Cognitive networked sensing and big data

Cognitive Networked Sensing and Big Data

Volumn 9781461445449, Issue , 2014, Pages 1-614

  Qiu, Robert ^a   Wicks, Michael ^b  

^a TENNESSEE TECHNOLOGICAL UNIVERSITY   (United States)

^b NONE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIG DATA; COGNITIVE RADIO; DATA HANDLING; REVIEWS; TESTBEDS;

COGNITIVE RADIO NETWORK; COGNITIVE SENSING; DISTRIBUTED SENSING; HARDWARE TESTBEDS; HIGH DIMENSIONAL DATA; HIGH MOBILITY; RESEARCH RESULTS; SOFTWARE-DEFINED RADIO IMPLEMENTATIONS;

DISTRIBUTED COMPUTER SYSTEMS;

EID: 84949177998     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-1-4614-4544-9     Document Type: Book

References (611)

1. N. Alon, M. Krivelevich, and V. Vu, "On the concentration of eigenvalues of random symmetric matrices," Israel Journal of Mathematics, vol. 131, no. 1, pp. 259-267, 2002.
2. V. Vu, "Concentration of non-lipschitz functions and applications," Random Structures & Algorithms, vol. 20, no. 3, pp. 262-316, 2002.
3. V. Vu, "Spectral norm of random matrices," Combinatorica, vol. 27, no. 6, pp. 721-736, 2007.
4. V. Mayer-Schönberger and K. Cukier, Big Data: A Revolution that will transform how we live, work and think. Eamon Dolan Book and Houghton Mifflin Hardcourt, 2013.
5. R. Qiu, Z. Hu, H. Li, and M. Wicks, Cognitiv Communications and Networking: Theory and Practice. John Wiley and Sons, 2012.
6. R. Qiu, Introduction to Smart Grid. John Wiley and Sons, 2014.
7. G. Lugosi, "Concentration-of-measure inequalities," 2009.
8. A. Leon-Garcia, Probability, Statistics, and Random Processing for Electrical Engineering. Pearson-Prentice Hall, third edition ed., 2008.
9. T. Tao, Topics in Random Matrix Thoery. American Mathematical Society, 2012.
10. N. Nguyen, P. Drineas, and T. Tran, "Tensor sparsification via a bound on the spectral norm of random tensors," arXiv preprint arXiv:1005.4732, 2010.
11. W. Hoeffding, "Probability inequalities for sums of bounded random variables," Journal of the American Statistical Association, pp. 13-30, 1963.
12. G. Bennett, "Probability inequalities for the sum of independent random variables," Journal of the American Statistical Association, vol. 57, no. 297, pp. 33-45, 1962.
13. A. Van Der Vaart and J. Wellner, Weak Convergence and Empirical Processes. SpringerVerlag, 1996.
14. F. Lin, R. Qiu, Z. Hu, S. Hou, J. Browning, and M. Wicks, "Generalized fmd detection for spectrum sensing under low signal-to-noise ratio," IEEE Communications Letters, to appear. [18, 221, 226, 227]
15. E. Carlen, "Trace inequalities and quantum entropy: an introductory course," Entropy and the quantum: Arizona School of Analysis with Applications, March 16-20, 2009, University of Arizona, vol. 529, 2010.
16. F. Zhang, Matrix Theory. Springer Ver, 1999.
17. K. Abadir and J. Magnus, Matrix Algebra. Cambridge Press, 2005.
18. D. S. Bernstein, Matrix Mathematics: Theory, Facts, and Formulas. Princeton University Press, 2009.
19. J. A. Tropp, "User-friendly tail bounds for sums of random matrices." Preprint, 2011.
20. N. J. Higham, Functions of Matrices: Theory and Computation. Society for Industrial and Applied Mathematics, 2008.
21. L. Trefethen and M. Embree, Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators. Princeton University Press, 2005.
22. R. Bhatia, Positive Definite Matrices. Princeton University Press, 2007.
23. R. Bhatia, Matrix analysis. Springer, 1997.
24. A. W. Marshall, I. Olkin, and B. C. Arnold, Inequalities: Theory of Majorization and Its Applications. Springer Verl, 2011.
25. D. Watkins, Fundamentals of Matrix Computations. Wiley, third ed., 2010.
26. J. A. Tropp, "On the conditioning of random subdictionaries," Applied and Computational Harmonic Analysis, vol. 25, no. 1, pp. 1-24, 2008.
27. M. Ledoux and M. Talagrand, Probability in Banach spaces. Springer, 1991.
28. J. A. Tropp, J. N. Laska, M. F. Duarte, J. K. Romberg, and R. G. Baraniuk, "Beyond nyquist: Efficient sampling of sparse bandlimited signals," Information Theory, IEEE Transactions on, vol. 56, no. 1, pp. 520-544, 2010.
29. J. Nelson, "Johnson-lindenstrauss notes," tech. rep., Technical report, MIT-CSAIL, Available at web.mit.edu/minilek/www/jl notes.pdf, 2010.
30. H. Rauhut, "Compressive sensing and structured random matrices," Theoretical foundations and numerical methods for sparse recovery, vol. 9, pp. 1-92, 2010.
31. F. Krahmer, S. Mendelson, and H. Rauhut, "Suprema of chaos processes and the restricted isometry property," arXiv preprint arXiv:1207.0235, 2012.
32. R. Latala, "On weak tail domination of random vectors," Bull. Pol. Acad. Sci. Math., vol. 57, pp. 75-80, 2009.
33. W. Bednorz and R. Latala, "On the suprema of bernoulli processes," Comptes Rendus Mathematique, 2013.
34. B. Gnedenko and A. Kolmogorov, Limit Distributions for Sums Independent Random Variables. Addison-Wesley, 1954.
35. R. Vershynin, "A note on sums of independent random matrices after ahlswede-winter." http://www-personal.umich.edu/∼romanv/teaching/reading-group/ahlswede-winter.pdf. Seminar Notes. [31, 91]
36. R. Ahlswede and A. Winter, "Strong converse for identification via quantum channels," Information Theory, IEEE Transactions on, vol. 48, no. 3, pp. 569-579, 2002.
37. T. Fine, Probability and Probabilistic Reasoning for Electrical Engineering. Pearson-Prentice Hall, 2006.
38. R. Oliveira, "Sums of random hermitian matrices and an inequality by rudelson," Elect. Comm. Probab, vol. 15, pp. 203-212, 2010.
39. T. Rockafellar, Conjugative duality and optimization. Philadephia: SIAM, 1974.
40. D. Petz, "A suvery of trace inequalities." Functional Analysis and Operator Theory, 287-298, Banach Center Publications, 30 (Warszawa), 1994. www.renyi.hu/∼petz/pdf/64.pdf.
41. R. Vershynin, "Golden-thompson inequality." www-personal.umich.edu/∼romanv/teaching/reading-group/golden-thompson.pdf. Seminar Notes. [39]
42. I. Dhillon and J. Tropp, "Matrix nearness problems with bregman divergences," SIAM Journal on Matrix Analysis and Applications, vol. 29, no. 4, pp. 1120-1146, 2007.
43. J. Tropp, "From joint convexity of quantum relative entropy to a concavity theorem of lieb," in Proc. Amer. Math. Soc, vol. 140, pp. 1757-1760, 2012.
44. G. Lindblad, "Expectations and entropy inequalities for finite quantum systems," Communications in Mathematical Physics, vol. 39, no. 2, pp. 111-119, 1974.
45. E. G. Effros, "A matrix convexity approach to some celebrated quantum inequalities," vol. 106, pp. 1006-1008, National Acad Sciences, 2009.
46. E. Carlen and E. Lieb, "A minkowski type trace inequality and strong subadditivity of quantum entropy ii: convexity and concavity," Letters in Mathematical Physics, vol. 83, no. 2, pp. 107-126, 2008.
47. T. Rockafellar, Conjugate duality and optimization. SIAM, 1974. Regional conference series in applied mathematics.
48. S. Boyd and L. Vandenberghe, Convex optimization. Cambridge Univ Pr, 2004.
49. J. Tropp, "Freedman's inequality for matrix martingales," Electron. Commun. Probab, vol. 16, pp. 262-270, 2011.
50. E. Lieb, "Convex trace functions and the wigner-yanase-dyson conjecture," Advances in Mathematics, vol. 11, no. 3, pp. 267-288, 1973.
51. V. I. Paulsen, Completely Bounded Maps and Operator Algebras. Cambridge Press, 2002.
52. T. M. Cover and J. A. Thomas, Elements of Information Theory. New York: John Wiley. [44]
53. J. Tropp, "User-friendly tail bounds for sums of random matrices," Foundations of Computational Mathematics, vol. 12, no. 4, pp. 389-434, 2011.
54. F. Hansen and G. Pedersen, "Jensen's operator inequality," Bulletin of the London Mathematical Society, vol. 35, no. 4, pp. 553-564, 2003.
55. P. Halmos, Finite-Dimensional Vector Spaces. Springer, 1958.
56. V. De la Peña and E. Giné, Decoupling: from dependence to independence. Springer Verlag, 1999.
57. R. Vershynin, "A simple decoupling inequality in probability theory," May 2011.
58. P. Billingsley, Probability and Measure. Wiley, 2008.
59. R. Dudley, Real analysis and probability, vol. 74. Cambridge University Press, 2002.
60. M. A. Arcones and E. Giné, "On decoupling, series expansions, and tail behavior of chaos processes," Journal of Theoretical Probability, vol. 6, no. 1, pp. 101-122, 1993.
61. D. L. Hanson and F. T. Wright, "A bound on tail probabilities for quadratic forms in independent random variables," The Annals of Mathematical Statistics, pp. 1079-1083, 1971.
62. S. Boucheron, G. Lugosi, and P. Massart, "Concentration inequalities using the entropy method," The Annals of Probability, vol. 31, no. 3, pp. 1583-1614, 2003.
63. T. Tao, Topics in Random Matrix Theory. Amer Mathematical Society, 2012.
64. E. Wigner, "Distribution laws for the roots of a random hermitian matrix," Statistical Theories of Spectra: Fluctuations, pp. 446-461, 1965.
65. M. Mehta, Random matrices, vol. 142. Academic press, 2004.
66. D. Voiculescu, "Limit laws for random matrices and free products," Inventiones mathemati-cae, vol. 104, no. 1, pp. 201-220, 1991.
67. J. Wishart, "The generalised product moment distribution in samples from a normal multi-variate population," Biometrika, vol. 20, no. 1/2, pp. 32-52, 1928.
68. P. Hsu, "On the distribution of roots of certain determinantal equations," Annals of Human Genetics, vol. 9, no. 3, pp. 250-258, 1939.
69. U. Haagerup and S. Thorbjørnsen, "Random matrices with complex gaussian entries," Expositiones Mathematicae, vol. 21, no. 4, pp. 293-337, 2003.
70. A. Erdelyi, W. Magnus, Oberhettinger, and F. Tricomi, eds., Higher Transcendental Functions, Vol. 1-3. McGraw-Hill, 1953.
71. J. Harer and D. Zagier, "The euler characteristic of the moduli space of curves," Inventiones Mathematicae, vol. 85, no. 3, pp. 457-485, 1986.
72. R. Vershynin, "Introduction to the non-asymptotic analysis of random matrices," Arxiv preprint arXiv:1011.3027v5, July 2011.
73. D. Garling, Inequalities: a journey into linear analysis. Cambridge University Press, 2007.
74. V. Buldygin and S. Solntsev, Asymptotic behaviour of linearly transformed sums of random variables. Kluwer, 1997.
75. J. Kahane, Some random series of functions. Cambridge Univ Press, 2nd ed., 1985.
76. M. Rudelson, "Lecture notes on non-asymptotic theory of random matrices," arXiv preprint arXiv:1301.2382, 2013.
77. V. Yurinsky, Sums and Gaussian vectors. Springer-Verlag, 1995.
78. U. Haagerup, "The best constants in the khintchine inequality," Studia Math., vol. 70, pp. 231-283, 1981.
79. R. Latala, P. Mankiewicz, K. Oleszkiewicz, and N. Tomczak-Jaegermann, "Banach-mazur distances and projections on random subgaussian polytopes," Discrete & Computational Geometry, vol. 38, no. 1, pp. 29-50, 2007.
80. E. D. Gluskin and S. Kwapien, "Tail and moment estimates for sums of independent random variable," Studia Math., vol. 114, pp. 303-309, 1995.
81. M. Talagrand, The generic chaining: upper and lower bounds of stochastic processes. Springer Verlag, 2005.
82. M. Talagrand, Upper and Lower Bounds for Stochastic Processes, Modern Methods and Classical Problems. Springer-Verlag, in press. Ergebnisse der Mathematik. [75, 199]
83. R. M. Dudley, "The sizes of compact subsets of hilbert space and continuity of gaussian processes," J. Funct. Anal, vol. 1, no. 3, pp. 290-330, 1967.
