Bruce Edward Hajek is a Professor in the

Coordinated Science Laboratory The Coordinated Science Laboratory (CSL) is a major scientific research laboratory at the University of Illinois Urbana-Champaign. With deep roots in information technology, CSL has invented and deployed many landmark innovations, such as the el ...

, the head of the Department of Electrical and Computer Engineering, and the Leonard C. and Mary Lou Hoeft Chair in Engineering at the

University of Illinois at Urbana-Champaign The University of Illinois Urbana-Champaign (U of I, Illinois, University of Illinois, or UIUC) is a public land-grant research university in Illinois in the twin cities of Champaign and Urbana. It is the flagship institution of the Univ ...

. He does research in communication networking,

auction theory Auction theory is an applied branch of economics which deals with how bidders act in auction markets and researches how the features of auction markets incentivise predictable outcomes. Auction theory is a tool used to inform the design of real-w ...

, stochastic analysis,

combinatorial optimization Combinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, where the set of feasible solutions is discrete or can be reduced to a discrete set. Typical combi ...

machine learning Machine learning (ML) is a field of inquiry devoted to understanding and building methods that 'learn', that is, methods that leverage data to improve performance on some set of tasks. It is seen as a part of artificial intelligence. Machine ...

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 a ...

, and

bioinformatics Bioinformatics () is an interdisciplinary field that develops methods and software tools for understanding biological data, in particular when the data sets are large and complex. As an interdisciplinary field of science, bioinformatics combi ...

Background, education, and positions

Bruce Hajek attended

Willowbrook High School Willowbrook High School (WBHS) is a public four-year high school in Villa Park, Illinois, a western suburb of Chicago, Illinois. The school is located approximately half a mile north of Illinois Route 38 on Ardmore Ave. It is a part of the DuPage ...

Villa Park Villa Park is a football stadium in Aston, Birmingham, England, with a seating capacity of 42,682. It has been the home of Premier League side Aston Villa since 1897. The ground is less than a mile from both Witton and Aston railway station ...

Illinois Illinois ( ) is a U.S. state, state in the Midwestern United States, Midwestern United States. Its largest metropolitan areas include the Chicago metropolitan area, and the Metro East section, of Greater St. Louis. Other smaller metropolita ...

. In 1973, he won the USA Mathematical Olympiad. In the same year, he graduated from high school. He entered the

(UIUC) to study computer science, but later he switched his major to mathematics. After working in Summer 1975 at

Brookhaven National Laboratory Brookhaven National Laboratory (BNL) is a United States Department of Energy national laboratory located in Upton, Long Island, and was formally established in 1947 at the site of Camp Upton, a former U.S. Army base and Japanese internment c ...

with

Herbert Robbins Herbert Ellis Robbins (January 12, 1915 – February 12, 2001) was an American mathematician and statistician. He did research in topology, measure theory, statistics, and a variety of other fields. He was the co-author, with Richard Co ...

, he graduated in 1976 with a BS in mathematics from

UIUC The University of Illinois Urbana-Champaign (U of I, Illinois, University of Illinois, or UIUC) is a public land-grant research university in Illinois in the twin cities of Champaign and Urbana. It is the flagship institution of the Uni ...

and received an

NSF NSF may stand for: Political organizations *National Socialist Front, a Swedish National Socialist party *NS-Frauenschaft, the women's wing of the former German Nazi party *National Students Federation, a leftist Pakistani students' political gr ...

Graduate Research Fellowship. He completed his MS degree in electrical engineering in 1977, again from

, and then took his Fellowship to

UC Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public university, public land-grant university, land-grant research university in Berkeley, California. Established in 1868 as the University of Californi ...

, where he received his PhD in 1979 under

Eugene Wong Eugene Wong (born December 24, 1934 in Nanking, China) is a Chinese-American computer scientist and mathematician. Wong's career has spanned academia, university administration, government and the private sector. Together with Michael Stonebra ...

. The same year, he returned to the department of

in Electrical & Computer Engineering, starting as an assistant professor and then becoming an associate professor (1982) and then a professor (1985). He was named the Leonard C. and Mary Lou Hoeft Chair in Engineering in 2006. Since 1986, he has been a recurring visitor at

Cambridge University , mottoeng = Literal: From here, light and sacred draughts. Non literal: From this place, we gain enlightenment and precious knowledge. , established = , other_name = The Chancellor, Masters and Schola ...

