Related papers: Computing with Coloured Tangles
An abundance of real-world problems manifest as covering edges and/or vertices of a graph with cliques that are optimized for some objectives. We consider different structural parameters of graph, and design fixed-parameter tractable…
K\"onig's edge coloring theorem says that a bipartite graph with maximal degree $n$ has an edge coloring with no more than $n$ colors. We explore the computability theory and Reverse Mathematics aspects of this theorem. Computable bipartite…
Parameterized quantum circuits play a key role in quantum computing. Measuring the suitability of such a circuit for solving a class of problems is needed. One such promising measure is the expressivity of a circuit, which is defined in two…
This paper explores the application of a new algebraic method of edge coloring, called complex coloring, to the scheduling problems of input queued switches. The proposed distributed parallel scheduling algorithm possesses two important…
We investigate the computational power of particle methods, a well-established class of algorit hms with applications in scientific computing and computer simulation. The computational power of a compute model determines the class of…
We propose and investigate a unifying class of sparse random graph models, based on a hidden coloring of edge-vertex incidences, extending an existing approach, Random graphs with a given degree distribution, in a way that admits a…
In this paper we consider clustering problems in which each point is endowed with a color. The goal is to cluster the points to minimize the classical clustering cost but with the additional constraint that no color is over-represented in…
Can the cross product be generalized? Why are the trace and determinant so important in matrix theory? What do all the coefficients of the characteristic polynomial represent? This paper describes a technique for `doodling' equations from…
We first prove that the set of domino tilings of a fixed finite figure is a distributive lattice, even in the case when the figure has holes. We then give a geometrical interpretation of the order given by this lattice, using (not…
Topology has emerged as a fundamental property of many systems, manifesting in cosmology, condensed matter, high-energy physics and waves. Despite the rich textures, the topology has largely been limited to low dimensional systems that can…
Persistent homology is a popular tool in Topological Data Analysis. It provides numerical characteristics of data sets which reflect global geometric properties. In order to be useful in practice, for example for feature generation in…
The study of neural computation aims to understand the function of a neural system as an information processing machine. Neural systems are undoubtedly complex, necessitating principled and automated tools to abstract away details to…
Consider a universal Turing machine that produces a partial or total function (or a binary stream), based on the answers to the binary queries that it makes during the computation. We study the probability that the machine will produce a…
Although there is a somewhat standard formalization of computability on countable sets given by Turing machines, the same cannot be said about uncountable sets. Among the approaches to define computability in these sets, order-theoretic…
Communication topology is a crucial part of a distributed control implementation for cyber-physical systems, yet is typically treated as a constraint within control design problems rather than a design variable. We propose a data-driven…
Herein we develop category-theoretic tools for understanding network-style diagrammatic languages. The archetypal network-style diagrammatic language is that of electric circuits; other examples include signal flow graphs, Markov processes,…
We investigate the usage of rule dependency graphs and their colorings for characterizing and computing answer sets of logic programs. This approach provides us with insights into the interplay between rules when inducing answer sets. We…
Traditional Turing machines are semantically poor, they only concern the syntactic manipulation of symbols, discarding the mathematical semantics behind the symbols. This semantic deficiency is considered the root cause of the three major…
In this paper, we will present some ideas to use 3D topology for quantum computing. Topological quantum computing in the usual sense works with an encoding of information as knotted quantum states of topological phases of matter, thus being…
Coloured probability tree models are statistical models coding conditional independence between events depicted in a tree graph. They are more general than the very important class of context-specific Bayesian networks. In this paper, we…