The goal of this thesis is the development and the analysis of numerical methods for problems where the unknown is a curve on a smooth manifold. In particular, the thesis is structured around the three following problems: homotopy continuation, curve inter ...
The recent rise in both popularity and performance of large language models has garnered considerable interest regarding their applicability to education. Technologies like ChatGPT, which can engage in human-like dialog, have already disrupted educational ...
An automated music composition and generation system for automatically harmonizing digital pieces of music using an automated music composition and generation engine for multi-voice music harmonization, including a system-user interface configured to input ...
Functional and structural connectivity alterations in short- and long-range projections have been reported across neurodevelopmental disorders (NDD). Interhemispheric callosal projection neurons (CPN) represent one of the major long-range projections in th ...
In this work, we present, analyze, and implement a class of multilevel Markov chain Monte Carlo(ML-MCMC) algorithms based on independent Metropolis--Hastings proposals for Bayesian inverse problems. In this context, the likelihood function involves solving ...
This thesis is dedicated to the analysis of a subclass of interfacial flows, columnlike free-interface flows, from two view angles: (i) the symmetry breaking under geometry-induced or external forces, (ii) their stability against infinitesimal disturbances ...
Many natural and industrial processes involve fluid flow at a three phase interface between liquid, solid and gas. When the liquid is forced to move rapidly over the solid surface, the physical mechanisms governing contact line motions are multi-phase and ...
Local modifications of a computational domain are often performed in order to simplify the meshing process and to reduce computational costs and memory requirements. However, removing geometrical features of a domain often introduces a non-negligible error ...
Witness encryption is a cryptographic primitive which encrypts a message under an instance of an NP language and decrypts the ciphertext using a witness associated with that instance. In the current state of the art, most of the witness encryption construc ...
Global spectral methods offer the potential to compute solutions of partial differential equations numerically to very high accuracy. In this work, we develop a novel global spectral method for linear partial differential equations on cubes by extending th ...
