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, mathematical structure, structure, space, Mathematica ...

known for his contributions to the theory of

stochastic processes In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables in a probability space, where the index of the family often has the interpretation of time. Stoc ...

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 th ...

and

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

, 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 o ...

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

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

Princeton University Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...

(1953) on a treatise on ''

Mathematical logic Mathematical logic is the study of Logic#Formal logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic com ...

''. He then worked for

Bell Labs Nokia Bell Labs, commonly referred to as ''Bell Labs'', is an American industrial research and development company owned by Finnish technology company Nokia. With headquarters located in Murray Hill, New Jersey, Murray Hill, New Jersey, the compa ...

until 1986, contributing to

Kalman filter In statistics and control theory, Kalman filtering (also known as linear quadratic estimation) is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, to produce estimates of unk ...

theory as well as the Beneš network, a

permutation network In mathematics, a permutation of a set can mean one of two different things: * an arrangement of its members in a sequence or linear order, or * the act or process of changing the linear order of an ordered set. An example of the first meanin ...

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 in the City of New York, commonly referred to as Columbia University, is a Private university, private Ivy League research university in New York City. Established in 1754 as King's College on the grounds of Trinity Churc ...

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

IEEE Fellow , the Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers (IEEE) is an American 501(c)(3) public charity professional organization for electrical engineering, electronics engineering, and ot ...

(1991) for "contributions to the structure of telephone connecting networks,

stochastic control Stochastic control or stochastic optimal control is a sub field of control theory that deals with the existence of uncertainty either in observations or in the noise that drives the evolution of the system. The system designer assumes, in a Bayesi ...

, and

nonlinear filtering In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathem ...

". The ''Benesfest'' was celebrated at

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

Millburn, New Jersey Millburn is a suburban Township (New Jersey), township in southwestern Essex County, New Jersey, Essex County, within the U.S. state of New Jersey, and part of the New York metropolitan area. As of the 2020 United States census, the township's ...

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

mountain climber Mountaineering, mountain climbing, or alpinism is a set of outdoor activities that involves ascending mountains. Mountaineering-related activities include traditional outdoor climbing, skiing, and traversing via ferratas that have become mounta ...

and member of the

American Alpine Club The American Alpine Club (AAC) is a non-profit member organization with more than 26,000 members. The club is housed in the American Mountaineering Center (AMC) in Golden, Colorado. Through its members, the AAC advocates for American climbers d ...

, 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 1939 to 1948. During the first six years of his second stint, he led the Czec ...

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. Be ...

. Emilie Benes Brzezinski, a sculptor, was his sister. His first wife Janet was the daughter of

Philip Franklin Philip Franklin (October 5, 1898 – January 27, 1965) was an American mathematician and professor whose work was primarily focused in analysis. Dr. Franklin received a B.S. in 1918 from City College of New York (who later awarded him ...

and niece of

Norbert Wiener Norbert Wiener (November 26, 1894 – March 18, 1964) was an American computer scientist, mathematician, and philosopher. He became a professor of mathematics at the Massachusetts Institute of Technology ( MIT). A child prodigy, Wiener late ...

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 ...

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

Academic Press Academic Press (AP) is an academic book publisher founded in 1941. It launched a British division in the 1950s. Academic Press was acquired by Harcourt, Brace & World in 1969. Reed Elsevier said in 2000 it would buy Harcourt, a deal complete ...

, 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 phil ...

, 3(2):33–36, April 1951 (review). *''A Partial Model for

Quine Quine may refer to: * Quine (computing), a program that produces its source code as output * Quine's paradox, in logic * Quine (surname), people with the surname ** Willard Van Orman Quine (1908–2000), American philosopher and logician See al ...

's "

New Foundations In mathematical logic, New Foundations (NF) is a non-well-founded, finitely axiomatizable set theory conceived by Willard Van Orman Quine as a simplification of the theory of types of ''Principia Mathematica''. Definition The well-formed fo ...

"'', 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 The ''Bell Labs Technical Journal'' was the in-house scientific journal for scientists of Bell Labs, published yearly by the IEEE society. The journal was originally established as ''The Bell System Technical Journal'' (BSTJ) in New York by the Am ...