84. X. Fernique, "Régularité des trajectoires des fonctions aléatoires gaussiennes," Ecole d'Eté de Probabilités de Saint-Flour IV-1974, pp. 1-96, 1975.
85. M. Talagrand, "Regularity of gaussian processes," Acta mathematica, vol. 159, no. 1, pp. 99-149, 1987.
86. R. Bhattacharya and R. Rao, Normal approximation and asymptotic expansions, vol. 64. Society for Industrial & Applied, 1986.
87. L. Chen, L. Goldstein, and Q. Shao, Normal Approximation by Stein's Method. Springer, 2010.
88. A. Kirsch, An introduction to the mathematical theory of inverse problems, vol. 120. Springer Science+ Business Media, 2011.
89. D. Porter and D. S. Stirling, Integral equations: a practical treatment, from spectral theory to applications, vol. 5. Cambridge University Press, 1990.
90. U. Grenander, Probabilities on Algebraic Structures. New York: Wiley, 1963.
91. N. Harvey, "C&o 750: Randomized algorithms winter 2011 lecture 11 notes." http://www.math.uwaterloo.ca/∼harvey/W11/, Winter 2011.
92. N. Harvey, "Lecture 12 concentration for sums of random matrices and lecture 13 the ahlswede-winter inequality." http://www.cs.ubc.ca/∼nickhar/W12/, Febuary 2012. Lecture Notes for UBC CPSC 536N: Randomized Algorithms. [87, 89, 90, 95]
93. M. Rudelson, "Random vectors in the isotropic position," Journal of Functional Analysis, vol. 164, no. 1, pp. 60-72, 1999.
94. A. Wigderson and D. Xiao, "Derandomizing the ahlswede-winter matrix-valued chernoff bound using pessimistic estimators, and applications," Theory of Computing, vol. 4, no. 1, pp. 53-76, 2008.
95. D. Gross, Y. Liu, S. Flammia, S. Becker, and J. Eisert, "Quantum state tomography via compressed sensing," Physical review letters, vol. 105, no. 15, p. 150401, 2010.
96. D. DUBHASHI and D. PANCONESI, Concentration of measure for the analysis of randomized algorithms. Cambridge Univ Press, 2009.
97. H. Ngo, "Cse 694: Probabilistic analysis and randomized algorithms." http://www.cse.buffalo. edu/∼hungngo/classes/2011/Spring-694/lectures/l4.pdf, Spring 2011. SUNY at Buffalo. [97]
98. O. Bratteli and D. W. Robinson, Operator Algebras amd Quantum Statistical Mechanics I. Springer-Verlag, 1979.
99. D. Voiculescu, K. Dykema, and A. Nica, Free Random Variables. American Mathematical Society, 1992.
100. P. J. Schreiner and L. L. Scharf, Statistical Signal Processing of Complex-Valued Data: The Theory of Improper and Noncircular Signals. Ca, 2010.
101. J. Lawson and Y. Lim, "The geometric mean, matrices, metrics, and more," The American Mathematical Monthly, vol. 108, no. 9, pp. 797-812, 2001.
102. D. Gross, "Recovering low-rank matrices from few coefficients in any basis," Information Theory, IEEE Transactions on, vol. 57, no. 3, pp. 1548-1566, 2011.
103. B. Recht, "A simpler approach to matrix completion," Arxiv preprint arxiv:0910.0651, 2009.
104. B. Recht, "A simpler approach to matrix completion," The Journal of Machine Learning Research, vol. 7777777, pp. 3413-3430, 2011.
105. R. Ahlswede and A. Winter, "Addendum to strong converse for identification via quantum channels," Information Theory, IEEE Transactions on, vol. 49, no. 1, p. 346, 2003.
106. R. Latala, "Some estimates of norms of random matrices," AMERICAN MATHEMATICAL SOCIETY, vol. 133, no. 5, pp. 1273-1282, 2005.
107. Y. Seginer, "The expected norm of random matrices," Combinatorics Probability and Computing, vol. 9, no. 2, pp. 149-166, 2000.
108. P. Massart, Concentration Inequalities and Model Selection. Springer, 2007.
109. M. Ledoux and M. Talagrand, Probability in Banach Spaces: Isoperimetry and Processes. Springer, 1991.
110. R. Motwani and P. Raghavan, Randomized Algorithms. Cambridge Univ Press, 1995.
111. A. Gittens and J. Tropp, "Tail bounds for all eigenvalues of a sum of random matrices," Arxiv preprint arXiv:1104.4513, 2011.
112. E. Lieb and R. Seiringer, "Stronger subadditivity of entropy," Physical Review A, vol. 71, no. 6, p. 062329, 2005.
113. D. Hsu, S. Kakade, and T. Zhang, "Tail inequalities for sums of random matrices that depend on the intrinsic dimension," 2011.
114. B. Schoelkopf, A. Sola, and K. Mueller, Kernl principal compnent analysis, ch. Kernl principal compnent analysis, pp. 327-352. MIT Press, 1999.
115. A. Magen and A. Zouzias, "Low rank matrix-valued chernoff bounds and approximate matrix multiplication," in Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1422-1436, SIAM, 2011.
116. S. Minsker, "On some extensions of bernstein's inequality for self-adjoint operators," Arxiv preprint arXiv:1112.5448, 2011.
117. G. Peshkir and A. Shiryaev, "The khintchine inequalities and martingale expanding sphere of their action," Russian Mathematical Surveys, vol. 50, no. 5, pp. 849-904, 1995.
118. N. Tomczak-Jaegermann, "The moduli of smoothness and convexity and the rademacher averages of trace classes," Sp (1 [p¡.) Studia Math, vol. 50, pp. 163-182, 1974.
119. p (1¡ p¡∞)," CR Acad. Sci. Paris, vol. 303, pp. 289-292, 1986.
120. G. Pisier, "Non-commutative vector valued lp-spaces and completely p-summing maps," Astérisque, vol. 247, p. 131, 1998.
121. A. Buchholz, "Operator khintchine inequality in non-commutative probability," Mathematische Annalen, vol. 319, no. 1, pp. 1-16, 2001.
122. A. So, "Moment inequalities for sums of random matrices and their applications in optimization," Mathematical programming, vol. 130, no. 1, pp. 125-151, 2011.
123. N. Nguyen, T. Do, and T. Tran, "A fast and efficient algorithm for low-rank approximation of a matrix," in Proceedings of the 41st annual ACM symposium on Theory of computing, pp. 215-224, ACM, 2009.
124. N. Nguyen, P. Drineas, and T. Tran, "Matrix sparsification via the khintchine inequality," 2009.
125. M. de Carli Silva, N. Harvey, and C. Sato, "Sparse sums of positive semidefinite matrices," 2011.
126. L. Mackey, M. Jordan, R. Chen, B. Farrell, and J. Tropp, "Matrix concentration inequalities via the method of exchangeable pairs," Arxiv preprint arXiv:1201.6002, 2012.
127. L. Rosasco, M. Belkin, and E. D. Vito, "On learning with integral operators," The Journal of Machine Learning Research, vol. 11, pp. 905-934, 2010.
128. L. Rosasco, M. Belkin, and E. De Vito, "A note on learning with integral operators," [144, 289]
129. P. Drineas and A. Zouzias, "A note on element-wise matrix sparsification via matrix-valued chernoff bounds," Preprint, 2010.
130. R. CHEN, A. GITTENS, and J. TROPP, "The masked sample covariance estimator: An analysis via matrix concentration inequalities," Information and Inference: A Journal of the IMA, pp. 1-19, 2012.
131. M. Ledoux, The Concentration of Measure Pheonomenon. American Mathematical Society, 2000.
132. D. Donoho et al., "High-dimensional data analysis: The curses and blessings of dimensionality," AMS Math Challenges Lecture, pp. 1-32, 2000.
133. S. Chatterjee, "Stein's method for concentration inequalities," Probability theory and related fields, vol. 138, no. 1, pp. 305-321, 2007.
134. B. Laurent and P. Massart, "Adaptive estimation of a quadratic functional by model selection," The annals of Statistics, vol. 28, no. 5, pp. 1302-1338, 2000.
135. G. Raskutti, M. Wainwright, and B. Yu, "Minimax rates of estimation for high-dimensional linear regression over¡ formula formulatype=," Information Theory, IEEE Transactions on, vol. 57, no. 10, pp. 6976-6994, 2011.
136. L. Birgé and P. Massart, "Minimum contrast estimators on sieves: exponential bounds and rates of convergence," Bernoulli, vol. 4, no. 3, pp. 329-375, 1998.
137. I. Johnstone, State of the Art in Probability and Statastics, vol. 31, ch. Chi-square oracle inequalities, pp. 399-418. Institute of Mathematical Statistics, ims lecture notes ed., 2001.
138. M. Wainwright, "Sharp thresholds for high-dimensional and noisy sparsity recovery using¡ formula formulatype=," Information Theory, IEEE Transactions on, vol. 55, no. 5, pp. 2183-2202, 2009.
139. A. Amini and M. Wainwright, "High-dimensional analysis of semidefinite relaxations for sparse principal components," in Information Theory, 2008. ISIT 2008. IEEE International Symposium on, pp. 2454-2458, IEEE, 2008.
140. W. Johnson and G. Schechtman, "Remarks on talagrand's deviation inequality for rademacher functions," Functional Analysis, pp. 72-77, 1991.
141. M. Ledoux, The concentration of measure phenomenon, vol. 89. Amer Mathematical Society, 2001.
142. M. Talagrand, "A new look at independence," The Annals of probability, vol. 24, no. 1, pp. 1-34, 1996.
143. S. Chatterjee, "Matrix estimation by universal singular value thresholding," arXiv preprint arXiv:1212.1247, 2012.
144. R. Bhatia, C. Davis, and A. McIntosh, "Perturbation of spectral subspaces and solution of linear operator equations," Linear Algebra and its Applications, vol. 52, pp. 45-67, 1983.
145. K. Davidson and S. Szarek, "Local operator theory, random matrices and banach spaces," Handbook of the geometry of Banach spaces, vol. 1, pp. 317-366, 2001.
146. A. DasGupta, Probability for Statistics and Machine Learning. Springer, 2011.
147. W. Hoeffding, "A combinatorial central limit theorem," The Annals of Mathematical Statistics, vol. 22, no. 4, pp. 558-566, 1951.
148. M. Talagrand, "Concentration of measure and isoperimetric inequalities in product spaces," Publications Mathematiques de l'IHES, vol. 81, no. 1, pp. 73-205, 1995.
149. M. Ledoux, "Deviation inequalities on largest eigenvalues," Geometric aspects of functional analysis, pp. 167-219, 2007.
150. H. Rauhut, Theoretical Foundations and Numerical Method for Sparse Recovery, ch. Compressed Sensing and Structured Random Matrices, pp. 1-92. Berlin/New York: De Gruyter, 2010.
151. J.-M. Azäis and M. Wschebor, Level sets and extrema of random processes and fields. Wiley, 2009.
152. G. Pisier, The volume of convex bodies and Banach space geometry, vol. 94. Cambridge Univ Pr, 1999.
153. Y. Gordon, A. Litvak, S. Mendelson, and A. Pajor, "Gaussian averages of interpolated bodies and applications to approximate reconstruction," Journal of Approximation Theory, vol. 149, no. 1, pp. 59-73, 2007.
154. J. Matousek, Lectures on discrete geometry, vol. 212. Springer, 2002.
155. S. Negahban and M. Wainwright, "Estimation of (near) low-rank matrices with noise and high-dimensional scaling," The Annals of Statistics, vol. 39, no. 2, pp. 1069-1097, 2011.
156. P. Zhang and R. Qiu, "Glrt-based spectrum sensing with blindly learned feature under rank-1 assumption," IEEE Trans. Communications. to appear. [177, 233, 347, 514]
157. P. Zhang, R. Qiu, and N. Guo, "Demonstration of Spectrum Sensing with Blindly Learned Feature," IEEE Communications Letters, vol. 15, pp. 548-550, May 2011.
158. S. Hou, R. Qiu, J. P. Browning, and Wick, "Spectrum sensing in cognitive radio with robust principal component analysis," in IEEE Waveform Diversity and Design Conference 2012, (Kauai, Hawaii), January 2012.
159. S. Hou, R. Qiu, J. P. Browning, and M. C. Wicks, "Spectrum sensing in cognitive radio with subspace matching," in IEEE Waveform Diversity and Design Conference 2012, (Kauai, Hawaii), January 2012.
160. S. Hou, R. Qiu, Z. Chen, and Z. Hu, "SVM and Dimensionality Reduction in Cognitive Radio with Experimental Validation," Arxiv preprint arXiv:1106.2325, submitted to EURASIP Journal on Advances in Signal Processing, 2011.
