Uncertainty principles, extractors, and explicit embeddings of l2 into l1

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn , Issue , 2007, Pages 615-620

  Indyk, Piotr ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Extractors; Norm embeddings; Uncertainty principles

Indexed keywords

EXTRACTORS; NORM EMBEDDINGS; UNCERTAINTY PRINCIPLES;

COMPUTATIONAL METHODS; UNCERTAINTY ANALYSIS;

EMBEDDED SYSTEMS;

EID: 35448994781     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1250790.1250881     Document Type: Conference Paper

References (33)

1. D. Achlioptas. Database-friendly random projections. Proceedings of the Symposium on Principles of Database Systems, pages 274-281, 2001.
2. N. Ailon and B. Chazelle. Approximate nearest neighbors and the Fast Johnson-Lindenstrauss Transform. Proceedings of the Symposium on Theory of Computing, 2006.
3. S. Artstein-Avidan and V. D. Milman. Logarithmic reduction of the level of randomness in some probabilistic geometric constructions. Journal of Functional Analysis, 235:297-329, 2006.
4. A. R. Calderbank, P. J. Cameron, W. M. Kantor, and J. J. Seidel. Z4-Kerdock codes, orthogonal spreads and extremal euclidean line-sets. Proceedings of the London Mathematical Society, 2000.
5. P. J. Cameron and J.J. Seidel. Quadratic forms over GF(2). Indag. Math. 1973.
6. E. Candes, J. Romberg, and T. Tao. Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE Transactions on Information Theory, 52:489-509, 2006.
7. D. Donoho. Compressed sensing. IEEE Transactions on Information Theory, 52(4):1289-1306, 2006.
8. D. Donoho and X. Huo. Uncertainty principles and ideal atomic decomposition. Transactions on Information Theory, 47:2845-2862, 2001.
9. D. Donoho and P. Stark. Uncertainty principles and signal recovery. SIAM Journal on Applied Mathematics, 1989.
10. A. Dvoretzky. A theorem on convex bodies and applications to banach spaces. Proceedings of the National Academy of Sciences USA, 45:223-226, 1959.
11. T. Figiel, J. Lindenstrauss, and V. D. Milman. The dimension of almost spherical sections of convex bodies. Acta Mathematica, 139:53-94, 1977.
12. R. Gribonval and M. Nielsen. Sparse representations in unions of bases. IEEE Transactions on Information Theory, 2003.
13. V. Guruswami, C. Umans, and S. Vadhan. Extractors and condensers from univariate polynomials. IEEE Conference on Communication Complexity, 2007.
14. R. W. Heath, T. Strohmer, and A. J. Paulraj. On quasi-orthogonal signatures for CDMA systems. IEEE Transactions on Information Theory, 52:1217-1226, 2006.
15. P. Indyk. Dimensionality reduction techniques for proximity problems. Proceedings of the Ninth ACM-SIAM Symposium on Discrete Algorithms, 2000.
16. P. Indyk. Stable distributions, pseudorandom generators, embeddings and data stream computation. Proceedings of the Symposium on Foundations of Computer Science, 2000.
17. P. In W. B. Johnson and J. Lindenstrauss, editors, Handbook of the Geometry of Banach Spaces, pages 837-870. Elsevier, 2001.
18. N. Linial, E. London, and Y. Rabinovich. The geometry of graphs and some of its algorithmic applications. Proceedings of 85th Annual IEEE Symposium on Foundations of Computer Science, pages 577-591, 1994.
19. Yu. Liubarskii and R. Vershynin. Uncertainty principles and vector quantization. Manuscript, 2006.
20. S. Lovett and S. Sodin. Almost euclidean sections of the n-dimensional cross-polytope using o(n) random bits. ECCC Report TR.07-012, 2007.
21. J. Matoušek. Collection of open problems on low-distortion embeddings of finite metric spaces. Available at http://kam.mff.cunl.cz/ ~matousek/metrop.ps.gz, 2004.
22. V. Milman. Topics in asymptotic geometric analysis. GAFA - Geometric and Functional Analysis, pages 792-815, 2000.
23. V.D. Milman. A new proof of the theorem of A. Dvoretzky on sections of convex bodies. Fund. Anal. Appl., 1971.
24. R. Raz, O. Reingold, and S. Vadhan. Extracting all the randomness and reducing the error in trevisan's extractors. Proceedings of the Symposium on Theory of Computing, 1999.
25. O. Regev and R. Rosen. Lattice problems and norm embeddings. Proceedings of the Symposium on Theory of Computing, 2006.
26. W. Rudin. Trigonometric series with gaps. J. Math. Mech., 9:203-227, 1960.
27. G. Schechtman. Random embeddings of euclidean spaces in sequence spaces. Israel J. Math., 40:187-192, 1981.
28. R. Shaltiel. Recent developments in extractors. In Current trends in theoretical computer science. The Challenge of the New Century. Vol 1: Algorithms and Complexity, 2004.
29. S. Szarek. Convexity, complexity and high dimensions. Proceedings of the International Congress of Mathematicians (manuscript available from the author's home page), 2006.
30. J. Tropp. Topics in sparse approximation. Ph.D. dissertation, Computational and Applied Mathematics, UT-Austin, 2004.
31. A. Wigderson and D. Zuckerman. Expanders that beat the eigenvalue bound: Explicit constructions and applications. Combinatorica, 1999.
32. W.K. Wooters and B. D. Fields. Optimal state-determination by mutually unbiased measurements. Annals of Physics, 191:363-381, 1989.
33. D. Zuckerman. Randomness-optimal oblivious sampling. Random Structures and Algorithms, 11:345-367, 1997.