, 37, pp. 211–258, 1958 *''Fluctuations of telephone traffic'',

, 38, pp. 965–974, 1959 *''Transition probabilities for telephone traffic'',

38. pp. 211–258, 1959 *''A Sufficient Set of Statistics for a Simple Telephone Exchange Model'',

, 38, pp. 939–964, 1959 *''General Stochastic Processes in Traffic Systems with One Server'',

, 39, pp. 127–160, 1960 *''Transition Probabilities for Telephone Traffic'',

, 39, pp. 1297–1320, 1960 *''Covariance function of simple trunk group, with applications to traffic measurement'',

, 1961 *''Heuristic Remarks and Mathematical Problems Regarding the Theory of Switching Systems'',

, vol. 41, pp. 1201–1247, 1962 *''On Rearrangeable Three-Stage Connecting Networks'',

, vol. XLI, Sep. 1962, No. 5, pp. 1481–1491. *''A "Renewal" Limit Theorem for General

Stochastic processes In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables in a probability space, where the index of the family often has the interpretation of time. Stoc ...

'', Ann. Math. Statist. Volume 33, Number 1, 98–113, 1962 *''Growth, Complexity and Performance of Telephone Connecting Networks'',

, Vol. 62, No. 3, pp. 499–539, February 1963, *''Optimal Rearrangeable Multistage Connecting Networks'',

, vol. 43, pp. 1641–1656, 1964 *''Permutation groups, complexes and rearrangeable connecting network'',

, 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'' was the in-house scientific journal for scientists of Bell Labs, published yearly by the IEEE society. The journal was originally established as ''The Bell System Technical Journal'' (BSTJ) in New York by the Am ...

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

SIAM Thailand, officially the Kingdom of Thailand and historically known as Siam (the official name until 1939), is a country in Southeast Asia on the Mainland Southeast Asia, Indochinese Peninsula. With a population of almost 66 million, it spa ...

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

Markov process In probability theory and statistics, a Markov chain or Markov process is a stochastic process describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, ...

es'', Proc. Amer.Math. Soc., 18:1058–1061, 1967. *''On some proposed models for traffic in connecting networks'',

, 46:105–116, 1967 *Benes and Lawrence Shepp, ''Wiener Integrals Associated with

Diffusion processes Molecular diffusion is the motion of atoms, molecules, or other particles of a gas or liquid at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid, size and density (or their product, ...

'',

Theory of Probability Probability theory or probability calculus 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 expre ...

, 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 personal secretive thoughts and as open book to personal therapy or used to feel connected to onesel ...

, 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'',

, vol.45, pp. 407–420, 1975 *''Proving the rearrangeability of connecting networks by group calculations'',

, 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'',

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'',

, 57(1):111–149, 1978 *Benes, Lawrence Shepp 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 René (''Born again (Christianity), born again'' or ''reborn'' in French language, French) is a common given name, first name in French-speaking, Spanish-speaking, and German-speaking countries. It derives from the Latin name Renatus. René is th ...

and V. E. Benes, ''Recursive non-linear estimation of a diffusion acting as the rate of an observed

Poisson process In probability theory, statistics and related fields, a Poisson point process (also known as: Poisson random measure, Poisson random point field and Poisson point field) is a type of mathematical object that consists of Point (geometry), points ...

IEEE The Institute of Electrical and Electronics Engineers (IEEE) is an American 501(c)(3) organization, 501(c)(3) public charity professional organization for electrical engineering, electronics engineering, and other related disciplines. The IEEE ...

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

Stochastics Stochastic (; ) is the property of being well-described by a random probability distribution. ''Stochasticity'' and ''randomness'' are technically distinct concepts: the former refers to a modeling approach, while the latter describes phenomena; in ...

, 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 In filtering theory the Zakai equation is a linear stochastic partial differential equation for the un-normalized density of a hidden state. In contrast, the Kushner equation gives a non-linear stochastic partial differential equation for the nor ...

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 Optica three times a month. It was established in 1962 with John N. Howard as founding editor-in-chief and Patricia Wakeling as managing editor. Wakeling worked on the journal ...

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

Moshe Zakai Moshe Zakai (; December 22, 1926 – November 27, 2015) was a Distinguished Professor at the Technion, Israel in electrical engineering, member of the Israel Academy of Sciences and Humanities and Rothschild Prize winner. Biography Moshe Zak ...

, 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 Fellows 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