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The {\em acyclic chromatic number} of a graph is the least number of colors needed to properly color its vertices so that none of its cycles has only two colors. The {\em acyclic chromatic index} is the analogous graph parameter for edge…
Colour refinement is a basic algorithmic routine for graph isomorphism testing, appearing as a subroutine in almost all practical isomorphism solvers. It partitions the vertices of a graph into "colour classes" in such a way that all…
The basic tool for solving problems in metric geometry and isotonic regression is the metric projection onto closed convex cones. Isotonicity of these projections with respect to a given order relation can facilitate finding the solutions…
Color centers play key roles in applications, including, e.g., solid state lighting and quantum information technology, for which the coupling between their optical and vibrational properties is crucial. Established methodologies for…
Grayscale images are fundamental to many image processing applications like data compression, feature extraction, printing and tone mapping. However, some image information is lost when converting from color to grayscale. In this paper, we…
The "reconfiguration problem" for circular colourings asks, given two $(p,q)$-colourings $f$ and $g$ of a graph $G$, is it possible to transform $f$ into $g$ by changing the colour of one vertex at a time such that every intermediate…
In trichromats, color vision entails the projection of an infinite-dimensional space (the one containing all possible electromagnetic power spectra) onto the 3-dimensional space that modulates the activity of the three types of cones. This…
We define vertex-colourings for edge-partitioned digraphs, which unify the theory of P-partitions and proper vertex-colourings of graphs. We use our vertex-colourings to define generalized chromatic functions, which merge the chromatic…
We obtain tilings with a singular point by applying conformal maps on regular tilings of the Euclidean plane, and determine its symmetries. The resulting tilings are then symmetrically colored by applying the same conformal maps on…
We consider solutions to the $4$-color problem for the vertices of sphere triangulations with degree sequence $6,...,6,4,4,4,4,4,4$. We sort these solutions into combinatorial types and show that each generic type $\tau$ is parametrized by…
Coloured graphical models are Gaussian statistical models determined by an undirected coloured graph. These models can be described by linear spaces of symmetric matrices. We outline a relationship between the symmetries of the graph and…
Cylindrical algebraic decomposition (CAD) is an important tool for the study of real algebraic geometry with many applications both within mathematics and elsewhere. It is known to have doubly exponential complexity in the number of…
Many well-known combinatorial optimization problems can be stated over the set of acyclic orientations of an undirected graph. For example, acyclic orientations with certain diameter constraints are closely related to the optimal solutions…
Advances in multimodal characterization methods fuel a generation of increasing immense hyper-dimensional datasets. Color mapping is employed for conveying higher dimensional data in two-dimensional (2D) representations for human…
Covering from photography to depth and spectral estimation, diverse computational imaging (CI) applications benefit from the versatile modulation of coded apertures (CAs). The light wave fields as space, time, or spectral can be modulated…
We present a method for analytic continuation of retarded Green functions, including Euclidean Green functions computed using lattice QCD. The method is based on conformal maps and construction of an interpolation function which is analytic…
We consider the problem of coloring the vertices of a large sparse random graph with a given number of colors so that no adjacent vertices have the same color. Using the cavity method, we present a detailed and systematic analytical study…
Color representation is essential in computer vision and human-computer interaction. There are multiple color models available. The choice of a suitable color model is critical for various applications. This paper presents a review of color…
We propose a perceptual chromatic adaptation transform for white balance that makes use of split-quaternions. The novelty of the present work, which is motivated by a recently developed quantum-like model of color perception, consists at…
Circular-harmonic spectra are a compact representation of local image features in two dimensions. It is well known that the computational complexity of such transforms is greatly reduced when polar separability is exploited in steerable…