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.

We present a theoretical analysis of the Weak Adversarial Networks (WAN) method, recently proposed in [1, 2], as a method for approximating the solution of partial differential equations in high dimensions and tested in the framework of inverse problems. In a very general abstract framework.

Analogies between financial markets and critical phenomena have long been observed empirically. So far, no convincing theory has emerged that can explain these empirical observations. Here, we take a step towards such a theory by modeling financial markets as a lattice gas.

Wave propagation and scattering problems are of huge importance in many applications in science and engineering - e.g., in seismic and medical imaging and more generally in acoustics and electromagnetics.

In this short course, we will introduce some elements in deriving the hp a posteriori error estimate for a high-order unfitted finite element method for elliptic interface problems. The key ingredient is an hp domain inverse estimate, which allows us to prove a sharp lower bound of the hp a posteriori error estimator.

Due to a variety of potential barriers to sample acquisition, many of the datasets encountered in important classification applications, ranging from tumor identification to facial recognition, are characterized by small samples of high-dimensional data. In such situations, linear classifiers are popular as they have less risk of overfitting while being faster and more interpretable than non-linear classifiers. They are also easier to understand and implement for the inexperienced practitioner.

One of the fundamental problems in population genetics and molecular evolution is to understand the drivers of genetic change in a population: which mutations affect the ability of an organism to survive, reproduce, and pass its genes to the next generation, while which mutations are mere "passengers" that do not affect this ability? In principle, the evolutionary history of a population contains information of the effects of mutations (deleterious, beneficial or neutral) occurring in the population.

This thesis focuses on Global Navigation Satellite Systems (GNSS)-based localization and attitude determination, essential for navigation and control systems in various platforms. Carrier-phase observations from GNSS signals are more accurate than pseudo-range, but resolving integer ambiguities in carrier-phase data is challenging. The thesis proposes three attitude determination methods based on an optimized GNSS attitude model with nonlinear constraints. Additionally, a joint solution for real-time kinematic positioning and attitude determination is proposed, leveraging the correlation between GNSS data in these two problems. Riemannian optimization is applied to improve the accuracy and ambiguity resolution in both localization and attitude determination.

GNSS PPP-RTK is an integer ambiguity resolution enabled precise point positioning concept originally developed for use with the ultra-precise CDMA-based Global Navigation Satellite System carrier-phase signals. In this presentation, we first present the classical principles of PPP-RTK as they apply to the CDMA-based global and regional satellite navigation systems GPS, BeiDou, Galileo, QZSS and IRNSS.

High-accuracy indoor localization and tracking systems are essential for many modern applications and technologies. However, accurate location estimation of moving targets is challenging. This thesis addresses the challenges in indoor localization and tracking systems and proposes several solutions. A novel signal design, which we named Differential Zadoff-Chu, allows us to develop algorithms that accurately estimate the distances of static and moving targets even under random Doppler shifts. The results show that the proposed algorithms outperform the state-of-the-art in terms of both accuracy and complexity.

This event has been postponed from 20th July to 27th July. Stochastic optimization refers to the minimization/maximization of an objective function in the presence of randomness. The randomness may appear in objective functions, constraints, or optimization methods. It has the advantage of dealing with uncertainties that deterministic optimizers cannot solve or cannot solve efficiently. In this work, we discuss the implementation of stochastic optimization methods in solving target positioning problems and tackling key issues in location-based applications.

In this thesis, we focus on precisely analyzing the high dimensional error performance of such regularized convex optimization problems under the presence of different impairments (such as uncertainties and/or correlations) in the measurement matrix, which has independent Gaussian entries. The precise nature of our analysis allows performance comparison between different types of these estimators and enables us to optimally tune the involved hyperparameters. In particular, we study the performance of some of the most popular cases in linear inverse problems, such as the Least Squares (LS), Regularized Least Squares (RLS), LASSO, Elastic Net, and their box-constrained variants.

The Internet of Things (IoT) is a foundational building block for the upcoming information revolution and imminent smart-world era. Particularly, the IoT bridges the cyber domain to everything and anything within our physical world which enables unprecedented ubiquitous monitoring, connectivity, and smart control. In this Ph.D. defense, we present Unmanned Aerial Vehicles (UAVs) enabled IoT network designs for enhanced estimation, detection, and connectivity. The utilization of UAVs can offer an extra level of flexibility which results in more advanced and efficient connectivity and data aggregation for the IoT devices.

Tareq Al-Naffouri is a professor of Electrical Engineering (EE) and Principale investigator of the Information System Lab (ISL). He is also an active member of the Sensor Initiative (SI) at the King Abdullah University of Sciences and Technology, Saudi Arabia.

Random matrix theory is an outstanding mathematical tool that has demonstrated its usefulness in many areas ranging from wireless communication to finance and economics. The main motivation behind its use comes from the fundamental role that random matrices play in modeling unknown and unpredictable physical quantities. In many situations, meaningful metrics expressed as scalar functionals of these random matrices arise naturally. Along this line, the present work consists in leveraging tools from random matrix theory in an attempt to answer fundamental questions related to applications from statistical signal processing and machine learning.