Exploratory data analysis and computational techiques are fundamental to understand modern modern statistical methods. Introduce modern techniques of data analysis with concomitant using of computer. Using statistical packages. Institute of Mathematics ans Statistics (IME) São Paulo main campus 1. Exploratory data analysis (univariate and multivariate): position measurements, dispersion, asymmetry, robust measures, bivariate measures, association between variables, outliers identification, processing variables, graphics. 2. Linear Regression Models, Regression Tough and Smoothing Methods. 3. Stochastic Simulation: inversion methods, rejection, composition and resampling methods. 4. Numerical Optimization: Newton-Raphson, scoring, quasi-Newton. 5. EM Algorithm. 6. “Bootstrap” and “Jacknife”. 7. Monte Carlo methods and Gaussian quadratures Denise Aparecida Botter, Eduardo Jordao Neves, Anatoli Iambartsev 40 MAE5704 8 Tests, Lists of exercises and seminars https://www.ime.usp.br/en

Stochastic processes are natural models for phenomena occurring in time and for spatial systems. Modeling natural phenomena using stochastic processes requires the knowledge of specific inferential and statistical model selection tools. Moreover, stochastic processes have also been used as computational tools in statistical inference, as exemplified by Monte-Carlo Markov chain algorithms for sampling probability distributions. To present basic notions of statistical inference for some important classes of stochastic processes. Institute of Mathematics ans Statistics (IME) São Paulo main campus 1) Statistical inference for Markov chains. Maximum likelihood estimation. Estimation of the order of the chain. 2) Statistical inference for stochastic chains with memory of variable length. The algorithm Context. 3) Context tree selection using the Bayesian Information Criterion (BIC). The algorithm_CTW. 4) Statistical inference for hidden Markov models. 5) Gibbs states. Interaction graph selection and maximum likelihood estimation for the_Ising_model. 6) Simulations using Monte-Carlo Markov chains (MCMC)._Glauber_dynamics, Gibbs sampler, Metropolis algorithm. 7) Perfect simulation algorithms. Jefferson Antonio Galves, Florencia Graciela Leonardi 40 MAE5741 8 Students will be evaluated through projects, seminars, exercise lists and write tests, https://www.ime.usp.br/en

The general treatment of Probability Theory requires its formulation in abstract spaces, in the framework introduced by Kolmogorov. Introduce the basics of Probability Theory into abstract spaces, including the necessary elements of Measure Theory, in the framework formulated by Kolmogorov. Institute of Mathematics ans Statistics (IME) São Paulo main campus 1. Probability Spaces: (a) Lebesgue-Stieltjes Measure, Carath_dory Extension Theorem; (b) Measures of Probability, Random Variables; (c) Integration, Expectation, Convergence Theorems; (d) Product measures, Fubini’s theorem; (e) Independence; (f) Kolmogorov Extension Theorem; (g) Radon-Nikodym Theorem, Conditional Expectation. 2. Laws of Large Numbers: (a) Convergence in Probability and Almost Sure Convergence; (b) Weak Law of Large Numbers; (c) Borel-Cantelli lemmas; (d) Strong Law of Large Numbers. 3. Central Limit Theorem: (a) Convergence in Distribution; (b) Characteristic Functions; (c) TLC for Random Variables I.I.D; (d) TLC for Triangular Arrangements. Vladimir Belitsky, Miguel Natalio Abadi, Anatoli Iambartsev 50 MAE5811 8 Exam and exercises, with the possibility of collecting an article at the end of the course. https://www.ime.usp.br/en

The formal study of the asymptotic properties of estimators and test statistics is fundamental to understand and propose modern statistical methods. To discuss formally asymptotic theory of statistical methods. Institute of Mathematics ans Statistics (IME) São Paulo main campus 1. Order of magnitudes and Taylor series. 2. Weak and strong convergence laws of the estimators. Univariate and multivariate cases. Slutsky’s Theorem. 3. Central limit Theorems _ Univariate, Multivariate and Martingales. Cram_r-Wold’s Theorem. Hajek-Sidak’ s Theorem and applications to regression models. Delta method and variance stabilizing transformations. 4. Asymptotic expansions. 5. Applications. Antonio Carlos Pedroso de Lima, Alexandre Galv_o Patriota 50 MAE5835 8 Exams, Worksheets and Seminars https://www.ime.usp.br/en

