SYLABI OF DIFFERENT COURSES
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Representation of Information, Number systems, integer and floating point representation, character codes (ASCII, EBCDIC). Error detection, Correction codes. Basic Building blocks: Boolean Algebra, Combinational logic design, flip-flops, registers, ALU; Arithmetic and Logic Operations Organization of Control Units. Memory: types and organization, Peripheral Devices. I/O devices (Video terminals and printers) and controllers. Storage Devices (Tape and disks). Programmed interrupt control mechanisms. I/O controllers, Bus bandwidths. Assembly Language Programming; Programmers model of a machine.
Example of a typical 16 to 32 bit processor. Registers, Addressing modes, Instruction set, use of an assembly language for specific programs for typical problems like: Table Search, subroutines, Symbolic and numeric manipulations and I/O.
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ADVANCED MATHEMATICAL TECHNIQUES
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Statistical methods : Measurements, parametric and non-parametric estimators, Point estimators of parameters; Distribution of estimators, Test of hypotheses; Linear regression.
Stochastic theory : Random variables and processes, Special classes - Markov sequences and processes, and Poisson processes; Correlation functions and spectral decomposition; Sampling and quantization of random signals.
Differential equations : Basic methods of solution, Runge-Kutta methods; Adaptive methods; Introduction to partial differential equations (PDE), Relaxation and spectral methods; Stability analysis.
Integral transforms : Generalized Fourier series, Fourier transform, Discrete Fourier transform, Fast Fourier transform; Laplace transform, causality and stability in the s-domain; z-Transform, Relation to Fourier and Laplace transforms.
Signal processing : Linear systems, Continuous-time and discrete-time systems, Frequency response, convolution and impulse response of a LTI system; Differential and difference equations and frequency response in terms of 'State Variables'.
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Integration and Differentiation : Numerical integration, Simpson's rule, Gaussian quadrature, Monte Carlo integration, multidimensional integrals, numerical differentiation.
Interpolation and extrapolation : Polynomial interpolation, Use of rational functions, Continued fraction methods, Application of Fourier transform; Extrapolation and inverse interpolation, Cubic spline.
Matrices : System of linear equations, Inversion and LU-decomposition; Eigen-values and eigen-vectors; Complex matrices and generalized eigen-value problem.
Methods of least squares : Statistical description of data, uncertainties and their propagation; Method of maximum likelihood and method of least squares; Linear least-squares fit to data, Nonlinear fit to data.
Catastrophe theory : Extrema of functions and stability analysis, Bifurcations, Hysteresis, Tunneling phenomenon.
Graphical Representation of Results : Basic ingredients of computer graphics, Functions with multiple variables and their representation.
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Problem Analysis, flow Charts, decision tables. Pseudo codes and Algorithms, High level language and Programmer's Model of Computer System.
Algorithmic Programming Language: Representation of integers, reals, characters, constants and variables, arithmetic expressions and their evaluation using rules of hierarchy. Assignment statements, Logical constants variables and expression Control structures - sequencing alteration, iteration. Arrays, Manipulating vectors and matrices. Subroutines overhead cost, interpretation of the variances.
Introduction to computerized accounting system : Coding logic and codes required, master files, transaction files, Introduction to documents used for data collection Processing of different files and output obtained.
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Fundamental Notations: Primitive and Composite Data types, Time and Space Complexity of Algorithms, Sorting Algorithms. Data Structures: Stacks, Queues, Arrays, Linked Lists, Trees and Graphs.
Union-Find Structure, Advanced Data structure used in Computational Geometry and Graph theory.
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MONTE CARLO TECHNIQUES & MOLECULAR DYNAMICS
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Monte Carlo Technique
Generation of random numbers, uniform distribution, linear congruence method; Tests for randomness : Frequency and run tests; Random numbers with a given distribution, Rejection technique, Metropolis algorithm. Data simulation and hypothesis testing, Estimate of confidence region with Monte Carlo methods.
Applications of MC technique : Molecular diffusion, Brownian motion; Percolation; Critical phenomena and Ising model; Random matrix ensembles; Path integrals in quantum mechanics; Fractals.
Molecular Dynamics
Newtonian and Hamiltonian dynamics; Phase-space trajectories, Fundamental distributions; Elements of sampling theory, Periodic boundary conditions; Conservation principles.
Kinematics of collisions; Collision times, Simulation algorithm, Phase diagrams, Unpredictability; Finite-difference methods, Euler's method, Algorithm for molecular dynamics, Reliability of trajectories.
