Related papers: Using GXWeb for Theorem Proving and Mathematical M…
This work proposes xGEMs or manifold guided exemplars, a framework to understand black-box classifier behavior by exploring the landscape of the underlying data manifold as data points cross decision boundaries. To do so, we train an…
ZX-Calculus is a versatile graphical language for quantum computation equipped with an equational theory. Getting inspiration from Geometry of Interaction, in this paper we propose a token-machine-based asynchronous model of both pure…
Graph Neural Networks (GNNs) have achieved significant success across various applications. However, their complex structures and inner workings can be challenging for non-AI experts to understand. To address this issue, this study presents…
We present a graphical simulation tool for visually and interactively exploring the processing of various events handled by an operating system when running a program. Our graphical simulator is available for use on the web and locally by…
The geometry automated theorem proving area distinguishes itself by a large number of specific methods and implementations, different approaches (synthetic, algebraic, semi-synthetic) and different goals and applications (from research in…
Teaching precise mathematical reasoning can be very hard. It is very easy for a student to make a subtle mistake in a proof which invalidates it, but it is often hard for the teacher to pinpoint and explain the problem in the (often…
This paper lays the foundations for a unified framework for numerically and computationally applying methods drawn from a range of currently distinct geometrical approaches to statistical modelling. In so doing, it extends information…
Extension of the open-source simulation package GSEIM for power electronics applications is presented. Recent developments in GSEIM, including those oriented specifically towards power electronic circuits, are described. Some examples of…
We present the specification for a modeling language, VoxML, which encodes semantic knowledge of real-world objects represented as three-dimensional models, and of events and attributes related to and enacted over these objects. VoxML is…
Molecular visualization software has long supported research and education in chemical and structural sciences, but consumer devices constrained to 2D inputs and outputs pose two major challenges: they poorly convey 3D nature, and 3D…
In this paper, we introduce a system called GamePad that can be used to explore the application of machine learning methods to theorem proving in the Coq proof assistant. Interactive theorem provers such as Coq enable users to construct…
This article introduces Globular, an online proof assistant for the formalization and verification of proofs in higher-dimensional category theory. The tool produces graphical visualizations of higher-dimensional proofs, assists in their…
In this manuscript, we propose to expand the use of scientific repositories such as Zenodo and HEP Data, in particular in order to better examine multi-parametric solutions of physical models. The implementation of interactive web-based…
Explainable deep learning models are advantageous in many situations. Prior work mostly provide unimodal explanations through post-hoc approaches not part of the original system design. Explanation mechanisms also ignore useful textual…
Dynamic geometry systems (DGS) have become basic tools in many areas of geometry as, for example, in education. Geometry Automated Theorem Provers (GATP) are an active area of research and are considered as being basic tools in future…
Spreadsheets are end-user programs and domain models that are heavily employed in administration, financial forecasting, education, and science because of their intuitive, flexible, and direct approach to computation. As a result,…
In this paper we make some considerations about using a dynamic geometry software for teaching history of mathematica at university level. After a short introduction to the software GeoGebra, we discuss four activities. The first is an…
In this paper we present a short overview of the new Wolfram Mathematica package intended for elementary "in-basis" tensor and differential-geometric calculations. In contrast to alternatives our package is designed to be easy-to-use,…
Invariant and equivariant models incorporate the symmetry of an object to be estimated (here non-parametric regression functions $f : \mathcal{X} \rightarrow \mathbb{R}$). These models perform better (with respect to $L^2$ loss) and are…
Mathematical proof is undoubtedly the cornerstone of mathematics. The emergence, in the last years, of computing and reasoning tools, in particular automated geometry theorem provers, has enriched our experience with mathematics immensely.…