Vaclav E. Benes
Encyclopedia
Václav Edvard "Vic" Beneš (born 1930) is a Czech-American mathematician, known for his contributions to the theory of stochastic processes, queueing theory
and control theory
, as well as the design of telecommunications switch
es.
He studied under John Kemeny and gained a doctorate in mathematics
at Princeton University
(1953) on a treatise on Mathematical logic
.
He then worked for Bell Labs
until 1987, contributing to Kalman filter
theory as well as the Beneš network, a permutation network of the Clos network
type. In the 1980s he held a position at Columbia University
as well.
Since 1987 he continued to publish independently.
He was elected IEEE Fellow
(1990) for "contributions to the structure of telephone connecting networks, stochastic control
, and nonlinear filtering".
The Benesfest was celebrated at Columbia University
(2000) to honor his 70th birthday. He resides in Millburn, New Jersey
(since 1985) where he has been a long-time mountain climber member of the American Alpine Club
, and currently heads the local historical society.
Queueing theory
Queueing theory is the mathematical study of waiting lines, or queues. The theory enables mathematical analysis of several related processes, including arriving at the queue, waiting in the queue , and being served at the front of the queue...
and control theory
Control theory
Control theory is an interdisciplinary branch of engineering and mathematics that deals with the behavior of dynamical systems. The desired output of a system is called the reference...
, as well as the design of telecommunications switch
Switch
In electronics, a switch is an electrical component that can break an electrical circuit, interrupting the current or diverting it from one conductor to another....
es.
He studied under John Kemeny and gained a doctorate in mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
at Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
(1953) on a treatise on Mathematical logic
Mathematical logic
Mathematical logic is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic. The field includes both the mathematical study of logic and the applications of formal logic to other areas of mathematics...
.
He then worked for Bell Labs
Bell Labs
Bell Laboratories is the research and development subsidiary of the French-owned Alcatel-Lucent and previously of the American Telephone & Telegraph Company , half-owned through its Western Electric manufacturing subsidiary.Bell Laboratories operates its...
until 1987, contributing to Kalman filter
Kalman filter
In statistics, the Kalman filter is a mathematical method named after Rudolf E. Kálmán. Its purpose is to use measurements observed over time, containing noise and other inaccuracies, and produce values that tend to be closer to the true values of the measurements and their associated calculated...
theory as well as the Beneš network, a permutation network of the Clos network
Clos network
In the field of telecommunications, a Clos network is a kind of multistage circuit switching network, first formalized by Charles Clos in 1953, which represents a theoretical idealization of practical multi-stage telephone switching systems. Clos networks are required when the physical circuit...
type. In the 1980s he held a position at Columbia University
Columbia University
Columbia University in the City of New York is a private, Ivy League university in Manhattan, New York City. Columbia is the oldest institution of higher learning in the state of New York, the fifth oldest in the United States, and one of the country's nine Colonial Colleges founded before the...
as well.
Since 1987 he continued to publish independently.
He was elected IEEE Fellow
IEEE Fellow
An IEEE member is elevated to the grade of IEEE Fellow for "unusual distinction in the profession and shall be conferred by the Board of Directors upon a person with an extraordinary record of accomplishments in any of the IEEE fields of interest"...
(1990) for "contributions to the structure of telephone connecting networks, stochastic control
Stochastic control
Stochastic control is a subfield of control theory which deals with the existence of uncertainty in the data. The designer assumes, in a Bayesian probability-driven fashion, that a random noise with known probability distribution affects the state evolution and the observation of the controllers...
, and nonlinear filtering".
The Benesfest was celebrated at Columbia University
Columbia University
Columbia University in the City of New York is a private, Ivy League university in Manhattan, New York City. Columbia is the oldest institution of higher learning in the state of New York, the fifth oldest in the United States, and one of the country's nine Colonial Colleges founded before the...
(2000) to honor his 70th birthday. He resides in Millburn, New Jersey
Millburn, New Jersey
Millburn is a township in Essex County, New Jersey, United States. As of the 2010 United States Census, the township population was 20,149.Millburn Township was created as a township by an act of the New Jersey Legislature on March 20, 1857, from portions of Springfield Township.Millburn also...
(since 1985) where he has been a long-time mountain climber member of the American Alpine Club
American Alpine Club
The American Alpine Club, or AAC, was founded in 1902 by Charles Ernest Fay, and is the leading national organization in the United States devoted to mountaineering, climbing, and the multitude of issues facing climbers...