161. P. Massart, "Concentration inequalities and model selection," 2007.
162. L. Birgé, "An alternative point of view on lepski's method," Lecture Notes-Monograph Series, pp. 113-133, 2001.
163. N. Karoui, "Operator norm consistent estimation of large-dimensional sparse covariance matrices," The Annals of Statistics, pp. 2717-2756, 2008.
164. P. Loh and M. Wainwright, "High-dimensional regression with noisy and missing data: Provable guarantees with non-convexity," arXiv preprint arXiv:1109.3714, 2011.
165. E. Meckes, "Approximation of projections of random vectors," Journal of Theoretical Probability, vol. 25, no. 2, pp. 333-352, 2012.
166. A. Efimov, "Modulus of continuity," Encyclopaedia of Mathematics. Springer, 2001.
167. V. Milman and G. Schechtman, Asymptotic theory of finite dimensional normed spaces, vol. 1200. Springer Verlag, 1986.
168. E. Meckes, "Projections of probability distributions: A measure-theoretic dvoretzky theorem," Geometric Aspects of Functional Analysis, pp. 317-326, 2012.
169. O. Bousquet, "A bennett concentration inequality and its application to suprema of empirical processes," Comptes Rendus Mathematique, vol. 334, no. 6, pp. 495-500, 2002.
170. O. Bousquet, Concentration inequalities and empirical processes theory applied to the analysis of learning algorithms. PhD thesis, PhD thesis, Ecole Polytechnique, 2002.
171. S. Boucheron, G. Lugosi, and O. Bousquet, "Concentration inequalities," Advanced Lectures on Machine Learning, pp. 208-240, 2004.
172. M. Ledoux, "On talagrand's deviation inequalities for product measures," ESAIM: Probability and statistics, vol. 1, pp. 63-87, 1996.
173. P. Massart, "About the constants in talagrand's concentration inequalities for empirical processes," Annals of Probability, pp. 863-884, 2000.
174. E. Rio, "Inégalités de concentration pour les processus empiriques de classes de parties," Probability Theory and Related Fields, vol. 119, no. 2, pp. 163-175, 2001.
175. S. Boucheron, O. Bousquet, G. Lugosi, and P. Massart, "Moment inequalities for functions of independent random variables," The Annals of Probability, vol. 33, no. 2, pp. 514-560, 2005.
176. S. Boucheron, O. Bousquet, G. Lugosi, et al., "Theory of classification: A survey of some recent advances," ESAIM Probability and statistics, vol. 9, pp. 323-375, 2005.
177. S. Boucheron, G. Lugosi, P. Massart, et al., "On concentration of self-bounding functions," Electronic Journal of Probability, vol. 14, no. 64, pp. 1884-1899, 2009.
178. S. Boucheron, P. Massart, et al., "A high-dimensional wilks phenomenon," Probability theory and related fields, vol. 150, no. 3, p. 405, 2011.
179. A. Connes, "Classification of injective factors," Ann. of Math, vol. 104, no. 2, pp. 73-115, 1976.
180. A. Guionnet and O. Zeitouni, "Concentration of the spectral measure for large matrices," Electron. Comm. Probab, vol. 5, pp. 119-136, 2000.
181. I. N. Bronshtein, K. A. Semendiaev, and K. A. Hirsch, Handbook of mathematics. Van Nostrand Reinhold New York, NY, 5th ed., 2007.
182. A. Khajehnejad, S. Oymak, and B. Hassibi, "Subspace expanders and matrix rank minimization," arXiv preprint arXiv:1102.3947, 2011.
183. M. Meckes, "Concentration of norms and eigenvalues of random matrices," Journal of Functional Analysis, vol. 211, no. 2, pp. 508-524, 2004.
184. C. Davis, "All convex invariant functions of hermitian matrices," Archiv der Mathematik, vol. 8, no. 4, pp. 276-278, 1957.
185. L. Li, "Concentration of measure for random matrices." private communication, October 2012. Tenneessee Technological University. [207]
186. N. Berestycki and R. Nickl, "Concentration of measure," tech. rep., Technical report, University of Cambridge, 2009.
187. R. A. Horn and C. R. Johnson, Matrix Analysis. Cambridge University Press, 1994.
188. Y. Zeng and Y. Liang, "Maximum-minimum eigenvalue detection for cognitive radio," in IEEE 18th International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC) 2007, pp. 1-5, 2007.
189. V. Petrov and A. Brown, Sums of independent random variables, vol. 197. Springer-Verlag Berlin, 1975.
190. M. Meckes and S. Szarek, "Concentration for noncommutative polynomials in random matrices," in Proc. Amer. Math. Soc, vol. 140, pp. 1803-1813, 2012.
191. G. W. Anderson, "Convergence of the largest singular value of a polynomial in independent wigner matrices," arXiv preprint arXiv:1103.4825, 2011.
192. E. Meckes and M. Meckes, "Concentration and convergence rates for spectral measures of random matrices," Probability Theory and Related Fields, pp. 1-20, 2011.
193. R. Serfling, "Approximation theorems of mathematical statistics (wiley series in probability and statistics)," 1981.
194. R. Latala, "Some estimates of norms of random matrices," Proceedings of the American Mathematical Society, pp. 1273-1282, 2005.
195. S. Lang, Real and functional analysis. 1993.
196. A. Guntuboyina and H. Leeb, "Concentration of the spectral measure of large wishart matrices with dependent entries," Electron. Commun. Probab, vol. 14, pp. 334-342, 2009.
197. M. Ledoux, "Concentration of measure and logarithmic sobolev inequalities," Seminaire de probabilites XXXIII, pp. 120-216, 1999.
198. Z. Bai, "Methodologies in spectral analysis of large-dimensional random matrices, a review," Statist. Sinica, vol. 9, no. 3, pp. 611-677, 1999.
199. B. Delyon, "Concentration inequalities for the spectral measure of random matrices," Electronic Communications in Probability, pp. 549-562, 2010.
200. F. Lin, R. Qiu, Z. Hu, S. Hou, J. P. Browning, and M. C. Wicks," Cognitive Radio Network as Sensors: Low Signal-to-Noise Ratio Collaborative Spectrum Sensing," in IEEE Waveform Diversity and Design Conference, 2012. Kauai, Hawaii. [226]
201. S. Chatterjee, "Fluctuations of eigenvalues and second order poincaré inequalities," Probability Theory and Related Fields, vol. 143, no. 1, pp. 1-40, 2009.
202. S. Chatterjee, "A new method of normal approximation," The Annals of Probability, vol. 36, no. 4, pp. 1584-1610, 2008.
203. I. Johnstone, "High dimensional statistical inference and random matrices," Arxiv preprint math/0611589, 2006.
204. T. Jiang, "Approximation of haar distributed matrices and limiting distributions of eigenvalues of jacobi ensembles," Probability theory and related fields, vol. 144, no. 1, pp. 221-246, 2009.
205. R. Bhatia, L. Elsner, and G. Krause, "Bounds for the variation of the roots of a polynomial and the eigenvalues of a matrix," Linear Algebra and Its Applications, vol. 142, pp. 195-209, 1990.
206. N. Gozlan, "A characterization of dimension free concentration in terms of transportation inequalities," The Annals of Probability, vol. 37, no. 6, pp. 2480-2498, 2009.
207. P. Deift and D. Gioev, Random matrix theory: invariant ensembles and universality, vol. 18. Amer Mathematical Society, 2009.
208. G. W. Anderson, A. Guionnet, and O. Zeitouni, An Introduction to Random Matrices. Cambridge University Press, 2010.
209. R. Speicher, Free probability theory and non-crossing partitions. 39 Seminaire Lotharingien de Combinatoire, 1997.
210. V. Kargin, "A concentration inequality and a local law for the sum of two random matrices," Probability Theory and Related Fields, pp. 1-26, 2010.
211. H. Weyl, "Das asymptotische verteilungsgesetz der eigenwerte linearer partieller differentialgleichungen (mit einer anwendung auf die theorie der hohlraumstrahlung)," Mathematische Annalen, vol. 71, no. 4, pp. 441-479, 1912.
212. A. Horn, "Eigenvalues of sums of hermitian matrices," Pacific J. Math, vol. 12, no. 1, 1962.
213. S. Chatterjee, "Concentration of haar measures, with an application to random matrices," Journal of Functional Analysis, vol. 245, no. 2, pp. 379-389, 2007.
214. S. Chatterjee and M. Ledoux, "An observation about submatrices," Electronic Communications in Probability, vol. 14, pp. 495-500, 2009.
215. E. Wigner, "On the distribution of the roots of certain symmetric matrices," The Annals of Mathematics, vol. 67, no. 2, pp. 325-327, 1958.
216. A. Soshnikov, "Universality at the edge of the spectrum of in wigner random matrices," Communications in mathematical physics, vol. 207, pp. 897-733, 1999.
217. A. Soshnikov, "Poisson statistics for the largest eigenvalues of wigner random matrices with heavy tails," Electron. Comm. Probab, vol. 9, pp. 82-91, 2004.
218. A. Soshnikov, "A note on universality of the distribution of the largest eigenvalues in certain sample covariance matrices," Journal of Statistical Physics, vol. 108, no. 5, pp. 1033-1056, 2002.
219. A. Soshnikov, "Level spacings distribution for large random matrices: Gaussianfluctuations," Annals of mathematics, pp. 573-617, 1998.
220. A. Soshnikov and Y. Fyodorov, "On the largest singular values of random matrices with independent cauchy entries," Journal of mathematical physics, vol. 46, p. 033302, 2005.
221. T. Tao and V. Vu, "Random covariance matrices: Universality of local statistics of eigenvalues," Arxiv preprint arxiv:0912.0966, 2009.
222. Z. Füredi and J. Komlós, "The eigenvalues of random symmetric matrices," Combinatorica, vol. 1, no. 3, pp. 233-241, 1981.
223. M. Krivelevich and V. Vu, "Approximating the independence number and the chromatic number in expected polynomial time," Journal of combinatorial optimization, vol. 6, no. 2, pp. 143-155, 2002.
224. A. Guionnet, "Lecture notes, minneapolis," 2012.
225. C. Bordenave, P. Caputo, and D. Chafäi, "Spectrum of non-hermitian heavy tailed random matrices," Communications in Mathematical Physics, vol. 307, no. 2, pp. 513-560, 2011.
226. A. Guionnet and B. Zegarlinski, "Lectures on logarithmic sobolev inequalities," S éminaire de Probabilités, XXXVI, vol. 1801, pp. 1-134, 1801.
227. D. Ruelle, Statistical mechanics: rigorous results. Amsterdam: Benjamin, 1969.
228. T. Tao and V. Vu, "Random matrices: Sharp concentration of eigenvalues," Arxiv preprint arXiv:1201.4789, 2012.
229. N. El Karoui, "Concentration of measure and spectra of random matrices: applications to correlation matrices, elliptical distributions and beyond," The Annals of Applied Probability, vol. 19, no. 6, pp. 2362-2405, 2009.
230. N. El Karoui, "The spectrum of kernel random matrices," The Annals of Statistics, vol. 38, no. 1, pp. 1-50, 2010.
231. M. Talagrand, "New concentration inequalities in product spaces," Inventiones Mathematicae, vol. 126, no. 3, pp. 505-563, 1996.
232. L. Birgé and P. Massart, "Gaussian model selection," Journal of the European Mathematical Society, vol. 3, no. 3, pp. 203-268, 2001.
233. L. Birgé and P. Massart, "Minimal penalties for gaussian model selection," Probability theory and related fields, vol. 138, no. 1, pp. 33-73, 2007.
234. P. Massart, "Some applications of concentration inequalities to statistics," in Annales-Faculte des Sciences Toulouse Mathematiques, vol. 9, pp. 245-303, Université Paul Sabatier, 2000.
235. I. Bechar, "A bernstein-type inequality for stochastic processes of quadratic forms of gaussian variables," arXiv preprint arXiv:0909.3595, 2009.
236. K. Wang, A. So, T. Chang, W. Ma, and C. Chi, "Outage constrained robust transmit optimization for multiuser miso downlinks: Tractable approximations by conic optimization," arXiv preprint arXiv:1108.0982, 2011.
237. M. Lopes, L. Jacob, and M. Wainwright, "A more powerful two-sample test in high dimensions using random projection," arXiv preprint arXiv:1108.2401, 2011.
238. W. Beckner, "A generalized poincaré inequality for gaussian measures," Proceedings of the American Mathematical Society, pp. 397-400, 1989.
239. M. Rudelson and R. Vershynin, "Invertibility of random matrices: unitary and orthogonal perturbations," arXiv preprint arXiv:1206.5180, June 2012. Version 1. [257, 334]
240. T. Tao and V. Vu, "Random matrices: Universality of local eigenvalue statistics," Acta mathematica, pp. 1-78, 2011.
241. T. Tao and V. Vu, "Random matrices: The distribution of the smallest singular values," Geometric And Functional Analysis, vol. 20, no. 1, pp. 260-297, 2010.
