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**,

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 *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,

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*,

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

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,

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.,

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,

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

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*,

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

Logo - ps file format