Fundamental concepts and current research in natural language processing. Algorithms for processing linguistic information. Computational properties of human languages. Analysis at the level of morphology, syntax, and semantics. Modern quantitative techniques of using large corpora, statistical models, and machine learning applied to problems of acquisition, disambiguation and parsing. Applications such as machine translation and question answering.

Introduction to cryptographic concepts. Symmetric encryption, the public-key breakthrough, one-way functions, hash functions, random numbers, digital signatures, zero-knowledge proofs, modern cryptographic protocols, multi-party computation. Everyday use examples including online commerce, BitTorrent peer-to-peer file sharing, and hacking some old encryption schemes.

Advanced topics in data structures, algorithms, and their computational complexity. Asymptotic complexity measures. Graph representations, topological order and algorithms. Forests and trees. Minimum spanning trees. Bipartite matching. Union-find data structure. Heaps. Hashing. Amortized complexity analysis. Randomized algorithms. Introduction to NP-completeness and approximation algorithms. The shortest path methods. Network flow problems.

Algorithms, models, representations, and databases for collecting and analyzing biological data to draw inferences. Overview of available molecular biological databases. Sequence analysis, alignment, database similarity searches. Phylogenetic trees. Discovering patterns in protein sequences and structures. Protein 3D structure prediction: homology modeling, protein folding, representation for macromolecules, simulation methods. Protein-protein interaction networks, regulatory networks, models and databases for signaling networks, data mining for signaling networks.

Tools and techniques for ensuring software reliability. Specification formalisms and languages. Modeling tools and languages. Unit and integration testing. Automated testing and verification tools and algorithms. Mathematical representations for programs and executions. Hoare logic. Specification using modular contracts: Preconditions, postconditions, loop and object invariants. Ownership systems. Automated test generation. Model-based testing. Coverage metrics for testing adequacy. Type and effect systems for reliable software. Software model checkers. Static analysis. Concurrent/multi-threaded programs. Correctness criteria for concurrent programs: race-freedom, atomicity, linearizability and serializability. Testing, verification and debugging tools for concurrent programs.

Presentation of research topics to introduce the students into thesis research.

The following objectives will be met through extensive reading, writing and discussion both in and out of class.Build a solid background in academic discourse, both written and spoken. Improve intensive and extensive critical reading skills. Foster critical and creative thinking. Build fundamental academic writing skills including summary, paraphrase, analysis, synthesis. Master cohesiveness as well as proper academic citation when incorporating the work of others.

Network flow models and optimization problems. Algorithms and applications. Minimum spanning tree problem. Shortest path problems. Maximum flow problems, minimum cuts in undirected graphs and cut-trees. The minimum cost network flow problem. Matching problems. Generalized flows. Multicommodity flows and solution by Lagrangean relaxation, column generation and Dantzig-Wolfe decomposition. Network design problems including the Steiner tree problem and the multicommodity capacitated network design problem; their formulations, branch-and-cut approaches and approximation algorithms.

Geometric, physics-based, and probabilistic modeling methodology and associated computational tools for interactive simulation: computer programming, numerical methods, graphical modeling and programming, physics-based and probabilistic modeling techniques.

Fundamental concepts of modeling, control sensing, and intelligence of robotic systems. Robotic manipulators and mobile robots. Forward and inverse kinematics, trajectory planning, dynamics, control, and programming of robotic manipulators. Hardware components of mobile robots, visual and navigational sensors, pose estimation, navigation, and reasoning in mobile robots. Hands-on experience with robotic arms and mobile robots in a laboratory environment.

Provides hands-on teaching experience to graduate students in undergraduate courses. Reinforces students' understanding of basic concepts and allows them to communicate and apply their knowledge of the subject matter.

Discrete and continuous random variables and processes, functions of random variables, independence of random variables. Central Limit Theorem. Discrete-time random processes, continuous-time random processes, stationary random processes, ergodicity, auto and cross correlation functions, power spectral density; spectral estimation, white noise processes, Markov chains.

Sound and human speech systems, phonetics and phonology, speech signal representations, role of pitch and formants, pitch-scale and time-scale modifications, basics of speech coding and VoIP systems, fundamentals of pattern and speech recognition, search algorithms for speech recognition.

Linear Algebra Review, Normal Matrices, Quadratic Forms and Semidefinite Matrices, Inner Product and Norm Spaces, State Space Descriptions for Continuous and Discrete Time Systems, Controllability, Observability, Stability, Realization Theory.