242. T. Tao and V. Vu, "On random±1 matrices: singularity and determinant," Random Structures & Algorithms, vol. 28, no. 1, pp. 1-23, 2006.
243. J. Silverstein and Z. Bai, "On the empirical distribution of eigenvalues of a class of large dimensional random matrices," Journal of Multivariate analysis, vol. 54, no. 2, pp. 175-192, 1995.
244. J. Von Neumann, Mathematische grundlagen der quantenmechanik, vol. 38. Springer, 1995.
245. J. Cadney, N. Linden, and A. Winter, "Infinitely many constrained inequalities for the von neumann entropy," Information Theory, IEEE Transactions on, vol. 58, no. 6, pp. 3657-3663, 2012.
246. H. Araki and E. Lieb, "Entropy inequalities," Communications in Mathematical Physics, vol. 18, no. 2, pp. 160-170, 1970.
247. E. Lieb and M. Ruskai, "A fundamental property of quantum-mechanical entropy," Physical Review Letters, vol. 30, no. 10, pp. 434-436, 1973.
248. E. Lieb and M. Ruskai, "Proof of the strong subadditivity of quantum-mechanical entropy," Journal of Mathematical Physics, vol. 14, pp. 1938-1941, 1973.
249. N. Pippenger, "The inequalities of quantum information theory," Information Theory, IEEE Transactions on, vol. 49, no. 4, pp. 773-789, 2003.
250. T. Chan, "Recent progresses in characterising information inequalities," Entropy, vol. 13, no. 2, pp. 379-401, 2011.
251. T. Chan, D. Guo, and R. Yeung, "Entropy functions and determinant inequalities," in Information Theory Proceedings (ISIT), 2012 IEEE International Symposium on, pp. 1251-1255, IEEE, 2012.
252. R. Yeung, "Facts of entropy," IEEE Information Theory Society Newsletter, pp. 6-15, December 2012.
253. C. Williams and M. Seeger, "The effect of the input density distribution on kernel-based classifiers," in Proceedings of the 17th International Conference on Machine Learning, Citeseer, 2000.
254. J. Shawe-Taylor, N. Cristianini, and J. Kandola, "On the concentration of spectral properties," Advances in neural information processing systems, vol. 1, pp. 511-518, 2002.
255. J. Shawe-Taylor, C. Williams, N. Cristianini, and J. Kandola, "On the eigenspectrum of the gram matrix and the generalization error of kernel-pca," Information Theory, IEEE Transactions on, vol. 51, no. 7, pp. 2510-2522, 2005.
256. Y. Do and V. Vu, "The spectrum of random kernel matrices," arXiv preprint arXiv:1206.3763, 2012.
257. X. Cheng and A. Singer, "The spectrum of random inner-product kernel matrices," arXiv:1202.3155v1 [math.PR], p. 40, 2012.
258. N. Ross et al., "Fundamentals of stein's method," Probability Surveys, vol. 8, pp. 210-293, 2011.
259. Z. Chen and J. Dongarra, "Condition numbers of gaussian random matrices," Arxiv preprint arXiv:0810.0800, 2008.
260. M. Junge and Q. Zeng, "Noncommutative bennett and rosenthal inequalities," Arxiv preprint arXiv:1111.1027, 2011.
261. A. Giannopoulos, "Notes on isotropic convex bodies," Warsaw University Notes, 2003.
262. Y. D. Burago, V. A. Zalgaller, and A. Sossinsky, Geometric inequalities, vol. 1988. Springer Berlin, 1988.
263. R. Schneider, Convex bodies: the Brunn-Minkowski theory, vol. 44. Cambridge Univ Pr, 1993.
264. V. Milman and A. Pajor, "Isotropic position and inertia ellipsoids and zonoids of the unit ball of a normed n-dimensional space," Geometric aspects of functional analysis, pp. 64-104, 1989.
265. C. Borell, "The brunn-minkowski inequality in gauss space," Inventiones Mathematicae, vol. 30, no. 2, pp. 207-216, 1975.
266. R. Kannan, L. Lovász, and M. Simonovits, "Random walks and an o∗(n5) volume algorithm for convex bodies," Random structures and algorithms, vol. 11, no. 1, pp. 1-50, 1997.
267. O. Guédon and M. Rudelson, "Lp-moments of random vectors via majorizing measures," Advances in Mathematics, vol. 208, no. 2, pp. 798-823, 2007.
268. C. Borell, "Convex measures on locally convex spaces," Arkiv för Matematik, vol. 12, no. 1, pp. 239-252, 1974.
269. C. Borell, "Convex set functions ind-space," Periodica Mathematica Hungarica, vol. 6, no. 2, pp. 111-136, 1975.
270. A. Prékopa, "Logarithmic concave measures with application to stochastic programming," Acta Sci. Math.(Szeged), vol. 32, no. 197, pp. 301-3, 1971.
271. S. Vempala, "Recent progress and open problems in algorithmic convex geometry," in =IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010), Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2010.
272. G. Paouris, "Concentration of mass on convex bodies," Geometric and Functional Analysis, vol. 16, no. 5, pp. 1021-1049, 2006.
273. J. Bourgain, "Random points in isotropic convex sets," Convex geometric analysis, Berkeley, CA, pp. 53-58, 1996.
274. S. Mendelson and A. Pajor, "On singular values of matrices with independent rows," Bernoulli, vol. 12, no. 5, pp. 761-773, 2006.
275. S. Alesker, "Phi 2-estimate for the euclidean norm on a convex body in isotropic position," Operator theory, vol. 77, pp. 1-4, 1995.
276. F. Lust-Piquard and G. Pisier, "Non commutative khintchine and paley inequalities," Arkiv f ör Matematik, vol. 29, no. 1, pp. 241-260, 1991.
277. F. Cucker and D. X. Zhou, Learning theory: an approximation theory viewpoint, vol. 24. Cambridge University Press, 2007.
278. V. Koltchinskii and E. Giné, "Random matrix approximation of spectra of integral operators," Bernoulli, vol. 6, no. 1, pp. 113-167, 2000.
279. S. Mendelson, "On the performance of kernel classes," The Journal of Machine Learning Research, vol. 4, pp. 759-771, 2003.
280. R. Kress, Linear Integral Equations. Berlin: Springer-Verlag, 1989.
281. G. W. Hanson and A. B. Yakovlev, Operator theory for electromagnetics: an introduction. Springer Verlag, 2002.
282. R. C. Qiu, Z. Hu, M. Wicks, L. Li, S. J. Hou, and L. Gary, "Wireless Tomography, Part II: A System Engineering Approach," in 5th International Waveform Diversity & Design Conference, (Niagara Falls, Canada), August 2010.
283. R. C. Qiu, M. C. Wicks, L. Li, Z. Hu, and S. J. Hou, "Wireless Tomography, Part I: A NovelApproach to Remote Sensing," in 5th International Waveform Diversity & Design Conference, (Niagara Falls, Canada), August 2010.
284. E. De Vito, L. Rosasco, A. Caponnetto, U. De Giovannini, and F. Odone, "Learning from examples as an inverse problem," Journal of Machine Learning Research, vol. 6, no. 1, p. 883, 2006.
285. E. De Vito, L. Rosasco, and A. Toigo, "Learning sets with separating kernels," arXiv preprint arXiv:1204.3573, 2012.
286. E. De Vito, V. Umanità, and S. Villa, "An extension of mercer theorem to matrix-valued measurable kernels," Applied and Computational Harmonic Analysis, 2012.
287. E. De Vito, L. Rosasco, and A. Toigo, "A universally consistent spectral estimator for the support of a distribution," [290]
288. R. Latala, "Weak and strong moments of random vectors," Marcinkiewicz Centenary Volume, Banach Center Publ., vol. 95, pp. 115-121, 2011.
289. R. Latala, "Order statistics and concentration of lr norms for log-concave vectors," Journal of Functional Analysis, 2011.
290. R. Adamczak, R. Latala, A. E. Litvak, A. Pajor, and N. Tomczak-Jaegermann, "Geometry of log-concave ensembles of random matrices and approximate reconstruction," Comptes Rendus Mathematique, vol. 349, no. 13, pp. 783-786, 2011.
291. R. Adamczak, R. Latala, A. E. Litvak, K. Oleszkiewicz, A. Pajor, and N. Tomczak-Jaegermann, "A short proof of paouris' inequality," arXiv preprint arXiv:1205.2515, 2012.
292. J. Bourgain, "On the distribution of polynomials on high dimensional convex sets," Geometric aspects of functional analysis, pp. 127-137, 1991.
293. B. Klartag, "An isomorphic version of the slicing problem," Journal of Functional Analysis, vol. 218, no. 2, pp. 372-394, 2005.
294. S. Bobkov and F. Nazarov, "On convex bodies and log-concave probability measures with unconditional basis," Geometric aspects of functional analysis, pp. 53-69, 2003.
295. S. Bobkov and F. Nazarov, "Large deviations of typical linear functionals on a convex body with unconditional basis," Progress in Probability, pp. 3-14, 2003.
296. A. Giannopoulos, M. Hartzoulaki, and A. Tsolomitis, "Random points in isotropic unconditional convex bodies," Journal of the London Mathematical Society, vol. 72, no. 3, pp. 779-798, 2005.
297. G. Aubrun, "Sampling convex bodies: a random matrix approach," Proceedings of the American Mathematical Society, vol. 135, no. 5, pp. 1293-1304, 2007.
298. R. Adamczak, "A tail inequality for suprema of unbounded empirical processes with applications to markov chains," Electron. J. Probab, vol. 13, pp. 1000-1034, 2008.
299. R. Adamczak, A. Litvak, A. Pajor, and N. Tomczak-Jaegermann, "Sharp bounds on the rate of convergence of the empirical covariance matrix," Comptes Rendus Mathematique, 2011.
300. R. Adamczak, R. Latala, A. E. Litvak, A. Pajor, and N. Tomczak-Jaegermann, "Tail estimates for norms of sums of log-concave random vectors," arXiv preprint arXiv:1107.4070, 2011.
301. R. Adamczak, A. E. Litvak, A. Pajor, and N. Tomczak-Jaegermann, "Quantitative estimates of the convergence of the empirical covariance matrix in log-concave ensembles," Journal of the American Mathematical Society, vol. 23, no. 2, p. 535, 2010.
302. Z. Bai and Y. Yin, "Limit of the smallest eigenvalue of a large dimensional sample covariance matrix," The annals of Probability, pp. 1275-1294, 1993.
303. R. Kannan, L. Lovász, and M. Simonovits, "Isoperimetric problems for convex bodies and a localization lemma," Discrete & Computational Geometry, vol. 13, no. 1, pp. 541-559, 1995.
304. G. Paouris, "Small ball probability estimates for log-concave measures," Trans. Amer. Math. Soc, vol. 364, pp. 287-308, 2012.
305. J. A. Clarkson, "Uniformly convex spaces," Transactions of the American Mathematical Society, vol. 40, no. 3, pp. 396-414, 1936.
306. Y. Gordon, "Gaussian processes and almost spherical sections of convex bodies," The Annals of Probability, pp. 180-188, 1988.
307. n. Springer, 1988. Geometric aspects of functional analysis (1986/87), 84-106, Lecture Notes in Math., 1317.
308. R. Adamczak, O. Guedon, R. Latala, A. E. Litvak, K. Oleszkiewicz, A. Pajor, and N. Tomczak-Jaegermann, "Moment estimates for convex measures," arXiv preprint arXiv:1207.6618, 2012.
309. A. Pajor and N. Tomczak-Jaegermann, "Chevet type inequality and norms of sub-matrices," [303]
310. N. Srivastava and R. Vershynin, "Covariance estimation for distributions with 2+\ epsilon moments," Arxiv preprint arXiv:1106.2775, 2011.
311. M. Rudelson and R. Vershynin, "Sampling from large matrices: An approach through geometric functional analysis," Journal of the ACM (JACM), vol. 54, no. 4, p. 21, 2007.
312. A. Frieze, R. Kannan, and S. Vempala, "Fast monte-carlo algorithms for finding low-rank approximations," Journal of the ACM (JACM), vol. 51, no. 6, pp. 1025-1041, 2004.
313. P. Drineas, R. Kannan, and M. Mahoney, "Fast monte carlo algorithms for matrices i: Approximating matrix multiplication," SIAM Journal on Computing, vol. 36, no. 1, p. 132, 2006.
314. P. Drineas, R. Kannan, and M. Mahoney, "Fast monte carlo algorithms for matrices ii: Computing a low-rank approximation to a matrix," SIAM Journal on Computing, vol. 36, no. 1, p. 158, 2006.
315. P. Drineas, R. Kannan, M. Mahoney, et al., "Fast monte carlo algorithms for matrices iii: Computing a compressed approximate matrix decomposition," SIAM Journal on Computing, vol. 36, no. 1, p. 184, 2006.
316. P. Drineas and R. Kannan, "Pass efficient algorithms for approximating large matrices," in Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms, pp. 223-232, Society for Industrial and Applied Mathematics, 2003.
