**Detail BioComputing Elective Course Description**

The biomedical signal processing course provides an application-intensive approach to biomedical signal processing and application of mathematical tools. Topics include a review of signals and systems theory, Fourier analysis, sampling theorem, discrete signal processing, noise characteristics of real-world bio-signals such as biologic, sensor, electronics and digital processing noise, linear and adaptive filtering, wavelet transforms, denoising, compression, classification and feature extraction applications to 1D and image biosignals, review of practical considerations in medical device design as relates to signal processing such as scalability, robustness, testability, algorithm complexity and regulatory issues.**Reference books and materials** [1] Najarian, K., and Splinter, R., Biomedical signal and Image processing, CRC, 2006 [2] Bruce, E. N., Biomedical Signal processing and Signal Modeling, Wiley & Sons, 2001 [3] Reddy, Biomedical Signal Processing: Principles and Techniques, Tata McGraw Hill, 2005 [4] Rangayyan, R. M., Biomedical Signal Analysis: A Case Study Approach, IEEE Press, 2002

The digital image processing course examines the properties of digital images and the method of processing. Topics include 2-D sequences and systems, separable systems, properties of digital images, image formation, sampling, time and frequency representation of images, transformation techniques including Fourier, z transform, difference equations, and wavelets transform, human visual system including perception, vision properties, color, and sensors, image enhancement, image restoration, geometrical image modification, filtering, and edge detection, binary image processing, morphological image processing, halftoning and edge detection, image coding and compression models for loss-free, lossless, and lossy compressions, motion estimation and compensation, compression standards and formats.**Reference books and materials** [1] Gonzalez, R. C., and Woods, R. E., Digital Image Processing, Prentice Hall, 2008 [2] Jahne, B., Digital Image Processing, Springer, 2005 [3] Pitas, I., Digital Image Processing Algorithms and Applications, Wiley-IEEE, 2000 [4] Acharya, T., and Ray, A. K., Image Processing: Principles and Applications, Wiley, 2005 [5] Nixon, M. S., and Aguado, A. S., Feature Extraction and Image Processing, 2nd Ed., Elsevier, 2008

The theory of computations course provides the fundamental complexity theory and models useful for solving computational problems. Topics include basic computational theory, computational models including nondeterministic alternating and probabilistic machines, Boolean circuits, complexity classes related to models of computing including NP, polynomial hierarchy, BPP among others, complete problems, interactive proof systems and probabilistic proofs, randomized algorithms, structural complexity and complexity hierarchy.**Reference books and materials** [1] Ross, S. M., Simulation, Academic Press, 2006 [2] Goldreich, O., Computational Complexity: A Conceptual Perspective, Cambridge Press, 2008 [3] Arora, S., and Barack, B., Computational Complexity: A Modern Approach, Cambridge University Press, 2009 [4] Zimand,M., Computational Complexity: A Quantitative Perspective, Elsevier, 2004

The algorithms for computational biology course provide the background knowledge useful for the design of algorithms for analysis of biological systems. Topics include vector geometry, matrix algebra and recursive relationship, algorithm concepts and optimization, basic biological techniques for predicting interactions, databases, graph algorithm libraries, network topological properties, phylogenetic profiles, predicting function including integer programming, modularity, partitioning heuristics, spectral partitioning and dense sub-graph detection, network searching and alignments, speeding-up searches and color coding, random models of biological networks including duplication model, small world, preferential attachment models, evolving modularity, generating random graphs, dynamic networks, linear programming algorithm, semi-definite, side chain packing, and phylogenetic trees and reassortment detection algorithm.**Reference books and materials** [1] Gusfield, D., Algorithms on Strings, Trees, and Sequences: Computer and Computational Biology, Cambridge University Press, 1997 [2] Pevzner, P., Computational Molecular Biology: An Algorithmic Approach, MIT Press, 2000 [3] Jiang, T., Xu, W., and Zhang, M. Q., Current Topics in Computational Molecular Biology, MIT Press, 2002 [4] Deonier, R. C., Tavare, S., and Waterman, M. S., Computational Genome Analysis, 1st Ed., 2005