Dynamic properties; Time correlation functions, Transport coefficients, Static and dynamic structure; Thermodynamic response functions.
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Integral wavelet transform, Time-frequency analysis; Inversion and duals; Classification of wavelets : Multi-resolution analysis, splines and wavelets; wavelet decompositions and re-constructions;
Gabor transform, Short-time Fourier transforms and uncertainty principle; dyadic wavelets and inversions, Frames, Wavelet series;
Cardinal spline spaces, Two-scale relation, Interpolatory display algorithm, Computation of cardinal splines; Spline approximate formulae, Spline interpolation formulae.
Scaling functions and Wavelets : Multi-resolution analysis, Direct-sum decompositions, Linear-phase filtering, Compactly supported wavelets.
Orthogonal wavelets and examples; Orthogonal two-scale symbols; Wavelet packets, Orthogonal decomposition of wavelet series;
Application to signal and image processing; Use in pattern recognition and neural networks.
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Neuro-physiological background: dynamics of neurons and synapses, from biology to information processing.
Modelling: neuron as perceptron, beyond the basic perceptron, building blocks for attractor neural networks; two state neural models;
Hebb's learning rule; dynamics of discrete neurons; synchronous and asynchronous dynamics; noise and its role in the retrieval of information; memory catastrophe and the ways out of it.
Optimization theory; Simulated annealing; Genetic Algorithms: biological background and its adaptation to the optimization problem;
Examples of applications - spin glass as a case study; building a classifier system; the schema theorem.
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Perfect spatial order and lattice symmetries; Positional and topological disorder; Self-similarity and dilatory symmetry;
Fractals - meaning and types; fractal dimensions;
Percolation - meaning and definitions; bond and site percolation; critical parameters; ultrametric structure of percolation; fractal nature of percolation cluster;
Synergetics - meaning and examples; stochasticity and predictability - statistical mechanics, quantum fluctuations.
Chaos; limit cycles; bifurcation; attractors; Lyapunov exponents; discrete maps; Self organization.
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Common classes of mathematical models: Cellular automata (CA) as an alternative to differential equations in modeling physical problems, different types of CA, Statistical mechanics of CA, Local and global properties of elementary CA.
Algebraic properties of CA; Additive CA, CA over the ring Zp of integers modulo p (p being a prime number) ; Higher dimensional and order CA; Non-additive CA.
Universality and complexity of CA; Qualitative classification; Class 1, 2, 3, and 4 of CA; Totalistic CA.
Physics-like models of computation; CA equivalent to universal Turing machine; CA machines CAM6 and CAM7; A computer architectural view on CA; CA complexity trade-offs.
Pattern generation and image processing using CA; Soliton-like behavior in CA; Realization of FIR and IIR digital filters using filter-automata.
CA of fluids; Thermodynamics and hydrodynamics using simple models of CA; CA for fluid dynamics modeling.
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Diakoptics : Topological and algebraic structures, Underlying physics; Need of diakoptics for computational considerations; Tearing and partitioning of topological and algebraic structures.
Isolation of subdivisions : Tieless subdivisions, Intersection network, Diakoptics of nonlinear structures and for optimization problems. Topological models of elastic field.
Electric circuit models of partial differential equations : Combined diffusion and wave terms; Pyramiding super-system solutions; Diakoptics for eigen value problems and time varying problems.
Integer programming : Matrix games; Games of strategy and chance; Triadic games and coalitions, Iterated games, Prisoner's dilemma models.
Artificial neural networks as learning circuits : Network architecture, Back-propagation algorithms; Associative learning; Hebb - , Kohonen - , and Elman learners; Self-organization in neural networks; Hopfield model.
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Digital image processing : problems and applications, image representation and models,image enhancement, image restoration and analysis, image reconstruction from projections and image coding, data compression.
2-d systems and related mathematical preliminaries: linear systems and shift invariance, Fourier Transform (FT) correlation, optimal modulation transfer function (MTF), random processes, stationarity, statistical independence, orthogonality.
Image perception : light and related quantities, MTF of visual system and visibility function, mono-chrome vision models, image fidelity, color difference measures, color vision model and temporal properties of vision, image quality evaluation.
Image sampling and quantization : image scanning and TV standards, image display and recording, 1-d and 2-d sampling theory, reconstruction from samples, practical limitations of sampling and reconstruction, image quantization, optimum quantizers, visual quantization.
Image transforms : 2-d orthogonal and unitary transforms, 1-d and 2-d discrete FT (DFT), the Hadamad transform, the KL transform, singular value decomposition (SVD) transform.
