Model-based Feature Engineering of Atrial Fibrillation

Atrial Fibrillation (AF) is the most common tachyarrhythmia in the heart. Irregular RR intervals and the absence of a P wave before the QRS complex characterize AF. Although many studies have been done to detect atrial fibrillation, many aspects of this intricate disease need further analysis. AF is often diagnosed by the interpretation of multi...

On the connection between uniqueness from samples and stability in Gabor phase retrieval

Gabor phase retrieval is the problem of reconstructing a signal from only the magnitudes of its Gabor transform. Previous findings suggest a possible link between unique solvability of the discrete problem (recovery from measurements on a lattice) and stability of the continuous problem (recovery from measurements on an open subset of R<sup>2...

The relativistic dynamics of labor economics: An economic engineering treatment

In this thesis, the analogy between the special theory of relativity and the dynamics of a laborer is developed in the context of labor economics. At the basis of this analogy stands an individual laborer who cannot supply more than 24$hours of labor in a day. This represents the theoretical limit to the flow of labor services (velocity). We...

Non-chaotic limit sets in multi-agent learning

Non-convergence is an inherent aspect of adaptive multi-agent systems, and even basic learning models, such as the replicator dynamics, are not guaranteed to equilibriate. Limit cycles, and even more complicated chaotic sets are in fact possible even in rather simple games, including variants of the Rock-Paper-Scissors game. A key challenge...

Classification of De novo post-operative and persistent atrial fibrillation using multi-channel ECG recordings

Atrial fibrillation (AF) is the most sustained arrhythmia in the heart and also the most common complication developed after cardiac surgery. Due to its progressive nature, timely detection of AF is important. Currently, physicians use a surface electrocardiogram (ECG) for AF diagnosis. However, when the patient develops AF, its various...

Poincaré-Bendixson Limit Sets in Multi-Agent Learning

A key challenge of evolutionary game theory and multi-agent learning is to characterize the limit behavior of game dynamics. Whereas convergence is often a property of learning algorithms in games satisfying a particular reward structure (e.g., zero-sum games), even basic learning models, such as the replicator dynamics, are not guaranteed to...

Persistence of periodic traveling waves and Abelian integrals

It is well known that the existence of traveling wave solutions (TWS) for many partial differential equations (PDE) is a consequence of the fact that an associated planar ordinary differential equation (ODE) has certain types of solutions defined for all time. In this paper we address the problem of persistence of TWS of a given PDE under small...

Atrial Fibrillation classification from a short single lead ECG recording

This thesis focuses on classifying AF and Normal rhythm ECG recordings. AF is a common arrhythmia occurring in millions of people every year, which could lead to blood clots, stroke or even heart failure. When AF is occurring, the P waves are often absent and RR intervals are often irregular. <br/><br/>This thesis proposes a new Poincaré plot...

The Extended Tisserand-Poincaré graph for multi-body trajectory design

The decision on the dynamical model used to design a spacecraft’s trajectory is a fundamental choice influenced by many factors. The complexity of such a model affects the accuracy of the designed trajectory but also the difficulty of the design process. One approach to simplify this task consists of splitting the trajectory design process into...

Connecting hyperbolic invariant manifolds at variations of the Poincaré section orientation: A numerical investigation into novel transfer solutions connecting collinear periodic libration point orbits through their associated manifold structures

The three-body problem (3BP) formulated by I. Newton has inspired many great mathematicians like L. Euler (1707-1783), J.L. Lagrange (1736-1813), K.G.J. Jacobi (1804-1851), W.R. Hamilton (1805-1865) and J.H. Poincaré (1854-1912) to develop mathematical studies, methods and theories in an attempt to solve this problem. Although these concepts...

On lunar collision orbits: New methodologies for Moon-to-Moon transfer design

Many interplanetary missions massively leverage the lunar gravitational pull in the so-called low-energy regime to converge to their aim, saving consistent amount of fuel. Among these, two future Japanese spacecraft are expected to repeatedly encounter the Moon along their trajectories to either facilitate the escape from the Earth–Moon system...

1:1 Ground-track resonance in a uniformly rotating 4th degree and order gravitational field

Using a gravitational field truncated at the 4th degree and order, the 1:1 ground-track resonance is studied. To address the main properties of this resonance, a 1-degree of freedom (1-DOF) system is firstly studied. Equilibrium points (EPs), stability and resonance width are obtained. Different from previous studies, the inclusion of non...

Linear stability and bifurcations of periodic Lagrange orbits in the Elliptic Restricted 3-Body Problem: An investigation at L1/L2 in the Earth-Moon system

The Three Body Problem (3BP) has been one of the main celestial mechanics problems in the past few centuries, for a long time studied by both engineers and mathematicians. Its practical purpose is to describe the motion of three particles only under their mutual gravitational interaction, thus it actually represents a ‘model’ of the real...

Modeling and analysis of periodic orbits around a contact binary asteroid

The existence and characteristics of periodic orbits (POs) in the vicinity of a contact binary asteroid are investigated with an averaged spherical harmonics model. A contact binary asteroid consists of two components connected to each other, resulting in a highly bifurcated shape. Here, it is represented by a combination of an ellipsoid and a...