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Claude E. Shannon
Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American mathematician, electrical engineer, and cryptographer known as a "father of information theory". As a 21-year-old master's degree student at the Massachusetts Institute of Technology (MIT), he wrote his thesis demonstrating that electrical applications of Boolean algebra could construct any logical numerical relationship. Shannon contributed to the field of cryptanalysis for national defense of the United States during World War II, including his fundamental work on codebreaking and secure telecommunications. Biography Childhood The Shannon family lived in Gaylord, Michigan, and Claude was born in a hospital in nearby Petoskey. His father, Claude Sr. (1862–1934), was a businessman and for a while, a judge of probate in Gaylord. His mother, Mabel Wolf Shannon (1890–1945), was a language teacher, who also served as the principal of Gaylord High School. Claude Sr. was a descendant of New Jersey se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Petoskey, Michigan
Petoskey ( ) is a city in the U.S. state of Michigan. It is the county seat and largest city in Emmet County. Part of Northern Michigan, Petoskey is a popular Midwestern resort town, as it sits on the shore of Little Traverse Bay, a bay of Lake Michigan. At the 2020 census, Petoskey's population was 5,877. History Odawa inhabitants The Little Traverse Bay area was long inhabited by indigenous peoples, including the Odawa people. The name ''Petoskey'' is said to mean "where the light shines through the clouds" in the language of the Odawa. After the 1836 Treaty of Washington, Odawa Chief Ignatius Petosega (1787–1885) took the opportunity to purchase lands near the Bear River. Petosega's father was Antoine Carre, a French Canadian fur trader and his mother was Odawa. Early Presbyterian missions By the 1850s, several religious groups had established missions near the Little Traverse Bay. A Mormon offshoot had been based at Beaver Island, the Jesuit missionaries had been ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
A Mathematical Theory Of Communication
"A Mathematical Theory of Communication" is an article by mathematician Claude E. Shannon published in '' Bell System Technical Journal'' in 1948. It was renamed ''The Mathematical Theory of Communication'' in the 1949 book of the same name, a small but significant title change after realizing the generality of this work. It became one of the most cited scientific articles and gave rise to the field of information theory. Publication The article was the founding work of the field of information theory. It was later published in 1949 as a book titled ''The Mathematical Theory of Communication'' (), which was published as a paperback in 1963 (). The book contains an additional article by Warren Weaver, providing an overview of the theory for a more general audience. Contents Shannon's article laid out the basic elements of communication: *An information source that produces a message *A transmitter that operates on the message to create a signal which can be sent through a channel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Entropy In Thermodynamics And Information Theory
The mathematical expressions for thermodynamic entropy in the statistical thermodynamics formulation established by Ludwig Boltzmann and J. Willard Gibbs in the 1870s are similar to the information entropy by Claude Shannon and Ralph Hartley, developed in the 1940s. Equivalence of form of the defining expressions The defining expression for entropy in the theory of statistical mechanics established by Ludwig Boltzmann and J. Willard Gibbs in the 1870s, is of the form: : S = - k_\text \sum_i p_i \ln p_i , where p_i is the probability of the microstate ''i'' taken from an equilibrium ensemble. The defining expression for entropy in the theory of information established by Claude E. Shannon in 1948 is of the form: : H = - \sum_i p_i \log_b p_i , where p_i is the probability of the message m_i taken from the message space ''M'', and ''b'' is the base of the logarithm used. Common values of ''b'' are 2, Euler's number , and 10, and the unit of entropy is shannon (or bit) for ''b''&n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edge Coloring
In graph theory, an edge coloring of a graph is an assignment of "colors" to the edges of the graph so that no two incident edges have the same color. For example, the figure to the right shows an edge coloring of a graph by the colors red, blue, and green. Edge colorings are one of several different types of graph coloring. The edge-coloring problem asks whether it is possible to color the edges of a given graph using at most different colors, for a given value of , or with the fewest possible colors. The minimum required number of colors for the edges of a given graph is called the chromatic index of the graph. For example, the edges of the graph in the illustration can be colored by three colors but cannot be colored by two colors, so the graph shown has chromatic index three. By Vizing's theorem, the number of colors needed to edge color a simple graph is either its maximum degree or . For some graphs, such as bipartite graphs and high-degree planar graphs, the number of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Digital Subscriber Line
