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Parametric Computer-aided design (CAD) enables the creation of reusable models by integrating variables into geometric properties, facilitating customization without a complete redesign. However, creating parametric designs in…
Despite high-dimensionality of images, the sets of images of 3D objects have long been hypothesized to form low-dimensional manifolds. What is the nature of such manifolds? How do they differ across objects and object classes? Answering…
Cylindrical Algebraic Decomposition (CAD) is a key tool in computational algebraic geometry, best known as a procedure to enable Quantifier Elimination over real-closed fields. However, it has a worst case complexity doubly exponential in…
Representing images and videos with Symmetric Positive Definite (SPD) matrices and considering the Riemannian geometry of the resulting space has proven beneficial for many recognition tasks. Unfortunately, computation on the Riemannian…
Caffe provides multimedia scientists and practitioners with a clean and modifiable framework for state-of-the-art deep learning algorithms and a collection of reference models. The framework is a BSD-licensed C++ library with Python and…
Summary: The Smith Waterman (SW) algorithm, which produces the optimal pairwise alignment between two sequences, is frequently used as a key component of fast heuristic read mapping and variation detection tools, but current implementations…
Geometric Machine Learning (GML) has shown that respecting non-Euclidean geometry in data spaces can significantly improve performance over naive Euclidean assumptions. In parallel, Quantum Machine Learning (QML) has emerged as a promising…
Coupled wave equations are popular tool for investigating longitudinal dynamical effects in semiconductor lasers, for example, sensitivity to delayed optical feedback. We study a model that consists of a hyperbolic linear system of partial…
Manifolds discovered by machine learning models provide a compact representation of the underlying data. Geodesics on these manifolds define locally length-minimising curves and provide a notion of distance, which are key for reduced-order…
We propose a new diagrammatic modeling language, DML. The paradigm used is that of the category theory and in particular of the pushout tool. We show that most of the object-oriented structures can be described with this tool and have many…
Machine learning has enabled the prediction of quantum chemical properties with high accuracy and efficiency, allowing to bypass computationally costly ab initio calculations. Instead of training on a fixed set of properties, more recent…
The MORPHOLO C++ extended Library allows to convert a specific stereoscopic snapshot into a Native multi-view image through morphing algorithms taking into account display calibration data for specific slanted lenticular 3D monitors.…
Shape analysis and compuational anatomy both make use of sophisticated tools from infinite-dimensional differential manifolds and Riemannian geometry on spaces of functions. While comprehensive references for the mathematical foundations…
This dissertation focuses on the design and the implementation of domain-specific compilers for linear algebra matrix equations. The development of efficient libraries for such equations, which lie at the heart of most software for…
This paper explores the relationship between C++ templates and partial evaluation. Templates were designed to support generic programming, but unintentionally provided the ability to perform compile-time computations and code generation.…
The problem of identifying geometric structure in data is a cornerstone of (unsupervised) learning. As a result, Geometric Representation Learning has been widely applied across scientific and engineering domains. In this work, we…
Due to their high computational cost, geophysical applications are typically designed to run in large computing systems. Because of that, such applications must implement several high-performance techniques to use the computational…
As quantum computing hardware systems continue to advance, the research and development of performant, scalable, and extensible software architectures, languages, models, and compilers is equally as important in order to bring this novel…
We present solidfmm, a highly optimised C++ library for the solid harmonics as they are needed in fast multipole methods. The library provides efficient, vectorised implementations of the translation operations M2M, M2L, and L2L, and is…
Representing graphs as sets of node embeddings in certain curved Riemannian manifolds has recently gained momentum in machine learning due to their desirable geometric inductive biases, e.g., hierarchical structures benefit from hyperbolic…