Image enhancement : point operators, histogram modeling, spatial operators, transform domain operators, multi-spectral image enhancement, color image enhancement.
Image filtering and restoration : image observation/degradation models, inverse and Wiener filtering, Fourier domain filters, filtering based on image transforms, interpolation and smoothing splines, generalized inverses, digital processing of speckle images, maximum entropy and Bayesian methods.
Image analysis and computer vision : spatial feature extraction, transform features, edge detection, boundary extraction, boundary representation, region representation, moment based representation, structure, shape features, texture, scene matching and detection, image segmentation, image understanding.
Image data compression : motivation, pixel coding, predictive coding techniques, transform coding of images, theory and algorithms, hybrid coding and vector DPCM, video coding, inter-frame coding, coding of 2 tone images, image coding standards, JBIG, JPEG and MPEG-I and II.
Advanced topics : image representation and models, scale space, pyramids, sub-bands, wavelets, image processing, software, and hardware.
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Efficiency of algorithms; Asymptotic Notation; Analysis of Algorithms; Solving recurrences; Application of data structures; Greedy Algorithms, Spanning trees, shortest paths, knapsack problem, scheduling problem; Divide-and-conquer, binary search, sorting; Dynamic programming principle of optimality; Graph Algorithms, BFS, DFS, Back tracking, Branch and Bound; Computation Complexity, reductions and introduction to NP-completeness; Examples and brief overview of heuristic, probabilistic and parallel algorithms, String Matching methods.
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Introduction to File Structures; Fundamental File Processing Operations; Physical Files and Logical Files, Opening files, Closing Files, Reading and Writing, Seeking. Secondary Storage and System Software; Disks, Magnetic Tape, Disk Versus Tape, Buffer Management, I/O in UNIX. Fundamental File Structure Concepts; Field and Record Organization, Record Access, File Access and File Organization. Organizing Files for Performance; Data Compression, Reclaiming Space in Files, Key sorting. Indexing; Consequential Processing and the Sorting of Large Files; B-Trees and Other Tree-structured File Organizations; The B+ Tree Family and Indexed Sequential File Access; Hashing; Extendible Hashing;
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Statistical Pattern Recognition
Introduction, Gaussian model, discriminant functions, classifier performance, risk and errors.
Supervised learning using parametric and non-parametric approaches, ML estimation, Bayesian parameter estimation approach, Parzen windows, k-nn estimation.
Un-supervised learning and clustering, the clustering concept, c-means algorithm, learning vector
quantization, clustering strategies, a hierarchical clustering procedure.
Syntactic Patter Recognition
Introduction to formal languages, string languages for pattern recognition, selection of pattern primitives, pattern grammars. PDL, transition network grammar for pattern description, automated transition nets (ATNs)
Higher dimensional grammars, Web and graph grammars, tree grammars, grammar describing 3-d objects.
Syntax analysis as a recognition procedure, parsing, top-down parsing, bottom-up parsing, Cocke-Younger-Kasami (CKY) parsing algorithm, Earley's parsing algorithms, LL(k) and LR(k) grammars.
Stochastic languages for syntactic pattern recognition, basic formulation, probability measures associated with linear and context-free grammars, languages accepted by stochastic automata, stochastic programmed and indexed grammars.
Structural Pattern Recognition
Imaging model, radiometric models, geometric models, sampling and quantization, tessellation, image models.
Graphs and grid, fundamentals of graph theory, basic algorithms for graphs, fundamental discrete geometry, connectivity and topology, segmentation : edge, region and texture.
Boundary representation, projection, Fourier descriptors, region representation, shape descriptors, mask and moments, thinning, MAT, scene analysis method
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Introduction: History, Advantages, Application, I/O Devices Graphic Packages, Languages. 2D Graphics: Drawing Elementary figures, Polygon Filling, Transformations, Windowing and clipping, Display file segmentation. Interactive Graphics: Interactive input techniques, Event handling, Input functions; 3D Graphics and Realism: Mathematical Preliminaries, Curves and Surfaces, Clipping, Hidden line and surface removal, rendering, real-time graphics; Interactive , Procedural elements for Computer Graphics. McGraw Hill Book Company, 2nd Edition, 1985. Introduction to Visualization, Tools for Visualization, Applications etc.
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Digital models for the speech signal, time-domain models for speech processing, linear predictive coding of speech, man-machine communication by voice, hypothesizing and verifying words for speech recognition.
Prosodic aids to speech recognition syntax, semantics and pragmatics, the HWIM speech understanding system, the Harpy speech understanding system, the Hearsay-II speech understanding system.
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