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We study the generalisation of Baxter's three-colour problem to a random lattice. Rephrasing the problem as a matrix model problem we discuss the analyticity structure and the critical behaviour of the resulting matrix model. Based on a set…
In this work we study the polytope associated with a 0,1-integer programming formulation for the Equitable Coloring Problem. We find several families of valid inequalities and derive sufficient conditions in order to be facet-defining…
Solid-state quantum emitters have emerged as a leading quantum memory for quantum networking applications. However, standard optical characterization techniques are neither efficient nor repeatable at scale. In this work, we introduce and…
Handling various objects with different colors is a significant challenge for image colorization techniques. Thus, for complex real-world scenes, the existing image colorization algorithms often fail to maintain color consistency. In this…
Cylindrical algebraic decomposition (CAD) is an important tool for the investigation of semi-algebraic sets, with applications within algebraic geometry and beyond. We recently reported on a new implementation of CAD in Maple which…
We find an arc-parameterization of the contour on which an given analytic function has constant modulus. This contour is seen to satisfy a differential equation which we explicitly give.
We present the Unit Region Encoding of floorplans, which is a unified and compact geometry-aware encoding representation for various applications, ranging from interior space planning, floorplan metric learning to floorplan generation…
Quantum harmonic analysis extends classical harmonic analysis by integrating quantum mechanical observables, replacing functions with operators and classical convolution structures with their noncommutative counterparts. This paper explores…
This article makes the key observation that when using cylindrical algebraic decomposition (CAD) to solve a problem with respect to a set of polynomials, it is not always the signs of those polynomials that are of paramount importance but…
A unification of characteristic mode decomposition for all method-of-moment formulations of field integral equations describing free-space scattering is derived. The work is based on an algebraic link between impedance and transition…
Image colorization, the task of adding colors to grayscale images, has been the focus of significant research efforts in computer vision in recent years for its various application areas such as color restoration and automatic animation…
Self-similar solutions of the coherent diffusion equation are derived and measured. The set of real similarity solutions is generalized by the introduction of a nonuniform phase surface, based on the elegant Gaussian modes of optical…
Automatic color enhancement is aimed to adaptively adjust photos to expected styles and tones. For current learned methods in this field, global harmonious perception and local details are hard to be well-considered in a single model…
There are two problems Analytical Geometry with facing anyone who studies this discipline: define the nature of the locus represented by the general equation 2do degree in two or three variables: That curve represents the plane? What…
The investigation of colour symmetries for periodic and aperiodic systems consists of two steps. The first concerns the computation of the possible numbers of colours and is mainly combinatorial in nature. The second is algebraic and…
One of the toughest problems in Ramsey theory is to determine the existence of monochromatic arithmetic progressions in groups whose elements have been colored. We study the harder problem to not only determine the existence of…
Graphs are a fundamental abstraction in computer science and discrete mathematics, where information is encoded in their combinatorial structure. Graph-reduction techniques aim at simplifying graphs while preserving selected structural…
We establish range characterizations, or data consistency conditions, for an integral transform that maps a function to its weighted integrals over conical surfaces in $\mathbb{R}^n$. We consider two different geometries for the cone…
This paper discusses ways to categorify chromatic, dichromatic and Penrose polynomials, including categorifications of integer evaluations of chromatic polynomials. We show that with an appropriate choice of variables the coefficients of…
Counterfactual explanations (CEs) aim to enhance the interpretability of machine learning models by illustrating how alterations in input features would affect the resulting predictions. Common CE approaches require an additional model and…