood around that point in which every loop (i.e., a continuous map from the unit circle \( S^1 \) to the space) can be contracted to a point within that neighborhood, provided the loop is sufficiently small.
In mathematics, particularly in the field of algebraic topology, the concept of a "sphere spectrum" refers to a particular type of structured object that arises in stable homotopy theory. The sphere spectrum is a central object that provides a foundation for the study of stable homotopy groups of spheres, stable cohomology theories, and many other constructions in stable homotopy. To understand the sphere spectrum, it's helpful to start with the notion of spectra in stable homotopy theory.
Daniel Quillen was an American mathematician known for his significant contributions to algebraic K-theory, homotopy theory, and the study of higher categories. He was born on January 27, 1933, and passed away on April 30, 2011. Quillen's work in K-theory, which concerns the study of vector bundles and their relationships to algebraic topology, has had a profound impact on both pure mathematics and theoretical physics.
The degree of an algebraic variety is a fundamental concept in algebraic geometry that provides a measure of its complexity and size. Specifically, it reflects how intersections with linear subspaces behave in relation to the variety.
"Arrangement" can refer to several concepts depending on the context. Here are some of the common meanings: 1. **General Meaning**: In a broad sense, arrangement refers to the act of organizing or ordering items, ideas, or people in a specific way or system. This could apply to anything from organizing files to planning a schedule. 2. **Musical Arrangement**: In music, an arrangement refers to the adaptation of a piece of music for a particular instrument or group of instruments.
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