317. P. Drineas, A. Frieze, R. Kannan, S. Vempala, and V. Vinay, "Clustering large graphs via the singular value decomposition," Machine Learning, vol. 56, no. 1, pp. 9-33, 2004.
318. V. Mil'man, "New proof of the theorem of a. dvoretzky on intersections of convex bodies," Functional Analysis and its Applications, vol. 5, no. 4, pp. 288-295, 1971.
319. K. Ball, "An elementary introduction to modern convex geometry," Flavors of geometry, vol. 31, pp. 1-58, 1997.
320. R. Vershynin, "Approximating the moments of marginals of high-dimensional distributions," The Annals of Probability, vol. 39, no. 4, pp. 1591-1606, 2011.
321. P. Youssef, "Estimating the covariance of random matrices," arXiv preprint arXiv:1301.6607, 2013.
322. M. Rudelson and R. Vershynin, "Smallest singular value of a random rectangular matrix," Communications on Pure and Applied Mathematics, vol. 62, no. 12, pp. 1707-1739, 2009.
323. R. Vershynin, "Spectral norm of products of random and deterministic matrices," Probability theory and related fields, vol. 150, no. 3, p. 471, 2011.
324. O. Feldheim and S. Sodin, "A universality result for the smallest eigenvalues of certain sample covariance matrices," Geometric And Functional Analysis, vol. 20, no. 1, pp. 88-123, 2010.
325. M. Lai and Y. Liu, "The probabilistic estimates on the largest and smallest q-singular values of pre-gaussian random matrices," submitted to Advances in Mathematics, 2010.
326. T. Tao and V. Vu, "Random matrices: The distribution of the smallest singular values," Geometric And Functional Analysis, vol. 20, no. 1, pp. 260-297, 2010.
327. D. CHAFAI, "Singular values of random matrices," Lecture Notes, November 2009. Univer-sité Paris-Est Marne-la-Vallée. []
328. M. LAI and Y. LIU, "A study on the largest and smallest q-singular values of random matrices," []
329. A. Litvak and O. Rivasplata, "Smallest singular value of sparse random matrices," Arxiv preprint arXiv:1106.0938, 2011.
330. R. Vershynin, "Invertibility of symmetric random matrices," Arxiv preprint arXiv:1102.0300, 2011.
331. H. Nguyen and V. Vu, "Optimal inverse littlewood-offord theorems," Advances in Mathematics, 2011.
332. Y. Eliseeva, F. Götze, and A. Zaitsev, "Estimates for the concentration functions in the littlewood-offord problem," Arxiv preprint arXiv:1203.6763, 2012.
333. S. Mendelson and G. Paouris, "On the singular values of random matrices," Preprint, 2012.
334. J. Silverstein, "The smallest eigenvalue of a large dimensional wishart matrix," The Annals of Probability, vol. 13, no. 4, pp. 1364-1368, 1985.
335. M. Rudelson and R. Vershynin, "Non-asymptotic theory of random matrices: extreme singular values," Arxiv preprint arXiv:1003.2990, 2010.
336. G. Aubrun, "A sharp small deviation inequality for the largest eigenvalue of a random matrix," S éminaire de Probabilités XXXVIII, pp. 320-337, 2005.
337. G. Bennett, L. Dor, V. Goodman, W. Johnson, and C. Newman, "On uncomplemented subspaces of lp, 1¡ p¡ 2," Israel Journal of Mathematics, vol. 26, no. 2, pp. 178-187, 1977.
338. A. Litvak, A. Pajor, M. Rudelson, and N. Tomczak-Jaegermann, "Smallest singular value of random matrices and geometry of random polytopes," Advances in Mathematics, vol. 195, no. 2, pp. 491-523, 2005.
339. S. Artstein-Avidan, O. Friedland, V. Milman, and S. Sodin, "Polynomial bounds for large bernoulli sections of l1 n," Israel Journal of Mathematics, vol. 156, no. 1, pp. 141-155, 2006.
340. M. Rudelson, "Lower estimates for the singular values of random matrices," Comptes Rendus Mathematique, vol. 342, no. 4, pp. 247-252, 2006.
341. M. Rudelson and R. Vershynin, "The littlewood-offord problem and invertibility of random matrices," Advances in Mathematics, vol. 218, no. 2, pp. 600-633, 2008.
342. R. Vershynin, "Some problems in asymptotic convex geometry and random matrices motivated by numerical algorithms," Arxiv preprint cs/0703093, 2007.
343. M. Rudelson and O. Zeitouni, "Singular values of gaussian matrices and permanent estimators," arXiv preprint arXiv:1301.6268, 2013.
344. Y. Yin, Z. Bai, and P. Krishnaiah, "On the limit of the largest eigenvalue of the large dimensional sample covariance matrix," Probability Theory and Related Fields, vol. 78, no. 4, pp. 509-521, 1988.
345. Z. Bai and J. Silverstein, "No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices," The Annals of Probability, vol. 26, no. 1, pp. 316-345, 1998.
346. Z. Bai and J. Silverstein, "Exact separation of eigenvalues of large dimensional sample covariance matrices," The Annals of Probability, vol. 27, no. 3, pp. 1536-1555, 1999.
347. H. Nguyen and V. Vu, "Random matrices: Law of the determinant," Arxiv preprint arXiv:1112.0752, 2011.
348. A. Rouault, "Asymptotic behavior of random determinants in the laguerre, gram and jacobi ensembles," Latin American Journal of Probability and Mathematical Statistics (ALEA), vol. 3, pp. 181-230, 2007.
349. N. Goodman, "The distribution of the determinant of a complex wishart distributed matrix," Annals of Mathematical Statistics, pp. 178-180, 1963.
350. O. Friedland and O. Giladi, "A simple observation on random matrices with continuous diagonal entries," arXiv preprint arXiv:1302.0388, 2013.
351. J. Bourgain, V. H. Vu, and P. M. Wood, "On the singularity probability of discrete random matrices," Journal of Functional Analysis, vol. 258, no. 2, pp. 559-603, 2010.
352. T. Tao and V. Vu, "From the littlewood-offord problem to the circular law: universality of the spectral distribution of random matrices," Bulletin of the American Mathematical Society, vol. 46, no. 3, p. 377, 2009.
353. R. Adamczak, O. Guédon, A. Litvak, A. Pajor, and N. Tomczak-Jaegermann, "Smallest singular value of random matrices with independent columns," Comptes Rendus Mathematique, vol. 346, no. 15, pp. 853-856, 2008.
354. R. law Adamczak, O. Guédon, A. Litvak, A. Pajor, and N. Tomczak-Jaegermann, "Condition number of a square matrix with iid columns drawn from a convex body," Proc. Amer. Math. Soc., vol. 140, pp. 987-998, 2012.
355. L. Erdos, B. Schlein, and H.-T. Yau, "Wegner estimate and level repulsion for wigner random matrices," International Mathematics Research Notices, vol. 2010, no. 3, pp. 436-479, 2010.
356. B. Farrell and R. Vershynin, "Smoothed analysis of symmetric random matrices with continuous distributions," arXiv preprint arXiv:1212.3531, 2012.
357. A. Maltsev and B. Schlein, "A wegner estimate for wigner matrices," Entropy and the Quantum II, vol. 552, p. 145, 2011.
358. H. H. Nguyen, "Inverse littlewood-offord problems and the singularity of random symmetric matrices," Duke Mathematical Journal, vol. 161, no. 4, pp. 545-586, 2012.
359. H. H. Nguyen, "On the least singular value of random symmetric matrices," Electron. J. Probab., vol. 17, pp. 1-19, 2012.
360. R. Vershynin, "Invertibility of symmetric random matrices," Random Structures & Algorithms, 2012.
361. A. Sankar, D. Spielman, and S. Teng, "Smoothed analysis of the condition numbers and growth factors of matrices," SIAM J. Matrix Anal. Appl., vol. 2, pp. 446-476, 2006.
362. T. Tao and V. Vu, "Smooth analysis of the condition number and the least singular value," Mathematics of Computation, vol. 79, no. 272, pp. 2333-2352, 2010.
363. K. P. Costello and V. Vu, "Concentration of random determinants and permanent estimators," SIAM Journal on Discrete Mathematics, vol. 23, no. 3, pp. 1356-1371, 2009.
364. T. Tao and V. Vu, "On the permanent of random bernoulli matrices," Advances in Mathematics, vol. 220, no. 3, pp. 657-669, 2009.
365. A. H. Taub, "John von neumann: Collected works, volume v: Design of computers, theory of automata and numerical analysis," 1963.
366. S. Smale, "On the efficiency of algorithms of analysis," Bull. Amer. Math. Soc.(NS), vol. 13, 1985.
367. A. Edelman, "Eigenvalues and condition numbers of random matrices," SIAM Journal on Matrix Analysis and Applications, vol. 9, no. 4, pp. 543-560, 1988.
368. S. J. Szarek, "Condition numbers of random matrices," J. Complexity, vol. 7, no. 2, pp. 131-149, 1991.
369. D. Spielman and S. Teng, "Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time," Journal of the ACM (JACM), vol. 51, no. 3, pp. 385-463, 2004.
370. L. Erdos, "Universality for random matrices and log-gases," arXiv preprint arXiv:1212.0839, 2012.
371. J. Von Neumann and H. Goldstine, "Numerical inverting of matrices of high order," Bull. Amer. Math. Soc, vol. 53, no. 11, pp. 1021-1099, 1947.
372. A. Edelman, Eigenvalues and condition numbers of random matrices. PhD thesis, Massachusetts Institute of Technology, 1989.
373. P. Forrester, "The spectrum edge of random matrix ensembles," Nuclear Physics B, vol. 402, no. 3, pp. 709-728, 1993.
374. -1/2)," Comptes Rendus Mathematique, vol. 346, no. 15, pp. 893-896, 2008.
375. V. Vu and T. Tao, "The condition number of a randomly perturbed matrix," in Proceedings of the thirty-ninth annual ACM symposium on Theory of computing, pp. 248-255, ACM, 2007.
376. J. Lindeberg, "Eine neue herleitung des exponentialgesetzes in der wahrscheinlichkeitsrechnung," Mathematische Zeitschrift, vol. 15, no. 1, pp. 211-225, 1922.
377. A. Edelman and B. Sutton, "Tails of condition number distributions," simulation, vol. 1, p. 2, 2008.
378. T. Sarlos, "Improved approximation algorithms for large matrices via random projections," in Foundations of Computer Science, 2006. FOCS'06. 47th Annual IEEE Symposium on, pp. 143-152, IEEE, 2006.
379. T. Tao and V. Vu, "Random matrices: the circular law," Arxiv preprint arXiv:0708.2895, 2007.
380. N. Pillai and J. Yin, "Edge universality of correlation matrices," arXiv preprint arXiv:1112.2381, 2011.
381. N. Pillai and J. Yin, "Universality of covariance matrices," arXiv preprint arXiv:1110.2501, 2011.
382. Z. Bao, G. Pan, and W. Zhou, "Tracy-widom law for the extreme eigenvalues of sample correlation matrices," 2011.
383. I. Johnstone, "On the distribution of the largest eigenvalue in principal components analysis," The Annals of statistics, vol. 29, no. 2, pp. 295-327, 2001.
384. S. Hou, R. C. Qiu, J. P. Browning, and M. C. Wicks, "Spectrum Sensing in Cognitive Radio with Subspace Matching," in IEEE Waveform Diversity and Design Conference, January 2012.
385. S. Hou and R. C. Qiu, "Spectrum sensing for cognitive radio using kernel-based learning," arXiv preprint arXiv:1105.2978, 2011.
386. S. Dallaporta, "Eigenvalue variance bounds for wigner and covariance random matrices," Random Matrices: Theory and Applications, vol. 1, no. 03, 2011.
387. Ø. Ryan, A. Masucci, S. Yang, and M. Debbah, "Finite dimensional statistical inference," Information Theory, IEEE Transactions on, vol. 57, no. 4, pp. 2457-2473, 2011.
388. R. Couillet and M. Debbah, Random Matrix Methods for Wireless Communications. Cambridge University Press, 2011.
389. A. Tulino and S. Verdu, Random matrix theory and wireless communications. now Publishers Inc., 2004.
390. R. Müller, "Applications of large random matrices in communications engineering," in Proc. Int. Conf. on Advances Internet, Process., Syst., Interdisciplinary Research (IPSI), Sveti Stefan, Montenegro, 2003.
391. G. E. Pfander, H. Rauhut, and J. A. Tropp, "The restricted isometry property for time-frequency structured random matrices," Probability Theory and Related Fields, pp. 1-31, 2011.
392. T. T. Cai, L. Wang, and G. Xu, "Shifting inequality and recovery of sparse signals," Signal Processing, IEEE Transactions on, vol. 58, no. 3, pp. 1300-1308, 2010.