, and currently heads the local historical society.
Books
- General stochastic processes in the theory of queues (Addison-WesleyAddison-WesleyAddison-Wesley was a book publisher in Boston, Massachusetts, best known for its textbooks and computer literature. As well as publishing books, Addison-Wesley also distributed its technical titles through the Safari Books Online e-reference service...
, 1963) - Mathematical Theory of Connecting Networks and Telephone Traffic (Academic PressAcademic PressAcademic Press is an academic book publisher. Originally independent, it was acquired by Harcourt, Brace & World in 1969. Reed Elsevier bought Harcourt in 2000, and Academic Press is now an imprint of Elsevier....
, 1965)
Journal publications
- Mr. MayoBernard MayoBernard Mayo was an English philosopher.He worked at University of Birmingham until 1968, when he joined University of St...
on “Rules” of language, Philosophical StudiesPhilosophical StudiesPhilosophical Studies is a peer-reviewed academic journal for philosophy in the analytic tradition. The journal is devoted to the publication of papers in exclusively analytic philosophy and welcomes papers applying formal techniques to philosophical problems...
, 3(2):33–36, April 1951 (review). - A Partial Model for QuineWillard Van Orman QuineWillard Van Orman Quine was an American philosopher and logician in the analytic tradition...
's "New FoundationsNew FoundationsIn mathematical logic, New Foundations is an axiomatic set theory, conceived by Willard Van Orman Quine as a simplification of the theory of types of Principia Mathematica. Quine first proposed NF in a 1937 article titled "New Foundations for Mathematical Logic"; hence the name...
", The Journal of Symbolic Logic, Vol. 19, No. 3, pp. 197–200, September 1954 - On the Consistency of an Axiom of Enumerability, J. Symb. Log. 20(1):29–30, 1955
- On queues with Poisson arrivals, Ann. Math. Statist., vol. 28, pp. 670–677, 1956
- On Trunks with Negative Exponential Holding Times Serving a Renewal Process, Bell System Technical JournalBell System Technical JournalThe Bell System Technical Journal was the in-house scientific journal of Bell Labs that was published from 1922 to 1983.- Notable papers :...
, 37, pp. 211–258, 1958 - Fluctuations of telephone traffic, Bell System Technical JournalBell System Technical JournalThe Bell System Technical Journal was the in-house scientific journal of Bell Labs that was published from 1922 to 1983.- Notable papers :...
, 38, pp. 965–974, 1959 - Transition probabilities for telephone traffic, Bell System Technical JournalBell System Technical JournalThe Bell System Technical Journal was the in-house scientific journal of Bell Labs that was published from 1922 to 1983.- Notable papers :...
38. pp. 211–258, 1959 - A Sufficient Set of Statistics for a Simple Telephone Exchange Model, Bell System Technical JournalBell System Technical JournalThe Bell System Technical Journal was the in-house scientific journal of Bell Labs that was published from 1922 to 1983.- Notable papers :...
, 38, pp. 939–964, 1959 - General Stochastic Processes in Traffic Systems with One Server, Bell System Technical JournalBell System Technical JournalThe Bell System Technical Journal was the in-house scientific journal of Bell Labs that was published from 1922 to 1983.- Notable papers :...
, 39, pp. 127–160, 1960 - Transition Probabilities for Telephone Traffic, Bell System Technical JournalBell System Technical JournalThe Bell System Technical Journal was the in-house scientific journal of Bell Labs that was published from 1922 to 1983.- Notable papers :...
, 39, pp. 1297–1320, 1960 - Covariance function of simple trunk group, with applications to traffic measurement, Bell System Technical JournalBell System Technical JournalThe Bell System Technical Journal was the in-house scientific journal of Bell Labs that was published from 1922 to 1983.- Notable papers :...
, 1961 - Heuristic Remarks and Mathematical Problems Regarding the Theory of Switching Systems, Bell System Technical JournalBell System Technical JournalThe Bell System Technical Journal was the in-house scientific journal of Bell Labs that was published from 1922 to 1983.- Notable papers :...
, vol. 41, pp. 1201–1247, 1962 - On Rearrangeable Three-Stage Connecting Networks, Bell System Technical JournalBell System Technical JournalThe Bell System Technical Journal was the in-house scientific journal of Bell Labs that was published from 1922 to 1983.- Notable papers :...