Data is at the center of the so-called fourth paradigm of scientific research that will spawn new sciences useful to the society. Data is also the new and extremely strong driving force behind many present-day applications, such as smart city, manufacturing informatics, and societal security, to name a few. It is thus imperative that our students know how to handle data, analyze data, use data and draw insights from data. This course aims at acquainting the students with the analytical foundation of data handling techniques. The course consists of a series of seminar talks with substantial student participation, in the form of research and presentation in response to posted questions about main topics in data analytics and modeling. 1. Scope Broad topics covered in the course include: •Regression & curve fitting •Probability distribution & parameter estimation •Mixture models, latent variable models & hybrid distributions •Hidden Markov models, Markov random fields, & graphic models •Pattern recognition & decision theory •Neural networks and deep learning Well spend 2-3 weeks on each topic (some may take up to 4 weeks). 2. Format For each topic, a number of questions to help students learn the subject will be posted in advance. Individual student will be assigned to conduct research, answer specific questions and return with presentations to the class. Each student presentation is of duration ~20 min, followed by ~10 min questions and discussion. Students who are assigned to address specific questions have one week time to prepare for the presentation. Common questions shared by all topics are: – What are the problems that gave rise to the particular topic & concept? (The original motivation) – What problems beyond the original motivation will the topic and the related techniques be able to solve? (New and novel applications) – What are the problem formulations with relevant assumptions that have been proposed? (The methodology and formulation) – What are the ensemble of techniques that were developed to solve the problem? (The tools and capabilities) – How do these techniques solve the problem or contribute to the solutions? (The solution mechanism) – What are the limitations of the solutions proposed so far? Any remaining open problems in the topic? (Research opportunities) In addition to these common questions, some topic-specific questions may also be posted and addressed in student presentations. After all posted questions about a subject are addressed in student presentations, one or two commentary sessions by the lecturer on the subject will follow so as to complete the systematic development of understanding of the subject. The course will be primarily conducted in English. To reflect the applicability of the subject matter to local problems, local languages may also be used as the circumstance calls for it. No official textbook is assigned in this course. Students are expected to conduct research with all university provided resources (e.g., books in the library) and information available on the web. Class notes by the lecturer will be distributed in due course. 3. Prerequisite Both graduate and undergraduate students can enroll in the class, as long as they have completed engineering mathematics courses, particularly Probability and Statistics or the equivalent. Overall, students will be exposed to data analytic topics and their historical perspectives, learn to ask and analyze related problems, understand the modeling techniques and their origins, and conceive of new applications and research opportunities. College of Electrical Engineering & Computer Science No written test will be given in the special course. Student presentations are evaluated by the class and moderated by the lecturer. JUANG BIING-HWANG Thursday 234 CSIE5610 3

Data is at the center of the so-called fourth paradigm of scientific research that will spawn new sciences useful to the society. Data is also the new and extremely strong driving force behind many present-day applications, such as smart city, manufacturing informatics, and societal security, to name a few. It is thus imperative that our students know how to handle data, analyze data, use data and draw insights from data. This course aims at acquainting the students with the analytical foundation of data handling techniques. The course consists of a series of seminar talks with substantial student participation, in the form of research and presentation in response to posted questions about main topics in data analytics and modeling. 1. Scope Broad topics covered in the course include: •Regression & curve fitting •Probability distribution & parameter estimation •Mixture models, latent variable models & hybrid distributions •Hidden Markov models, Markov random fields, & graphic models •Pattern recognition & decision theory •Neural networks and deep learning Well spend 2-3 weeks on each topic (some may take up to 4 weeks). 2. Format For each topic, a number of questions to help students learn the subject will be posted in advance. Individual student will be assigned to conduct research, answer specific questions and return with presentations to the class. Each student presentation is of duration ~20 min, followed by ~10 min questions and discussion. Students who are assigned to address specific questions have one week time to prepare for the presentation. Common questions shared by all topics are: – What are the problems that gave rise to the particular topic & concept? (The original motivation) – What problems beyond the original motivation will the topic and the related techniques be able to solve? (New and novel applications) – What are the problem formulations with relevant assumptions that have been proposed? (The methodology and formulation) – What are the ensemble of techniques that were developed to solve the problem? (The tools and capabilities) – How do these techniques solve the problem or contribute to the solutions? (The solution mechanism) – What are the limitations of the solutions proposed so far? Any remaining open problems in the topic? (Research opportunities) In addition to these common questions, some topic-specific questions may also be posted and addressed in student presentations. After all posted questions about a subject are addressed in student presentations, one or two commentary sessions by the lecturer on the subject will follow so as to complete the systematic development of understanding of the subject. The course will be primarily conducted in English. To reflect the applicability of the subject matter to local problems, local languages may also be used as the circumstance calls for it. No official textbook is assigned in this course. Students are expected to conduct research with all university provided resources (e.g., books in the library) and information available on the web. Class notes by the lecturer will be distributed in due course. 3. Prerequisite Both graduate and undergraduate students can enroll in the class, as long as they have completed engineering mathematics courses, particularly Probability and Statistics or the equivalent. Overall, students will be exposed to data analytic topics and their historical perspectives, learn to ask and analyze related problems, understand the modeling techniques and their origins, and conceive of new applications and research opportunities. College of Electrical Engineering & Computer Science No written test will be given in the special course. Student presentations are evaluated by the class and moderated by the lecturer. JUANG BIING-HWANG Thursday 234 CSIE5610 3