393. E. Candes, "The Restricted Isometry Property and Its Implications for Compressed Sensing," Comptes rendus-Mathematique, vol. 346, no. 9-10, pp. 589-592, 2008.
394. E. Candes, J. Romberg, and T. Tao, "Stable Signal Recovery from Incomplete and Inaccurate Measurements," Comm. Pure Appl. Math, vol. 59, no. 8, pp. 1207-1223, 2006.
395. S. Foucart, "A note on guaranteed sparse recovery via t\-minimization," Applied and Computational Harmonic Analysis, vol. 29, no. 1, pp. 97-103, 2010.
396. S. Foucart, "Sparse recovery algorithms: sufficient conditions in terms of restricted isometry constants," Approximation Theory XIII: San Antonio 2010, pp. 65-77, 2012.
397. D. Needell and J. A. Tropp, "Cosamp: Iterative signal recovery from incomplete and inaccurate samples," Applied and Computational Harmonic Analysis, vol. 26, no. 3, pp. 301-321, 2009.
398. T. Blumensath and M. E. Davies, "Iterative hard thresholding for compressed sensing," Applied and Computational Harmonic Analysis, vol. 27, no. 3, pp. 265-274, 2009.
399. S. Foucart, "Hard thresholding pursuit: an algorithm for compressive sensing," SIAM Journal on Numerical Analysis, vol. 49, no. 6, pp. 2543-2563, 2011.
400. R. Baraniuk, M. Davenport, R. DeVore, and M. Wakin, "A Simple Proof of the Restricted Isometry Property for Random Matrices." Submitted for publication, January 2007.
401. D. L. Donoho and J. Tanner, "Counting faces of randomly-projected polytopes when the projection radically lowers dimension," J. Amer. Math. Soc, vol. 22, no. 1, pp. 1-53, 2009.
402. M. Rudelson and R. Vershynin, "On sparse reconstruction from fourier and gaussian measurements," Communications on Pure and Applied Mathematics, vol. 61, no. 8, pp. 1025-1045, 2008.
403. H. Rauhut, J. Romberg, and J. A. Tropp, "Restricted isometries for partial random circulant matrices," Applied and Computational Harmonic Analysis, vol. 32, no. 2, pp. 242-254, 2012.
404. G. E. Pfander and H. Rauhut, "Sparsity in time-frequency representations," Journal of Fourier Analysis and Applications, vol. 16, no. 2, pp. 233-260, 2010.
405. G. Pfander, H. Rauhut, and J. Tanner, "Identification of Matrices having a Sparse Representation," in Preprint, 2007.
406. E. Candes and T. Tao, "Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?," IEEE Transactions on Information Theory, vol. 52, no. 12, pp. 5406-5425, 2006.
407. S. Mendelson, A. Pajor, and N. Tomczak-Jaegermann, "Uniform uncertainty principle for bernoulli and subgaussian ensembles," Constructive Approximation, vol. 28, no. 3, pp. 277-289, 2008.
408. A. Cohen, W. Dahmen, and R. DeVore, "Compressed Sensing and Best k-Term Approximation," in Submitted for publication, July, 2006.
409. S. Foucart, A. Pajor, H. Rauhut, and T. Ullrich, "The gelfand widths of lp-balls for 0
410. A. Y. Garnaev and E. D. Gluskin, "The widths of a euclidean ball," in Dokl. Akad. Nauk SSSR, vol. 277, pp. 1048-1052, 1984.
411. W. B. Johnson and J. Lindenstrauss, "Extensions of lipschitz mappings into a hilbert space," Contemporary mathematics, vol. 26, no. 189-206, p. 1, 1984.
412. F. Krahmer and R. Ward, "New and improved johnson-lindenstrauss embeddings via the restricted isometry property," SIAM Journal on Mathematical Analysis, vol. 43, no. 3, pp. 1269-1281, 2011.
413. N. Alon, "Problems and results in extremal combinatorics-i," Discrete Mathematics, vol. 273, no. 1, pp. 31-53, 2003.
414. N. Ailon and E. Liberty, "An almost optimal unrestricted fast johnson-lindenstrauss transform," in Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 185-191, SIAM, 2011.
415. D. Achlioptas, "Database-friendly random projections," in Proceedings of the twentieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems, pp. 274-281, ACM, 2001.
416. D. Achlioptas, "Database-friendly random projections: Johnson-lindenstrauss with binary coins," Journal of computer and System Sciences, vol. 66, no. 4, pp. 671-687, 2003.
417. N. Ailon and B. Chazelle, "Approximate nearest neighbors and the fast johnson-lindenstrauss transform," in Proceedings of the thirty-eighth annual ACM symposium on Theory of computing, pp. 557-563, ACM, 2006.
418. N. Ailon and B. Chazelle, "The fast johnson-lindenstrauss transform and approximate nearest neighbors," SIAM Journal on Computing, vol. 39, no. 1, pp. 302-322, 2009.
419. G. Lorentz, M. Golitschek, and Y. Makovoz, "Constructive approximation, volume 304 of grundlehren math. wiss," 1996.
420. R. I. Arriaga and S. Vempala, "An algorithmic theory of learning: Robust concepts and random projection," Machine Learning, vol. 63, no. 2, pp. 161-182, 2006.
421. K. L. Clarkson and D. P. Woodruff, "Numerical linear algebra in the streaming model," in Proceedings of the 41st annual ACM symposium on Theory of computing, pp. 205-214, ACM, 2009.
422. S. Dasgupta and A. Gupta, "An elementary proof of a theorem of johnson and lindenstrauss," Random Structures & Algorithms, vol. 22, no. 1, pp. 60-65, 2002.
423. P. Frankl and H. Maehara, "The johnson-lindenstrauss lemma and the sphericity of some graphs," Journal of Combinatorial Theory, Series B, vol. 44, no. 3, pp. 355-362, 1988.
424. P. Indyk and R. Motwani, "Approximate nearest neighbors: towards removing the curse of dimensionality," in Proceedings of the thirtieth annual ACM symposium on Theory of computing, pp. 604-613, ACM, 1998.
425. D. M. Kane and J. Nelson, "A derandomized sparse johnson-lindenstrauss transform," arXiv preprint arXiv:1006.3585, 2010.
426. J. Matoušek, "On variants of the johnson-lindenstrauss lemma," Random Structures & Algorithms, vol. 33, no. 2, pp. 142-156, 2008.
427. M. Rudelson and R. Vershynin, "Geometric approach to error-correcting codes and reconstruction of signals," International Mathematics Research Notices, vol. 2005, no. 64, p. 4019, 2005.
428. J. Vybí ral, "A variant of the johnson-lindenstrauss lemma for circulant matrices," Journal of Functional Analysis, vol. 260, no. 4, pp. 1096-1105, 2011.
429. A. Hinrichs and J. Vybí ral, "Johnson-lindenstrauss lemma for circulant matrices," Random Structures & Algorithms, vol. 39, no. 3, pp. 391-398, 2011.
430. H. Rauhut, K. Schnass, and P. Vandergheynst, "Compressed Sensing and Redundant Dictionaries," IEEE Transactions on Information Theory, vol. 54, no. 5, pp. 2210-2219, 2008.
431. W. U. Bajwa, J. Haupt, A. M. Sayeed, and R. Nowak, "Compressed channel sensing: A new approach to estimating sparse multipath channels," Proceedings of the IEEE, vol. 98, no. 6, pp. 1058-1076, 2010.
432. J. Chiu and L. Demanet, "Matrix probing and its conditioning," SIAM Journal on Numerical Analysis, vol. 50, no. 1, pp. 171-193, 2012.
433. G. E. Pfander, "Gabor frames in finite dimensions," Finite Frames, pp. 193-239, 2012.
434. J. Haupt, W. U. Bajwa, G. Raz, and R. Nowak, "Toeplitz compressed sensing matrices with applications to sparse channel estimation," Information Theory, IEEE Transactions on, vol. 56, no. 11, pp. 5862-5875, 2010.
435. K. Gröchenig, Foundations of time-frequency analysis. Birkhäuser Boston, 2000.
436. F. Krahmer, G. E. Pfander, and P. Rashkov, "Uncertainty in time-frequency representations on finite abelian groups and applications," Applied and Computational Harmonic Analysis, vol. 25, no. 2, pp. 209-225, 2008.
437. J. Lawrence, G. E. Pfander, and D. Walnut, "Linear independence of gabor systems in finite dimensional vector spaces," Journal of Fourier Analysis and Applications, vol. 11, no. 6, pp. 715-726, 2005.
438. B. M. Sanandaji, T. L. Vincent, and M. B. Wakin, "Concentration of measure inequalities for compressive toeplitz matrices with applications to detection and system identification," in Decision and Control (CDC), 2010 49th IEEE Conference on, pp. 2922-2929, IEEE, 2010.
439. B. M. Sanandaji, T. L. Vincent, and M. B. Wakin, "Concentration of measure inequalities for toeplitz matrices with applications," arXiv preprint arXiv:1112.1968, 2011.
440. B. M. Sanandaji, M. B. Wakin, and T. L. Vincent, "Observability with random observations," arXiv preprint arXiv:1211.4077, 2012.
441. M. Meckes, "On the spectral norm of a random toeplitz matrix," Electron. Comm. Probab, vol. 12, pp. 315-325, 2007.
442. R. Adamczak, "A few remarks on the operator norm of random toeplitz matrices," Journal of Theoretical Probability, vol. 23, no. 1, pp. 85-108, 2010.
443. R. Calderbank, S. Howard, and S. Jafarpour, "Construction of a large class of deterministic sensing matrices that satisfy a statistical isometry property," Selected Topics in Signal Processing, IEEE Journal of, vol. 4, no. 2, pp. 358-374, 2010.
444. Y. Plan, Compressed sensing, sparse approximation, and low-rank matrix estimation. PhD thesis, California Institute of Technology, 2011.
445. R. Vershynin, "Math 280 lecture notes," 2007.
446. B. Recht, M. Fazel, and P. A. Parrilo, "Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization," SIAM review, vol. 52, no. 3, pp. 471-501, 2010.
447. R. Vershynin, "On large random almost euclidean bases," Acta Math. Univ. Comenianae, vol. 69, no. 2, pp. 137-144, 2000.
448. E. L. Lehmann and G. Casella, Theory of point estimation, vol. 31. Springer, 1998.
449. S. Negahban, P. Ravikumar, M. Wainwright, and B. Yu, "A unified framework for high-dimensional analysis of m-estimators with decomposable regularizers," arXiv preprint arXiv:1010.2731, 2010.
450. A. Agarwal, S. Negahban, and M. Wainwright, "Fast global convergence of gradient methods for high-dimensional statistical recovery," arXiv preprint arXiv:1104.4824, 2011.
451. B. Recht, M. Fazel, and P. Parrilo, "Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization," in Arxiv preprint arXiv:0706.4138, 2007.
452. H. Lütkepohl, "New introduction to multiple time series analysis," 2005.
453. A. Agarwal, S. Negahban, and M. Wainwright, "Noisy matrix decomposition via convex relaxation: Optimal rates in high dimensions," arXiv preprint arXiv:1102.4807, 2011.
454. C. Meyer, Matrix analysis and applied linear algebra. SIAM, 2000.
455. M. McCoy and J. Tropp, "Sharp recovery bounds for convex deconvolution, with applications," Arxiv preprint arXiv:1205.1580, 2012.
456. V. Chandrasekaran, S. Sanghavi, P. A. Parrilo, and A. S. Willsky, "Rank-sparsity incoherence for matrix decomposition," SIAM Journal on Optimization, vol. 21, no. 2, pp. 572-596, 2011.
457. V. Koltchinskii, "Von neumann entropy penalization and low-rank matrix estimation," The Annals of Statistics, vol. 39, no. 6, pp. 2936-2973, 2012.
458. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information. Cambridge Press, 10th edition ed., 2010.
459. S. Sra, S. Nowozin, and S. Wright, eds., Optimization for machine learning. MIT Press, 2012. Chapter 4 (Bertsekas) Incremental Gradient, Subgradient, and Proximal Method for Convex Optimization: A Survey. [440, 441]
460. M. Rudelson, "Contact points of convex bodies," Israel Journal of Mathematics, vol. 101, no. 1, pp. 93-124, 1997.
461. D. Blatt, A. Hero, and H. Gauchman, "A convergent incremental gradient method with a constant step size," SIAM Journal on Optimization, vol. 18, no. 1, pp. 29-51, 2007.
462. M. Rabbat and R. Nowak, "Quantized incremental algorithms for distributed optimization," Selected Areas in Communications, IEEE Journal on, vol. 23, no. 4, pp. 798-808, 2005.
463. E. Candes, Y. Eldar, T. Strohmer, and V. Voroninski, "Phase retrieval via matrix completion," Arxiv preprint arXiv:1109.0573, 2011.
