The concept of a graph minor is a fundamental notion in graph theory, particularly in the study of graph structure and graph algorithms. A graph \( H \) is said to be a **minor** of another graph \( G \) if \( H \) can be formed from \( G \) by performing a series of operations that includes: 1. **Edge Deletion**: Removing edges from the graph. 2. **Vertex Deletion**: Removing vertices and incident edges from the graph.
3D pose estimation refers to the process of determining the spatial configuration of an object or a person in three-dimensional space. This typically involves estimating the 3D coordinates of key points (joints or landmarks) on the object or body being analyzed, which can then be used to understand its orientation, position, and movement.
Triangulation in computer vision refers to the method of determining the position of a point in 3D space by using the geometric principles derived from two or more observations of that point from different camera viewpoints. It is a fundamental technique used in various applications such as 3D reconstruction, camera calibration, and depth estimation. ### How Triangulation Works 1. **Multiple Camera Views**: Triangulation typically uses two or more cameras capturing images of the same scene from different angles.
GEUP (Geometric Modeling and Computational Geometry) is a software tool and platform designed for geometric modeling, particularly in educational contexts. It is often used in engineering, mathematics, and computer science courses to help students understand concepts related to geometry and spatial visualization. Specific features of GEUP may include: 1. **Interactive Geometry**: Users can create and manipulate geometric figures in a visual environment, allowing for real-time exploration of geometric principles.
Aram Arutyunov is not a widely known public figure or concept, and there might not be substantial information readily available about him.
The T-criterion, also known as the T-test, is a statistical method used to determine if there are significant differences between the means of two groups or a single group's mean compared to a known value. It is commonly employed in hypothesis testing to assess whether the observed data deviates significantly from the null hypothesis, which typically states that there is no effect or no difference.
A **unitary matrix** is a complex square matrix \( U \) that satisfies the condition: \[ U^\dagger U = U U^\dagger = I \] where \( U^\dagger \) is the conjugate transpose (also known as the Hermitian transpose) of \( U \), and \( I \) is the identity matrix of the same dimension as \( U \).
The term "operator system" can refer to different concepts depending on the context. Here are a few interpretations: 1. **Mathematical Operator Systems**: In mathematics, particularly in functional analysis and operator algebra, an operator system is a certain type of self-adjoint space of operators on a Hilbert space that has a structure similar to that of a C*-algebra but is more general.
A **Pro-p group** is a type of mathematical object in the field of group theory, particularly in the area of profinite groups. More specifically, a Pro-p group is a topological group that is both locally compact and totally disconnected, and it is defined as an inverse limit of finite groups whose orders are powers of a prime \( p \).
Geocomputation is a field that combines geographic information science (GIS) with computational techniques to analyze and model spatial data. It integrates methods from disciplines such as statistics, computer science, and geography to solve complex spatial problems. Geocomputation encompasses a wide range of techniques, including: 1. **Spatial Analysis**: Investigating spatial relationships and patterns in data.
Yamb is a dice game that is similar to Yahtzee. It's played with five dice and involves players trying to achieve specific combinations that score points, such as three of a kind, four of a kind, full house, and others, ultimately aiming to maximize their score over a series of turns. In Yamb, players take turns rolling the dice, and they have a limited number of rolls (usually three) per turn to try to achieve the best combination possible.
Brain simulation refers to computational and experimental techniques used to create models of the brain's structure and functionality. These simulations aim to replicate the processes of the brain, facilitating a deeper understanding of its operations, including neuronal activity, neural networks, and behavioral responses. There are several approaches and applications in brain simulation: 1. **Computational Models**: These models use mathematical and computational frameworks to simulate the behavior of neurons and networks of neurons.
The cotangent bundle is a fundamental construction in differential geometry and symplectic geometry. It is particularly important in the study of manifolds and classical mechanics. Given a smooth manifold \( M \), the cotangent bundle, denoted \( T^*M \), is the vector bundle whose fibers at each point consist of the cotangent vectors (or covectors) at that point.
A Merkle tree, also known as a binary hash tree, is a data structure that is used to efficiently and securely verify the integrity of large sets of data. It is named after Ralph Merkle, who first published the concept in the 1970s. Here's how a Merkle tree works: 1. **Leaf Nodes**: Data is divided into chunks, and each chunk is hashed using a cryptographic hash function (like SHA-256).
The Eötvös experiment, named after the Hungarian physicist Loránd Eötvös, is a fundamental experiment that tested the equivalence principle, which is a key component of Einstein's theory of general relativity. The equivalence principle states that gravitational mass (the mass that determines the strength of the gravitational force) and inertial mass (the mass that determines how an object accelerates when subjected to a force) are equivalent.
The Wilson quotient is a concept in number theory related to Wilson's theorem. Wilson's theorem states that a natural number \( p \) is a prime if and only if \[ (p-1)! \equiv -1 \, (\text{mod } p). \] The Wilson quotient is computed using the factorial of \( p-1 \) and is specifically defined for prime numbers. It can be expressed as: \[ W(p) = \frac{(p-1)!

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