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.

Living in the booming age of information, we have to rely on powerful information retrieval tools to seek the unique piece of desired knowledge from such a big data world, like using personalized search engines and recommendation systems. In this thesis, we aim at advancing the development of the methodologies and principles of mining heterogeneous information networks through learning entity relations from a pairwise learning to rank optimization perspective. More specifically we first show the connections of different relation learning objectives modified from different ranking metrics including both pairwise and list-wise objectives. We prove that most of popular ranking metrics can be optimized in the same lower bound. Secondly, we propose the class-imbalance problem imposed by entity relation comparison in ranking objectives, and prove that class-imbalance problems can lead to frequency clustering and gradient vanishment problems. As a response, we indicate out that developing a fast adaptive sampling method is very essential to boost the pairwise ranking model. To model the entity dynamic dependency, we propose to unify the individual-level interaction and union-level interactions, and result in a multi-order attentive ranking model to improve the preference inference from multiple views.

This talk will introduce two novel models we developed for automatic HG generation in two different settings, positive-negative learning and positive-unlabeled learning. We demonstrate the efficacy of the proposed model on three real-world datasets constructed from biomedical publications.

Research and experimentation in various scientific fields are based on the knowledge and ideas from scholarly literature. The advancement of research and development has, thus, strengthened the importance of literary analysis and understanding. However, in recent years, researchers have been facing massive scholarly documents published at an exponentially increasing rate. Analyzing this vast number of publications is far beyond the capability of individual researchers. This dissertation is motivated by the need for large scale analyses of the exploding number of scholarly literature for scientific knowledge discovery and information retrieval. In the first part of this dissertation, the interdependencies between scholarly literature are studied. First, I develop Delve -- a data-driven search engine supported by our designed semi-supervised edge classification method. This system enables users to search and analyze the relationship between datasets and scholarly literature. Based on the Delve system, I propose to study information extraction as a node classification problem in attributed networks. Specifically, if we can learn the research topics of documents (nodes in a network), we can aggregate documents by topics and retrieve information specific to each topic (e.g., top-k popular datasets).

The proposed method, called PREMA, leverages low-rank tensor factorization tools to provide recovery guarantees under certain conditions. PREMA is flexible in the sense that it can perform the disaggregation task on data that have missing entries, i.e., partially observed. The proposed method considers challenging scenarios: i) the available views of the data are aggregated in two dimensions, i.e., double aggregation, and ii) the aggregation patterns are unknown. Experiments on real data from different domains, i.e., sales data from retail companies, crime counts, and weather observations, are presented to showcase the effectiveness of PREMA.

In this talk, the speaker will provide a high-level introduction to his recent research on IoT endpoint security. Firstly, he will introduce requirements followed by a discussion on cryptographic algorithm implementation. He will mainly focus on an overview of efficient cryptography for IoT endpoints and system privacy issues. Then he will discuss security management approaches, positives, negatives and challenges to resolve, linking to the endpoint device security section with regards to realistic device needs/capabilities.

The goal of this thesis is to pave the way towards the next generation of recommendation systems tackling such real-world challenges to improve the user experience while giving good recommendations.