464. E. Candes, T. Strohmer, and V. Voroninski, "Phaselift: Exact and stable signal recovery from magnitude measurements via convex programming," Arxiv preprint arXiv:1109.4499, 2011.
465. E. Candès and B. Recht, "Exact matrix completion via convex optimization," Foundations of Computational Mathematics, vol. 9, no. 6, pp. 717-772, 2009.
466. J. Cai, E. Candes, and Z. Shen, "A singular value thresholding algorithm for matrix completion," Arxiv preprint Arxiv:0810.3286, 2008.
467. E. Candes and T. Tao, "The power of convex relaxation: Near-optimal matrix completion," Information Theory, IEEE Transactions on, vol. 56, no. 5, pp. 2053-2080, 2010.
468. A. Alfakih, A. Khandani, and H. Wolkowicz, "Solving euclidean distance matrix completion problems via semidefinite programming," Computational optimization and applications, vol. 12, no. 1, pp. 13-30, 1999.
469. M. Fukuda, M. Kojima, K. Murota, K. Nakata, et al., "Exploiting sparsity in semidefinite programming via matrix completion i: General framework," SIAM Journal on Optimization, vol. 11, no. 3, pp. 647-674, 2001.
470. R. Keshavan, A. Montanari, and S. Oh, "Matrix completion from a few entries," Information Theory, IEEE Transactions on, vol. 56, no. 6, pp. 2980-2998, 2010.
471. C. Johnson, "Matrix completion problems: a survey," in Proceedings of Symposia in Applied Mathematics, vol. 40, pp. 171-198, 1990.
472. E. Candes and Y. Plan, "Matrix completion with noise," Proceedings of the IEEE, vol. 98, no. 6, pp. 925-936, 2010.
473. A. Chai, M. Moscoso, and G. Papanicolaou, "Array imaging using intensity-only measurements," Inverse Problems, vol. 27, p. 015005, 2011.
474. L. Tian, J. Lee, S. Oh, and G. Barbastathis, "Experimental compressive phase space tomography," Optics Express, vol. 20, no. 8, pp. 8296-8308, 2012.
475. Y. Lu and M. Vetterli, "Sparse spectral factorization: Unicity and reconstruction algorithms," in Acoustics, Speech and Signal Processing (ICASSP), 2011 IEEE International Conference on, pp. 5976-5979, IEEE, 2011.
476. J. Fienup, "Phase retrieval algorithms: a comparison," Applied Optics, vol. 21, no. 15, pp. 2758-2769, 1982.
477. A. Sayed and T. Kailath, "A survey of spectral factorization methods," Numerical linear algebra with applications, vol. 8, no. 6-7, pp. 467-496, 2001.
478. C. Beck and R. D'Andrea, "Computational study and comparisons of lft reducibility methods," in American Control Conference, 1998. Proceedings of the 1998, vol. 2, pp. 1013-1017, IEEE, 1998.
479. M. Mesbahi and G. Papavassilopoulos, "On the rank minimization problem over a positive semidefinite linear matrix inequality," Automatic Control, IEEE Transactions on, vol. 42, no. 2, pp. 239-243, 1997.
480. K. Toh, M. Todd, and R. Tütüncü, "Sdpt3-a matlab software package for semidefinite programming, version 1.3," Optimization Methods and Software, vol. 11, no. 1-4, pp. 545-581, 1999.
481. M. Grant and S. Boyd, "Cvx: Matlab software for disciplined convex programming," Available httpstanford edu boydcvx, 2008.
482. S. Becker, E. Candès, and M. Grant, "Templates for convex cone problems with applications to sparse signal recovery," Mathematical Programming Computation, pp. 1-54, 2011.
483. 1 minimization," Journal of Fourier Analysis and Applications, vol. 14, no. 5, pp. 877-905, 2008.
484. M. Fazel, H. Hindi, and S. Boyd, "Log-det heuristic for matrix rank minimization with applications to hankel and euclidean distance matrices," in American Control Conference, 2003. Proceedings of the 2003, vol. 3, pp. 2156-2162, Ieee, 2003.
485. M. Fazel, Matrix rank minimization with applications. PhD thesis, PhD thesis, Stanford University, 2002.
486. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics. Cambridge University Press, 1995.
487. Z. Hu, R. Qiu, J. Browning, and M. Wicks, "A novel single-step approach for self-coherent tomography using semidefinite relaxation," IEEE Geoscience and Remote Sensing Letters. to appear. [449]
488. M. Grant and S. Boyd, "Cvx: Matlab software for disciplined convex programming, version 1.21." http://cvxr.com/cvx, 2010.
489. H. Ohlsson, A. Y. Yang, R. Dong, and S. S. Sastry, "Compressive phase retrieval from squared output measurements via semidefinite programming," arXiv preprint arXiv:1111.6323, 2012.
490. A. Devaney, E. Marengo, and F. Gruber, "Time-reversal-based imaging and inverse scattering of multiply scattering point targets," The Journal of the Acoustical Society of America, vol. 118, pp. 3129-3138, 2005.
491. L. Lo Monte, D. Erricolo, F. Soldovieri, and M. C. Wicks, "Radio frequency tomography for tunnel detection," Geoscience and Remote Sensing, IEEE Transactions on, vol. 48, no. 3, pp. 1128-1137, 2010.
492. O. Klopp, "Noisy low-rank matrix completion with general sampling distribution," Arxiv preprint arXiv:1203.0108, 2012.
493. R. Foygel, R. Salakhutdinov, O. Shamir, and N. Srebro, "Learning with the weighted trace-norm under arbitrary sampling distributions," Arxiv preprint arXiv:1106.4251, 2011.
494. R. Foygel and N. Srebro, "Concentration-based guarantees for low-rank matrix reconstruction," Arxiv preprint arXiv:1102.3923, 2011.
495. V. Koltchinskii and P. Rangel, "Low rank estimation of similarities on graphs," Arxiv preprint arXiv:1205.1868, 2012.
496. E. Richard, P. Savalle, and N. Vayatis, "Estimation of simultaneously sparse and low rank matrices," in Proceeding of 29th Annual International Conference on Machine Learning, 2012.
497. H. Ohlsson, A. Yang, R. Dong, and S. Sastry, "Compressive phase retrieval from squared output measurements via semidefinite programming," Arxiv preprint arXiv:1111.6323, 2011.
498. A. Fannjiang and W. Liao, "Compressed sensing phase retrieval," in Proceedings of IEEE Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, 2011.
499. A. Fannjiang, "Absolute uniqueness of phase retrieval with random illumination," Arxiv preprint arXiv:1110.5097, 2011.
500. S. Oymak and B. Hassibi, "Recovering jointly sparse signals via joint basis pursuit," Arxiv preprint arXiv:1202.3531, 2012.
501. Z. Wen, C. Yang, X. Liu, and S. Marchesini, "Alternating direction methods for classical and ptychographic phase retrieval," []
502. H. Ohlsson, A. Yang, R. Dong, and S. Sastry, "Compressive phase retrieval via lifting," [456]
503. K. Jaganathan, S. Oymak, and B. Hassibi, "On robust phase retrieval for sparse signals," in Communication, Control, and Computing (Allerton), 2012 50th Annual Allerton Conference on, pp. 794-799, IEEE, 2012.
504. Y. Chen, A. Wiesel, and A. Hero, "Robust shrinkage estimation of high-dimensional covariance matrices," Signal Processing, IEEE Transactions on, vol. 59, no. 9, pp. 4097-4107, 2011.
505. E. Levina and R. Vershynin, "Partial estimation of covariance matrices," Probability Theory and Related Fields, pp. 1-15, 2011.
506. S. Marple, Digital Spectral Analysis with Applications. Prentice-Hall, 1987.
507. C. W. Therrien, Discrete Random Signals and Statistical Signal Processing. Prentice-Hall, 1992.
508. H. Xiao and W. Wu, "Covariance matrix estimation for stationary time series," Arxiv preprint arXiv:1105.4563, 2011.
509. A. Rohde, "Accuracy of empirical projections of high-dimensional gaussian matrices," arXiv preprint arXiv:1107.5481, 2011.
510. K. Jurczak, "A universal expectation bound on empirical projections of deformed random matrices," arXiv preprint arXiv:1209.5943, 2012.
511. A. Amini, "High-dimensional principal component analysis," 2011.
512. L. Vandenberghe and S. Boyd, "Semidefinite programming," SIAM review, vol. 38, no. 1, pp. 49-95, 1996.
513. D. Paul and I. M. Johnstone, "Augmented sparse principal component analysis for high dimensional data," arXiv preprint arXiv:1202.1242, 2012.
514. Q. Berthet and P. Rigollet, "Optimal detection of sparse principal components in high dimension," Arxiv preprint arXiv:1202.5070, 2012.
515. A. d'Aspremont, F. Bach, and L. Ghaoui, "Approximation bounds for sparse principal component analysis," Arxiv preprint arXiv:1205.0121, 2012.
516. A. d'Aspremont, L. El Ghaoui, M. Jordan, and G. Lanckriet, A direct formulation for sparse PCA using semidefinite programming, vol. 49. SIAM Review, 2007.
517. H. Zou, T. Hastie, and R. Tibshirani, "Sparse principal component analysis," Journal of computational and graphical statistics, vol. 15, no. 2, pp. 265-286, 2006.
518. P. Bickel and E. Levina, "Covariance regularization by thresholding," The Annals of Statistics, vol. 36, no. 6, pp. 2577-2604, 2008.
519. T. Cai, C. Zhang, and H. Zhou, "Optimal rates of convergence for covariance matrix estimation," The Annals of Statistics, vol. 38, no. 4, pp. 2118-2144, 2010.
520. N. El Karoui, "Spectrum estimation for large dimensional covariance matrices using random matrix theory," The Annals of Statistics, vol. 36, no. 6, pp. 2757-2790, 2008.
521. S. Geman, "The spectral radius of large random matrices," The Annals of Probability, vol. 14, no. 4, pp. 1318-1328, 1986.
522. J. Baik, G. Ben Arous, and S. Péché, "Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices," The Annals of Probability, vol. 33, no. 5, pp. 1643-1697, 2005.
523. T. Tao, "Outliers in the spectrum of iid matrices with bounded rank perturbations," Probability Theory and Related Fields, pp. 1-33, 2011.
524. F. Benaych-Georges, A. Guionnet, M. Maida, et al., "Fluctuations of the extreme eigenvalues of finite rank deformations of random matrices," Electronic Journal of Probability, vol. 16, pp. 1621-1662, 2010.
525. F. Bach, S. Ahipasaoglu, and A. d'Aspremont, "Convex relaxations for subset selection," Arxiv preprint ArXiv:1006.3601, 2010.
526. E. J. Candès and M. A. Davenport, "How well can we estimate a sparse vector?," Applied and Computational Harmonic Analysis, 2012.
527. E. Candes and T. Tao, "The Dantzig Selector: Statistical Estimation When p is much larger than n," Annals of Statistics, vol. 35, no. 6, pp. 2313-2351, 2007.
528. F. Ye and C.-H. Zhang, "Rate minimaxity of the lasso and dantzig selector for the lq loss in lr balls," The Journal of Machine Learning Research, vol. 9999, pp. 3519-3540, 2010.
529. E. Arias-Castro, "Detecting a vector based on linear measurements," Electronic Journal of Statistics, vol. 6, pp. 547-558, 2012.
530. E. Arias-Castro, E. Candes, and M. Davenport, "On the fundamental limits of adaptive sensing," arXiv preprint arXiv:1111.4646, 2011.
531. E. Arias-Castro, S. Bubeck, and G. Lugosi, "Detection of correlations," The Annals of Statistics, vol. 40, no. 1, pp. 412-435, 2012.
532. E. Arias-Castro, S. Bubeck, and G. Lugosi, "Detecting positive correlations in a multivariate sample," 2012.
533. A. B. Tsybakov, Introduction to nonparametric estimation. Springer, 2008.
534. L. Balzano, B. Recht, and R. Nowak, "High-dimensional matched subspace detection when data are missing," in Information Theory Proceedings (ISIT), 2010 IEEE International Symposium on, pp. 1638-1642, IEEE, 2010.
535. L. K. Balzano, Handling missing data in high-dimensional subspace modeling. PhD thesis, UNIVERSITY OF WISCONSIN, 2012.
536. L. L. Scharf, Statistical Signal Processing. Addison-Wesley, 1991.
537. L. L. Scharf and B. Friedlander, "Matched subspace detectors," Signal Processing, IEEE Transactions on, vol. 42, no. 8, pp. 2146-2157, 1994.
538. S. Hou, R. C. Qiu, M. Bryant, and M. C. Wicks, "Spectrum Sensing in Cognitive Radio with Robust Principal Component Analysis," in IEEE Waveform Diversity and Design Conference, January 2012.
539. C. McDiarmid, "On the method of bounded differences," Surveys in combinatorics, vol. 141, no. 1, pp. 148-188, 1989.
540. M. Azizyan and A. Singh, "Subspace detection of high-dimensional vectors using compres-sive sampling," in IEEE SSP, 2012.
