Dirk Nuyens' Homepage @ cs.kuleuven.be

My Homepage

Welcome on Dirk Nuyens's Personal Computer Science Department Homepage.

Topics on this Site are: Research, About Me and Other Things.

• Research

  I work in the field of high dimensional quasi-Monte Carlo integration. More specifically I work on the construction of rank-1 lattice rules. You can find some recent work in the list below. The more recent work is listed on top, so for a good understanding you may want to read bottom up.

  1. Graphs of double character sums

     As a graphical experiment I am plotting a visual interpretation of a certain double character sum layed out on a circle. This then clearly shows symmetry and gives rise to other visual deducible properties.

     

  2. PhD thesis

     I defended my PhD thesis on April 20th 2007.

  3. Matlab codes for fast construction

     Some Matlab codes for the fast construction of good lattice rules and good lattice sequences can be found on my code page. They work also with Octave.

  4. The December 2005 Cover of AMS Notices
     » more info and images on separate page

     The December issue of Notices of the AMS contains an image of the component-by-component matrix on the cover by me as well as a one page explanation of these matrices as accompaniment to an article by Ian Sloan and Frances Kuo. The image below is not the cover art, but the beautiful situation for n=90.

     

  5. Using Embedded Lattice Rules as Finite Sequences

     In joint work with Frances Y. Kuo and Roland Cools we construct embedded lattice rules which can be used as a finite low-discrepancy sequence.

     

     You can download a preprint of “Constructing embedded lattice rules for multivariate integration”.

     To be published in SIAM Journal on Scientific Computing.

  6. Fast CBC Construction for Different Kernels and Polynomial Lattice Rules
     » more info and Matlab code on separate page

     The techniques on which the fast construction algorithm relies are independent of the kernel of the reproducing kernel Hilbert space, and thus the algorithm can also be applied to more exotic kernels. More over, the fast construction algorithm can directly be applied for polynomial lattice rules. We also supply a Matlab implementation of the fast algorithm for prime n.

     You can download a preprint of “Fast Component-by-Component Construction, A Reprise for Different Kernels” which appears in the MC2QMC2004 proceedings.

  7. Fast CBC Construction for (Non-)Prime Lattice Rules

     The fast construction algorithm has been extended to work for any number of points. The construction cost for general n remains O(sn log(n)) for n points in s dimensions.

     You can download a preprint of “Fast Component-by-Component Construction of Rank-1 Lattice Rules With a Non-Prime Number of Points” to appear in the Dagstuhl 2004 issue of Journal of Complexity.

  8. Fast CBC Construction for Lattice Rules with a Prime Number of Points

     The component-by-component (CBC) construction algorithm is a nice way to construct lattice rules which are extensible in the dimension. However the straight forward construction cost of this algorithm is O(s²n²), which is intractable for n and s large. We show a fast construction algorithm with time complexity O(sn log(n)) and memory complexity O(n).

     “Fast Algorithms for Component-By-Component Construction of Rank-1 Lattice Rules in Shift-Invariant Reproducing Kernel Hilbert Spaces” (AMS link) which appears in Mathematics of Computation. There is also an extended version on this server as a TW-report with extra tables.

• About Me

  1. My Research Interests

     • Quasi-Monte Carlo (qMC) in general.
     • Lattice rules.
     • Component-by-component construction of lattice rules.
     • The concepts of information based complexity (IBC).
     • Quantum algorithms and complexity.
     • Financial mathematics.
     • And a little bit off topic: computer languages and optimization (of code and human effort).

  2. My Publication List

     You can get an automated listing from our publication database.

  3. Contact Info

     My address: Dirk Nuyens, Department of Computer Science, K.U.Leuven, Celestijnenlaan 200A, B-3001 Heverlee.

     My email address in a harder to read font, as an image, and hopefully not easy machine decipherable:

  4. Past Events

     • iciam07: 6th International Congres on Industrial and Applied Mathematics, 16 - 20 July, 2007, ETH Zürich, Swiss.
     • naconf2007: Numerical Analysis Conference 2007, Tuesday 26th June - Friday 29th June, 2007, University of Dundee, Scotland, UK. The last Dundee...
     • Second Workshop on High-dimensional Approximation, hda07, 19 - 22 February 2007, Australian National University, Canberra, Australia.
     • Algorithms and Complexity for Continuous Problems, Seminar 06391, 24 - 29 September 2006, Dagstuhl.
     • International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCQMC2006, 14 - 18 August 2006, Ulm University, Germany.
     • SIAM Conference on Financial Mathematics and Engineering, FM2006, Boston, USA, July 9-12, 2006,
     • Symposium on Optimisation and Data Analysis, ODA05, 21 - 23 September 2005, Australian National University, Canberra, Australia.
     • naconf2005: Numerical Analysis Conference 2005, Tuesday 28 June - Friday July 1, 2005, University of Dundee, Scotland, UK.
     • Software Environments for Numerical Problems, November 17 - 18 2004, Gent.
     • Algorithms and Complexity for Continuous Problems, Seminar 04401, September 26 - October 1 2004, Dagstuhl.
     • ICCAM-2004, Leuven, Belgium.
     • MC2QMC2004 in Juan-les-Pins, France.
     • IVth IMACS Seminar on Monte Carlo Methods MCM-2003, Special session on high dimensional integration, 15-19 September 2003, Berlin.

  5. My MsTheses's

     My thesis as industrial engineer EE was about approximate string matching to find duplicates in marketing databases and was rewarded the Information Technology Prize 1998. My thesis as civil engineer CS was about simulation techniques for quantum computers.

  6. My Music

     My favorite hobby is playing music. I own several synthesizers: an Ensoniq TS-12, a Kurzweil K2500S and a Ronald JV80. As well as an acoustic piano and a Rhodes Stage 73 piano. The website of my old band Torn is still online.

• Other Things

  1. Liene

     Liene was born at April 22th. These are some older pictures at 16 weeks pregnancy.

     

  2. Some Pictures from My Recent Trip to Australia and New Zealand

     Some of the pictures will be put on line soon. As a preview my collection of license plates photographed at the National University of Australia during ODA05. Every state seems to have a slogan put on the plate: Canberra - The nation's capital; NSW - The premier state; Queensland - Sunshine state (Although it rained for the 2 days we were in Brisbane); Victoria - The place to be; Southern Australia - The festival state.

     
     

  3. Some Notes for the Numerical Mathematics Sessions (in Dutch)

  4. Some Notes for the Scientific Software Design Course (in Dutch)

© Copyright Dirk Nuyens. Page generated on 2008/05/10. XHTML and CSS compliant (please mail any irregularities). Disclaimer: I've learned to speak for myself, please learn to live with the mistakes.