12 research outputs found
Mathematical models as research data via flexiformal theory graphs
Mathematical modeling and simulation (MMS) has now been established as an essential part
of the scientific work in many disciplines. It is common to categorize the involved
numerical data and to some extent the corresponding scientific software as research
data. But both have their origin in mathematical models, therefore any holistic approach
to research data in MMS should cover all three aspects: data, software, and
models. While the problems of classifying, archiving and making accessible are largely
solved for data and first frameworks and systems are emerging for software, the question
of how to deal with mathematical models is completely open.
In this paper we propose a solution -- to cover all aspects of mathematical models: the
underlying mathematical knowledge, the equations, boundary conditions, numeric
approximations, and documents in a flexi\-formal framework, which has enough structure to
support the various uses of models in scientific and technology workflows.
Concretely we propose to use the OMDoc/MMT framework to formalize mathematical models
and show the adequacy of this approach by modeling a simple, but non-trivial model: van
Roosbroeck's drift-diffusion model for one-dimensional devices. This formalization -- and
future extensions -- allows us to support the modeler by e.g. flexibly composing models,
visualizing Model Pathway Diagrams, and annotating model equations in documents as
induced from the formalized documents by flattening. This directly solves some of the
problems in treating MMS as "research data'' and opens the way towards more MKM
services for models
Interoperability in the OpenDreamKit Project: The Math-in-the-Middle Approach
OpenDreamKit --- "Open Digital Research Environment Toolkit for the
Advancement of Mathematics" --- is an H2020 EU Research Infrastructure project
that aims at supporting, over the period 2015--2019, the ecosystem of
open-source mathematical software systems. From that, OpenDreamKit will deliver
a flexible toolkit enabling research groups to set up Virtual Research
Environments, customised to meet the varied needs of research projects in pure
mathematics and applications.
An important step in the OpenDreamKit endeavor is to foster the
interoperability between a variety of systems, ranging from computer algebra
systems over mathematical databases to front-ends. This is the mission of the
integration work package (WP6). We report on experiments and future plans with
the \emph{Math-in-the-Middle} approach. This information architecture consists
in a central mathematical ontology that documents the domain and fixes a joint
vocabulary, combined with specifications of the functionalities of the various
systems. Interaction between systems can then be enriched by pivoting off this
information architecture.Comment: 15 pages, 7 figure
Interoperability in the OpenDreamKit project : the Math-in-the-Middle approach
OpenDreamKit - "Open Digital Research Environment Toolkit for the Advancement of Mathematics" - is an H2020 EU Research Infrastructure project that aims at supporting, over the period 2015-2019, the ecosystem of open-source mathematical software systems. OpenDreamKit will deliver a flexible toolkit enabling research groups to set up Virtual Research Environments, customised to meet the varied needs of research projects in pure mathematics and applications. An important step in the OpenDreamKit endeavor is to foster the interoperability between a variety of systems, ranging from computer algebra systems over mathematical databases to front-ends. This is the mission of the integration work package. We report on experiments and future plans with the Math-in-the-Middle approach. This architecture consists of a central mathematical ontology that documents the domain and xes a joint vocabulary, or even a language, going beyond existing systems such as OpenMath, combined with specifications of the functionalities of the various systems. Interaction between systems can then be enriched by pivoting around this architecture.Postprin
Argumentation Theory for Mathematical Argument
To adequately model mathematical arguments the analyst must be able to
represent the mathematical objects under discussion and the relationships
between them, as well as inferences drawn about these objects and relationships
as the discourse unfolds. We introduce a framework with these properties, which
has been used to analyse mathematical dialogues and expository texts. The
framework can recover salient elements of discourse at, and within, the
sentence level, as well as the way mathematical content connects to form larger
argumentative structures. We show how the framework might be used to support
computational reasoning, and argue that it provides a more natural way to
examine the process of proving theorems than do Lamport's structured proofs.Comment: 44 pages; to appear in Argumentatio
Making Presentation Math Computable
This Open-Access-book addresses the issue of translating mathematical expressions from LaTeX to the syntax of Computer Algebra Systems (CAS). Over the past decades, especially in the domain of Sciences, Technology, Engineering, and Mathematics (STEM), LaTeX has become the de-facto standard to typeset mathematical formulae in publications. Since scientists are generally required to publish their work, LaTeX has become an integral part of today's publishing workflow. On the other hand, modern research increasingly relies on CAS to simplify, manipulate, compute, and visualize mathematics. However, existing LaTeX import functions in CAS are limited to simple arithmetic expressions and are, therefore, insufficient for most use cases. Consequently, the workflow of experimenting and publishing in the Sciences often includes time-consuming and error-prone manual conversions between presentational LaTeX and computational CAS formats. To address the lack of a reliable and comprehensive translation tool between LaTeX and CAS, this thesis makes the following three contributions. First, it provides an approach to semantically enhance LaTeX expressions with sufficient semantic information for translations into CAS syntaxes. Second, it demonstrates the first context-aware LaTeX to CAS translation framework LaCASt. Third, the thesis provides a novel approach to evaluate the performance for LaTeX to CAS translations on large-scaled datasets with an automatic verification of equations in digital mathematical libraries. This is an open access book