541. M. Davenport, M. Wakin, and R. Baraniuk, "Detection and estimation with compressive measurements," tech. rep., Tech. Rep. TREE0610, Rice University ECE Department, 2006, 2006.
542. J. Paredes, Z. Wang, G. Arce, and B. Sadler, "Compressive matched subspace detection," in Proc. 17th European Signal Processing Conference, Glasgow, Scotland, pp. 120-124, Citeseer, 2009.
543. J. Haupt and R. Nowak, "Compressive sampling for signal detection," in Acoustics, Speech and Signal Processing, 2007. ICASSP 2007. IEEE International Conference on, vol. 3, pp. III-1509, IEEE, 2007.
544. A. James, "Distributions of matrix variates and latent roots derived from normal samples," The Annals of Mathematical Statistics, pp. 475-501, 1964.
545. S. Balakrishnan, M. Kolar, A. Rinaldo, and A. Singh, "Recovering block-structured activations using compressive measurements," arXiv preprint arXiv:1209.3431, 2012.
546. R. Muirhead, Aspects of Mutivariate Statistical Theory. Wiley, 2005.
547. S. Vempala, The random projection method, vol. 65. Amer Mathematical Society, 2005.
548. C. Helstrom, "Quantum detection and estimation theory," Journal of Statistical Physics, vol. 1, no. 2, pp. 231-252, 1969.
549. C. Helstrom, "Detection theory and quantum mechanics," Information and Control, vol. 10, no. 3, pp. 254-291, 1967.
550. J. Sharpnack, A. Rinaldo, and A. Singh, "Changepoint detection over graphs with the spectral scan statistic," arXiv preprint arXiv:1206.0773, 2012.
551. D. Ramí rez, J. Ví a, I. Santamaŕia, and L. Scharf, "Locally most powerful invariant tests for correlation and sphericity of gaussian vectors," arXiv preprint arXiv:1204.5635, 2012.
552. A. Onatski, M. Moreira, and M. Hallin, "Signal detection in high dimension: The multispiked case," arXiv preprint arXiv:1210.5663, 2012.
553. A. Nemirovski, "On tractable approximations of randomly perturbed convex constraints," in Decision and Control, 2003. Proceedings. 42nd IEEE Conference on, vol. 3, pp. 2419-2422, IEEE, 2003.
554. A. Nemirovski, "Regular banach spaces and large deviations of random sums," Paper in progress, E-print: http://www2.isye.gatech.edu/nemirovs, 2004.
555. D. De Farias and B. Van Roy, "On constraint sampling in the linear programming approach to approximate dynamic programming," Mathematics of operations research, vol. 29, no. 3, pp. 462-478, 2004.
556. G. Calafiore and M. Campi, "Uncertain convex programs: randomized solutions and confidence levels," Mathematical Programming, vol. 102, no. 1, pp. 25-46, 2005.
557. E. Erdoʇan and G. Iyengar, "Ambiguous chance constrained problems and robust optimization," Mathematical Programming, vol. 107, no. 1, pp. 37-61, 2006.
558. M. Campi and S. Garatti, "The exact feasibility of randomized solutions of uncertain convex programs," SIAM Journal on Optimization, vol. 19, no. 3, pp. 1211-1230, 2008.
559. A. Nemirovski and A. Shapiro, "Convex approximations of chance constrained programs," SIAM Journal on Optimization, vol. 17, no. 4, pp. 969-996, 2006.
560. A. Nemirovski, "Sums of random symmetric matrices and quadratic optimization under orthogonality constraints," Mathematical programming, vol. 109, no. 2, pp. 283-317, 2007.
561. S. Janson, "Large deviations for sums of partly dependent random variables," Random Structures & Algorithms, vol. 24, no. 3, pp. 234-248, 2004.
562. S. Cheung, A. So, and K. Wang, "Chance-constrained linear matrix inequalities with dependent perturbations: A safe tractable approximation approach," Preprint, 2011.
563. A. Ben-Tal and A. Nemirovski, "On safe tractable approximations of chance-constrained linear matrix inequalities," Mathematics of Operations Research, vol. 34, no. 1, pp. 1-25, 2009.
564. A. Gershman, N. Sidiropoulos, S. Shahbazpanahi, M. Bengtsson, and B. Ottersten, "Convex optimization-based beamforming," Signal Processing Magazine, IEEE, vol. 27, no. 3, pp. 62-75, 2010.
565. Z. Luo, W. Ma, A. So, Y. Ye, and S. Zhang, "Semidefinite relaxation of quadratic optimization problems," Signal Processing Magazine, IEEE, vol. 27, no. 3, pp. 20-34, 2010.
566. E. Karipidis, N. Sidiropoulos, and Z. Luo, "Quality of service and max-min fair transmit beamforming to multiple cochannel multicast groups," Signal Processing, IEEE Transactions on, vol. 56, no. 3, pp. 1268-1279, 2008.
567. Z. Hu, R. Qiu, and J. P. Browning, "Joint Amplify-and-Forward Relay and Cooperative Jamming with Probabilistic Security Consideration," 2013. submitted to IEEE COMMUNICATIONS LETTERS. [547]
568. H.-M. Wang, M. Luo, X.-G. Xia, and Q. Yin, "Joint cooperative beamforming and jamming to secure af relay systems with individual power constraint and no eavesdropper's csi," Signal Processing Letters, IEEE, vol. 20, no. 1, pp. 39-42, 2013.
569. Y. Yang, Q. Li, W.-K. Ma, J. Ge, and P. Ching, "Cooperative secure beamforming for af relay networks with multiple eavesdroppers," Signal Processing Letters, IEEE, vol. 20, no. 1, pp. 35-38, 2013.
570. D. Ponukumati, F. Gao, and C. Xing, "Robust peer-to-peer relay beamforming: A probabilistic approach," 2013.
571. S. Kandukuri and S. Boyd, "Optimal power control in interference-limited fading wireless channels with outage-probability specifications," Wireless Communications, IEEE Transactions on, vol. 1, no. 1, pp. 46-55, 2002.
572. S. Ma and D. Sun, "Chance constrained robust beamforming in cognitive radio networks," 2013.
573. D. Zhang, Y. Hu, J. Ye, X. Li, and X. He, "Matrix completion by truncated nuclear norm regularization," in Computer Vision and Pattern Recognition (CVPR), 2012 IEEE Conference on, pp. 2192-2199, IEEE, 2012.
574. K.-Y. Wang, T.-H. Chang, W.-K. Ma, A.-C. So, and C.-Y. Chi, "Probabilistic sinr constrained robust transmit beamforming: A bernstein-type inequality based conservative approach," in Acoustics, Speech and Signal Processing (ICASSP), 2011 IEEE International Conference on, pp. 3080-3083, IEEE, 2011.
575. K.-Y. Wang, T.-H. Chang, W.-K. Ma, and C.-Y. Chi, "A semidefinite relaxation based conservative approach to robust transmit beamforming with probabilistic sinr constraints," in Proc. EUSIPCO, pp. 23-27, 2010.
576. K. Yang, J. Huang, Y. Wu, X. Wang, and M. Chiang, "Distributed robust optimization (dro) part i: Framework and example," 2008.
577. K. Yang, Y. Wu, J. Huang, X. Wang, and S. Verdú, "Distributed robust optimization for communication networks," in INFOCOM 2008. The 27th Conference on Computer Communications. IEEE, pp. 1157-1165, IEEE, 2008.
578. M. Chen and M. Chiang, "Distributed optimization in networking: Recent advances in combinatorial and robust formulations," Modeling and Optimization: Theory and Applications, pp. 25-52, 2012.
579. G. Calafiore, F. Dabbene, and R. Tempo, "Randomized algorithms in robust control," in Decision and Control, 2003. Proceedings. 42nd IEEE Conference on, vol. 2, pp. 1908-1913, IEEE, 2003.
580. R. Tempo, G. Calafiore, and F. Dabbene, Randomized algorithms for analysis and control of uncertain systems. Springer, 2004.
581. X. Chen, J. Aravena, and K. Zhou, "Risk analysis in robust control-making the case for probabilistic robust control," in American Control Conference, 2005. Proceedings of the 2005, pp. 1533-1538, IEEE, 2005.
582. Z. Zhou and R. Cogill, "An algorithm for state constrained stochastic linear-quadratic control," in American Control Conference (ACC), 2011, pp. 1476-1481, IEEE, 2011.
583. A. M.-C. So and Y. J. A. Zhang, "Distributionally robust slow adaptive ofdma with soft qos via linear programming," in IEEE J. Sel. Areas Commun.[Online]. Available: http://www1. se.cuhk.edu.hk/∼manchoso. [558]
584. C. Boutsidis and A. Gittens, "Im@articlegittens2012var, title=Var (Xjk), author=GITTENS, A., year=2012," arXiv preprint arXiv:1204.0062, 2012.
585. A. GITTENS, "Var (xjk)," 2012.
586. M. Magdon-Ismail, "Using a non-commutative bernstein bound to approximate some matrix algorithms in the spectral norm," Arxiv preprint arXiv:1103.5453, 2011.
587. M. Magdon-Ismail, "Row sampling for matrix algorithms via a non-commutative bernstein bound," Arxiv preprint arXiv:1008.0587, 2010.
588. C. Faloutsos, T. Kolda, and J. Sun, "Mining large time-evolving data using matrix and tensor tools," in ICDM Conference, 2007.
589. M. Mahoney, "Randomized algorithms for matrices and data," Arxiv preprint arXiv:1104.5557, 2011.
590. R. Ranganathan, R. Qiu, Z. Hu, S. Hou, Z. Chen, M. Pazos-Revilla, and N. Guo, Communication and Networking in Smart Grids, ch. Cognitive Radio Network for Smart Grid. Auerbach Publications, Taylor & Francis Group, CRC, 2013.
591. R. C. Qiu, Z. Chen, N. Guo, Y. Song, P. Zhang, H. Li, and L. Lai, "Towards a real-time cognitive radio network testbed: architecture, hardware platform, and application to smart grid," in Networking Technologies for Software Defined Radio (SDR) Networks, 2010 Fifth IEEE Workshop on, pp. 1-6, IEEE, 2010.
592. R. Qiu, Z. Hu, Z. Chen, N. Guo, R. Ranganathan, S. Hou, and G. Zheng, "Cognitive radio network for the smart grid: Experimental system architecture, control algorithms, security, and microgrid testbed," Smart Grid, IEEE Transactions on, no. 99, pp. 1-18, 2011.
593. R. Qiu, C. Zhang, Z. Hu, and M. Wicks, "Towards a large-scale cognitive radio network testbed: Spectrum sensing, system architecture, and distributed sensing," Journal of Communications, vol. 7, pp. 552-566, July 2012.
594. E. Estrada, The structure of complex networks: theory and applications. Oxford University Press, 2012.
595. M. Newman, Network: An Introduction. Oxford University Press, 2010.
596. M. Newman, "The structure and function of complex networks," SIAM review, vol. 45, no. 2, pp. 167-256, 2003.
597. M. Newman and M. Girvan, "Finding and evaluating community structure in networks," Physical review E, vol. 69, no. 2, p. 026113, 2004.
598. S. Strogatz, "Exploring complex networks," Nature, vol. 410, no. 6825, pp. 268-276, 2001.
599. A. Barrat, M. Barthelemy, and A. Vespignani, Dynamical processes on complex networks. Cambridge University Press, 2008.
600. M. Franceschetti and R. Meester, Random networks for communication: from statistical physics to information systems. Cambridge University Press, 2007.
601. P. Van Mieghem, Graph spectra for complex networks. Cambridge University Press, 2011.
602. D. Cvekovic, M. Doob, and H. Sachs, Spectra of graphs: theory and applications. Academic Press, 1980.
603. C. Godsil and G. Royle, Algebraic graph theory. Springer, 2001.
604. F. Chung and M. Radcliffe, "On the spectra of general random graphs," the electronic journal of combinatorics, vol. 18, no. P215, p. 1, 2011.
605. R. Oliveira, "Concentration of the adjacency matrix and of the laplacian in random graphs with independent edges," arXiv preprint arXiv:0911.0600, 2009.
606. R. Oliveira, "The spectrum of random k-lifts of large graphs (with possibly large k)," arXiv preprint arXiv:0911.4741, 2009.
607. A. Gundert and U. Wagner, "On laplacians of random complexes," in Proceedings of the 2012 symposuim on Computational Geometry, pp. 151-160, ACM, 2012.
608. L. Lu and X. Peng, "Loose laplacian spectra of random hypergraphs," Random Structures & Algorithms, 2012.
609. F. Chung, Speatral graph theory. American Mathematical Society, 1997.
610. B. Osting, C. Brune, and S. Osher, "Optimal data collection for improved rankings expose well-connected graphs," arXiv preprint arXiv:1207.6430, 2012.