, vol. XLI, Sep. 1962, No. 5, pp. 1481–1491. - A "Renewal" Limit Theorem for General Stochastic processes, Ann. Math. Statist. Volume 33, Number 1, 98–113, 1962
- Growth, Complexity and Performance of Telephone Connecting Networks, Bell System Technical JournalBell System Technical JournalThe Bell System Technical Journal was the in-house scientific journal of Bell Labs that was published from 1922 to 1983.- Notable papers :...
, Vol. 62, No. 3, pp. 499–539, February 1963, - Optimal Rearrangeable Multistage Connecting Networks, Bell System Technical JournalBell System Technical JournalThe Bell System Technical Journal was the in-house scientific journal of Bell Labs that was published from 1922 to 1983.- Notable papers :...
, vol. 43, pp. 1641–1656, 1964 - Permutation groups, complexes and rearrangeable connecting network, Bell System Technical JournalBell System Technical JournalThe Bell System Technical Journal was the in-house scientific journal of Bell Labs that was published from 1922 to 1983.- Notable papers :...
, 43, 4:1619–1640, 1964. - Index Reduction of FMFrequency modulationIn telecommunications and signal processing, frequency modulation conveys information over a carrier wave by varying its instantaneous frequency. This contrasts with amplitude modulation, in which the amplitude of the carrier is varied while its frequency remains constant...
Waves by Feed-Back and Power-Law Nonlinearities, Bell Labs Technical JournalBell Labs Technical JournalThe Bell Labs Technical Journal is the in-house scientific journal for scientists of Bell Labs/Alcatel-Lucent. It is published quarterly by John Wiley & Sons. The editor is Alice E...
, Vol.XLIV, No.4, pp. 581–601, April 1965 - Programming and control problems arising from optimal routing in telephone networks, SIAM Journal on Control, 4(??):6–18, 1966
- Existence of finite invariant measures for Markov processMarkov processIn probability theory and statistics, a Markov process, named after the Russian mathematician Andrey Markov, is a time-varying random phenomenon for which a specific property holds...
es, Proc. Amer.Math. Soc., 18:1058–1061, 1967. - On some proposed models for traffic in connecting networks, Bell System Technical JournalBell System Technical JournalThe Bell System Technical Journal was the in-house scientific journal of Bell Labs that was published from 1922 to 1983.- Notable papers :...
, 46:105–116, 1967 - Benes and Lawrence SheppLawrence SheppLawrence Shepp is an American mathematician, specialising in statistics and computational tomography.Shepp obtained his PhD from Princeton University with a dissertation entitled Recurrent Sums of Random Variables. His advisor was William Feller. He joined Bell Laboratories in 1962. He joined...
, Wiener Integrals Associated with Diffusion processes, Theory of Probability, 13, pages 498–501, 1968 - Finite Regular Invariant Measures for FellerWilliam FellerWilliam Feller born Vilibald Srećko Feller , was a Croatian-American mathematician specializing in probability theory.-Early life and education:...
Processes, Journal of Applied Probability, Vol. 5, No. 1, pages 203–209, April 1968 - Existence of optimal strategies based on specified information, for a class of stochastic decision problems, SIAM Journal on Control, 8(??):179–188, 1970
- Existence of optimal stochastic control laws, SIAM Journal on Control 9(?):446–475, 1971
- Applications of group theory to connecting networks, Bell System Technical JournalBell System Technical JournalThe Bell System Technical Journal was the in-house scientific journal of Bell Labs that was published from 1922 to 1983.- Notable papers :...
, vol.45, pp.407–420, 1975 - Proving the rearrangeability of connecting networks by group calculations, Bell System Technical JournalBell System Technical JournalThe Bell System Technical Journal was the in-house scientific journal of Bell Labs that was published from 1922 to 1983.- Notable papers :...
, vol.45, pp.421–434, 1975 - Full "bang" to reduce predicted miss is optimal, SIAM Journal on Control, 15(?):52–83, 1976
- On KailathThomas KailathThomas Kailath is an Indian electrical engineer, information theorist, control engineer, entrepreneur and the Hitachi America Professor of Engineering, Emeritus, at Stanford University...
's innovation conjecture, Bell System Technical JournalBell System Technical JournalThe Bell System Technical Journal was the in-house scientific journal of Bell Labs that was published from 1922 to 1983.- Notable papers :...
