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In this work, we develop a novel mathematical framework for universal digital quantum computation using algebraic probability theory. We rigorously define quantum circuits as finite sequences of elementary quantum gates and establish their…
The complexities of today's materials simulations demand computer codes which are both powerful and highly flexible. A researcher should be able to readily choose different geometries, different materials and different algorithms without…
Generalised planning (GP) refers to the task of synthesising programs that solve families of related planning problems. We introduce a novel, yet simple method for GP: given a set of training problems, for each problem, compute an optimal…
Image processing is a fundamental task in computer vision, which aims at enhancing image quality and extracting essential features for subsequent vision applications. Traditionally, task-specific models are developed for individual tasks…
Reconfigurable computing refers to the use of processors, such as Field Programmable Gate Arrays (FPGAs), that can be modified at the hardware level to take on different processing tasks. A reconfigurable computing platform describes the…
With the soaring demand for high-performing integrated circuits, 3D integrated circuits (ICs) have emerged as a promising alternative to traditional planar structures. Unlike existing 3D ICs that stack 2D layers, a full 3D IC features cubic…
The integration of machine learning techniques in materials discovery has become prominent in materials science research and has been accompanied by an increasing trend towards open-source data and tools to propel the field. Despite the…
We propose a new probabilistic framework that allows mobile robots to autonomously learn deep, generative models of their environments that span multiple levels of abstraction. Unlike traditional approaches that combine engineered models…
Domain generalization (DG) strives to address distribution shifts across diverse environments to enhance model's generalizability. Current DG approaches are confined to acquiring robust representations with continuous features, specifically…
This paper presents a method to obtain geometric registrations between high-genus ($g\geq 1$) surfaces. Surface registration between simple surfaces, such as simply-connected open surfaces, has been well studied. However, very few works…
The increasing demand for Fourier transforms on geometric algebras has resulted in a large variety. Here we introduce one single straight forward definition of a general geometric Fourier transform covering most versions in the literature.…
Understanding how nano- or micro-scale structures and material properties can be optimally configured to attain specific functionalities remains a fundamental challenge. Photonic metasurfaces, for instance, can be spectrally tuned through…
Programming requires much more than just writing code in a programming language. It is usually done in the context of a stateful environment, by interacting with a system through a graphical user interface. Yet, this wide space of…
This work deals with the optimization of computer programs targeting Graphics Processing Units (GPUs). The goal is to lift, from programmers to optimizing compilers, the heavy burden of determining program details that are dependent on the…
The area of geometry with its very strong and appealing visual contents and its also strong and appealing connection between the visual content and its formal specification, is an area where computational tools can enhance, in a significant…
This paper presents a cognitive typology of reuse processes, and a cognitive typology of documenting processes. Empirical studies on design with reuse and on software documenting provide evidence for a generalized cognitive model. First,…
Formal methods for verification of programs are extended to testing of programs. Their combination is intended to lead to benefits in reliable program development, testing, and evolution. Our geometric theory of testing is intended to serve…
There has been a lot of recent interest in mining patterns from graphs. Often, the exact structure of the patterns of interest is not known. This happens, for example, when molecular structures are mined to discover fragments useful as…
The $k$-dimensional coding schemes refer to a collection of methods that attempt to represent data using a set of representative $k$-dimensional vectors, and include non-negative matrix factorization, dictionary learning, sparse coding,…
Conventional coded computing frameworks are predominantly tailored for structured computations, such as matrix multiplication and polynomial evaluation. Such tasks allow the reuse of tools and techniques from algebraic coding theory to…