. In the 2009-2010 academic year, he was appointed a Rothschild Distinguished Visiting Fellow at the

Isaac Newton Institute for Mathematical Sciences The Isaac Newton Institute for Mathematical Sciences is an international research institute for mathematics and its many applications at the University of Cambridge. It is named after one of the university's most illustrious figures, the mathemat ...

Cambridge Cambridge ( ) is a university city and the county town in Cambridgeshire, England. It is located on the River Cam approximately north of London. As of the 2021 United Kingdom census, the population of Cambridge was 145,700. Cambridge bec ...

Service and leadership

From 1990 to 1993, Hajek served as the

editor-in-chief An editor-in-chief (EIC), also known as lead editor or chief editor, is a publication's editorial leader who has final responsibility for its operations and policies. The highest-ranking editor of a publication may also be titled editor, managing ...

for the ''

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 operation ...

Transactions on Information Theory''. In 1995, he served as the president of the

Information Theory Society. He has mentored 18 PhD students, including IBM

CEO A chief executive officer (CEO), also known as a central executive officer (CEO), chief administrator officer (CAO) or just chief executive (CE), is one of a number of corporate executives charged with the management of an organization especially ...

Arvind Krishna.

Research

Random fields

Bruce Hajek's PhD dissertation, titled ''Stochastic Integration, Markov Property and Measure Transformation of Random Fields'', studied

random field In physics and mathematics, a random field is a random function over an arbitrary domain (usually a multi-dimensional space such as \mathbb^n). That is, it is a function f(x) that takes on a random value at each point x \in \mathbb^n(or some other ...

s of three types: continuous-parameter

Markov random field In the domain of physics and probability, a Markov random field (MRF), Markov network or undirected graphical model is a set of random variables having a Markov property described by an undirected graph. In other words, a random field is said to b ...

s, continuous-parameter

s admitting stochastic-integral representations, and

s "arising from transformations of

absolutely continuous In calculus, absolute continuity is a smoothness property of functions that is stronger than continuity and uniform continuity. The notion of absolute continuity allows one to obtain generalizations of the relationship between the two central ope ...

measures". This work on

s has been recognized by others. In 1987, Hajek and Toby Berger showed that, under weak assumptions, a

whose entries take values in a finite-order field can be written as a component-wise sum of two independent

s with -valued components, with one of these two

s being

independent and identically distributed In probability theory and statistics, a collection of random variables is independent and identically distributed if each random variable has the same probability distribution as the others and all are mutually independent. This property is usua ...

according to a

nondegenerate In mathematics, a degenerate case is a limiting case of a class of objects which appears to be qualitatively different from (and usually simpler than) the rest of the class, and the term degeneracy is the condition of being a degenerate case. T ...

probability measure.

Communication networks

Hajek's work has significantly furthered the integration of computers and

communications system A communications system or communication system is a collection of individual telecommunications networks, transmission systems, relay stations, tributary stations, and terminal equipment usually capable of interconnection and interoperati ...

s. His many papers have taken the chaotic field of communication networking and given it a coherence and conceptual structure that it previously lacked. In the early 1980s, he led research that proved the stability of dynamically controlled ALOHA multiple access. He and his students also developed algorithms for dynamic routing and transmission scheduling. These innovations showed that determinism in service time minimizes waiting time in network queues. In relation to these achievements, he was inducted to the

National Academy of Engineering The National Academy of Engineering (NAE) is an American nonprofit, non-governmental organization. The National Academy of Engineering is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy ...

in 1999 "for contributions to stochastic systems,

communication networks A telecommunications network is a group of nodes interconnected by telecommunications links that are used to exchange messages between the nodes. The links may use a variety of technologies based on the methodologies of circuit switching, messag ...

, and

control Control may refer to: Basic meanings Economics and business * Control (management), an element of management * Control, an element of management accounting * Comptroller (or controller), a senior financial officer in an organization * Controllin ...

