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

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

Ein Beitrag zur Berücksichtigung von pseudoelastischem Werkstoffverhalten in der Modellierung tubulärer Kontinuumsroboter

Die Arbeit widmet sich der elastokinematischen Modellierung tubulärer Kontinuumsroboter aus Nickel-Titan-Röhrchen. Besonderes Augenmerk liegt dabei auf der Berücksichtigung des nichtlinearen und hysteresebehafteten Werkstoffverhaltens der Nickel-Titan-Legierung und dessen Einfluss auf das mechanische Verhalten tubulärer Kontinuumsmechanismen. Einleitend erfolgt eine Motivation zur potentiellen Anwendung tubulärer Kontinuumsroboter in der Medizin, eine Gegenüberstellung unterschiedlicher Kanülen zur aktiven Trajektorienverfolgung sowie die Darlegung des Standes der Forschung von tubulären Kontinuumsrobotern. Die Modellierung wird dann in mehreren Stufen, aus zum Teil verschachtelten, Teilmodellen aufgebaut. Zunächst wird die Werkstoffcharakteristik der Nickel-Titan-Legierung durch ein nichtlineares Werkstoffmodell mit Hystereseberücksichtigung abgebildet und mit Messungen verglichen. Darauf aufbauend wird ein Bauteilmodell hergeleitet, welches einzelne Nickel-Titan-Röhrchen unter reiner Biegung abbilden kann. Anschließend erfolgt die Betrachtung der Auswirkung der Werkstoffhysterese auf die Gleichgewichtslage tubulärer Kontinuumsmechanismen sowie die Bestimmung von Gleichgewichtskrümmungen und Übergangswinkeln. Diese Teilmodelle werden aus einer numerischen Kontaktsimulation einer einfachen Röhrchenkombination mit linearelastischem Werkstoffverhalten abgeleitet. Eine Gesamtkinematik führt die, aus den Teilmodellen gewonnenen, kinematischen Zustände zu einer Beschreibung des Bewegungsverhaltens des gesamten Kontinuumsmechanismus zusammen. Zur Beurteilung der Modellqualität erfolgen Messungen der Trajektorie der Röhrchenenden eines tubulären Kontinuumsmechanismus aus zwei Röhrchen. Es wird gezeigt, dass es mit der Modellierungsweise möglich ist, die gesamte Trajektorie für eine maximale Kanülenlänge von 70 mm mit einer maximalen euklidischen Abweichung von etwa 2 mm abzubilden. Die Kalibrierung der kinematischen Zustände reduziert die maximale euklidische Abweichung deutlich unter 1 mm. Basierend auf dem nichtlinearen Bauteilmodell und der berechneten Gleichgewichtslage erfolgt eine modellbasierte Bestimmung der erforderlichen Antriebskräfte zum Verschieben der Röhrchen und der Vergleich dieser mit Messungen. Die Arbeit schließt mit der Beschreibung aller verwendeten Experimentalaufbauten ab. Dazu gehören die Antriebseinheit zur Verschiebung der Röhrchen, eine schwenkbare Austrittsbuchse zur Erhöhung der Bewegungsfreiheit tubulärer Kontinuumsmechanismen, ein Stereokamera-Messsystem zur Trajektorienmessung und ein Kraftmesssystem zur Bestimmung der erforderlichen Antriebskräfte.This thesis addresses the elastokinematic modeling of tubular continuum robots comprised of nickel-titanium tubes. Particular attention is paid to the nonlinear and hysteretic material behaviour of nickel-titanium and its influence on the mechanical behaviour of tubular continuum mechanisms. Initially, a potential application of tubular continuum robots in medicine is motivated. It is followed by a comparison of different cannulas for active following of trajectories and a statement of the state of the research on tubular continuum robots. The modelling is then built up in several stages of partially nested submodels. First, the material characteristic of the nickel-titanium alloy is represented by a nonlinear material constitutive law with hysteresis. Based on this, a structural element constitutive law is derived, which represents single nickel-titanium tubes under pure bending. Subsequently, the effect of the material hysteresis on the equilibrium conformation of tubular continuum mechanisms and the determination of equilibrium curvatures and transition angles is considered. These submodels are derived from a numerical contact simulation of a simple tube combination with linear elastic material behaviour. The kinematic states, obtained from the submodels, are then combined into an overall kinematic formulation of the entire continuum mechanisms motion behaviour. Trajectory measurements of the tube ends of a tubular continuum mechanism made of two tubes are conducted to assess the model quality. The measurements show that the modelling method is able to map the entire trajectory for a maximum cannula length of 70 mm, with a maximum euclidean deviation of approximately 2 mm. The calibration of the kinematic states reduces the maximum euclidean deviation to well below 1 mm. Finally, based on the non-linear structural element constitutive law and the calculated equilibrium conformation, a model-based determination of the required driving forces for moving the tubes is presented and compared to measurements. The work concludes with a description of all employed experimental setups. These include the drive unit for displacing the tubes, a pivotable outlet bushing to increase the freedom of movement of tubular continuum mechanisms, a stereo camera measurement system for trajectory measurement and a force measurement system for determining the required driving forces

