Selected Online Publications

Monograph:    Probability Distributions in Quantum Statistical Mechanics (PDF)

Papers:  (Available as .pdf unless otherwise specified)

Wavelet sampling and generalization in neural networks (with Z. Zhang), Neurocomputing, 11-May, DOI: 10.1016/j.neucom.2017.04.054, May 11, 2017.


An application of spectral regularization machine learning and cancer classification (with L. Raphael), Excursions in Harmonic Analysis 5, Norbert Wiener Center, 129, 2017.


Functional analytic regularization in machine learning (with Y. Fan and L. Raphael), preprint, 2017


Differentiation and integration of machine learning feature vectors  (with X. Mu and A. Pavel), Machine Learning and Applications 16, IEEE, Washington, DOI: 10.1109/ICMLA.2016.010, 2016


On the average uncertainty for systems with nonlinear coupling (with K. Nelson and S. Umarov), Physica A, Oct. 27, 2016, DOI:  10.1016/j.physa.2016.09.046, 2016.


A Method for Interpolation Wavelet Construction Using Orthogonal Scaling Functions (with Z. Zhang), SPA 2016, Warsaw, 20-35, 2016.

Unique Recovery from Edge Information (with B. Allen), Sampling Theory and Applications 2015, IEEE, Washington, DC., 2015.

On Relating Interpolation Wavelets to Interpolation Scaling Functions in Multiresolution Analyses (with Z. Zhang),  Circuits, Systems & Signal Processing  34, June 2015, 1947-1976. DOI 10.1007/s00034-014-9937-8, 2015.

Real-time simulation of large open quantum spin systems driven by dissipation (with D. Banerjee, F.-J. Jiang and U.-J. Wiese) Phys. Rev. B (Rapid Communications) 90, 241104(R) Published 2 December. DOI: 10.1103/PhysRevB.90.241104, 2014.

The Marr conjecture in one dimension and uniqueness of wavelet transforms ArXiv:1401.0542v2 [math.FA] 2014.

On the probabilistic continuous complexity conjecture  Posted 2012 arXiv:1212.1263

Ensemble machine methods for analysis of transcription factor and DNA interactions (with Y. Fan and C. DeLisi), preprint 2014.

Computational methods for analysis of transcriptional networks (with Y. Fan and C. DeLisi), Springer Handbook of Bioinformatics, Springer-Verlag, Berlin, 327-354, 2014.

Current trends in genome-wide association studies (with T. Yang and C. DeLisi), in Data Mining for Systems Biology, Hiroshi Mamitsuka and Minoru Kanehisa, eds., Springer-Verlag, 2012.

Pathway-based classification of cancer subtypes (with S. Kim and C. DeLisi), Biology Direct (2012), 7:21 doi:10.1186/1745-6150-7-21; Published: 3 July 2012.

On some integrated approaches to inference (with L. Plaskota), technical report (2011).

Empirical normalization for quadratic discriminant analysis and classifying cancer subtypes (with N. Nikolaev), Machine Learning and Applications 10 (2011), IEEE, Washington, 374-379.

Top scoring pairs for feature selection in machine learning with applications to cancer outcome prediction  (with P. Shi, S. Ray and Q. Zhu), BMC Bioinformatics, 12:375 (2011). DOI:10.1186/1471-2105-12-375

Combinations of newly confirmed glioma-associated loci link regions on chromosomes 1 and 9 to increased disease risk (with T. Yang and C. DeLisi), BMC Medical Genomics 4:63 doi:10.1186/1755-8794-4-63 (2011).

Regularization techniques for machine learning on graphs and networks with biological applications (with Y. Fan, S. Kim, L. Raphael, and C. DeLisi, Communications in Mathematical Analysis 8 (3; Special Volume in Honor of Peter Lax) (2010), 136-145.

Smoothing gene expression using biological networks (with Y. Fan, S. Kim,  and C. DeLisi), Machine Learning and Applications 9, IEEE, Washington DC. (2010)

A new phylogenetic diversity measure generalizing the Shannon index (with B. Allen and Y. Bar Yam,  American Naturalist 174 (2009),236-243.


Ensemble machine methods for DNA binding (with Y. Fan, and C. DeLisi), Machine Learning and Applications 7,  M. Wani, et al., eds.  IEEE, Washington (2008),709-716.  Algorithm available here.