Digital subscriber line (DSL; originally digital subscriber loop) is a family of technologies that are used to transmit digital data over telephone lines. In telecommunications marketing, the term DSL is widely understood to mean asymmetric digital subscriber line (ADSL), the most commonly installed DSL technology, for Internet access. DSL service can be delivered simultaneously with wired telephone service on the same telephone line since DSL uses higher frequency bands for data. On the customer premises, a DSL filter on each non-DSL outlet blocks any high-frequency interference to enable simultaneous use of the voice and DSL services. The bit rate of consumer DSL services typically ranges from 256 kbit/s to over 100 Mbit/s in the direction to the customer (downstream), depending on DSL technology, line conditions, and service-level implementation. Bit rates of 1 Gbit/s have been reached. In ADSL, the data throughput in the upstream direction (the direction ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Digital Electronics
Digital electronics is a field of electronics involving the study of digital signals and the engineering of devices that use or produce them. This is in contrast to analog electronics and analog signals. Digital electronic circuits are usually made from large assemblies of logic gates, often packaged in integrated circuits. Complex devices may have simple electronic representations of Boolean logic functions. History The binary number system was refined by Gottfried Wilhelm Leibniz (published in 1705) and he also established that by using the binary system, the principles of arithmetic and logic could be joined. Digital logic as we know it was the brain-child of George Boole in the mid 19th century. In an 1886 letter, Charles Sanders Peirce described how logical operations could be carried out by electrical switching circuits.Peirce, C. S., "Letter, Peirce to A. Marquand", dated 1886, '' Writings of Charles S. Peirce'', v. 5, 1993, pp. 541–3. GooglPreview See Burks, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Compression
In information theory, data compression, source coding, or bit-rate reduction is the process of encoding information using fewer bits than the original representation. Any particular compression is either lossy or lossless. Lossless compression reduces bits by identifying and eliminating statistical redundancy. No information is lost in lossless compression. Lossy compression reduces bits by removing unnecessary or less important information. Typically, a device that performs data compression is referred to as an encoder, and one that performs the reversal of the process (decompression) as a decoder. The process of reducing the size of a data file is often referred to as data compression. In the context of data transmission, it is called source coding; encoding done at the source of the data before it is stored or transmitted. Source coding should not be confused with channel coding, for error detection and correction or line coding, the means for mapping data onto a signal. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Chess
Computer chess includes both hardware (dedicated computers) and software capable of playing chess. Computer chess provides opportunities for players to practice even in the absence of human opponents, and also provides opportunities for analysis, entertainment and training. Computer chess applications that play at the level of a chess master or higher are available on hardware from supercomputers to smart phones. Standalone chess-playing machines are also available. Stockfish, GNU Chess, Fruit, and other free open source applications are available for various platforms. Computer chess applications, whether implemented in hardware or software, utilize different strategies than humans to choose their moves: they use heuristic methods to build, search and evaluate trees representing sequences of moves from the current position and attempt to execute the best such sequence during play. Such trees are typically quite large, thousands to millions of nodes. The computational speed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boolean Algebra
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values ''true'' and ''false'', usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses logical operators such as conjunction (''and'') denoted as ∧, disjunction (''or'') denoted as ∨, and the negation (''not'') denoted as ¬. Elementary algebra, on the other hand, uses arithmetic operators such as addition, multiplication, subtraction and division. So Boolean algebra is a formal way of describing logical operations, in the same way that elementary algebra describes numerical operations. Boolean algebra was introduced by George Boole in his first book ''The Mathematical Analysis of Logic'' (1847), and set forth more fully in his '' An Investigation of the Laws of Thought'' (1854). According to Huntington, the term "Boolean algebra" wa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Block Cipher
In cryptography, a block cipher is a deterministic algorithm operating on fixed-length groups of bits, called ''blocks''. Block ciphers are specified cryptographic primitive, elementary components in the design of many cryptographic protocols and are widely used to encryption, encrypt large amounts of data, including in data exchange protocols. A block cipher uses blocks as an unvarying transformation. Even a secure block cipher is suitable for the encryption of only a single block of data at a time, using a fixed key. A multitude of block cipher modes of operation, modes of operation have been designed to allow their repeated use in a secure way to achieve the security goals of confidentiality and authentication, authenticity. However, block ciphers may also feature as building blocks in other cryptographic protocols, such as universal hash functions and pseudorandom number generators. Definition A block cipher consists of two paired algorithms, one for encryption, , and the othe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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