Related papers: Grout: A 1-Dimensional Substitution Tiling Space P…
Coroutine, as a powerful programming construct, is widely used in asynchronous applications to replace thread-based programming or the callback hell. Using coroutines makes code more readable and maintainable, for its ability to transfer…
This paper develops new combinatorial approaches to analyze and compute special set partitions, called complementary set partitions, which are fundamental in the study of generalized cumulants. Moving away from traditional graph-based and…
We discuss the architecture and design principles that underpin the latest version of SKIRT, a state-of-the-art open source code for simulating continuum radiation transfer in dusty astrophysical systems, such as spiral galaxies and…
We design an algorithm to find certain partial permutation representations of a finitely presented group $G$ (the bricks) that may be combined to a transitive permutation representation of $G$ (the mosaic) on the disjoint union.
We study the rotational structures of aperiodic tilings in Euclidean space of arbitrary dimension using topological methods. Classical topological approaches to the study of aperiodic patterns have largely concentrated just on translational…
A number of novel programming languages and libraries have been proposed that offer simpler-to-use models of concurrency than threads. It is challenging, however, to devise execution models that successfully realise their abstractions…
Preparing problems for execution on quantum computers can require many compilation steps. Automated compilation software is useful not only for easier and faster problem execution, but also for facilitating the comparison between different…
We present a suite of algorithmic techniques for handling substitution tilings by treating a tile's hierarchy of supertiles in a purely combinatorial fashion using finite state automata. The resulting techniques are very convenient for…
We introduce the Insertion Chain Complex, a higher-dimensional extension of insertion graphs, as a new framework for analyzing finite sets of words. We study its topological and combinatorial properties, in particular its homology groups,…
Visualizing changes over time is fundamental to learning from the past and anticipating the future. However, temporal semantics can be complicated, and existing visualization tools often struggle to accurately represent these complexities.…
The North American Linear Collider Detector group has developed simulation and analysis program packages. LCDROOT is one of the packages, and is based on ROOT and the C++ programing language to maximally benefit from object oriented…
An algorithm is presented that formalizes different steps in a classical Supersymmetric (SUSY) calculation. Based on the algorithm Dill, a symbolic software package, that can perform the calculations, is developed in the Mathematica…
In this paper we provide, first, a general symbolic algorithm for computing the symmetries of a given rational surface, based on the classical differential invariants of surfaces, i.e. Gauss curvature and mean curvature. In practice, the…
Abstracting Gradual Typing (AGT) is a systematic approach to designing gradually-typed languages. Languages developed using AGT automatically satisfy the formal semantic criteria for gradual languages identified by Siek et al. [2015].…
We study the topology and dynamics of subshifts and tiling spaces associated to non-primitive substitutions in one dimension. We identify a property of a substitution, which we call tameness, in the presence of which most of the possible…
e use Prolog as a flexible meta-language to provide executable specifications of some fundamental mathematical objects and their transformations. In the process, isomorphisms are unraveled between natural numbers and combinatorial objects…
The introduced package MoebInv contains two CPP libraries for symbolic, numeric and graphical manipulations in non-Euclidean geometry. The first library cycle implements basic geometric operations on cycles, which are the zero sets of…
This is a tutorial in applied and computational topology and topological data analysis. It is illustrated with numerous computational examples that utilize Gudhi library. It is under constant development, so please do not consider this…
A generic rectangulation is a partition of a rectangle into finitely many interior-disjoint rectangles, such that no four rectangles meet in a point. In this work we present a versatile algorithmic framework for exhaustively generating a…
An effort has been made to show mathematicians some new ideas applied to image analysis. Gray images are presented as tilings. Based on topological properties of the tiling, a number of gray convex hulls: maximal, minimal, and oriented ones…