55:7, pp. 981–1001, 1976 - Nonexistence of strong nonanticipating solutions to stochastic DEs: implications for functional DEs, filtering, and control. Stochastic Processes Applied 5:3, 243–263., 1977
- Reduction of network states under symmetries, Bell System Technical JournalBell System Technical JournalThe Bell System Technical Journal was the in-house scientific journal of Bell Labs that was published from 1922 to 1983.- Notable papers :...
, 57(1):111–149, 1978 - Benes, Lawrence SheppLawrence SheppLawrence Shepp is an American mathematician, specialising in statistics and computational tomography.Shepp obtained his PhD from Princeton University with a dissertation entitled Recurrent Sums of Random Variables. His advisor was William Feller. He joined Bell Laboratories in 1962. He joined...
and Hans S. Witsenhausen, Some Solvable Stochastic Control Problems, Stochastics 4, 39–83, 1980 - Least-Squares Estimator for Frequency Shift Position Modulation in White Noise, pp. 1289–1296, Sept. 1980
- René K. Boell and V. E. Benes, Recursive non-linear estimation of a diffusion acting as the rate of an observed Poisson processPoisson processA Poisson process, named after the French mathematician Siméon-Denis Poisson , is a stochastic process in which events occur continuously and independently of one another...
, IEEE Trans. Information Theory, vol. 26: (5), pp. 561–575, 1980. - Exact Finite Dimensional Filters for Certain Diffusions with Nonlinear Drift, Stochastics, 5, pp. 65–92, 1981.
- Benes and Ioannis Karatzas, Estimation and control for linear, partially observable systems with non-gaussian initial distribution, In Stochastic Processes & Applications, 14, pages 233–248, 1981
- Benes and Karatzas, On the relation of Zakai equationZakai equationIn filtering theory the Zakai equation is a linear recursive filtering equation for the un-normalized density of a hidden state. In contrast, the Kushner equation gives a non-linear recursive equation for the normalized density of the hidden state...
and Mortensen's equation, SIAM Journal on Control and Optimization, 21 pp. 472–489, 1983 - Benes and Karatzas, Filtering of diffusions controlled through their conditional measures, Stochastics, 13, pp. 1–23, 1984
- R. A. Spanke and V. E. Benes, N-stage planar optical permutation network, Applied OpticsApplied OpticsApplied Optics is a peer-reviewed scientific journal published by the Optical Society of America three times a month. It was established in 1963 with John N. Howard as founding editor. The journal has four divisions of editorial scope: optical technology, information processing, lasers, photonics...
26, 1226–, 1987 - Quadratic approximation by linear systems controlled from partial observations, In Stochastic Analysis: Liber Amicorum for Moshe ZakaiMoshe ZakaiMoshe Zakai is Distinguished Professor at the Technion, Israel in Electrical Engineering, member of the Israel Academy of Sciences and Humanities and Rothschild Prize winner.- Biography :...
, Academic PressAcademic PressAcademic Press is an academic book publisher. Originally independent, it was acquired by Harcourt, Brace & World in 1969. Reed Elsevier bought Harcourt in 2000, and Academic Press is now an imprint of Elsevier....
, 1991 - Benes, Kurt Helmes and Raymond. W. Rishel, Pursuing a maneuvering target which uses a random process for its control, IEEE Trans. on Automatic Control, 40(2), 1995
- Benes and Robert J. ElliottRobert J. ElliottRobert James Elliott is a British-Canadian mathematician, known for his contributions to control theory, game theory, stochastic processes and mathematical finance.He was schooled at Swanwick, Derbyshire and studied mathematics...
, Finite dimensional risk sensitive information states, I.F.A.C. Symposium on Nonlinear Control System Design, Lake Tahoe, CA, 471–476, June 1995 - Benes and Robert J. ElliottRobert J. ElliottRobert James Elliott is a British-Canadian mathematician, known for his contributions to control theory, game theory, stochastic processes and mathematical finance.He was schooled at Swanwick, Derbyshire and studied mathematics...
, Finite-dimensional solutions of a modified Zakai equationZakai equationIn filtering theory the Zakai equation is a linear recursive filtering equation for the un-normalized density of a hidden state. In contrast, the Kushner equation gives a non-linear recursive equation for the normalized density of the hidden state...
, Mathematics of Control, Signals, and Systems, 9, 341–351, 1996 - Nonlinear filtering and optimal quality control, in Journal of Applied Mathematics and Stochastic Analysis, vol. 11, no. 3, pp. 225–230, 1998.