Gonçalo Morais


Área Científica de Matemática

Instituto Superior de Engenharia da Lisboa

Rua Conselheiro Emídio Navarro, 1

1959-007 Lisboa

phone: (+351) 218 317 000

fax: (+351) 218 317 001

email: gmorais@adm.isel.pt

Office: Building G, Room 1.10.2

[FSF Associate Member]
 Gonçalo Morais with Professor Strang

Images from NUMDE

Code

  1. NUMDE (Numerical Differential Equations Library), a general purpose library written in C/C++, to compute numerical solutions of Ordinary Differential Equations and to create graphical representations of the solutions. This code was used to generate the cover and some of the pictures inside the book Differential Equations and Linear Algebra by Professor Gilbert Strang
  2. Runge-Kutta algorithm in C, for pedagogical purposes: rungekutta.c
  3. Signal Processing over ECG in Python.
  4. Unidimensional Brownian Bridges in Julia
  5. Price of European and American Options using the Crank-Nicolson algoritm (in pure C). The results match the results in here.

Outline of Machine Learning Course (Fall 2018)

  1. Code and some basic notes

    1. Gradient descent.
    2. Capacity, Underfitting and Overfitting
    3. Stochastic Gradient Descent (part 1)
    4. Perceptrons
    5. Back Propagation in Artificial Neural Networks (SGD part 2)
    6. Back Propagation in action with this mini library of functions.
    7. Modular approach to Back Propagation. Requires this mini library of functions.
    8. Regularization in Artificial Neural Networks
    9. Convolutional Neural Networks
      1. Tensorflow Basics
      2. Introduction to Keras example 1
      3. Introduction to Keras example 2
      4. CNN on MNIST example
      5. CNN on Fashion MNIST example

  2. Case Studies projects

    1. Sports performance of NBA teams in regular season.
      1. Detailed explanation of Data Consolidation. The plain Python script.
    2. Principal Components Analysis and Autoencoders.
      1. Toy Model for PCA playground here. The Julia module to compute N-dimensional geometry. To see the pictures please go to PDF version of the file.
    3. Credit Risk in the context of Machine Learning.

Code for the Modeling Course (Spring 19)

All information here.

Gazeta de Matemática

  1. Gilbert Strang
  2. Rogério Martins
  3. Charles Fefferman
  4. André Neves
  5. Ingrid Daubechies
  6. Carles Simó
  7. Charles Johnson
  8. João Pedro Nunes
  9. Cédric Villani
  10. Henrique Leitão
  11. Mega Ferreira e Francisco Domingues

Publications

  1. Bounded Domains of Negative Multipliers, with Charles Johnson, to appear in Journal of Mathematical Analysis and Applications.
  2. Generalized synchronization in a system of several non-autonomous oscillators coupled by a medium, with Rogério Martins, Kybernetika, Volume: 51, Issue: 2, page 347-373.