Related papers: Using GXWeb for Theorem Proving and Mathematical M…
Graph Neural Networks (GNNs) are widely used in many modern applications, necessitating explanations for their decisions. However, the complexity of GNNs makes it difficult to explain predictions. Even though several methods have been…
This paper presents an intelligent tutoring system, GeoTutor, for Euclidean Geometry that is automatically able to synthesize proof problems and their respective solutions given a geometric figure together with a set of properties true of…
Statistical Shape Models of faces and various body parts are heavily used in medical image analysis, computer vision and visualization. Whilst the field is well explored with many existing tools, all of them aim at experts, which limits…
A learning environment, the tutor-web (http://tutor-web.net), has been developed and used for educational research. The system is accessible and free to use for anyone having access to the Web. It is based on open source software and the…
Symbolic computation is the science of computing with symbolic objects (terms, formulae, programs, algebraic objects, geometrical objects, etc). Powerful symbolic algorithms have been developed during the past decades and have played an…
The ZX-calculus is a graphical language for reasoning about ZX-diagrams, a type of tensor networks that can represent arbitrary linear maps between qubits. Using the ZX-calculus, we can intuitively reason about quantum theory, and optimise…
A freely available educational application (a mobile website) is presented. This provides access to educational material and drilling on selected topics within mathematics and statistics with an emphasis on tablets and mobile phones. The…
In order to implement a STEAM approach including the use of technology, namely the use of interactive mathematics software GeoGebra, in mathematics classes, in the lusophone space, the materials presented here were conceived, to be…
The field of geometric automated theorem provers has a long and rich history, from the early AI approaches of the 1960s, synthetic provers, to today algebraic and synthetic provers. The geometry automated deduction area differs from other…
Probabilistic graphical modeling is a branch of machine learning that uses probability distributions to describe the world, make predictions, and support decision-making under uncertainty. Underlying this modeling framework is an elegant…
XNMR is a system designed to explore the results of combining the well-founded semantics system XSB with the stable-models evaluator SMODELS. Its main goal is to work as a tool for fast and interactive exploration of knowledge bases.
Geospatial reasoning requires solving image-grounded problems over the complex spatial structure of a scene. However, developing this capability is hindered by the cost of annotating a vast and combinatorial question space. We propose GeoX,…
Geometrical modelling generally provides the geometrical description of a special structure and a set of services to "navigate" through its structure. HEP geometrical modellers are designed to handle high complexity detector geometries and…
Calculus and geometry are ubiquitous in the theoretical modelling of scientific phenomena, but have historically been very challenging to apply directly to real data as statistics. Diffusion geometry is a new theory that reformulates…
Proof assistants are computer softwares that allow us to write mathematical proofs so as to assess their correctness. In November 2021, I started the project of checking the simplicity of the alternating groups within the Lean theorem…
We introduce a system of software tools that can automatically prove or discover geometric inequalities. The system, called GeoGebra Discovery, consisting of an extended version of GeoGebra, a controller web service realgeom, and the…
GWR is a popular approach for investigating the spatial variation in relationships between response and predictor variables, and critically for investigating and understanding process spatial heterogeneity. The geographically weighted (GW)…
Realizing test scenarios through a tutoring system involve questions about architecture and didactic methods in such a system. Observing the fact that traditional tutoring systems normally are domain-static, this paper shows investigations…
We introduce TopoX, a Python software suite that provides reliable and user-friendly building blocks for computing and machine learning on topological domains that extend graphs: hypergraphs, simplicial, cellular, path and combinatorial…
This paper presents Geomancer, an open-source framework for geospatial feature engineering. It simplifies the acquisition of geospatial attributes for downstream, large-scale machine learning tasks. Geomancer leverages any geospatial…