Related papers: PyRigi -- a general-purpose Python package for the…
A d-dimensional framework is a graph and a map from its vertices to E^d. Such a framework is globally rigid if it is the only framework in E^d with the same graph and edge lengths, up to rigid motions. For which underlying graphs is a…
This paper investigates the use of graph rewriting systems as a modelling tool, and advocates the embedding of such systems in an interactive environment. One important application domain is the modelling of biochemical systems, where…
Space-filling experimental design techniques are commonly used in many computer modeling and simulation studies to explore the effects of inputs on outputs. This research presents raxpy, a Python package that leverages expressive annotation…
Graphs are pervasive in our everyday lives, with relevance to biology, the internet, and infrastructure, as well as numerous other applications. It is thus necessary to have an understanding as to how quickly a graph disintegrates, whether…
A two-dimensional direction-length framework $(G,p)$ consists of a multigraph $G=(V;D,L)$ whose edge set is formed of "direction" edges $D$ and "length" edges $L$, and a realisation $p$ of this graph in the plane. The edges of the framework…
A tutorial introduction to projective geometric algebra (PGA), a modern, coordinate-free framework for doing euclidean geometry. PGA features: uniform representation of points, lines, and planes; robust, parallel-safe join and meet…
An approximate formulation of a robust geometric program (RGP) as a convex program is proposed. Interest in using geometric programs (GPs) to model complex engineering systems has been growing, and this has motivated explicitly modeling the…
A bar-joint framework $(G,p)$ in $\mathbb{R}^d$ is rigid if the only edge-length preserving continuous motions of the vertices arise from isometries of $\mathbb{R}^d$. It is known that, when $(G,p)$ is generic, its rigidity depends only on…
Pykg2vec is an open-source Python library for learning the representations of the entities and relations in knowledge graphs. Pykg2vec's flexible and modular software architecture currently implements 16 state-of-the-art knowledge graph…
The flexibility of the DPG methodology is exposed by solving the linear elasticity equations under different variational formulations, including some with non-symmetric functional settings (different infinite-dimensional trial and test…
This work focuses on the bearing rigidity theory, namely the branch of knowledge investigating the structural properties necessary for multi-element systems to preserve the inter-units bearings when exposed to deformations. The original…
Grid diagrams are a combinatorial version of classical link diagrams, widely used in theoretical, computational and applied knot theory. Motivated by questions from (bio)-physical knot theory, we introduce GridPyM, a Sage compatible Python…
A standard practice in extragalactic population studies is the fitting of parametric models to galaxy images. From such fits, key structural parameters of galaxies such as total flux and effective radius (size) can be extracted. One of the…
We propose a novel method for large-scale image stitching that is robust against repetitive patterns and featureless regions in the imagery. In such cases, state-of-the-art image stitching methods easily produce image alignment artifacts,…
ruptures is a Python library for offline change point detection. This package provides methods for the analysis and segmentation of non-stationary signals. Implemented algorithms include exact and approximate detection for various…
CurvPy is an open-source Python library for automated curve fitting and regression analysis, aiming to make advanced statistical and machine learning techniques more accessible. This paper explores the mathematical foundations and…
From a dynamical viewpoint, basic phase transitions of statistical mechanics can be regarded as a breaking of ergodicity. While many random models exhibiting such transitions at the thermodynamics limit exist, finite-dimensional examples…
Reliable parameter extraction from experimental data is central to quantitative analysis in spectroscopy, diffraction, photoluminescence, chromatography, microscopy, and time-resolved measurements. We present FitED, a Python-based desktop…
A $d$-dimensional tensegrity framework $(T,p)$ is an edge-labeled geometric graph in ${\mathbb R}^d$, which consists of a graph $T=(V,B\cup C\cup S)$ and a map $p:V\to {\mathbb R}^d$. The labels determine whether an edge $uv$ of $T$…
A bar-and-joint framework is a finite set of points together with specified distances between selected pairs. In rigidity theory we seek to understand when the remaining pairwise distances are also fixed. If there exists a pair of points…