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Witsenhausen's Counterexample
Witsenhausen's counterexample, shown in the figure below, is a deceptively simple toy problem in decentralized stochastic control. It was formulated by Hans Witsenhausen in 1968. It is a counterexample to a natural conjecture that one can generalize a key result of centralized linear–quadratic–Gaussian control systems—that in a system with linear dynamics, Gaussian disturbance, and quadratic cost, affine (linear) control laws are optimal—to decentralized systems. Witsenhausen constructed a two-stage linear quadratic Gaussian system where two decisions are made by decision makers with decentralized information and showed that for this system, there exist nonlinear control laws that outperform all linear laws. The problem of finding the optimal control law remains unsolved.Ho, Yu-Chi, "Review of the Witsenhausen problem". ''Proceedings of the 47th IEEE Conference on Decision and Control (CDC)'', pp. 1611–1613, 2008. Statement of the counterexample The statement of the co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Toy Problem
In scientific disciplines, a toy problem or a puzzlelike problem is a problem that is not of immediate scientific interest, yet is used as an expository device to illustrate a trait that may be shared by other, more complicated, instances of the problem, or as a way to explain a particular, more general, problem solving technique. A toy problem is useful to test and demonstrate methodologies. Researchers can use toy problems to compare the performance of different algorithms. They are also good for game designing. For instance, while engineering a large system, the large problem is often broken down into many smaller toy problems which have been well understood in detail. Often these problems distill a few important aspects of complicated problems so that they can be studied in isolation. Toy problems are thus often very useful in providing intuition about specific phenomena in more complicated problems. As an example, in the field of artificial intelligence, classical puzzles, ga ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Information Theory
Information theory is the scientific study of the quantification (science), quantification, computer data storage, storage, and telecommunication, communication of information. The field was originally established by the works of Harry Nyquist and Ralph Hartley, in the 1920s, and Claude Shannon in the 1940s. The field is at the intersection of probability theory, statistics, computer science, statistical mechanics, information engineering (field), information engineering, and electrical engineering. A key measure in information theory is information entropy, entropy. Entropy quantifies the amount of uncertainty involved in the value of a random variable or the outcome of a random process. For example, identifying the outcome of a fair coin flip (with two equally likely outcomes) provides less information (lower entropy) than specifying the outcome from a roll of a dice, die (with six equally likely outcomes). Some other important measures in information theory are mutual informat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jeff S
Jeff is a masculine name, often a short form (hypocorism) of the English given name Jefferson or Jeffrey, which comes from a medieval variant of Geoffrey. Music * DJ Jazzy Jeff, American DJ/turntablist record producer Jeffrey Allen Townes * Excision (musician), Canadian dubstep producer and DJ Jeff Abel * Jeff Abercrombie, bassist for American rock band Fuel * Jeff Allen, English session drummer * Jeff Baxter, American guitarist for rock bands Steely Dan and The Doobie Brothers * Jeff Beal (born 1963), American composer of music for various media * Jeff Beck, electric guitarist * Jeff Buckley, American singer-songwriter * Jeff Coffin, saxophonist, bandleader, composer and educator * Jeff Current, lead singer of American alternative rock band Against All Will * Jeff Fatt, Australian musician and actor, formerly with the children's band The Wiggles * Jeff Gillan, an American journalist * Jeff Graham, Canadian radio DJ * Jeff Hanneman (1964–2013), American guitarist, foundin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yu-Chi Ho
Yu-Chi "Larry" Ho (; born March 1, 1934) is a Chinese-American mathematician, control theorist, and a professor at the School of Engineering and Applied Sciences, Harvard University. He is the co-author of ''Applied Optimal Control'', and an influential researcher in differential games, pattern recognition, and discrete event dynamic systems. Ho was elected a member of the National Academy of Engineering in 1987 for pioneering and sustained contributions to applied optimization, control, and systems engineering theory and application. Biography Education Yu-Chi Ho was born on March 1, 1934, in Shanghai, China, and left home at the age of 15 in 1949 to complete his high school education in Hong Kong. In 1950, Ho was accepted to the Massachusetts Institute of Technology and came to the U.S., where he received a B.S. in electrical engineering in the summer of 1953, at the age of 19. Ho later reported that his initial interests were in mechanical engineering, due to a childhood e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neural Networks
A neural network is a network or circuit of biological neurons, or, in a modern sense, an artificial neural network, composed of artificial neurons or nodes. Thus, a neural network is either a biological neural network, made up of biological neurons, or an artificial neural network, used for solving artificial intelligence (AI) problems. The connections of the biological neuron are modeled in artificial neural networks as weights between nodes. A positive weight reflects an excitatory connection, while negative values mean inhibitory connections. All inputs are modified by a weight and summed. This activity is referred to as a linear combination. Finally, an activation function controls the amplitude of the output. For example, an acceptable range of output is usually between 0 and 1, or it could be −1 and 1. These artificial networks may be used for predictive modeling, adaptive control and applications where they can be trained via a dataset. Self-learning resulting from e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discretization
