Related papers: PyRigi -- a general-purpose Python package for the…
A bar-joint framework $(G,p)$ in the Euclidean space $\mathbb{E}^d$ is globally rigid if it is the unique realisation, up to rigid congruences, of $G$ in $\mathbb{E}^d$ with the edge lengths of $(G,p)$. Building on key results of…
We present a survey of results concerning the use of inductive constructions to study the rigidity of frameworks. By inductive constructions we mean simple graph moves which can be shown to preserve the rigidity of the corresponding…
We show that universal rigidity of a generic bar and joint framework (G,p) in the line depends on more than the ordering of the vertices. In particular, we construct examples of one-dimensional generic frameworks with the same graph and…
Rigidity, arising in discrete geometry, is the property of a structure that does not flex. Laman provides a combinatorial characterization of rigid graphs in the Euclidean plane, and thus rigid graphs in the Euclidean plane have…
Interpreting machine learning models is challenging but crucial for ensuring the safety of deep networks in autonomous driving systems. Due to the prevalence of deep learning based perception models in autonomous vehicles, accurately…
We consider the rigidity and global rigidity of bar-joint frameworks in Euclidean $d$-space under additional dilation constraints in specified coordinate directions. In this setting we obtain a complete characterisation of generic rigidity.…
Pyrit is a field simulation software based on the finite element method written in Python to solve coupled systems of partial differential equations. It is designed as a modular software that is easily modifiable and extendable. The…
We give an algebraic characterization of when a $d$-dimensional periodic framework has no non-trivial, symmetry preserving, motion for any choice of periodicity lattice. Our condition is decidable, and we provide a simple algorithm that…
Data gridding is a common task in astronomy and many other science disciplines. It refers to the resampling of irregularly sampled data to a regular grid. We present cygrid, a library module for the general purpose programming language…
Programmable quantum systems based on Rydberg atom arrays have recently emerged as a promising testbed for combinatorial optimization. Indeed, the Maximum Weighted Independent Set problem on unit-disk graphs can be efficiently mapped to…
Isogeometric Analysis (IgA) is a spline based approach to the numerical solution of partial differential equations. There are two major issues that IgA was designed to address. The first issue is the exact representation of domains stemming…
Models for near-rigid shape matching are typically based on distance-related features, in order to infer matches that are consistent with the isometric assumption. However, real shapes from image datasets, even when expected to be related…
In this paper, we propose a perturbation framework to measure the robustness of graph properties. Although there are already perturbation methods proposed to tackle this problem, they are limited by the fact that the strength of the…
GeneralizIT is a Python package designed to streamline the application of Generalizability Theory (G-Theory) in research and practice. G-Theory extends classical test theory by estimating multiple sources of error variance, providing a more…
We study the classical problem of computing geometric thickness, i.e., finding a straight-line drawing of an input graph and a partition of its edges into as few parts as possible so that each part is crossing-free. Since the problem is…
We introduce pymovements: a Python package for analyzing eye-tracking data that follows best practices in software development, including rigorous testing and adherence to coding standards. The package provides functionality for key…
To facilitate flexible and efficient structural bioinformatics analyses, new functionality for three-dimensional structure processing and analysis has been introduced into PyCogent -- a popular feature-rich framework for sequence-based…
PySPH is an open-source, Python-based, framework for particle methods in general and Smoothed Particle Hydrodynamics (SPH) in particular. PySPH allows a user to define a complete SPH simulation using pure Python. High-performance code is…
This paper introduces layout-aware graph modeling for multimodal RAG. Different from traditional RAG methods that mostly deal with flat text chunks, the proposed method takes into account the relationship of multimodalities by using a graph…
We give a combinatorial characterization of generic frameworks that are minimally rigid under the additional constraint of maintaining symmetry with respect to a finite order rotation or a reflection. To establish these results we develop a…