4882 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 58, NO. 9, SEPTEMBER 2010
 A. Datta, R. Pal, A. Choudhary, and E. R. Dougherty, “Control
approaches for probabilistic gene regulatory networks,”
Process. Mag., vol. 24, no. 1, pp. 54–63, 2007.
 D. P. Bertsekas, Dynamic Programming and Optimal Control, 3rd
ed. Belmont, MA: Athena Scientiﬁc, 2005.
 B. Faryabi, A. Datta, and E. R. Dougherty, “On approximate stochastic
control in genetic regulatory networks,” IET Syst. Biol., vol. 1, no. 6,
pp. 361–368, 2007.
 G. Vahedi, B. Faryabi, J.-F. Chamberland, A. Data, and E. R.
Dougherty, “Intervention in gene regulatory networks via a stationary
mean-ﬁrst-passage-time control policy,” IEEE Trans. Biomed. Eng.,
pp. 2319–2331, Oct. 2008.
 X. Qian, I. Ivanov, N. Ghaffari, and E. R. Dougherty, “Intervention in
gene regulatory networks via greedy control policies based on long-run
behavior,” BMC Syst. Biol., 2009.
 S. A. Kauffman, “Metabolic stability and epigenesis in randomly con-
structed genetic nets,” J. Theoret. Biol., vol. 22, pp. 437–467, 1969.
 I. Shmulevich, E. R. Dougherty, S. Kim, and W. Zhang, “Probabilistic
boolean networks: A rule-based uncertainty model for gene regulatory
networks,” Bioinform., vol. 18, no. 2, pp. 261–274, 2002.
 R. Pal, A. Datta, and E. R. Dougherty, “Robust intervention in proba-
bilistic Boolean networks,” IEEE Trans. Signal Process., vol. 56, no.
3, pp. 1280–1294, 2008.
 E. R. Dougherty and I. Shmulevich, “Mappings between probabilistic
Boolean networks,” Signal Process., vol. 83, no. 4, pp. 799–809, 2003.
 I. Ivanov and E. R. Dougherty, “Reduction mappings between proba-
bilistic boolean networks,” EURASIP J. Acoust. Signal Process., vol.
1, no. 1, pp. 125–131, 2004.
 M. Brun, E. R. Dougherty, and I. Shmulevich, “Steady-state probabil-
ities for attractors in probabilistic Boolean networks,” Signal Process.,
vol. 85, no. 10, pp. 1993–2013, 2005.
 X. Qian and E. R. Dougherty, “On the long-run sensitivity of proba-
bilistic Boolean networks,” J. Theoret. Biol., pp. 560–577, 2009.
 J. J. Hunter, “Stationary distributions and mean ﬁrst passage times
of perturbed Markov chains,” Linear Algebra Appl., vol. 410, pp.
 P. J. Schweitzer, “Perturbation theory and ﬁnite Markov chains,” J.
Appl. Probab., vol. 5, pp. 401–413, 1968.
 J. Norris, Markov Chains. Cambridge, U.K.: Cambridge Univ. Press,
 N. Ghaffari, I. Ivanov, X. Qian, and E. R. Dougherty, “A CoD-based re-
duction algorithm for designing stationary control policies on Boolean
networks,” Bioinformatics, vol. 26, pp. 1556–1563, 2010.
 E. R. Dougherty, S. Kim, and Y. Chen, “Coeffcient of determination in
nonlinear signal processing,” Signal Process., vol. 80, pp. 2219–2235,
 R. Pal, I. Ivanov, A. Datta, and E. R. Dougherty, “Generating Boolean
networks with a prescribed attractor structure,” Bioinformatics, vol. 54,
no. 21, pp. 4021–4025, Nov. 2005.