In applied mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts. This process is usually carried out as a first step toward making them suitable for numerical evaluation and implementation on digital computers. Dichotomization is the special case of discretization in which the number of discrete classes is 2, which can approximate a continuous variable as a binary variable (creating a dichotomy for modeling purposes, as in binary classification). Discretization is also related to discrete mathematics, and is an important component of granular computing. In this context, ''discretization'' may also refer to modification of variable or category ''granularity'', as when multiple discrete variables are aggregated or multiple discrete categories fused. Whenever continuous data is discretized, there is always some amount of discretization error. The goal is to reduce the amount to a level conside ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NP-complete
In computational complexity theory, a problem is NP-complete when: # it is a problem for which the correctness of each solution can be verified quickly (namely, in polynomial time) and a brute-force search algorithm can find a solution by trying all possible solutions. # the problem can be used to simulate every other problem for which we can verify quickly that a solution is correct. In this sense, NP-complete problems are the hardest of the problems to which solutions can be verified quickly. If we could find solutions of some NP-complete problem quickly, we could quickly find the solutions of every other problem to which a given solution can be easily verified. The name "NP-complete" is short for "nondeterministic polynomial-time complete". In this name, "nondeterministic" refers to nondeterministic Turing machines, a way of mathematically formalizing the idea of a brute-force search algorithm. Polynomial time refers to an amount of time that is considered "quick" for a de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Tsitsiklis
John N. Tsitsiklis ( el, Γιάννης Ν. Τσιτσικλής; born 1958) is a Clarence J. Lebel Professor of Electrical Engineering with the Department of Electrical Engineering and Computer Science (EECS) at the Massachusetts Institute of Technology. He serves as the director of the Laboratory for Information and Decision Systems and is affiliated with the Institute for Data, Systems, and Society (IDSS), the Statistics and Data Science Center and the MIT Operations Research Center. Education Tsitsiklis received a B.S. degree in Mathematics (1980), and his B.S. (1980), M.S. (1981), and Ph.D. (1984) degrees in Electrical Engineering, all from the Massachusetts Institute of Technology in Cambridge, Massachusetts. Awards and honors Tsitsiklis was elected to the 2007 class of Fellows of the Institute for Operations Research and the Management Sciences. He won the "2016 ACM SIGMETRICS Achievement Award in recognition of his fundamental contributions to decentralized control and c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Christos Papadimitriou
Christos Charilaos Papadimitriou ( el, Χρήστος Χαρίλαος "Χρίστος" Παπαδημητρίου; born August 16, 1949) is a Greek theoretical computer scientist and the Donovan Family Professor of Computer Science at Columbia University. Education Papadimitriou studied at the National Technical University of Athens, where in 1972 he received his Bachelor of Arts degree in electrical engineering. He then pursued graduate studies at Princeton University, where he received his Ph.D. in electrical engineering and computer science in 1976 after completing a doctoral dissertation titled "The complexity of combinatorial optimization problems." Career Papadimitriou has taught at Harvard, MIT, the National Technical University of Athens, Stanford, UCSD, University of California, Berkeley and is currently the Donovan Family Professor of Computer Science at Columbia University. Papadimitriou co-authored a paper on pancake sorting with Bill Gates, then a Harvard undergra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Propagation Delay
Propagation delay is the time duration taken for a signal to reach its destination. It can relate to networking, electronics or physics. ''Hold time'' is the minimum interval required for the logic level to remain on the input after triggering edge of the clock pulse. Networking In computer networks, propagation delay is the amount of time it takes for the head of the signal to travel from the sender to the receiver. It can be computed as the ratio between the link length and the propagation speed over the specific medium. Propagation delay is equal to ''d / s'' where ''d'' is the distance and ''s'' is the wave propagation speed. In wireless communication, ''s''=''c'', i.e. the speed of light. In copper wire, the speed ''s'' generally ranges from .59c to .77c. This delay is the major obstacle in the development of high-speed computers and is called the interconnect bottleneck in IC systems. Electronics In electronics, digital circuits and digital electronics, the propagati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transmission Delay
In a network based on packet switching, transmission delay (or store-and-forward delay, also known as packetization delay) is the amount of time required to push all the packet's bits into the wire. In other words, this is the delay caused by the data-rate of the link. Transmission delay is a function of the packet's length and has nothing to do with the distance between the two nodes. This delay is proportional to the packet's length in bits, It is given by the following formula: :D_T = N/R seconds where :D_T is the transmission delay in seconds :''N'' is the number of bits, and :''R'' is the rate of transmission (say in bits per second) Most packet switched networks use store-and-forward transmission at the input of the link. A switch using store-and-forward transmission will receive (save) the entire packet to the buffer and check it for CRC errors or other problems before sending the first bit of the packet into the outbound link. Thus, store-and-forward packet switches int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tamer Basar
Tamer is a Turkish given name and surname. It means ''Competent soldier'' in Turkish. In Arabic (written as تامر), the name is more closely related to Tamr (as in dates). Persons Given name * Tamer Abdel Hamid, Egyptian football player * Tamer Ashor (born 1984), Egyptian singer and composer * Tamer Balci (1917–1993), Turkish actor * Tamer Basar, Turkish control theorist * Tamer Başoğlu, (born 1938) Turkish sculptor * Tamer Bayoumi, Egyptian taekwondo player and Olympian * Tamer El Said, Egyptian film director, producer, and writer * Tamer El-Sawy, Egyptian tennis player * Tamer Fernandes (born 1974), English football player * Tamer Hamed (born 1974), Egyptian swimmer and Olympian * Tamer Hassan, English actor of Turkish Cypriot descent * Tamer Hosny, Egyptian singer-songwriter * Tamer Karadağlı, Turkish actor * Tamer Moustafa (born 1982), Egyptian basketball player * Tamer Nafar, Arab Israeli rap artist * Tamer Oyguç, Turkish professional basketball player * Ta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
