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Discovering heterogeneous catalysts tailored for specific reaction intermediates remains a fundamental bottleneck in materials science. While traditional trial-and-error methods and recent generative models have shown promise, they struggle…
The evaluation of cell tracking results steers the development of tracking methods, significantly impacting biomedical research. This is quantitatively achieved by means of evaluation metrics. Unfortunately, current metrics favor local…
In ontology-mediated query answering, access to incomplete data sources is mediated by a conceptual layer constituted by an ontology, which can be formulated in a description logic (DL) or using existential rules. In the literature, there…
Training or fine-tuning large language model (LLM)-based systems often requires costly human feedback, yet there is limited understanding of how to minimize such intervention while maintaining strong error guarantees. We study this problem…
Matrix completion results deal with the question of when a partially specified symmetric matrix can be completed to a member of certain matrix cones. Results from positive semidefinite matrix completion and completely positive matrix…
Over the last few decades, many distinct lines of research aimed at automating mathematics have been developed, including computer algebra systems (CASs) for mathematical modelling, automated theorem provers for first-order logic, SAT/SMT…
Randomized compilation protocols have recently attracted attention as alternatives to traditional deterministic Trotter-Suzuki methods, potentially reducing circuit depth and resource overhead. These protocols determine gate application…
Constraint automata (CA) constitute a coordination model based on finite automata on infinite words. Originally introduced for modeling of coordinators, an interesting new application of CAs is implementing coordinators (i.e., compiling CAs…
We are interested in solving the Asymmetric Eigenvalue Complementarity Problem (AEiCP) by accelerated Difference-of-Convex (DC) algorithms. Two novel hybrid accelerated DCA: the Hybrid DCA with Line search and Inertial force (HDCA-LI) and…
Searching for potential active compounds in large databases is a necessary step to reduce time and costs in modern drug discovery pipelines. Such virtual screening methods seek to provide predictions that allow the search space to be…
Canonical Correlation Analysis (CCA) is a linear representation learning method that seeks maximally correlated variables in multi-view data. Non-linear CCA extends this notion to a broader family of transformations, which are more powerful…
Evolutionary clustering algorithms have considered as the most popular and widely used evolutionary algorithms for minimising optimisation and practical problems in nearly all fields. In this thesis, a new evolutionary clustering algorithm…
ChatGPT represents a significant milestone in the field of artificial intelligence (AI), finding widespread applications across diverse domains. However, its effectiveness in mathematical contexts has been somewhat constrained by its…
Identifying and selecting high-quality Metamorphic Relations (MRs) is a challenge in Metamorphic Testing (MT). While some techniques for automatically selecting MRs have been proposed, they are either domain-specific or rely on strict…
The Combustion Toolbox (CT) is a newly developed open-source thermochemical code designed to solve problems involving chemical equilibrium for both gas- and condensed-phase species. The kernel of the code is based on the theoretical…
Building on the successes of satisfiability modulo theories (SMT), Bj{\o}rner et al. initiated a research programme advocating Horn constraints as a suitable basis for automatic program verification. The notion of first-order constrained…
Large language models (LLMs) are prone to generating factually incorrect outputs. Recent work has applied conformal prediction to provide uncertainty estimates and statistical guarantees for the factuality of LLM generations. However,…
Formal Concept Analysis (FCA) allows to analyze binary data by deriving concepts and ordering them in lattices. One of the main goals of FCA is to enable humans to comprehend the information that is encapsulated in the data; however, the…
The accelerating adoption of Large Language Models (LLMs) in software engineering (SE) has brought with it a silent crisis: unsustainable computational cost. While these models demonstrate remarkable capabilities in different SE tasks, they…
Tokenization-free hierarchical models are emerging as a promising alternative to traditional Large Language Models (LLMs), addressing inherent preprocessing issues such as vocabulary design complexity, out-of-vocabulary (OOV) errors, and…