The bioinformatics course provides computational methods and development of algorithms to address problems in molecular biology. Topics include molecular genetics of DNA, RNA and protein, cellular organization, modern biochemical techniques such as cloning and DNA sequencing, bioinformatics problems, bioinformatics database, representing and retrieval of sequences, sequence comparison with dot matrices and dynamic programming, statistics of pattern appearance, multiple sequence alignment, sequence database searching, learning machine basics, phylogenetic tree construction and algorithms, representing and finding sequence features, RNA and protein structure prediction, gene prediction and annotation, gene finding, retrieving and displaying macromolecular structures, microarrays and gene expression analysis models and technologies, biomolecular computing.**Reference books and materials** [1] Xiong, J., Essential Bioinformatics, Cambridge University Press, 2006 [2] Mount, D. W., Bioinformatics: Sequence and Genome Analysis, CSHL Press, 2004 [3] Gautham, N., Bioinformatics: Databases and Algorithms, Alpha Science, 2006 [4] Baxevanis, A. D., and Francis Ouellette, B. F., Bioinformatics: A Practical Guide to the Analysis of Genes and Proteins, Wiley & Sons, 2001 [5] Pevsner, J., Bioinformatics and Functional Genomes, Wiley & Sons, 2003

The mathematical neurobiology course provides insight to the elements of neurophysiology and neuroanatomy for the development of quantitative models of nerve cell and brain phenomena and to develop and analyze several different mathematical models in neurobiology. Topics include difference equations, dynamical systems theory, ordinary differential equations and partial differential equations, linear membrane and cable theory, Rall's equivalent cylinder model of the nerve cell, determination of active membrane properties using linear theory, action potentials including Hodgkin-Huxley (HH) model and FitzHugh-Nagumo (FHN) model, asymptotic and computational determination of the action potential using the FHN equations, bursting phenomena in excitable cells, nonlinear waves of spreading cortical depression, and rotating waves in excitable media.**Reference books and materials** [1] Miftahof, R., Gil Nam, H., and Wingate, D. L., Mathematical Modeling and Simulation in Enteric Neurobiology, World Scientific, 2009 [2] Laing, C., and Lord, G. J., Stochastic Methods in Neuroscience, Oxford Press, 2010 [3] Poznanski, R. R., Modeling in Neurosciences: From Ironic Channels to Neural Networks, Harwood Academic Press, 1999 [4] Feng, J., Computational Neuroscience: A Comprehensive Approach, Chapman & Hall, 2004 [5] Ascoli, G. A., Computational Neuroanatomy: Principles and Trends, Human Press, 2002

The algorithm design course provides the basic concepts and principles to examine and design efficient algorithms for a variety of computational problems and applications. Topics include dynamic programming, methods of algorithm design and analysis including data structures, network flows, matching, and linear programming, ellipsoid algorithm, probabilistic algorithm techniques, approximation algorithms for NP problems, geometric algorithms, number theoretic algorithms, on-line computation, and parallel computing.**Reference books and materials** [1] Hopcroft, J. E., Motwani, R., and Ullman, J. D., Introduction to Automata Theory, Languages and Computation, 3rd Ed., Addison Wesley, 2006 [2] Cormen, T. H., Lieserson,C. E., Rivest, R. L., and Stein, C., Introduction to Algorithms, 3rd Ed., MIT Press, 2009 [3] Kleinberg, J., Algorithm Design, Person Education, 2006 [4] Goodrich, M. T., and Tamassia, R., Algorithm Design: Foundations, Analysis, and Internet Examples, Wiley, 2006 [5] Skiena, S. S., The Algorithm Design Manual, 3rd Ed., MIT Press, 2009

The analysis of genomic data course examines the approach for the analysis and display of large scale biological data sets using various algorithms and machine learning techniques. Topics include clustering techniques for gene expression and protein data analysis, machine learning techniques, biological networks, joint learning from multiple data sources, visualization issues for large scale biological data sets.**Reference books and materials** [1] Berrar, D. P., Dubitzky, W., and Granzow, M., A Practical Approach to Micro-array Data analysis, Springer, 2003 [2] Zhang, A., Advanced Analysis of Gene Expression Micro-array Data, World Scientific, 2006 [3] Allison, B. D., DNA Micro-arrays and Related Genomic Techniques: Designs, Analysis, and Interpretation of Experiments, Chapman & Hall, 2006 [4] Azuaje, F., and Dopazo, J., Data Analysis and Visualization in Genomics and Proteomics, Wiley & Sons, 2005