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Leonard E. Baum
Leonard Esau Baum (August 23, 1931 – August 14, 2017) was an American mathematician, known for the Baum–Welch algorithm and Baum–Sweet sequence. He graduated Phi Beta Kappa from Harvard University in 1953, and earned a Ph.D. in mathematics from Harvard in 1958, with a dissertation titled ''Derivations in Commutative Semi-Simple Banach Algebras''. He developed the Baum–Welch Algorithm with Lloyd Welch while working for the Communications Research Division of IDA. It enabled the development of speech recognition and had applications in cryptanalysis and genetics. He coined the motto of the Communications Research Division: "Bad ideas is good, good ideas is terrific, no ideas is terrible." Later, in the late 1970s and early 1980s, Baum used mathematical models for currency trading, working with Monemetrics, a predecessor of hedge fund management company Renaissance Technologies. He left the firm in 1984 amid steep losses. In his later years, he would participate in Go ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Baum–Welch Algorithm
In electrical engineering, statistical computing and bioinformatics, the Baum–Welch algorithm is a special case of the expectation–maximization algorithm used to find the unknown parameters of a hidden Markov model (HMM). It makes use of the forward-backward algorithm to compute the statistics for the expectation step. The Baum–Welch algorithm, the primary method for inference in hidden Markov models, is numerically unstable due to its recursive calculation of joint probabilities. As the number of variables grows, these joint probabilities become increasingly small, leading to the forward recursions rapidly approaching values below machine precision. History The Baum–Welch algorithm was named after its inventors Leonard E. Baum and Lloyd R. Welch. The algorithm and the Hidden Markov models were first described in a series of articles by Baum and his peers at the IDA Center for Communications Research, Princeton in the late 1960s and early 1970s. One of the first major a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Foreign Exchange Market
The foreign exchange market (forex, FX, or currency market) is a global decentralized or over-the-counter (OTC) market for the trading of currencies. This market determines foreign exchange rates for every currency. By trading volume, it is by far the largest market in the world, followed by the credit market. The main participants are the larger international banks. Financial centres function as anchors of trading between a range of multiple types of buyers and sellers around the clock, with the exception of weekends. As currencies are always traded in pairs, the market does not set a currency's absolute value, but rather determines its relative value by setting the market price of one currency if paid for with another. Example: 1 USD is worth 1.1 Euros or 1.2 Swiss Francs etc. The market works through financial institutions and operates on several levels. Behind the scenes, banks turn to a smaller number of financial firms known as "dealers", who are involve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harvard Graduate School Of Arts And Sciences Alumni
Harvard University is a private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher learning in the United States. Its influence, wealth, and rankings have made it one of the most prestigious universities in the world. Harvard was founded and authorized by the Massachusetts General Court, the governing legislature of colonial-era Massachusetts Bay Colony. While never formally affiliated with any denomination, Harvard trained Congregational clergy until its curriculum and student body were gradually secularized in the 18th century. By the 19th century, Harvard emerged as the most prominent academic and cultural institution among the Boston elite. Following the American Civil War, under Harvard president Charles William Eliot's long tenure from 1869 to 1909, Harvard developed multiple professional schools, which transform ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
21st-century American Mathematicians
File:1st century collage.png, From top left, clockwise: Jesus is crucified by Roman authorities in Judaea (17th century painting). Four different men ( Galba, Otho, Vitellius, and Vespasian) claim the title of Emperor within the span of a year; The Great Fire of Rome (18th-century painting) sees the destruction of two-thirds of the city, precipitating the empire's first persecution against Christians, who are blamed for the disaster; The Roman Colosseum is built and holds its inaugural games; Roman forces besiege Jerusalem during the First Jewish–Roman War (19th-century painting); The Trưng sisters lead a rebellion against the Chinese Han dynasty (anachronistic depiction); Boudica, queen of the British Iceni leads a rebellion against Rome (19th-century statue); Knife-shaped coin of the Xin dynasty., 335px rect 30 30 737 1077 Crucifixion of Jesus rect 767 30 1815 1077 Year of the Four Emperors rect 1846 30 3223 1077 Great Fire of Rome rect 30 1108 1106 2155 Boudic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Princeton, New Jersey
The Municipality of Princeton is a Borough (New Jersey), borough in Mercer County, New Jersey, United States. It was established on January 1, 2013, through the consolidation of the Borough of Princeton, New Jersey, Borough of Princeton and Princeton Township, New Jersey, Princeton Township, both of which are now defunct. As of the 2020 United States census, the borough's population was 30,681, an increase of 2,109 (+7.4%) from the 2010 United States census, 2010 census combined count of 28,572. In the 2000 United States census, 2000 census, the two communities had a total population of 30,230, with 14,203 residents in the borough and 16,027 in the township. Princeton was founded before the American Revolutionary War. The borough is the home of Princeton University, one of the world's most acclaimed research universities, which bears its name and moved to the community in 1756 from the educational institution's previous location in Newark, New Jersey, Newark. Although its associ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Go (game)