Caching and Reproducibility: Making Data Science experiments faster and FAIRer

Small to medium-scale data science experiments often rely on research software developed ad-hoc by individual scientists or small teams. Often there is no time to make the research software fast, reusable, and open access. The consequence is twofold. First, subsequent researchers must spend significant work hours building upon the proposed hypotheses or experimental framework. In the worst case, others cannot reproduce the experiment and reuse the findings for subsequent research. Second, suppose the ad-hoc research software fails during often long-running computationally expensive experiments. In that case, the overall effort to iteratively improve the software and rerun the experiments creates significant time pressure on the researchers. We suggest making caching an integral part of the research software development process, even before the first line of code is written. This article outlines caching recommendations for developing research software in data science projects. Our recommendations provide a perspective to circumvent common problems such as propriety dependence, speed, etc. At the same time, caching contributes to the reproducibility of experiments in the open science workflow. Concerning the four guiding principles, i.e., Findability, Accessibility, Interoperability, and Reusability (FAIR), we foresee that including the proposed recommendation in a research software development will make the data related to that software FAIRer for both machines and humans. We exhibit the usefulness of some of the proposed recommendations on our recently completed research software project in mathematical information retrieval.Comment: 8 pages, 1 tabl

Caching and Reproducibility: Making Data Science Experiments Faster and FAIRer

Small to medium-scale data science experiments often rely on research software developed ad-hoc by individual scientists or small teams. Often there is no time to make the research software fast, reusable, and open access. The consequence is twofold. First, subsequent researchers must spend significant work hours building upon the proposed hypotheses or experimental framework. In the worst case, others cannot reproduce the experiment and reuse the findings for subsequent research. Second, suppose the ad-hoc research software fails during often long-running computational expensive experiments. In that case, the overall effort to iteratively improve the software and rerun the experiments creates significant time pressure on the researchers. We suggest making caching an integral part of the research software development process, even before the first line of code is written. This article outlines caching recommendations for developing research software in data science projects. Our recommendations provide a perspective to circumvent common problems such as propriety dependence, speed, etc. At the same time, caching contributes to the reproducibility of experiments in the open science workflow. Concerning the four guiding principles, i.e., Findability, Accessibility, Interoperability, and Reusability (FAIR), we foresee that including the proposed recommendation in a research software development will make the data related to that software FAIRer for both machines and humans. We exhibit the usefulness of some of the proposed recommendations on our recently completed research software project in mathematical information retrieval

SKT5SciSumm -- A Hybrid Generative Approach for Multi-Document Scientific Summarization

Summarization for scientific text has shown significant benefits both for the research community and human society. Given the fact that the nature of scientific text is distinctive and the input of the multi-document summarization task is substantially long, the task requires sufficient embedding generation and text truncation without losing important information. To tackle these issues, in this paper, we propose SKT5SciSumm - a hybrid framework for multi-document scientific summarization (MDSS). We leverage the Sentence-Transformer version of Scientific Paper Embeddings using Citation-Informed Transformers (SPECTER) to encode and represent textual sentences, allowing for efficient extractive summarization using k-means clustering. We employ the T5 family of models to generate abstractive summaries using extracted sentences. SKT5SciSumm achieves state-of-the-art performance on the Multi-XScience dataset. Through extensive experiments and evaluation, we showcase the benefits of our model by using less complicated models to achieve remarkable results, thereby highlighting its potential in advancing the field of multi-document summarization for scientific text

TEIMMA: The First Content Reuse Annotator for Text, Images, and Math

This demo paper presents the first tool to annotate the reuse of text, images, and mathematical formulae in a document pair -- TEIMMA. Annotating content reuse is particularly useful to develop plagiarism detection algorithms. Real-world content reuse is often obfuscated, which makes it challenging to identify such cases. TEIMMA allows entering the obfuscation type to enable novel classifications for confirmed cases of plagiarism. It enables recording different reuse types for text, images, and mathematical formulae in HTML and supports users by visualizing the content reuse in a document pair using similarity detection methods for text and math