Review of multi-dimensional sampling theory, aliasing, and quantization, fundamentals of color, human visual system, 2-D Block transforms, DFT, DCT and wavelets. Image filtering, edge detection, enhancement, and restoration. Basic video file formats, resolutions, and bit rates for various digital video applications. Motion analysis and estimation using 2D and 3D models. Motion-compensated filtering methods for noise removal, de-interlacing, and resolution enhancement. Digital image and video compression methods and standards, including JPEG/JPEG2000 and MPEG-1/2 and 4. Content-based image and video indexing and MPEG-7.

Study of computational models of visual perception and their implementation in computer systems. Topics include: image formation; edge, corner and boundary extraction, segmentation, matching, pattern recognition and classification techniques; 3-D Vision: projection geometry, camera calibration, shape from stereo/silhouette/shading, model-based 3D object recognition; color texture, radiometry and BDRF; motion analysis.

Entropy, Relative Entropy and Mutual Information; Asymptotic Equipartition Theory; Entropy Rates of a Stochastic Process; Data Compression; Kolmogorov Complexity; Channel Capacity; Differential Entropy; The Gaussian Channel; Maximum Entropy and Spectral Estimation; Rate Distortion Theory, Network Information Theory.

Characterization of communication signals & systems, digital modulation schemes, optimum reception for the additive white Gaussian noise (AWGN) channel, signal design for band-limited channels, Nyquist criterion, intersymbol interference (ISI), optimum reception for channels with ISI and AWGN, linear equalization, decision feedback equalization, adaptive equalization, channel capacity & coding, linear block codes, convolutional codes, multichannel and multicarrier systems, spread spectrum signals for digital communications, multiuser communications. Design oriented exercises using computer aids.

Adaptive Filtering, LMS, RLS and Fast Algorithms, Array Signal Processing, Blind Algorithms & Subspace Methods for Channel Identification and Equalization, Convex Optimization and Its Applications, Multirate Signal Processing and Filter Banks.

The cellular concept, channel assignment strategies, frequency reuse, handoff strategies, interference sources, mobile radio propagation, large-scale path loss, small-scale fading and multipath, modulation techniques for mobile radio, diversity combining, transmit and receive antennas for wireless communication systems, multiple access techniques in wireless, wireless system design for delay intolerant services, wireless system design for delay tolerant services, error correction coding and ARQ schemes, wireless networking, wireless systems & standards: GSM, IS-95, cdma2000, W-CDMA, 3GPP2 1xEV-DO, 3GPP2 1xEV-DV, fourth generation wireless system proposals. Design oriented exercises using computer aids.

Issues in digital integrated circuit design. The devices. CMOS Inverter. Combinational logic gates in CMOS. Designing sequential logic circuits. Designing arithmetic building blocks. Timing issues in digital circuits. Memories and array structures. Design verification and testing. Design projects using computer aided design tools: SPICE, MAGIC, IRSIUM, OCTTOOLS. Project design requirements include architectural design, logic and timing verification, layout design, and test pattern generation. The resulting chips may be fabricated.

Introduction to mathematical formulations and computational techniques for the modeling and simulation of engineering and other kinds of systems, including electronic, mechanical, biological, biochemical, virtual, abstract and multi-domain dynamical systems. Applications from various engineering disciplines and the sciences. Matrix formulation of equations for linear problems. Formulation of equations for nonlinear problems & linearization. Numerical solution of linear algebraic equations. Gaussian elimination, computations with sparse & structured matrices. Floating point number representation & arithmetic. Numerical conditioning, ill-conditioned problems. Numerical solution of nonlinear algebraic equations. Fixed point iteration & Newton’s method in one dimension. Newton’s method for system of coupled nonlinear algebraic equations. Improving convergence of Newton’s method. Numerical solution of ordinary differential equations. Forward & backward Euler, trapezoidal rule. Multistep methods, accuracy & stability. Implicit vs explicit techniques, region of stability, stiff problems.

Review of electromagnetism; geometrical optics, analysis of optical systems; wave properties of light, Gaussian beams, beam optics; interaction of light with matter, spontaneous and stimulated emission, optical amplification, theory and applications of lasers, optical interactions in semiconductors, light emitting diodes and diode lasers; detectors, noise in detection systems; light propagation in anisotropic crystals, Pockels and Kerr effect, light modulators; nonlinear optics, second harmonic generation, phase matching, nonlinear optical materials.