Units of information are standardized measures used to quantify information content, data, or knowledge. Here are some key units and concepts: 1. **Bit**: The most basic unit of information. A bit can represent a binary value of 0 or 1. It is the foundational unit in computing and digital communications. 2. **Byte**: A group of 8 bits, which can represent 256 different values (ranging from 0 to 255).

"A Mathematical Theory of Communication" is a seminal paper written by Claude Shannon, published in 1948. It is widely regarded as the foundation of information theory. In this work, Shannon introduced a rigorous mathematical framework for quantifying information and analyzing communication systems. Key concepts from the theory include: 1. **Information and Entropy**: Shannon defined information in terms of uncertainty and introduced the concept of entropy as a measure of the average information content in a message.

Adjusted Mutual Information (AMI) is a measure used to evaluate the quality of clustering results compared to a ground truth classification. It is an adjustment of the Mutual Information (MI) metric, designed to account for the chance agreements that can occur in clustering processes. ### Definitions: 1. **Mutual Information (MI)**: MI quantifies the amount of information obtained about one random variable through another random variable.

Ernest Friedman-Hill is a notable figure in the field of computer science, particularly recognized for his work on rule-based systems and the Jess Rule Engine. Jess (Java Expert System Shell) is a knowledge-based system that allows for the creation and execution of complex rule-based applications. It is widely used in artificial intelligence, expert systems, and decision support systems.

"Ascendancy" typically refers to a position of dominance or influence over others. It describes a state where someone or something has rising power, control, or superiority in a particular context, often in politics, social structures, or competitive environments. For example, a political party might gain ascendancy over its rivals during an election cycle, or a particular ideology may achieve ascendancy in public discourse.

The Asymptotic Equipartition Property (AEP) is a fundamental concept in information theory that describes the behavior of large sequences of random variables. It essentially states that for a sufficiently large number of independent and identically distributed (i.i.d.) random variables, the joint distribution of those variables becomes concentrated around a typical set of outcomes, which have roughly the same probability. Formally, if \(X_1, X_2, \ldots, X_n\) are i.

Bandwidth extension (BWE) is a technique used in various fields like telecommunications, audio processing, and speech coding to expand the frequency range of a signal. It aims to enhance the quality and intelligibility of a signal by extending its effective bandwidth, especially when the original signal is limited in frequency range.

The Bretagnolle–Huber inequality is a result in probability theory and statistics that provides bounds on the tail probabilities of sums of independent random variables. It is particularly useful when dealing with distributions that are sub-exponential or have heavy tails.

Channel capacity is a fundamental concept in information theory that represents the maximum rate at which information can be reliably transmitted over a communication channel. More specifically, it refers to the highest data rate (measured in bits per second, bps) that can be achieved without significant errors as the length of transmission approaches infinity. The concept was introduced by Claude Shannon in his seminal 1948 paper "A Mathematical Theory of Communication.

Cobham's theorem is a result in number theory that pertains to the theory of formal languages and the classification of sequences of integers. Specifically, it addresses the distinction between sequences that are definable in a certain arithmetic system and those that are not.

The Common Data Model (CDM) is a standardized data framework that provides a common definition and structure for data across various applications and systems. It is primarily used to enable data interoperability, enhance data sharing, and simplify the process of integrating disparate data sources. CDM is particularly useful in industries such as healthcare, finance, and education, where managing and analyzing data from multiple sources is crucial.

A communication channel refers to the medium or method used to convey information between individuals or groups. It can encompass a wide range of formats and tools, including: 1. **Verbal Communication**: This includes face-to-face conversations, phone calls, video conferences, and speeches. 2. **Written Communication**: This includes emails, text messages, letters, reports, and social media posts.

Computational irreducibility is a concept introduced by Stephen Wolfram in his work on cellular automata and complex systems, particularly in his book "A New Kind of Science." It refers to the idea that certain complex systems cannot be easily predicted or simplified; instead, one must simulate or compute the system's evolution step by step to determine its behavior.

Conditional entropy is a concept from information theory that quantifies the amount of uncertainty or information required to describe the outcome of a random variable, given that the value of another random variable is known. It effectively measures how much additional information is needed to describe a random variable \( Y \) when the value of another variable \( X \) is known.

Differential entropy is a concept in information theory that extends the idea of traditional (or discrete) entropy to continuous probability distributions. While discrete entropy measures the uncertainty associated with a discrete random variable, differential entropy quantifies the uncertainty of a continuous random variable.

Distributed source coding is a concept in information theory that involves the compression of data coming from multiple, potentially correlated, sources. The idea is to efficiently encode the data in such a way that the decoders, which may have access to different parts of the data, are able to reconstruct the original data accurately without requiring all data to be transmitted to a central location.

A **paratopological group** is a mathematical structure that combines the concepts of group theory and topology, but with a relaxed condition on the topology. Specifically, a paratopological group is a set equipped with a group operation that is continuous in a weaker sense than standard topological groups.

Entropic uncertainty refers to a concept in quantum mechanics and information theory that quantifies the uncertainty or lack of predictability associated with measuring the state of a quantum system. It is often expressed in terms of entropy, particularly the Shannon entropy or the von Neumann entropy, which measure the amount of information that is missing or how uncertain we are about a particular variable.

In information theory, a constraint refers to a limitation or restriction that affects the way information is processed, transmitted, or represented. Constraints can come in various forms and can influence the structure of codes, the capacity of communication channels, and the efficiency of data encoding and compression. Here are some examples of constraints in information theory: 1. **Channel Capacity Constraints**: The maximum rate at which information can be transmitted over a communication channel without error is characterized by the channel's capacity.