ToDo-List & Ideas

# Roadmap

Here are some ideas we hope to cover/implement in the future.

### Time: Monday 3:00 pm CT

### Location: Zoom (Ether)

## Current schedule (2020 Fall)

Date | Person | Subject |
---|---|---|

Sep. 21 | George | Agent-based and non-markovian models of the spread of COVID-19 |

Oct. 05 | Kevin L. | PSLQ |

Oct. 19 | Paul | Linear Sum Assignment |

Nov. 09 | Mayisha | Graphing Temporal Dynamics in fMRI |

Nov. 16 | Abid | Homotopy Testing and Finding Shortest Homotopic Paths |

Nov. 30 | Greg | Persistent Homology |

Dec. 14 | Ryan | The magic of NUTS |

## Speaker Guidelines

**TL;DR** Do unto others as you would have them do unto you.

At minimum, an AIG presenter should prepare a few slides and an example code.

- The slides should explain: - what the algorithm is - how a minimum example works - why the algorithm might be practically useful
- A code that demonstrates the simplest problem the algorithm solves.
- Make a pull-request (PR) to the website repository to make your presentation and code eternal. Follow instructions in the README.md file.

The presentation should be 30-50 min if given without interruptions. Interactive elements are encouraged. e.g. a Jupyter notebook demo. with tweakable parameters given by the audience.

## Ideas for presentations

- Machine learning.
- Back propogation.
- Clustering.
~~Boltzmann machine.~~

- Control theory and signal processing.
- Model reduction.
~~Kalman filter.~~~~Hidden markov model.~~~~Proportional-integral (PI) controller.~~

- Stochastic algorithms.
- The Metropolis approach to sampling and alternatives
- Global balance (pentalty method).
- Quasi-random numbers.
- Ant Colony Optimization
- Parallel tempering.
- Stochastic hill climbing.
- Bayesian networks.
~~Simulated annealing~~~~Evolutionary, and genetics algorithms.~~~~Particle Swarm Optimization~~~~Belief propogation~~~~Gibbs sampling~~

- Encryption.
- Symmetric-key, Public-key (RSA) cryptography
- Cryptanalysis (breaking encryption).
- Hashing.

- Optimzation.
- Global Newton methods
- line search
- trust region
- iterative solution of linear equations
- matrix free

- Generalized minimal residual method (GMRES)
- preconditioning
- additive Schwarts
- Algebraic and geometric multi-grid
- Block Jacobi

- Quadratic optimization.
- Convex optmization.
- Steepest descent, Conjugate gradiant, Quasi-Newton, ….
- Noisy optimization.
- Compilers (fortan).
~~Simplex method.~~

- Global Newton methods
- Linear Algebra.
- Random matrix theory.
~~QR / SVD. principle component analysis~~~~Diagnolization~~, inversion.~~Lanczos~~~~Fast Fourier transforms (FFT).~~

- Numerical solutions to differential equations.
- Finite differences
~~Finite elements~~- Finite volumes
- Spectral elements
- PDE solvers (additional problems from multivariate)
- Energy conserving or time-reversal invariant versions.
~~Runge-Kutta and family.~~

- Data compression.
- Image compression techniques (one or more).
- Compressed sensing (probabilistic approach and connections to stat mech).
~~Compressed sensing (l-1 technique).~~

- Image Processing
- Image recognition
~~Automatic focus~~

- Visualization
~~Marching Cubes~~

- Quantum computing.
- Quantum annealing.
- Quantum error correction.
- Quantum encryption.
- Quantum stabilizers.
~~Grover algorithm.~~~~Shor algorithm.~~

- Parallelism.
- Parallel linear algebra.
- OpenMP and MPI
- GPU, Cuda, …

- Computer networks/the internet.
~~Google search bar, page rank.~~- The Internet protocal suite.
- Packet switching vs. cell-based switching.
- Mobile networks.
- Error detection and correction, Hamming codes.
- Internet security.
- Network routing.

- Classic CS algorithms
- Quicksort, Graph theory, …
~~Cellular atomata~~.~~Theory of computation~~(Turing, finite state machine, definition of language, regular expressions).~~complexity theory.~~