# Go is an abstract strategy game, abstract strategy board game for two players in which the aim is to fence off more territory than the opponent. The game was invented in China more than 2,500 years ago and is believed to be the oldest board game continuously played to the present day. A 2016 survey by the International Go Federation's 75 member nations found that there are over 46 million people worldwide who know how to play Go, and over 20 million current players, the majority of whom live in East Asia. The Game piece (board game), playing pieces are called ''Go equipment#Stones, stones''. One player uses the white stones and the other black stones. The players take turns placing their stones on the vacant intersections (''points'') on the #Boards, board. Once placed, stones may not be moved, but ''captured stones'' are immediately removed from the board. A single stone (or connected group of stones) is ''captured'' when surrounded by the opponent's stones on all Orthogona ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hedge Fund
A hedge fund is a Pooling (resource management), pooled investment fund that holds Market liquidity, liquid assets and that makes use of complex trader (finance), trading and risk management techniques to aim to improve investment performance and insulate returns from beta (finance), market risk. Among these portfolio (finance), portfolio techniques are short (finance), short selling and the use of leverage (finance), leverage and derivative (finance), derivative instruments. In the United States, financial regulations require that hedge funds be marketed only to institutional investors and high-net-worth individuals. Hedge funds are considered alternative investments. Their ability to use leverage and more complex investment techniques distinguishes them from regulated investment funds available to the retail market, commonly known as mutual funds and Exchange-traded fund, ETFs. They are also considered distinct from private-equity fund, private equity funds and other similar cl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Renaissance Technologies
Renaissance Technologies LLC (also known as RenTec or RenTech) is an American hedge fund based in East Setauket, New York, on Long Island, that specializes in systematic trading using quantitative models derived from mathematical and statistical analysis. Renaissance was founded in 1982 by James Simons, a mathematician who worked as a code breaker during the Cold War. In 1988, the firm established the Medallion Fund, a form of Leonard Baum's mathematical models expanded by algebraist James Ax, to explore correlations from which it could profit. The hedge fund was named Medallion in honor of the math awards Simons and Ax had won. Simons ran Renaissance until his retirement in late 2009. He continued to play a role at the firm as non-executive chairman until 2021. He remained invested in its funds, particularly the Medallion fund, until his death in 2024. The company is now run by Peter Brown (after Robert Mercer resigned). Both were computer scientists specializing in c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Genetics
Genetics is the study of genes, genetic variation, and heredity in organisms.Hartl D, Jones E (2005) It is an important branch in biology because heredity is vital to organisms' evolution. Gregor Mendel, a Moravian Augustinians, Augustinian friar working in the 19th century in Brno, was the first to study genetics scientifically. Mendel studied "trait inheritance", patterns in the way traits are handed down from parents to offspring over time. He observed that organisms (pea plants) inherit traits by way of discrete "units of inheritance". This term, still used today, is a somewhat ambiguous definition of what is referred to as a gene. Phenotypic trait, Trait inheritance and Molecular genetics, molecular inheritance mechanisms of genes are still primary principles of genetics in the 21st century, but modern genetics has expanded to study the function and behavior of genes. Gene structure and function, variation, and distribution are studied within the context of the Cell (bi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Baum–Sweet Sequence
In mathematics the Baum–Sweet sequence is an infinite automatic sequence of 0s and 1s defined by the rule: :''b''''n'' = 1 if the binary representation of ''n'' contains no block of consecutive 0s of odd length; :''b''''n'' = 0 otherwise; for ''n'' ≥ 0. For example, ''b''4 = 1 because the binary representation of 4 is 100, which only contains one block of consecutive 0s of length 2; whereas ''b''5 = 0 because the binary representation of 5 is 101, which contains a block of consecutive 0s of length 1. Starting at ''n'' = 0, the first few terms of the Baum–Sweet sequence are: :1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1 ... Historical motivation The properties of the sequence were first studied by Leonard E. Baum and Melvin M. Sweet in 1976. In 1949, Khinchin conjectured that there does not exist a non-quadratic algebraic real number having bounded partial quotients in its continued fraction expansion. A counterexample to this conjecture is still not known. Baum an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cryptanalysis
Cryptanalysis (from the Greek ''kryptós'', "hidden", and ''analýein'', "to analyze") refers to the process of analyzing information systems in order to understand hidden aspects of the systems. Cryptanalysis is used to breach cryptographic security systems and gain access to the contents of encrypted messages, even if the cryptographic key is unknown. In addition to mathematical analysis of cryptographic algorithms, cryptanalysis includes the study of side-channel attacks that do not target weaknesses in the cryptographic algorithms themselves, but instead exploit weaknesses in their implementation. Even though the goal has been the same, the methods and techniques of cryptanalysis have changed drastically through the history of cryptography, adapting to increasing cryptographic complexity, ranging from the pen-and-paper methods of the past, through machines like the British Bombes and Colossus computers at Bletchley Park in World War II, to the mathematically advanced ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
