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Chromatic Correlation Clustering (CCC) extends Correlation Clustering by assigning semantic colors to edges and requiring each cluster to receive a single color label. Unlike standard CC, whose LP relaxation has integrality gap 2 on…
We introduce a new graph invariant that measures fractional covering of a graph by cuts. Besides being interesting in its own right, it is useful for study of homomorphisms and tension-continuous mappings. We study the relations with…
In this article, the conversion of color RGB images to grayscale is covered by characterizing the mathematical operators used to project 3 color channels to a single one. Based on the fact that most operators assign each of the $256^3$…
We define the independence ratio and the chromatic number for bounded, self-adjoint operators on an L^2-space by extending the definitions for the adjacency matrix of finite graphs. In analogy to the Hoffman bounds for finite graphs, we…
A general (convex) polytope $P\subset\mathbb R^d$ and its edge-graph $G_P$ can have very distinct symmetry properties. We construct a coloring (of the vertices and edges) of the edge-graph so that the combinatorial symmetry group of the…
We investigate the completely positive semidefinite cone $\mathcal{CS}_+^n$, a new matrix cone consisting of all $n\times n$ matrices that admit a Gram representation by positive semidefinite matrices (of any size). In particular we study…
In a 2D conservative Hamiltonian system there is a formal integral $\Phi$ besides the energy H. This is not convergent near a stable periodic orbit, but it is convergent near an unstable periodic orbit. We explain this difference and we…
We prove lower and upper bounds for the chromatic number of certain hypergraphs defined by geometric regions. This problem has close relations to conflict-free colorings. One of the most interesting type of regions to consider for this…
Audio autoencoders learn useful, compressed audio representations, but their non-linear latent spaces prevent intuitive algebraic manipulation such as mixing or scaling. We introduce a simple training methodology to induce linearity in a…
We introduce methods for deriving analytic solutions from differential-algebraic systems of equations (DAEs), as well as methods for deriving governing equations for analytic characterization which is currently limited to very small systems…
A technique called analytic perturbation theory, which respects the required analytic properties, consistent with causality, is applied to the definition of the running coupling in the timelike region, to the description of inclusive…
Image forensics aims to detect the manipulation of digital images. Currently, splicing detection, copy-move detection and image retouching detection are drawing much attentions from researchers. However, image editing techniques develop…
This study investigates the cognitive plausibility of a pretrained multimodal model, CLIP, in recognizing emotions evoked by abstract visual art. We employ a dataset comprising images with associated emotion labels and textual rationales of…
There are many variations on partition functions for graph homomorphisms or colorings. The case considered here is a counting or hard constraint problem in which the range or color graph carries a free and vertex transitive Abelian group…
We explore the concept of a graph homomorphism through the lens of C$^*$-algebras and operator systems. We start by studying the various notions of a quantum graph homomorphism and examine how they are related to each other. We then define…
We conclude an investigation of Abrishami, Esperet, Giocanti, Hamman, Knappe and M\"oller studying the existence of periodic colourings of locally finite graphs. A colouring of a graph $\Gamma$ is periodic if the resulting coloured graph…
Color transfer is an image editing process that adjusts the colors of a picture to match a target picture's color theme. A natural color transfer not only matches the color styles but also prevents after-transfer artifacts due to image…
This study addresses the challenge of, without training or fine-tuning, controlling the global color aspect of images generated with a diffusion model. We rewrite the guidance equations to ensure that the outputs are closer to a known color…
This paper deals with the identification of the flux for a system of conservation laws in the specific example of analytic chromatography. The fundamental equations of chromatographic process are highly non linear. The state-of-the-art…
Cosmological correlators encode statistical properties of the initial conditions of our universe. Mathematically, they can often be written as Mellin integrals of a certain rational function associated to graphs, namely the flat space…