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Equational reasoning is among the most important tools that functional programming provides us. Curiously, relatively less attention has been paid to reasoning about monadic programs. In this report we derive a backtracking algorithm for…
Clustering problems have numerous applications and are becoming more challenging as the size of the data increases. In this paper, we consider designing clustering algorithms that can be used in MapReduce, the most popular programming…
Regular chains and triangular decompositions are fundamental and well-developed tools for describing the complex solutions of polynomial systems. This paper proposes adaptations of these tools focusing on solutions of the real analogue:…
Computed Tomography (CT) using synchrotron radiation is a powerful technique that, compared to lab-CT techniques, boosts high spatial and temporal resolution while also providing access to a range of contrast-formation mechanisms. The…
Outer approximation methods have long been employed to tackle a variety of optimization problems, including linear programming, in the 1960s, and continue to be effective for solving variational inequalities, general convex problems, as…
With the development of computer-aided diagnosis (CAD) and image scanning technology, Whole-slide Image (WSI) scanners are widely used in the field of pathological diagnosis. Therefore, WSI analysis has become the key to modern digital…
Deep models have been widely and successfully used in image manipulation detection, which aims to classify tampered images and localize tampered regions. Most existing methods mainly focus on extracting global features from tampered images,…
Computer-Aided Design (CAD) plays a foundational role in modern manufacturing and product development, often requiring designers to modify or build upon existing models. Converting 3D scans into parametric CAD representations--a process…
Quaternion symmetry is ubiquitous in the physical sciences. As such, much work has been afforded over the years to the development of efficient schemes to exploit this symmetry using real and complex linear algebra. Recent years have also…
Symplectic integrators are the established standard for long-term simulations of nearly-integrable Hamiltonian systems due to their preservation of geometric structures. However, they suffer from an inherent limitation: secular phase-shift…
Self-organising maps are a powerful tool for cluster analysis in a wide range of data contexts. From the pioneer work of Kohonen, many variants and improvements have been proposed. This review focuses on the last decade, in order to provide…
Image matching, which establishes correspondences between two-view images to recover 3D structure and camera geometry, serves as a cornerstone in computer vision and underpins a wide range of applications, including visual localization, 3D…
Large kernel systems are prone to be ill-conditioned. Pivoted Cholesky decomposition (PCD) render a stable and efficient solution to the systems without a perturbation of regularization. This paper proposes a new PCD algorithm by tuning…
The primal-dual optimization algorithm developed in Chambolle and Pock (CP), 2011 is applied to various convex optimization problems of interest in computed tomography (CT) image reconstruction. This algorithm allows for rapid prototyping…
An update of the ODEtools Maple package, for the analytical solving of 1st and 2nd order ODEs using Lie group symmetry methods, is presented. The set of routines includes an ODE-solver and user-level commands realizing most of the relevant…
Owing to their favorable scaling with dimensionality, Monte Carlo (MC) methods have become the tool of choice for numerical integration across the quantitative sciences. Almost invariably, efficient MC integration schemes are strictly…
Self organizing maps (SOMs) are widely-used for unsupervised classification. For this application, they must be combined with some partitioning scheme that can identify boundaries between distinct regions in the maps they produce. We…
We present different methods for symbolic computer algebra computations in higher dimensional (\ge9) Clifford algebras using the \Clifford\ and \Bigebra\ packages for \Maple(R). This is achieved using graded tensor decompositions,…
We consider several basic questions pertaining to the geometry of image of a general quadratic map. In general the image of a quadratic map is non-convex, although there are several known classes of quadratic maps when the image is convex.…
Studies in thermodynamics often require the reduction of some first or second order partial derivatives in terms of a smaller basic set. A simple algorithm to perform such a reduction is presented here, together with a review of earlier…