Václav Edvard "Vic" Beneš (born January 1, 1931) is a Czech-American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

, known for his contributions to the theory of stochastic processes,

queueing theory Queueing theory is the mathematical study of waiting lines, or queues. A queueing model is constructed so that queue lengths and waiting time can be predicted. Queueing theory is generally considered a branch of operations research because the ...

and

control theory Control theory is a field of mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a ...

, as well as the design of telecommunications

switch In electrical engineering, a switch is an electrical component that can disconnect or connect the conducting path in an electrical circuit, interrupting the electric current or diverting it from one conductor to another. The most common type of ...

es. He studied under John Kemeny and gained a doctorate in mathematics at

Princeton University Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the ...

(1953) on a treatise on ''

Mathematical logic Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal ...

''. He then worked for

Bell Labs Nokia Bell Labs, originally named Bell Telephone Laboratories (1925–1984), then AT&T Bell Laboratories (1984–1996) and Bell Labs Innovations (1996–2007), is an American industrial Research and development, research and scientific developm ...

until 1986, contributing to

Kalman filter For statistics and control theory, Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, and produces estima ...

theory as well as the Beneš network, a permutation network of the

Clos network In the field of telecommunications, a Clos network is a kind of multistage circuit-switching network which represents a theoretical idealization of practical, multistage switching systems. It was invented by Edson Erwin in 1938 and first formalize ...

type. In the 1980s he held a position at

Columbia University Columbia University (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manhatt ...

as well. He has continued to publish independently since 1989. He was elected

IEEE Fellow As of 2019, the Institute of Electrical and Electronics Engineers (IEEE) has 5,082 members designated Fellow, each of whom is associated with one of the 41 societies under the IEEE. The Fellow grade of membership is the highest level of membershi ...

(1991) for "contributions to the structure of telephone connecting networks, stochastic control, and nonlinear filtering". The ''Benesfest'' was celebrated at

(2001) to honor his 70th birthday. He resides in

Millburn, New Jersey Millburn is a suburban township in Essex County, New Jersey, United States. As of the 2010 United States census, the township's population was 20,149, reflecting an increase of 384 (+1.9%) from the 19,765 counted in the 2000 Census, which had ...

(since 1985) where he has been a long-time

mountain climber Mountaineering or alpinism, is a set of outdoor activities that involves ascending tall mountains. Mountaineering-related activities include traditional outdoor climbing, skiing, and traversing via ferratas. Indoor climbing, sport climbing, an ...

and member of the

American Alpine Club The American Alpine Club (AAC) is a non-profit member organization with more than 24,000 members. Its vision is to create "a united community of competent climbers and healthy climbing landscapes." The Club is housed in the American Mountaineerin ...

, and currently heads the local historical society. He is a relative of the former President of Czechoslovakia

Edvard Beneš Edvard Beneš (; 28 May 1884 – 3 September 1948) was a Czech politician and statesman who served as the president of Czechoslovakia from 1935 to 1938, and again from 1945 to 1948. He also led the Czechoslovak government-in-exile 1939 to 194 ...

and politician

Vojta Beneš Vojta Beneš (11 May 1878 – 20 November 1951) was a Czech educator, political leader in Czechoslovakia and brother of Edvard Beneš. Life and career Vojta Beneš was born in Kožlany, Bohemia, then a province of the Austro-Hungarian Empire. ...

Emilie Benes Brzezinski Emilie Beneš Brzezinski (born Emilie Anna Beneš; January 21, 1932 – July 22, 2022) was a Swiss-American sculptor and the wife of Zbigniew Brzezinski. Education and career Emilie Beneš was born in Geneva, Switzerland. She earned a fine ar ...

, a sculptor, was his sister. His first wife Janet was the daughter of Philip Franklin and niece of Norbert Wiener.

Books

*''General stochastic processes in the theory of queues'' (

Addison-Wesley Addison-Wesley is an American publisher of textbooks and computer literature. It is an imprint of Pearson PLC, a global publishing and education company. In addition to publishing books, Addison-Wesley also distributes its technical titles throu ...

, 1963) *''Mathematical Theory of Connecting Networks and Telephone Traffic'' (

Academic Press Academic Press (AP) is an academic book publisher founded in 1941. It was acquired by Harcourt, Brace & World in 1969. Reed Elsevier bought Harcourt in 2000, and Academic Press is now an imprint of Elsevier. Academic Press publishes referen ...

, 1965)

Journal publications

*'' Mr. Mayo on “Rules” of language'',

Philosophical Studies ''Philosophical 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 philo ...

, 3(2):33–36, April 1951 (review). *''A Partial Model for Quine's " New Foundations"'', 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 Journal, 37, pp. 211–258, 1958 *''Fluctuations of telephone traffic'', Bell System Technical Journal, 38, pp. 965–974, 1959 *''Transition probabilities for telephone traffic'', Bell System Technical Journal 38. pp. 211–258, 1959 *''A Sufficient Set of Statistics for a Simple Telephone Exchange Model'', Bell System Technical Journal, 38, pp. 939–964, 1959 *''General Stochastic Processes in Traffic Systems with One Server'', Bell System Technical Journal, 39, pp. 127–160, 1960 *''Transition Probabilities for Telephone Traffic'', Bell System Technical Journal, 39, pp. 1297–1320, 1960 *''Covariance function of simple trunk group, with applications to traffic measurement'', Bell System Technical Journal, 1961 *''Heuristic Remarks and Mathematical Problems Regarding the Theory of Switching Systems'', Bell System Technical Journal, vol. 41, pp. 1201–1247, 1962 *''On Rearrangeable Three-Stage Connecting Networks'', Bell System Technical Journal, 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 Journal, Vol. 62, No. 3, pp. 499–539, February 1963, *''Optimal Rearrangeable Multistage Connecting Networks'', Bell System Technical Journal, vol. 43, pp. 1641–1656, 1964 *''Permutation groups, complexes and rearrangeable connecting network'', Bell System Technical Journal, 43, 4:1619–1640, 1964. *''Index Reduction of FM Waves by Feed-Back and Power-Law Nonlinearities'',