 N. D. Price, J. Trent, A. K. El-Naggar, D. Cogdell, E. Taylor, K. K.
Hunt, R. E. Pollock, L. Hood, I. Shmulevich, and W. Zhang, “Highly
accurate two-gene classiﬁer for differentiating gastrointestinal stromal
tumors and leiomyosarcomas,” Proc. Nat. Acad. Sci., vol. 104, no. 9,
pp. 3414–3419, 2007.
 I. Shmulevich and W. Zhang, “Binary analysis and optimization-based
normalization of gene expression data,” Bioinform., vol. 18, no. 4, pp.
 R. Hashimoto, S. Kim, I. Shmulevich, W. Zhang, M. L. Bittner, and E.
R. Dougherty, “A directed-graph algorithm to grow genetic regulatory
subnetworks from seed genes based on strength of connection,” Bioin-
form., vol. 20, no. 8, pp. 1241–1247, 2004.
Ivan Ivanov received the Ph.D. degree in mathe-
matics from the University of South Florida, Tampa.
He is an Assistant Professor with the Department
of Veterinary Physiology and Pharmacology, Texas
A&M University, College Station, TX. His current
research is focused on genomic signal processing,
and, in particular, on modeling the genomic regu-
latory mechanisms and on mappings reducing the
complexity of the models of genomic regulatory
Plamen Simeonov received the Ph.D. degree in
mathematics from the University of South Florida,
He is an Associate Professor of mathematics with
the Department of Computer and Mathematical Sci-
ences, University of Houston-Downtown, Houston,
TX. His current research interests are in the areas
of analysis, approximation theory, potential theory,
orthogonal polynomials and special functions, com-
puter-aided geometric design, and biostatistics.
Noushin Ghaffari received the M.Sc. degree in
computer information systems from the University
of Houston—Clear Lake, TX, in 2006.
Currently, she is pursuing the Ph.D. degree with
the Department of Electrical and Computer Engi-
neering, Texas A&M University, College Station.
Her research interests include: genomic signal
processing, systems biology, and computational
biology; especially complexity reduction and control
of Genetic Regulatory Networks.
Xiaoning Qian received the Ph.D. degree in elec-
trical engineering from Yale University, New Haven,
CT, in 2005.
Currently, he is an Assistant Professor with the
Department of Computer Science and Engineering,
University of South Florida, Tampa. He was with
the Bioinformatics Training Program, Texas A&M
University, College Station. His current research
interests include computational biology, genomic
signal processing, and biomedical image analysis.
Edward R. Dougherty received the M.S. degree
in computer science from Stevens Institute of
Technology, Hoboken, NJ, the Ph.D. degree in math-
ematics from Rutgers University, New Brunswick,
NJ, and the Doctor Honoris Causa by the Tampere
University of Technology, Finland.
He is a Professor with the Department of Electrical
and Computer Engineering, Texas A&M Univer-
sity, College Station, where he holds the Robert
M. Kennedy ’26 Chair in Electrical Engineering
and is Director of the Genomic Signal Processing
Laboratory. He is also co-Director of the Computational Biology Division of
the Translational Genomics Research Institute, Phoenix, AZ, and is an Adjunct
Professor with the Department of Bioinformatics and Computational Biology,
University of Texas M. D. Anderson Cancer Center, Houston. He is author
of 15 books, editor of ﬁve others, and author of 250 journal papers. He has
contributed extensively to the statistical design of nonlinear operators for image
processing and the consequent application of pattern recognition theory to
nonlinear image processing. His current research in genomic signal processing
is aimed at diagnosis and prognosis based on genetic signatures and using gene
regulatory networks to develop therapies based on the disruption or mitigation
of aberrant gene function contributing to the pathology of a disease.
Dr. Dougherty is a fellow of SPIE, has received the SPIE President’s Award,
and served as the editor of the SPIE/IS&T Journal of Electronic Imaging.At
Texas A&M University received the Association of Former Students Distin-
guished Achievement Award in Research, been named Fellow of the Texas En-
gineering Experiment Station, and named Halliburton Professor of the Dwight
Look College of Engineering.
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