In topology, "collapse" generally refers to a process in which a space is transformed into a simpler space by identifying or merging certain points. More formally, it often involves a kind of equivalence relation on a topological space that leads to a new space, typically by collapsing a subspace of points into a single point or by collapsing all points in a certain way. One specific example of collapsing is the creation of a quotient space.
College women's basketball records and statistics in the United States encompass a wide range of achievements, including team and individual records for points, rebounds, assists, steals, and more. The governing body for college basketball in the United States is the National Collegiate Athletic Association (NCAA), which divides the teams into Division I, Division II, and Division III.
Combination tones are auditory phenomena that occur when two or more sounds are played together, leading to the perception of additional tones that are not present in the actual sound wave. These tones arise due to the nonlinear interaction of the sounds and can be categorized primarily into two types: 1. **Difference Tones**: These occur when two frequencies are played simultaneously, generating a tone that is equal to the difference between the two frequencies.
As of my last update in October 2023, there is no widely recognized figure or concept specifically known as "Joel Spruck." It is possible that "Joel Spruck" could refer to a private individual, a lesser-known figure, or a fictional character. If you have additional context or information regarding Joel Spruck, such as the field they are associated with (e.g., science, art, literature, etc.
Computational anatomy is an interdisciplinary field that combines principles from anatomy, mathematics, computer science, and image processing to analyze, model, and understand the structure of biological shapes and forms, particularly in the context of the human body and its variations. It focuses on the geometric and topological features of anatomical structures, leveraging computational techniques to study their variability and changes across different populations, health conditions, and developmental stages.
Computational statistics is a field that combines statistical theory and methodologies with computational techniques to analyze complex data sets and solve statistical problems. It involves the use of algorithms, numerical methods, and computer simulations to perform statistical analysis, particularly when traditional analytical methods are impractical or infeasible due to the complexity of the data or the model.
Cooperative binding refers to a phenomenon observed in biochemistry and molecular biology, where the binding of a ligand (such as a substrate, hormone, or other signaling molecules) to a protein influences the binding affinity of additional ligand molecules to the same protein. This can lead to a more significant response than would be expected from independent binding events.
In topology, a **covering space** is a topological space that "covers" another space in a specific, structured way. Formally, a covering space \( \tilde{X} \) of a space \( X \) is a space that satisfies the following conditions: 1. **Projection**: There is a continuous surjective map (called the covering map) \( p: \tilde{X} \to X \).
Quantum mysticism is a term that refers to a blend of concepts from quantum physics and mysticism or spirituality. It often involves the interpretation of quantum mechanics in a way that suggests parallels with mystical or spiritual experiences, though it can be controversial and is not widely accepted within the scientific community. Proponents of quantum mysticism might argue that principles such as non-locality, entanglement, or the observer effect in quantum mechanics support notions of interconnectedness and the profound nature of consciousness.
In a mathematical context, a **cusp** refers to a point on a curve where the curve has a sharp point or a singularity, which often results from the curve failing to be smooth at that location. In more detail: 1. **Geometry and Curves**: A cusp is typically associated with certain types of curves, such as the cusp of a cubic function or the cusps of a hypocycloid.
Dagfinn Føllesdal is a Norwegian philosopher known for his work in the fields of logic, philosophy of language, philosophy of mind, and theoretical computer science. He has made significant contributions to areas such as the nature of meaning, the philosophy of mathematics, and the cognitive sciences. Føllesdal has also been involved in various philosophical debates and has published numerous papers and books throughout his academic career.

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!
We have two killer features:
  1. 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-calculus
    Articles 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/derivative
  2. 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.
    Figure 2.
    You can publish local OurBigBook lightweight markup files to either https://OurBigBook.com or as a static website
    .
    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.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
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