Bell Labs Technical Journal The ''Bell Labs Technical Journal'' is the in-house scientific journal for scientists of Nokia Bell Labs, published yearly by the IEEE society. The managing editor is Charles Bahr. The journal was originally established as the ''Bell System Techn ...

, Vol.XLIV, No.4, pp. 581–601, April 1965 *''Programming and control problems arising from optimal routing in telephone networks'',

SIAM Thailand ( ), historically known as Siam () and officially the Kingdom of Thailand, is a country in Southeast Asia, located at the centre of the Indochinese Peninsula, spanning , with a population of almost 70 million. The country is bo ...

Journal on Control, 4(??):6–18, 1966 *''Existence of finite invariant measures for

Markov process A Markov chain or Markov process is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happe ...

es'', Proc. Amer.Math. Soc., 18:1058–1061, 1967. *''On some proposed models for traffic in connecting networks'', Bell System Technical Journal, 46:105–116, 1967 *Benes and

Lawrence Shepp Lawrence Alan Shepp (September 9, 1936 Brooklyn, NY – April 23, 2013, Tucson, AZ) was an American mathematician, specializing in statistics and computational tomography. Shepp obtained his PhD from Princeton University in 1961 with a disserta ...

, ''Wiener Integrals Associated with

Diffusion processes Molecular diffusion, often simply called diffusion, is the thermal motion of all (liquid or gas) particles at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid and the size (mass) of ...

'',

Theory of Probability Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set o ...

, 13, pages 498–501, 1968 *''Finite Regular Invariant Measures for Feller Processes'',

Journal of Applied Probability A journal, from the Old French ''journal'' (meaning "daily"), may refer to: *Bullet journal, a method of personal organization *Diary, a record of what happened over the course of a day or other period *Daybook, also known as a general journal, a ...

, Vol. 5, No. 1, pages 203–209, April 1968 *''Existence of optimal strategies based on specified information, for a class of stochastic decision problems'',

Journal on Control, 8(??):179–188, 1970 *''Existence of optimal stochastic control laws'',

Journal on Control 9(?):446–475, 1971 *''Applications of group theory to connecting networks'', Bell System Technical Journal, vol.45, pp. 407–420, 1975 *''Proving the rearrangeability of connecting networks by group calculations'', Bell System Technical Journal, vol.45, pp. 421–434, 1975 *''Full "bang" to reduce predicted miss is optimal'',

Journal on Control, 15(?):52–83, 1976 *''On Kailath's innovation conjecture'', Bell System Technical Journal 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 Journal, 57(1):111–149, 1978 *Benes,

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 process In probability, statistics and related fields, a Poisson point process is a type of random mathematical object that consists of points randomly located on a mathematical space with the essential feature that the points occur independently of one ...

IEEE The Institute of Electrical and Electronics Engineers (IEEE) is a 501(c)(3) professional association for electronic engineering and electrical engineering (and associated disciplines) with its corporate office in New York City and its operat ...

Trans. Information Theory, vol. 26: (5), pp. 561–575, 1980. *''Exact Finite Dimensional Filters for Certain Diffusions with Nonlinear Drift'',

Stochastics Stochastic (, ) refers to the property of being well described by a random probability distribution. Although stochasticity and randomness are distinct in that the former refers to a modeling approach and the latter refers to phenomena themselve ...

, 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 equation Zakai is a surname. Notable people with the surname include: *Johanan ben Zakai :''See Yohanan for more rabbis by this name''. Yohanan ben Zakkai ( he, יוֹחָנָן בֶּן זַכַּאי, ''Yōḥānān ben Zakkaʾy''; 1st century CE), s ...

and Mortensen's equation'',

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 Optics ''Applied Optics'' is a peer-reviewed scientific journal published by The Optical Society three times a month. It was established in 1962 with John N. Howard as founding editor-in-chief. The journal covers all aspects of optics, photonics, imagin ...

26, 1226–, 1987 *''Quadratic approximation by linear systems controlled from partial observations'', In Stochastic Analysis: Liber Amicorum for Moshe Zakai,

, 1991 *Benes, Kurt Helmes and Raymond. W. Rishel, ''Pursuing a maneuvering target which uses a random process for its control'',

Trans. on Automatic Control, 40(2), 1995 *Benes and Robert J. Elliott, ''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. Elliott, ''Finite-dimensional solutions of a modified

'', '' 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.

References

{{DEFAULTSORT:Benes, Vaclav E. 20th-century American mathematicians Queueing theorists Fellow Members of the IEEE Princeton University alumni Scientists at Bell Labs Place of birth missing (living people) Columbia University staff American people of Czech descent 1931 births Living people Control theorists Probability theorists