Regulatory analysis for exploring human disease progression (with D. Holloway and C. DeLisi), Biology Direct 3:24, 2008. Algorithm available here.


Building transcription factor classifiers and discovering relevant biological features,  (with D. Holloway and C. DeLisi), BiologyDirect 3:22, 30 May 2008. Algorithm available here.


SVMMotif:  A machine learning motif algorithm (with Y. Fan, D.Holloway and C. DeLisi), International Conference on Machine Learning and Applications 6, 573-580, IEEE, Washington, 2007. Algorithm available here.


Learning methods for DNA binding in computational biology (with D. Holloway, et al.) International Joint Conference on Neural Networks,  20, IEEE, Los Alamitos 1605, 2007.


Machine learning for regulatory analysis and transcription factor target prediction in yeast (with D. Holloway and C. DeLisi), Systems and Synthetic Biology 1 (2006), 25-46.                                                                                                              


Approximating functions in reproducing kernel Hilbert spaces via statistical learning theory (with L. Raphael), in Splines and Wavelets, G. Chen and M.J. Lai, eds, (2006) 270-286

Machine learning methods for transcription data integration (with D. Holloway and C.DeLisi),IBM Journal of Research and Development 50(2006), 631-644 (Abstract only - Journal link is here)

Information-based nonlinear approximation:  An average case setting (with L. Plaskota),  J. Complexity 21 (2005),211-228.

Extending Girosi's approximation estimates for functions in Sobolev spaces via statistical learning theory (with L. Raphael and D. Williams), J. Analysis and Applications 3 No. 2 (2005), 67-90.

Statistical likelihood representations of prior knowledge in machine learning (with L, Plaskota and A. Przybyszewski), Artificial Intelligence and Applications, M.H. Hamza, Ed., Innsbruck (2005), 467-472.

Integrating genomic data to predict transcription factor binding  (with D. Holloway and C. DeLisi), Genome Informatics 16 (2005), 83-94.

Machine learning and statistical MAP methods (with L. Plaskota and A. Przybyszewski), Intelligent Information Processing, Springer, Berlin (2005), 441-445.

Complexity of predictive neural networks (with L. Plaskota) Proceedings of International Conference on Complexity,  Y. Bar-Yam, Ed., Cambridge, MA (2003)

Sup-norm convergence rates of wavelet expansions in Besov Spaces (with L. Raphael), in Applicable Mathematics (2002), 193-203.

Pointwise wavelet convergence in Besov and uniformly local Sobolev Spaces  (with L. Raphael), J. Contemporary Math. Analysis 36 (2002), 51-68.

Complexity of neural network approximation with limited information:  a worst-case approach (with L. Plaskota), J. Complexity 17 (2001), 345-365.

Convergence rates of multiscale and wavelet expansions (with L. Raphael), in Wavelet Transforms and Time-FrequencySignal Analysis, American Mathematical Society CBMS Volume, L.Debnath, Ed. (2001), 37-65.

A characterization of wavelet convergence in Sobolev spaces (with L. Raphael), Applicable Analysis 78 (2001), 271-324.

Complexity of regularization RBF networks (with L. Plaskota), in Proceedings of International Joint Congress on Neural Networks,INNS, Washington (2001), 342-346.

Review of Complexity and Information, (by J.F. Traub and A.G. Werschulz), Bull. Amer. Math Soc. 37 (2000), 199-204.

Information complexity of neural networks (with L. Plaskota), Neural Networks 13 (2000),365-376.

Oscillation criteria for delay equations (with Y.Sficas and I. P. Stavroulakis), Proc. Am. Math. Soc. 128 (2000), 2989-2997.

Neural networks, radial basis functions, and complexity (with L. Plaskota), Proceedings of Bialowieza Conference on Statistical Physics, 1997, 122-145.

Exact smoothing properties of Schrodinger semigroups (with A. Gulisashvili), American J. Math. 118 (1996), 1215-1248

Pointwise convergence of wavelet expansions (with S. Kelly and L. Raphael), Bull. Amer. Math. Soc. 30 (1994), 87-94

Local convergence of wavelet expansions (with S. Kelly and L. Raphael), J. Functional Anal. 126 (1994), 102-138


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