Jorge Silva

Graduate Level: Ph.D degree in Electrical Engineering
University of Southern California

Minor in Mathematics:
math507A: Theory of Probability: Part I. (probability spaces; weak convergence, laws of large numbers, central limit theorem (CLT); stable and infinitely divisible laws; law of iterative logarithms, conditional expectation, Markov chains, stoping times...) [Varadhan 2001][Breiman 1992]
math507B: Theory of Probability: Part II. (martingales, stationary processes and ergodic theorems, CLT for Martingales, Brownian motion, Markov processes, pure jump processes, Poisson Processes, infinitesimal generators, Ito's stochastic integrals....)[Varadhan 2001][Breiman 1992]
math507A: Topics in Probability (Large Deviations). (Cramer's theorem, Sanov's theorem, contraction principle, general large deviation principle (LDP), Varadhan's lemma, weak LDP, LDP for Markov sequences...) [Hollander 2000]

Statistical Signal Processing:
ee562B: Random Processes in Engineering: Part II.(Narrow-band random processes, nonlinear operations on random processes, direct and transform methods, applications to communication receivers, continuous-time Markov chains, infinitesimal generators, applications to queueing problems, continuous-state continuous-time Markov processes, diffusion processes....)[Davenport et al][Karlin et al]
ee563: Estimation Theory. [Mendel 1995]

Communication:
ee565A: Information Theory. (Information quantities, properties and inequalities, asymptotic equipartition property (AEP), entropy rates, Kraft inequality and losless data compression, Huffman codes, Shannon-Fano-Elias codes, artimetic coding, channel capacity, Fano's inequality, rate-distorition theory, network information theory....)[Gray 1990] [Cover et al 1991]

Graduate Level: Master degree in Electrical Engineering (selected course work)
University of Southern California

Signal Processing and Statistical Signal Processing:
ee519: Speech Recognition and Processing for Multimedia.
ee559: Mathematical Pattern Recognition.
ee596: Wavelets.(Orthonormal bases, frames, discrete Wavelet transform (DWT), multirate filter bank, filter design, Wavelet Packets, continuous time wavelet, multi-resolution analysis, application to image processing....) [Vetterli et al 1995][Daubechies, 1992 ]
ee562A: Random Processes in Engineering, Part I.(Karhunen-Loeve expansions of random vectors, basic simualtion and whitening problem, convergences of random sequences, mean square calculus, basic detection and estiamtion problems, spectral theory of atationary random processes, linear systems with stochastic input....)[Gray et al 2004]

Communication:
ee599: Quantum Computation and Quantum Information.(Postulates of quantum mechanics, unitary transformations and time evolution, entangling interactions, measurement and interference, universal sets of quantum gates, Grover's search algorithm, decoherence and effect of environment) [Nielsen et al 2003]
ee564: Communication Theory. ( Baysean decision theory, decision theory to vector models of communication signals, communication in additive Gaussian noise, Karhuenen-Loeve expansion, sufficient statistics, correlation detection, matched filtering, additive-white-Gaussian-noise (AWGN) channel, random coding, sphere packing, Shannon's capacity theorem for the AWGN channel )[Wozencraft, 1965][Harry L. Van Trees]
ee568: Error Correcting Codes.(channel models, decoding methods, soft-in soft-out decoding, linear block codes, covolutional codes)

Electrical Engineering Degree (selected course work)
University of Chile

Minor in Mathematics:
MA38A: Analysis I: Topology and Complex Analysis.
MA48A: Analysis II: Measure Theory. (Mononotone class, filed and sigma fields, Borel sigma field, measures, extension of measures, measurable functions, Lebesgue integration, Radon-Nikodym theorem, Fubini's theorem, product spaces...) [Halmos 1951]
MA47A: Combinatorial Optimization, Algorithms and Complexity. (Graph theory,... )
MA44C: Markov chains. (Weak and strong Markov properties, invariant distributiuons, hitting times and absorption probabilities, recurrent and transient states, convergence to equilibrium, Ergodic resuls for Markov chains, continous time Markov processes) [Norris 1996][Breiman 1992]
MA54B: Information Theory and Ergodic Theory. (topologocal dynamical system and anbstract dynamical system, topological entropy, Shannon-Mc.Millan-Breiman theorem) [Petersen 1983]

Signal Processing:
EM753: Neural Networks Theory.
EL731: Digital Signal Processing.
EM755: Fussy Logic and Intelligent System.

Monographs References

Probability Theory:
Leo Breiman, "Probability," SIAM, 1992.
S.R.S. Varadhan, "Probability Theory," AMS, 2001.
F. den Hollander, "Large Deviation," AMS, 2000.
J.R Norris, "Markov Chains," Cambridge, 1996.
S. Kullback, "Information Theory and Statistics," Dover, 1967.
Karl Petersen, "Ergodic Theory," Cambridge, 1983.
P.R. Halmos,"Measure Theory," Van Nostrand, 1951.

Signal and Statistical Signal Processing:
M. Vetterli and J. Kovacevic, "Wavelet and Subband Coding." Englewood Cliffs, NY: Prentice-Hall, 1995.
I. Daubechies, "Ten Lectures on Wavelets," SIAM 1992.
R. M. Gray and L. D. Davisson, "Introduction to Statistical Signal Processing," Cambridge, 2004.
J.M. Mendel, "Lessons in Estimation Theory for Signal Processing, Communication, and Control," P. Hall, 1995.

Statistical Learning Theory and Pattern Recognition:
V. N. Vapnik, "Statistical Learning Theory." J. Wiley&Songs, 1998.
V. N. Vapnik, "The Nature of Statistical Learning Theory." Springer, 1999.
L. Devroye, L. Gyorfi and G. Lugosi, "A Probabilistic Theory of Pattern Recognition," Springer 1996.
R. O. Duda and P. E. Hart, "Pattern Classification and Scene Analysis," New York: Wiley, 1983.
L Breiman, J. Friedman, R. Olshen and C. Stone, "Classification and Regression Trees," Wadsworth, 1984.
L. Devroye and G. Lugosi, "Combinatorial Methods in Density Estiamtion," Springer-Verlag NY, 2001.

Information Theory:
C.E. Shannon and W. Weaver, "The Mathematical Theory of Communication," the Univ. of Illinois Press, 1949.
R. M. Gray, "Entropy and Information Theory. Springer," Verlag, New York, 1990.
T. M. Cover and J. A. Thomas," Elements of Information Theory. Wiley Interscience," New York, 1991.
R. G. Gallager,"Information Theory and Reliable Communication," J. Wiley&Songs, 1968.
D. J. C. MacKay, "Information Theory, Inference, and Learning Algorithms," Cambridge, 2003.

Communication:
J. M. Wozencraft and I. M. Jacobs," Principles of Communication System Engineering," Waveland Press, 1965.
Harry L. Van Trees," Detection, Estimation, and Modulation Theory," Wiley-Interscience.
W. B. Davenport and W. L. Root, "An Introduction to the Theory of Random Signals and Noise," IEEE Press.
S. Karlin and H. E. Taylor, "A First Course in Stochastic Processes," Academic Press
Michael A. Nielsen and Isaac L. Chuang," Quantum Computation and Quantum Information," Cambridge, 2003

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