1. Introduction of Queueing Model and Review of Markov Chain 2. Simple Markovian Birth and Death Queueing Models (M/M/1, etc) 3. Advanced Markovian Queueing Models 4. Jackson Queueing Networks 5. Models with General Arrival or Service Pattern (M/G/1, G/M/1) 6. Discrete-Time Queues and Applications in Networking To provide the basic knowledge in queueing models and the analysis capability of the queueing models in telecommunications, computers, and industrial engineering College of Electrical Engineering & Computer Science Midterm 45% Final Exam 45% Homework (including programming and simulations) 10% ZSEHONG TSAI Wednesday 789 EE5039 3

1. Review of Random Variables (Papoulis, Chaps. 1-7, and class note) 2. Introduction to Random Processes: General Concepts and Spectral Analysis (Papoulis, Chap. 9, and class note) 3. Gaussian Random Vectors and Gaussian Random Processes (Larson & Shubert, class note) 4. Signal Representation — Karhunen-Love Expansion (Papoulis, Chap. 11, and class note) 5. Narrowband Processes and Bandpass Systems (Davenport and Root, and class note) 6. Poisson Processes (Larson & Shubert, Leon-Garcia, and class note) 7. Markov Processes and Markov Chains (Larson & Shubert, Leon-Garcia, and class note) 8. Queuing Systems (Leon-Garcia) 9. Random Walk Processes and Brownian Motion Processes (Leon-Garcia) The purpose of this course is to provide students with a solid and pertinent mathematical background for thoroughly understanding digital communications and communication networks. It is a prerequisite for advanced study of numerous communication applications, including wireless communications, mobile communications, communication networks, spread spectrum communications, satellite communications, optical communications, radar and sonar signal processing, signal synchronization, etc. The students majoring in communications and networks are strongly recommended to take this course. The course consists of lectures organized in class notes. College of Electrical Engineering & Computer Science Prerequisite: Probability and Statistics. Grading Policy: There will be six homeworks, one every three weeks, one midterm exam, and one final exam. The grading policy is “Homeworks: 30%; Midterm: 35%; Final: 35%”. CHAR-DIR CHUNG Friday 789 EE5041 3

1. Review of Random Variables (Papoulis, Chaps. 1-7, and class note) 2. Introduction to Random Processes: General Concepts and Spectral Analysis (Papoulis, Chap. 9, and class note) 3. Gaussian Random Vectors and Gaussian Random Processes (Larson & Shubert, class note) 4. Signal Representation — Karhunen-Love Expansion (Papoulis, Chap. 11, and class note) 5. Narrowband Processes and Bandpass Systems (Davenport and Root, and class note) 6. Poisson Processes (Larson & Shubert, Leon-Garcia, and class note) 7. Markov Processes and Markov Chains (Larson & Shubert, Leon-Garcia, and class note) 8. Queuing Systems (Leon-Garcia) 9. Random Walk Processes and Brownian Motion Processes (Leon-Garcia) The purpose of this course is to provide students with a solid and pertinent mathematical background for thoroughly understanding digital communications and communication networks. It is a prerequisite for advanced study of numerous communication applications, including wireless communications, mobile communications, communication networks, spread spectrum communications, satellite communications, optical communications, radar and sonar signal processing, signal synchronization, etc. The students majoring in communications and networks are strongly recommended to take this course. The course consists of lectures organized in class notes. College of Electrical Engineering & Computer Science Prerequisite: Probability and Statistics. Grading Policy: There will be six homeworks, one every three weeks, one midterm exam, and one final exam. The grading policy is “Homeworks: 30%; Midterm: 35%; Final: 35%”. CHAR-DIR CHUNG Friday 789 EE5041 3

In this class, I will cover the basic techniques for design and analysis of algorithms. I will also give a brief introduction to advanced topics such as approximate algorithms and randomized algorithms. 1 Introduce different algorithm design techniques. 2 Teach the students how to evaluate the performance of different algorithms. College of Electrical Engineering & Computer Science Grading: Homework: 40% Midterm: 30% Final exam: 30% HO-LIN CHEN Tuesday 234 EE5048 3

In this class, I will cover the basic techniques for design and analysis of algorithms. I will also give a brief introduction to advanced topics such as approximate algorithms and randomized algorithms. 1 Introduce different algorithm design techniques. 2 Teach the students how to evaluate the performance of different algorithms. College of Electrical Engineering & Computer Science Grading: Homework: 40% Midterm: 30% Final exam: 30% HO-LIN CHEN Tuesday 234 EE5048 3

Logic synthesis is an automated process of generating logic circuits satisfying certain Boolean constraints and/or transforming logic circuits with respect to optimization objectives. It is an essential step in the design automation of VLSI systems and is crucial in extending the scalability of formal verification tools. This course introduces classic logic synthesis problems and solutions as well as some recent developments. This course is intended to introduce Boolean algebra, Boolean function representation and manipulation, logic circuit optimization, circuit timing analysis, formal verification, and other topics. The students may learn useful Boolean reasoning techniques for various applications even beyond logic synthesis. College of Electrical Engineering & Computer Science The prerequisite is the undergrad “Logic Design” course. Knowledge about data structures and programming would be helpful. JIE-HONG JIANG Friday 234 EEE5028 3