The research reported below was supported by the U.S.
National Science Foundation through the grants DMS-1056996 (CAREER),
CCF-1065494, and CCF-1248100 (INSPIRE), and by Yale University.
Needless to say, any opinions, findings and conclusions or
recomendations expressed in this material are those of the author(s) and do not
necessarily reflect the views of the National Science Foundation (NSF).
I try to keep links updated; however some links may not be to most recent
versions of documents. The copyrights of published papers belong to the
publisher in most cases, and consequently some of the journal links are behind
a paywall.
Most journal papers below are likely to have been reviewed for AMS's MathSciNet
here (subscription required).
O. Johnson, I. Kontoyiannis and M. Madiman:
"Information, Estimation and Approximation for Poisson and related channels".
S. Bobkov and M. Madiman:
"When can one invert Hölder's inequality? (and why one might care)".
M. Harrison, I. Kontoyiannis, and M. Madiman: "A Minimum Description
Length Proposal for Lossy Data Compression".
M. Madiman, A. R. Barron, A. M. Kagan and T. Yu: "Fundamental statistical limits for distributed
estimation: the case of a location parameter".
M. Madiman: "Determinant and trace inequalities for sums of positive-definite matrices".
M. Madiman and L. Wang: "Beyond the entropy power inequality, via rearrangements".
[arXiv]
M. Madiman and I. Kontoyiannis:
"The Ruzsa divergence for random elements in locally compact abelian groups".
Coming soon to an arXiv near you.
I. Kontoyiannis and M. Madiman:
"Sumset and Inverse Sumset Inequalities for Differential Entropy and Mutual Information".
Submitted, 2012.
[arXiv]
[pdf]
S. Bobkov and M. Madiman:
"On the problem of reversibility of the entropy power inequality".
Limit Theorems in Probability, Statistics and Number Theory,
Festschrift in honor of F. Götze's 60th birthday,
P. Eichelsbacher et al. (ed.),
Springer Proceedings in Mathematics and Statistics 42, pp. 61-74, Springer-Verlag, 2013.
[arXiv]
[pdf]
[book]
A. M. Kagan, Tinghui Yu, A. R. Barron and M. Madiman:
"Contribution to the theory of Pitman estimators".
Zapiski Nauchnykh Seminarov POMI, Special issue in honour of I. A. Ibragimov's 80th birthday,
Vol. 408, pp. 245-267, 2012.
[arXiv]
[pdf]
[journal]
M. Madiman, A. Marcus and P. Tetali: "Entropy and set cardinality inequalities
for partition-determined functions". Random Structures and Algorithms,
Vol. 40, pp. 399-424, 2012.
[arXiv]
[pdf]
[journal]
S. Bobkov and M. Madiman: "Reverse Brunn-Minkowski and reverse
entropy power inequalities for convex measures".
Journal of Functional Analysis, Vol. 262, no. 7, pp. 3309-3339, April 2012.
[arXiv]
[pdf]
[journal]
S. Bobkov and M. Madiman: "Concentration of the information in data with
log-concave distributions". Annals of Probability, Vol. 39, no. 4, pp. 1528-1543, 2011.
[arXiv]
[pdf]
[journal]
S. Bobkov and M. Madiman: "The entropy per coordinate of a random vector
is highly constrained under convexity conditions".
IEEE Transactions on Information Theory, Vol. 57, no. 8, pp. 4940-4954, August 2011.
[arXiv]
[pdf]
[journal]
S. Bobkov, M. Madiman and L. Wang:
"Fractional generalizations of Young and Brunn-Minkowski inequalities".
Contemporary Mathematics: Concentration, Functional Inequalities and Isoperimetry,
(ed. C. Houdré, M. Ledoux, E. Milman, and M. Milman), Vol. 545, pp. 35-53, American Mathematical Society, 2011.
[arXiv]
[pdf]
[book]
S. Bobkov and M. Madiman: "Dimensional behaviour of entropy and information".
Comptes Rendus de l'Académies des Sciences Paris, Série I Mathematique,
349, pp. 201-204, 2011.
[arXiv]
[pdf]
[journal]
O. Johnson, I. Kontoyiannis and M. Madiman:
"Log-concavity, ultra-log-concavity, and a maximum entropy
property of compound Poisson measures". Special issue for
Proceedings of Jubilee Conference on Discrete Mathematics (JCDM 2009)
edited by D. J. Kleitman, A. Shastri, V. T. Sós,
Discrete Applied Mathematics, 161(9), pp. 1232-1250, June 2013.
[arXiv]
[pdf]
[journal]
A. D. Barbour, O. Johnson, I. Kontoyiannis and M. Madiman:
"Compound Poisson Approximation via Information Functionals".
Electronic Journal of Probability, 15, paper no. 42, pp. 1344-1368, 2010.
[arXiv]
[pdf/journal]
M. Madiman and P. Tetali: "Information inequalities for joint distributions,
with interpretations and applications".
IEEE Transactions on Information Theory, 56, no. 6, pp.2699-2713, June 2010.
[arXiv]
[pdf]
[journal]
M. Madiman: "Cores of Cooperative Games in Information Theory".
EURASIP Journal on Wireless Communications and Networking,
Special issue on "Theory and Applications in
Multiuser/Multiterminal Communications", no. 318704, 2008.
[arXiv]
[pdf]
[journal]
M. Madiman and A. R. Barron: "Generalized Entropy Power Inequalities
and Monotonicity Properties of Information".
IEEE Transactions on Information Theory, 53, no. 7, pp.2317-2329, July 2007.
[arXiv]
[pdf]
[journal]
I. Kontoyiannis and M. Madiman:
"Measure concentration for compound Poisson distributions".
Electronic Communications in Probability, 11, pp.45-57, 2006.
[arXiv]
[pdf/journal]
I. Kontoyiannis and M. Madiman:
"The entropy of sums and Ruzsa's divergence on abelian group".
Proceedings of the 2013 Information Theory Workshop,
Seville, Spain, September 2013.
M. Madiman and L. Wang: "Unfolding
the entropy power inequality".
Proceedings of the 2013 Information Theory and Applications Workshop,
San Diego, California, February 2013.
M. Madiman: "On the Entropy of Sums".
Proceedings of the 2008 IEEE Information Theory Workshop,
Porto, Portugal, May 2008.
M. Madiman and P. Tetali: "
Sandwich Bounds for Joint Entropy".
Proceedings of the 2007 IEEE International Symposium on Information Theory,
Nice, France, July 2007.
M. Madiman: "Singularities in Mechanisms".
B.Tech. Thesis, Indian Institute of Technology-Bombay, 1999.
M. Madiman: "A Geometric Singular Perturbation Approach to the
Stabilization of an Inverted Pendulum on a Cart".
Unpublished Report, Brown University, December 2000.
M. Madiman: "Potential Formulations of Electromagnetism".
B.Tech. Seminar Report, Indian Institute of Technology-Bombay,
May 1998.
