We address the motion planning problem for smooth control-nonlinear systems by presenting a regularised version of the well-established homotopy continuation method. The proposed approach (inspired by Tikhonov regularisation in the Moore-Penrose pseudo-inverse theory) deal\tred{s} with the two issues of the classical method: the singularities of th...
This paper studies a mathematical model of opinion dynamics on social networks, which features continuous opinions and binary actions. The binary actions are a suitable quantization of the opinions, which evolve in continuous time. The model thus takes the form of a differential equation with discontinuous right-hand side: we explore the asymptotic...
Among all mosquito-transmitted diseases, dengue is one of the most widespread, causing millions on infections and thousands of deaths, especially in Latin America. Lately, the Sterile Insect Technique has been applied successfully to reduce wild mosquito populations in several regions, and therefore control the spread of mosquito-transmitted diseas...
Published in Journal of pharmacokinetics and pharmacodynamics
Mathematical modelling has become a key tool in pharmacological analysis, towards understanding dynamics of cell signalling and quantifying ligand-receptor interactions. Ordinary differential equation (ODE) models in receptor theory may be used to parameterise such interactions using timecourse data, but attention needs to be paid to the theoretica...
We explore potential management strategies for short-term mitigation efforts of cyanobacterial blooms informed by process-based dynamic models. We focus on the case where blooms are linked to the existence of alternative stable states, such that, under the same conditions but depending on the past, a lake may be dominated either by cyanobacteria (“...
Mathematics provides us with tools to capture and explain phenomena in everyday biology, even at the nanoscale. The most regularly applied technique to biology is differential equations. In this article, we seek to present how differential equation models of biological phenomena, particularly the flow through ion channels, can be used to motivate a...
One of the central questions in control theory is achieving stability through feedback control. This paper introduces a novel approach that combines Reinforcement Learning (RL) with mathematical analysis to address this challenge, with a specific focus on the Sterile Insect Technique (SIT) system. The objective is to find a feedback control that st...
The study of physical systems, modeled by partial differential equations (PDEs), represents a cornerstone of scientific research. These equations, describing the relation between some function and its partial derivatives across variables, are vital for modeling diverse phenomena, for eg fluid dynamics and heat transfer, with applications in various...
This paper presents a DC-DC buck converter topology with multi-output capability for stacks of electrolyzers. The converter operation and its behavior are explained through the derivation of differential equations. A control strategy is proposed to regulate the hydrogen production rate effectively. To alleviate the voltage rating requirements of th...
Deep learning has emerged as a transformative paradigm in the past decade, with major impact in various fields of artificial intelligence. However, the properties of this family of machine learning methods are not yet fully understood. In this PhD thesis, we present contributions, mostly theoretical in nature, to the field of deep learning. We stud...
