The Johnson–Lindenstrauss (JL) lemma is a result in mathematics and computer science that states that a set of high-dimensional points can be embedded into a lower-dimensional space in such a way that the distances between the points are approximately preserved. More formally, the lemma asserts that for any set of points in a high-dimensional Euclidean space, there exists a mapping to a lower-dimensional Euclidean space that maintains the pairwise distances between points within a small factor.
Minkowski distance is a generalization of several distance measures used in mathematics and machine learning to quantify the distance between two points in a vector space. It is defined in a way that encompasses different types of distance metrics by varying a parameter \( p \).
In mathematics, particularly in the field of category theory and algebra, a **tight span** is a concept used to describe a particular kind of "span" of a set in a metric or ordered structure. The idea of a tight span often arises in the context of generating a certain type of space in a minimal yet appropriate way. ### Definition: A tight span can be defined in more formal settings, such as in metric spaces and in the theory of posets (partially ordered sets).
Polyhedral space is a concept that arises in the context of geometry and topology, particularly in relation to spaces that can be decomposed into polyhedra or simplices. The term itself can refer to various structures and spaces depending on the context in which it is used.
A tablespoon is a unit of measurement commonly used in cooking and food preparation. 1. **Volume Measure**: In the United States, one tablespoon is equivalent to about 14.79 milliliters. In cooking, it is often used to measure liquid and dry ingredients. In the UK, a tablespoon is typically measured as 15 milliliters. 2. **Utensil**: A tablespoon also refers to the actual utensil used for measuring or serving food.
As of my last update in October 2023, there is no widely known figure or concept named Nataliya Kalashnykova in public discourse. It is possible that she is a private individual or a professional in a particular field that hasn't gained broad recognition.
Ecological metrics are quantitative measures used to assess the health, biodiversity, and functionality of ecosystems. These metrics help scientists, conservationists, and land managers evaluate ecological conditions, understand ecosystem dynamics, and monitor changes over time. The use of ecological metrics can be fundamental for evaluating the impacts of human activities, climate change, and conservation efforts.
Chemometrics is a field of study that employs mathematical and statistical methods to analyze chemical data. Its primary goal is to extract meaningful information from complex datasets generated in chemical research, including analytical chemistry, spectroscopy, chromatography, and other scientific disciplines. Key aspects of chemometrics include: 1. **Data Analysis**: Chemometric techniques help in interpreting data, especially when dealing with high-dimensional datasets, such as those from spectroscopic measurements.
The United States Army Command, Control, Communication, Computers, Cyber, Intelligence, Surveillance, and Reconnaissance Center, often abbreviated as C5ISR Center, is a key component of the U.S. Army’s efforts to enhance its capabilities in various areas of military operations.
Overtime rate refers to the additional pay that employees receive for hours worked beyond their standard work schedule, typically defined as over 40 hours in a week in the United States. The Fair Labor Standards Act (FLSA) mandates that non-exempt employees must be paid at least one and a half times (1.5 times) their regular hourly rate for overtime hours worked.
A Microelectromechanical System (MEMS) oscillator is a type of oscillator that integrates mechanical and electrical components at a microscale to generate periodic signals, typically in the form of voltage or current waves. These oscillators leverage the principles of MEMS technology, which combines microfabrication techniques with mechanical design to create tiny devices that can respond to electrical signals with mechanical motion.
Lavabit was an encrypted email service founded in 2004 by Ladar Levison. It gained significant attention in 2013 when it was revealed that the service had been used by whistleblower Edward Snowden to communicate securely. In August 2013, shortly after the Snowden revelations, Lavabit shut down its operations rather than comply with a court order that required it to hand over its users' encryption keys and other data.
Diego Rodríguez is a mathematician known for his contributions to various areas of mathematics. While specific details about his life and work may not be widely available or may vary depending on the context, individuals named Diego Rodríguez in academia often engage in research related to fields such as algebra, geometry, analysis, or other mathematical disciplines.
Graciela Salicrup is a scientist known for her work in the field of biological sciences, particularly in areas related to genetics and evolution. She has contributed to various research studies and publications, focusing on topics such as genetic diversity, conservation, and the ecological impacts of environmental changes.
Advanced silicon etching refers to a set of techniques and processes used in semiconductor manufacturing and microfabrication to selectively remove silicon from a substrate with high precision and control. This is crucial for creating the intricate patterns and structures found in integrated circuits, microelectromechanical systems (MEMS), and various nanotechnology applications.
Javier González Garza could refer to a few different individuals, but without additional context, it's difficult to determine exactly who you are referring to. He may be a public figure, academic, or professional in a specific field.
Fariborz Maseeh is an entrepreneur and philanthropist, best known for his contributions to technology and education. He is the founder of several companies, including **MassChallenge** and **the Maseeh College of Engineering and Computer Science** at Portland State University, which he supported through philanthropic efforts. Maseeh has been involved in various ventures, particularly in the fields of engineering and technology, and is recognized for his commitment to supporting innovation and education.
"Phantom Access" can refer to different concepts depending on the context, but it is often associated with network security and cybersecurity, particularly in the context of unauthorized or hidden access to computer networks or systems. 1. **In Cybersecurity**: Phantom Access may describe a situation where an attacker gains undetected access to a system or network. This can involve exploiting vulnerabilities, using malware, or employing social engineering tactics.
Microelectromechanical systems (MEMS) foundries are specialized facilities that fabricate MEMS devices, which integrate mechanical and electrical components at the microscale. Here is a list of some notable MEMS foundries and companies that are known for their MEMS fabrication capabilities: 1. **MEMSCAP** - A prominent MEMS foundry offering services for various MEMS applications, including sensors and actuators.
The GP5 chip refers to a specific microchip developed for various applications, often seen in smart devices and embedded systems. However, the context in which "GP5 chip" is used can vary widely, as different manufacturers may have similar naming conventions for their products. One well-known example is the GP5 chip from the company **Pioneer**, which is commonly associated with various automotive and consumer electronics applications, such as car infotainment systems.

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