In information theory, entropy is a measure of the uncertainty or unpredictability associated with a random variable or a probability distribution. It quantifies the amount of information that is produced on average by a stochastic source of data. The concept was introduced by Claude Shannon in his seminal 1948 paper "A Mathematical Theory of Communication.
The concept of **entropy rate** is rooted in information theory and is used to measure the average information production rate of a stochastic (random) process or a data source. In detail: 1. **Information Theory Context**: Entropy, introduced by Claude Shannon, quantifies the uncertainty or unpredictability of a random variable or source of information. The entropy \( H(X) \) of a discrete random variable \( X \) with possible outcomes \( x_1, x_2, ...
The error exponent is a concept in information theory that quantifies the rate at which the probability of error decreases as the length of the transmitted message increases. In the context of coding and communication systems, it provides a measure of how efficiently a coding scheme can minimize the risk of errors in the transmitted data.
"Everything is a file" is a concept in Unix and Unix-like operating systems (like Linux) that treats all types of data and resources as files. This philosophy simplifies the way users and applications interact with different components of the system, allowing for a consistent interface for input/output operations.
Fano's inequality is a result in information theory that provides a lower bound on the probability of error in estimating a message based on observed data. It quantifies the relationship between the uncertainty of a random variable and the minimal probability of making an incorrect estimation of that variable when provided with some information. More formally, consider a random variable \( X \) with \( n \) possible outcomes and another random variable \( Y \), which represents the "guess" or estimation of \( X \).
Fisher information is a fundamental concept in statistics that quantifies the amount of information that an observable random variable carries about an unknown parameter of a statistical model. It is particularly relevant in the context of estimation theory and is used to evaluate the efficiency of estimators.
A glossary of quantum computing is a compilation of terms and concepts commonly used in the field of quantum computing. Here are some key terms and their definitions: 1. **Quantum Bit (Qubit)**: The basic unit of quantum information, analogous to a classical bit, which can exist in a state of 0, 1, or both simultaneously due to superposition.
An index of information theory articles typically refers to a curated list or database of academic and research articles that focus on information theory, a branch of applied mathematics and electrical engineering that deals with the quantification, storage, and communication of information. Such indexes can help researchers, students, and practitioners find relevant literature on various topics within information theory, including but not limited to: 1. **Fundamental Principles**: Articles discussing the foundational concepts, like entropy, mutual information, and channel capacity.
Grey Relational Analysis (GRA) is a multi-criteria decision-making technique used primarily in situations where the information is incomplete, uncertain, or vague, which is often the case in real-world problems. It is a part of the broader field of Grey System Theory, developed by Prof. Julong Deng in the 1980s. ### Key Concepts of Grey Relational Analysis: 1. **Grey System Theory**: This theory deals with systems that have partially known and partially unknown information.
The log-sum inequality, also known as Jensen's inequality in the context of convex functions, relates to the properties of logarithmic functions and the concavity of such functions.
The "logic of information" is a concept that explores the principles, structures, and reasoning related to information, especially in terms of its representation, processing, and communication. It can intersect with various fields such as computer science, information theory, philosophy, and cognitive science. Here are some key aspects of the logic of information: 1. **Information Theory**: Developed by Claude Shannon, information theory deals with quantifying information, data transmission, and compression.
The Lovász number, denoted as \( \vartheta(G) \), is a graph parameter associated with a simple undirected graph \( G \). It is a meaningful quantity in the context of both combinatorial optimization and information theory. The Lovász number can be interpreted in several ways and is particularly important in the study of graph coloring, independent sets, and the performance of certain algorithms.
The Hartley function is a measure of information that is similar to the Shannon entropy but uses a different formulation. It was introduced by Ralph Hartley in 1928 and is particularly useful in the context of information theory, particularly when dealing with discrete random variables.
Health information-seeking behavior refers to the ways in which individuals search for, acquire, and utilize information related to health and health care. This behavior can encompass a variety of activities, including: 1. **Searching for Information**: Individuals may seek information from various sources such as healthcare providers, family, friends, media (TV, newspapers), and online platforms (websites, social media).
Human Information Interaction (HII) is a multidisciplinary field that explores how people interact with information, technology, and each other. It encompasses various aspects of human behavior, cognition, and design principles related to the retrieval, processing, and usage of information. The goal of HII is to enhance the effectiveness and efficiency of information interactions, ensuring that users can access, comprehend, and apply information in meaningful ways.
Hyper-encryption is not a widely recognized term in the field of cryptography or computer security as of my last update in October 2023. However, the term could be interpreted in several ways based on the components of the word "hyper" and "encryption." 1. **Advanced Encryption Techniques**: It might refer to highly sophisticated encryption methods that go beyond traditional encryption standards, perhaps incorporating multiple layers of encryption or utilizing advanced algorithms that enhance security.
The IMU Abacus Medal is an award presented by the International Mathematical Union (IMU) to recognize exceptional mathematical achievements, specifically in the area of mathematical education. The medal is given to individuals who have made significant contributions to the education and outreach of mathematics, aiming to inspire and promote mathematical activity across different communities. The Abacus Medal is part of the IMU's broader efforts to enhance the quality of mathematical education and to encourage the development of mathematics globally.
The term "ideal tasks" can have different meanings depending on the context in which it is used. Here are a few interpretations: 1. **Project Management**: In project management, ideal tasks might refer to tasks that are well-defined, achievable, and aligned with the overall goals of the project. These tasks often follow the SMART criteria: Specific, Measurable, Achievable, Relevant, and Time-bound.
Information behavior refers to the ways in which individuals seek, receive, organize, store, and use information. It encompasses a wide range of activities and processes that people engage in to find and utilize information in their daily lives, whether for personal, professional, academic, or social purposes. Key aspects of information behavior include: 1. **Information Seeking**: The processes and strategies individuals use to locate information.
Information content refers to the amount of meaningful data or knowledge that is contained within a message, signal, or system. In various fields, it can have slightly different interpretations: 1. **Information Theory**: In information theory, established by Claude Shannon, information content is often quantified in terms of entropy. Entropy measures the average amount of information produced by a stochastic source of data. It represents the uncertainty or unpredictability of a system and is typically expressed in bits.
Pinned article: ourbigbook/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 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.Figure 3. Visual Studio Code extension installation.Figure 5. . 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. - 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