". In 2003, he received the

Kobayashi Award "for the application of stochastic and probabilistic theory to improved understanding of computer-network behavior, particularly, the modeling and performance optimization of multiple-access channels." The citation for the 2015 ACM

SIGMETRICS SIGMETRICS is the Association for Computing Machinery's Special Interest Group on Measurement and Evaluation, which specializes in the field of performance analysis, measurement, and modeling of computer systems. It is also the name of an annual ...

Achievement Award says,

Simulated annealing

A large fraction of Hajek's citations comes from his work on

simulated annealing Simulated annealing (SA) is a probabilistic technique for approximating the global optimum of a given function. Specifically, it is a metaheuristic to approximate global optimization in a large search space for an optimization problem. It ...

. His most cited paper, ''Cooling schedules for optimal annealing'', gives a nice condition for convergence of

to global minima, depending on the annealing schedule.

Books

In 2015, Hajek collaborated with

Cambridge University Press Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by Henry VIII of England, King Henry VIII in 1534, it is the oldest university press A university press is an academic publishing hou ...

to publish as a book his course notes for his Random Processes course, ECE 534, at

. The book is titled ''Random Processes for Engineers''. He is also a co-author on the second edition of a more advanced book,

's ''Stochastic Processes in Engineering Systems'' (Springer, 1985).

Awards and honors

*2022 UC Berkeley EE Distinguished Alumni Award "for his prodigious and fundamental research contributions to stochastic processes, information theory, and communications and computer networks; for his sustained and worldwide influence as a beloved teacher and mentor; and for his major leadership role in electrical and computer engineering." *2015

Achievement Award "for contributions to stochastic analysis, optimization and control, which have provided unique mathematical insights into the performance of the Internet, wireless networks, and

peer-to-peer Peer-to-peer (P2P) computing or networking is a distributed application architecture that partitions tasks or workloads between peers. Peers are equally privileged, equipotent participants in the network. They are said to form a peer-to-peer n ...

networks such as BitTorrent." *2014 Aaron D. Wyner Distinguished Service Award of the

Information Theory Society "for his longstanding contributions as" an ditor-in-chief an "organizer of many conferences", a "chair of several key society committees and IEEE committees", and a "leader of the

society". *2006 Markov Lecturer, on

network coding In computer networking, linear network coding is a program in which intermediate nodes transmit data from source nodes to sink nodes by means of linear combinations. Linear network coding may be used to improve a network's throughput, efficiency, ...

and stochastic networks, for the

Institute for Operations Research and the Management Sciences The Institute for Operations Research and the Management Sciences (INFORMS) is an international society for practitioners in the fields of operations research (O.R.), management science, and analytics. It was established in 1995 with the merger of ...

Applied Probability Society *2003

IEEE Koji Kobayashi Computers and Communications Award The IEEE Koji Kobayashi Computers and Communications Award is a Technical Field Award of the IEEE established in 1986. This award has been presented annually since 1988 for outstanding contributions to the integration of computers and commun ...

, "for the application of stochastic and probabilistic theory to improved understanding of computer-network behavior, particularly, the modeling and performance optimization of multiple-access channels." *

, inducted in 1999 "for contributions to stochastic systems, communication networks, and control." *1992

Guggenheim Fellow Guggenheim Fellowships are grants that have been awarded annually since by the John Simon Guggenheim Memorial Foundation to those "who have demonstrated exceptional capacity for productive scholarship or exceptional creative ability in the ar ...

in Applied Mathematics *1991 COMCON Award for Contributions to the Theory of Communications *

Fellow, inducted in 1989 "for contributions to stochastic systems, communication networks, and control systems." *1985

Control Systems Society Outstanding Paper Award *1984

Presidential Young Investigator Award The Presidential Young Investigator Award (PYI) was awarded by the National Science Foundation of the United States Federal Government. The program operated from 1984 to 1991, and was replaced by the NSF Young Investigator (NYI) Awards and Presiden ...

for "stochastic algorithms and analysis for large communication networks." *1982 Donald P. Eckman Award for control theory, from the

American Automatic Control Council The American Automatic Control Council (AACC) is an organization founded in 1957 for research in control theory. AACC is a member of the International Federation of Automatic Control (IFAC) and is an association of the control systems divisions of ...

References

{{DEFAULTSORT:Hajek, Bruce Living people American electrical engineers Grainger College of Engineering alumni University of California, Berkeley alumni University of Illinois Urbana-Champaign faculty 1955 births