Mathematical content not related to the Work Packages of the DyCon ERC Project.

#### Available tutorials:

#### Multilevel Selective Harmonic Modulation via Optimal Control

The Multilevel Selective Harmonic Modulation problem is recast under the perspective of optimal control

#### Opening the black box of Deep Learning

The aim is then to open the black box of Deep Learning, and try to gain an intuition of what are these models doing. One of the most succesful mathematical theories in recent years has been connecting Deep Learning with Dynamical Systems.

#### Points of Interest Extraction and Prediction of Next Locations

In this project we tried first working on finding an algorithm that can help us define the points of interest of the users we have in the dataset. For that we implement an algorithm that can identify the users stop points.

#### Touchdown localization for the MEMS problem with variable dielectric permittivity

In this tutorial we study the localization of touchdown points in a mathematical model for micro-electro-mechanical systems (MEMS) with variable dielectric permittivity. We consider a device consisting of two conducting plates, connected to an electric circuit. The upper plate is rigid and fixed while the lower one is elastic and fixed only at the boundary. When a voltage (difference of potential between the two plates) is applied, the lower plate starts to bend and, if the voltage is large enough, the lower plate eventually touches the upper one. This is called touchdown phenomenon and our aim is to control the localization of touchdown points in the device by a suitable choice of the dielectric permittivity of the material.

#### Propagation of one and two-dimensional discrete waves under finite difference approximation

We analyze the propagation properties of the numerical versions of one and two-dimensional wave equations, semi-discretized in space by finite difference schemes, and we illustrate that numerical solutions may have unexpected behaviours with respect to the analytic ones.

#### Structured deformations of continua

A Multiscale Geometrical Basis for Variational Problems in Mechanics

#### An introduction to the moment method for optimal control problems for polynomial ODEs

The aim of this note is to explain how one can solve an optimal control problem with the moment method

#### Two Grids Filter Method for RPS Semi-Discretization

This work is regarding solving 1-d wave equation using RPS semi-discretization method and analysis corresponding dispersion relation.

#### WKB expansion for a fractional Schrödinger equation with applications to controllability

Theoretical and numerical analysis of the propagation of the solutions for a Schrödinger equation with fractional Laplacian, with application to the study of controllability properties.

#### Radial Basis Functions Interpolation

This is a set of Matlab functions to interpolate scattered data with Radial Basis Functions (RBF).