Instructor: Hazel Sive

License: Creative Commons BY-NC-SA

More information at http://ocw.mit.edu/terms

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Description: In search of better"burning fuels, or more accurate projections of climate change, researchers inevitably work through multiple models, sometimes at great cost.

In this seminar, Marzouk describes ways of managing uncertainty, which "is where a lot of idealizations of modeling meet the reality of the complex systems we're actually trying to study." Specifically, he aims to "quantify confidence in computational predictions, and use these predictions in design and decision"making;" learn from "noisy, indirect experimental observations," and refine and build models based on the most informative things observed and measured.

With formulas and graphs, Marzouk shows how he applies such methodologies as polynomial chaos expansion to "construct machinery that lets us propagate uncertainties, evaluate variances, evaluate any aspect of the probability distribution in the model output," in order "to apply robust formulations much more effectively." With statistical (Bayesian) inference and inverse problems, Marzouk extracts information from observational data to make models better, "backing out kinetic parameters working at microscale from macroscale data."

One real"world problem on which Marzouk has been applying his methods: ice sheet dynamics in west Antarctica, which pose "an enormous inference problem," due to unknowns about sliding friction, geothermal heat flux, and initial temperature of ice. Researchers "need to get a handle on this from the available data," he says. Another example involves solid oxide fuel cells, which suggest "a lot of potential as high efficiency conversion devices for vehicles or stationary power generation." Marzouk also hopes his modeling methods can help create better techniques for refining biomass for synthetic fuels.

About the Speaker(s):

Marzouk has been honored with a DOE Early Career Research Award, and several research fellowships.

Host(s): School of Engineering, Transportation@MIT

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Description: It's not every day that Euclid appears in public with "Alice and Bob," but in a lecture spanning a few thousand years,

Rivest makes quick work of the period before mid" 20th century, but credits the ancient Greeks for prime number factorization -- essential to cryptography -- and elementary ciphers. In the 18th and 19th century, mathematicians delved into number theory and extended techniques of factoring. The twentieth century, with its two world wars and technological advances, established the significance of cryptography on and off the battlefield. Alan Turing's Enigma machine not only helped the allies win World War II, but catalyzed development of the first generation of computers. MIT professor Claude Shannon, who worked with Turing and other cryptanalysts, went on to father the field of information science, leading to the digital age.

In the 1970s came development of public data encryption methods. Academics prevailed against U.S. government efforts to conceal means for encrypting data. In 1977, Rivest's group at MIT, which included Adi Shamir and Len Adleman, came up with RSA, an elegant algorithm for public"key cryptography that "relies on the difficulty of factoring" primes and which is still widely used. The group was so confident of its encryption method that they offered $100 for breaking a cipher"text based on a 129"digit product of primes. Rivest thought it would take "40 quadrillion years" to solve the challenge. "It was a bad estimate," he admits.

In fact, a combination of new algorithms and brute computing power cracked the text in 1994 ("The Magic Words are Squeamish Ossifrage"). Technological and theoretical advances have made possible improved encryption methods, and ways of authenticating and securing data. Faster computers may someday "make factoring a million"digit number easy," says Rivest. Work is even progressing on a quantum computer (it can only factor the number 15 so far). But code"breaking is also increasingly sophisticated, Rivest warns, as the internet opens up vast new areas of data to cyber"attack.

Rivest sees cryptography blossoming into applications for anonymity, password"based keys, and crypto for smart cards. He has been looking into probabilistic micropayment systems, and techniques to enhance the security and transparency of voting. "Maybe large prime numbers have a role to play in our democracy down the road," he says.

About the Speaker(s):

Rivest, whose research interests include cryptography, computer and network security, voting systems, and algorithms, is a member of the National Academy of Engineering, the National Academy of Sciences, and is a Fellow of the Association for Computing Machinery, the International Association for Cryptographic Research, and the American Academy of Arts and Sciences. Among other honors, Rivest, with Adi Shamir and Len Adleman, has been awarded the 2000 IEEE Koji Kobayashi Computers and Communications Award and the Secure Computing Lifetime Achievement Award.

Rivest is an inventor of the RSA public"key cryptosystem. He has extensive experience in cryptographic design and cryptanalysis, and has published numerous papers in these areas. He has served as a Director of the International Association for Cryptologic Research, the organizing body for the Eurocrypt and Crypto conferences, and as a Director of the Financial Cryptography Association.

He received a B.A. in Mathematics from Yale University in 1969, and a Ph.D. in Computer Science from Stanford University in 1974.

Host(s): Office of the President, Office of the President

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