Molecular communication (MC) is a promising paradigm for information transmission in complex environments, such as living cells and porous media. While most existing works consider standard diffusion, where the mean square displacement (MSD) of information molecules (IMs) scales linearly with time, this dissertation focuses on sub-diffusive dynamics in crowded and complex environments. The primary objectives of this research are to model, simulate, and analyze the performance of MC systems in sub-diffusive environments.

This dissertation examines the deployment of Low Earth Orbit (LEO) satellite networks to enhance Internet of Things (IoT) connectivity across extensive geographic regions, including remote and rural areas where terrestrial infrastructure is insufficient. Through a comprehensive study structured into three main areas, this research addresses uplink performance, energy sustainability, and security challenges associated with LEO satellite communications.

The aim of this thesis is to understand and analyze diffusive and thermal effects in multicomponent systems for gas mixtures through the perspective of partial differential equations. Starting from Class--II models of thermodynamics, diffusion equations are derived formally by a Chapman--Enskog expansion and the expansion is justified as a relaxation limit by means of the relative entropy method.

Numerous problems in scientific computing can be formulated as optimization problems of suitable parametric models over parameter spaces. Neural network and deep learning methods provide unique capabilities for building and optimizing such models, especially in high-dimensional settings.

Disordered sound fields are ubiquitous in our daily life – the sound in a room undergoes multiple scattering form such a sound field. These fields are inherently random and traditionally challenging to manipulate. In our research, we demonstrate that reconfigurable acoustic metasurfaces can effectively reshape reverberating sound fields. By actively adjusting the reflective phases, these metasurfaces can 're-sculpt' the acoustic environment. The specific acoustic metasurface we have developed includes 200 units of electronically tunable Helmholtz resonators. Each unit can switch between two phase states, allowing for dynamic control of reflected waves over a wide frequency range from 1000 to 1700 Hz. This tunability is achieved through individual control of each resonator, utilizing a series of feedback-driven optimization algorithms.

DNA replication is a fundamental cellular process and its precise regulation is crucial for maintaining genomic integrity. Inspired by the mathematical parallelism between DNA replication and the nucleation problem in one-dimensional crystal growth kinetics, we introduce a model that maps whole-genome replication dynamics based on the firing rate profiles of replication origins and fork movement.

We are excited to announce the upcoming Stochastic Numerics and Statistical Learning: Theory and Applications Workshop 2024, taking place at KAUST, Auditorium 0215 b/w B4&5, from May 19-30, 2024. Following the highly successful last two years edition, this year's workshop promises to be another engaging and insightful event for researchers, faculty members, and students interested in stochastic algorithms, statistical learning, optimization, and approximation. The 2024 workshop aims to build on the achievements of last year's event, which featured 30 talks, two mini-courses, and two poster sessions, attracting over 150 participants from various universities and research institutes. In 2022 and 2023, attendees had the opportunity to learn from through insightful talks, interactive mini-courses, and vibrant poster sessions. This year, the workshop will once again showcase contributions that offer mathematical foundations for algorithmic analysis or highlight relevant applications. Confirmed speakers include renowned experts from institutions such as Ecole Polytechnique, EPFL, Université Pierre et Marie Curie - Paris VI, CUHK Shenzhen, and Imperial College London, among others.

This thesis consists of three papers considering, in general, two challenges: the minimization of computational cost in the ensemble Kalman filtering (EnKF) method and the problem of tracking a rare event within the framework of the EnKF.

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The accurate numerical prediction of complex processes in medicine, science, and engineer

Recently, scientific machine learning (SciML) has expanded the capabilities of traditional numerical approaches by simplifying computational modeling and providing cost-effective surrogates. However, SciML models suffer from the absence of explicit error control, a computationally intensive training phase, and a lack of reliability in practice. In this talk, we will take the first steps toward addressing these challenges by exploring two different research directions.

Despite being small and simple structured in comparison to their victims, virus particles have the potential to harm severly and even kill highly developed species such as humans. To face upcoming virus pandemics, detailed quantitative biophysical understanding of intracellular virus replication mechanisms is crucial.

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Numerical approximation of partial differential equations involves parameter dependencies from problem formulation and numerical methods. We focus on two areas: least-squares finite element method with linear elasticity, studying its dependence on the Lamé parameter, and the Virtual Element Method, known for handling complex geometries where the stabilization parameter is analyzed.

Rare, low-probability events often lead to the biggest impacts. Therefore, the development of statistical approaches for modeling, predicting and quantifying environmental risks associated with natural hazards is of utmost importance. In this seminar, I will show how statistical deep-learning methods can help solve challenges that arise when modeling complex and massive spatiotemporal extremes data.

We will discuss the solution of eigenvalue problems associated with partial differential equations (PDE)s that can be written in the generalised form Ax = λMx, where the matrices A and/or M may depend on a scalar parameter. Parameter dependent matrices occur frequently when stabilised formulations are used for the numerical approximation of PDEs. With the help of classical numerical examples we will show that the presence of one (or both) parameters can produce unexpected results.

Growth is a fundamental process in biological systems and various technological applications, including epitaxial deposition and additive manufacturing. The interaction between growth and mechanics in deformable bodies leads to a wealth of very challenging mathematical questions. I will give a short overview of the key concepts of morphoelasticity, namely, the theory of elastic deformations in growing bodies.

Traveling wave solutions of reaction-diffusion systems have been studied to explain wave propagation phenomena in biological organisms.

Abstract

Neural operator methods provide a novel approach for solving or learning the complex mapp

Predicting the paths of animals poses a significant challenge, given the intricate nature of their behaviors, the impact of unpredictable environmental elements, individual differences, and the scarcity of precise data on their movements.

As more and more modern time series data sets are becoming high dimensional, the problem of classification in this context has received increasing attention. We propose a statistical framework for classifying multivariate stationary Gaussian time series where the number of covariates, the length of the series, and the sample size, all grow to infinity.

Hessian-dependent functionals play a pivotal role in a wide latitude of problems in mathematics. Arising in the context of differential geometry and probability theory, this class of problems find applications in the mechanics of deformable media (mostly in elasticity theory) and the modelling of slow viscous fluids. We study such functionals from three distinct perspectives.

In this work, we employ importance sampling (IS) techniques to track a small over-threshold probability of a running maximum associated with the solution of a stochastic differential equation (SDE) within the framework of ensemble Kalman filtering (EnKF).

Artificial materials represent composite media that can be meticulously engineered to exhibit unique wave propagation behaviors. Our research endeavors are driven by the intriguing principles underlying these materials, such as effective models, and their broad applications, including perfect absorption. In this presentation, I will outline our recent advancements in our innovative design strategies for novel artificial materials from both forward first-principle physics-based modeling and data-driven approaches. Specifically, I will highlight our pioneering work in the designs of double-zero-index materials for both electromagnetic and acoustic waves. Additionally, I will discuss our discovery of the acoustic Purcell effect for enhanced emission, as well as our development of analytic and numerical solutions for space-time modulated wave systems. Furthermore, I will delve into our practical solution for achieving broad frequency cloaking of invisibility. These accomplishments hold significant promise for a wide range of applications spanning sound control, communication, sensing, imaging and more.

In this work, we analyze the convergence rate of randomized quasi-Monte Carlo (RQMC) methods under Owen's boundary growth condition [Owen, 2006] via spectral analysis.