Mathematical Representations of the Architecture of Graphical User Interfaces

This text is an introduction to mathematical representations of graphical user interfaces, GUIs. Vectors are employed as a means to represent the state of a GUI and the user interaction with a GUI. These representations form a model of the behavior of a GUI over time. The usefulness of the model in testing and developing well-behaved GUIs is discussed and demonstrated by example

Workstation environment for wastewater treatment design using AI and mathematical models

This research explores the use of computer-based environments to facilitate environmental engineering decision making. A prototype system is developed for wastewater treatment plant design as an exploration tool to demonstrate the techniques and principles proposed. Several mathematical techniques, interactive graphic displays, and friendly user interfaces are used. The mathematical techniques are: (1) mass and water balances for an analysis program for wastewater treatment plant design, (2) a rule-based system for sludge bulking judgment, and (3) a standard processor for checking a design against existing design standards. The interactive graphic displays provide visual data for effective data manipulation, and the friendly user interfaces are designed for engineers who are not necessarily computer experts.U.S. Department of the InteriorU.S. Geological SurveyOpe

Towards a narrative-oriented framework for designing mathematical learning

This paper proposes a narrative-oriented approach to the design of educational activities, as well as a CSCL system to support them, in the context of learning mathematics. Both Mathematics and interface design seem unrelated to narrative. Mathematical language, as we know it, is devoid of time and person. Computer interfaces are static and non-linear. Yet, as Bruner (1986; 1990) and others show, narrative is a powerful cognitive and epistemological tool. The questions we wish to explore are - - If, and how, can mathematical meaning be expressed in narrative forms - without compromising rigour? - What are the narrative aspects of user interface? How can interface design be guided by notions of narrative? - How can we harness the power of narrative in teaching mathematics, in a CSCL environment? We begin by giving a brief account of the use of narrative in educational theory. We will describe the environment and tools used by the WebLabs project, and report on one of our experiments. We will then describe our narrative-oriented framework, by using it to analyze both the environment and the experiment described

AudioFunctions.web: Multimodal Exploration of Mathematical Function Graphs

We present AudioFunctions.web, a web app that uses sonifcation, earcons and speech synthesis to enable blind people to explore mathematical function graphs. The system is designed for personalized access through different interfaces (touchscreen, keyboard, touchpad and mouse) on both mobile and traditional devices, in order to better adapt to different user abilities and preferences. It is also publicly available as a web service and can be directly accessed from the teaching material through a hypertext link. An experimental evaluation with 13 visually impaired participants highlights that, while the usability of all the presented interaction modalities is high, users with different abilities prefer different interfaces to interact with the system. It is also shown that users with higher level of mathematical education are capable of better adapting to interaction modalities considered more diffcult by others

Advanced Proof Viewing in ProofTool

Sequent calculus is widely used for formalizing proofs. However, due to the proliferation of data, understanding the proofs of even simple mathematical arguments soon becomes impossible. Graphical user interfaces help in this matter, but since they normally utilize Gentzen's original notation, some of the problems persist. In this paper, we introduce a number of criteria for proof visualization which we have found out to be crucial for analyzing proofs. We then evaluate recent developments in tree visualization with regard to these criteria and propose the Sunburst Tree layout as a complement to the traditional tree structure. This layout constructs inferences as concentric circle arcs around the root inference, allowing the user to focus on the proof's structural content. Finally, we describe its integration into ProofTool and explain how it interacts with the Gentzen layout.Comment: In Proceedings UITP 2014, arXiv:1410.785

Scaling Up Automated Verification: A Case Study and a Formalization IDE for Building High Integrity Software

Component-based software verification is a difficult challenge because developers must specify components formally and annotate implementations with suitable assertions that are amenable to automation. This research investigates the intrinsic complexity in this challenge using a component-based case study. Simultaneously, this work also seeks to minimize the extrinsic complexities of this challenge through the development and usage of a formalization integrated development environment (F-IDE) built for specifying, developing, and using verified reusable software components. The first contribution is an F-IDE built to support formal specification and automated verification of object-based software for the integrated specification and programming language RESOLVE. The F-IDE is novel, as it integrates a verifying compiler with a user-friendly interface that provides a number of amenities including responsive editing for model-based mathematical contracts and code, assistance for design by contract, verification, responsive error handling, and generation of property-preserving Java code that can be run within the F-IDE. The second contribution is a case study built using the F-IDE that involves an interplay of multiple artifacts encompassing mathematical units, component interfaces, and realizations. The object-based interfaces involved are specified in terms of new mathematical models and non-trivial theories designed to encapsulate data structures and algorithms. The components are designed to be amenable to modular verification and analysis

Assessing the Quality of Mobile Graphical User Interfaces Using Multi-Objective Optimization

Aesthetic defects are a violation of quality attributes that are symptoms of bad interface design programming decisions. They lead to deteriorating the perceived usability of mobile user interfaces and negatively impact the Users eXperience (UX) with the mobile app. Most existing studies relied on a subjective evaluation of aesthetic defects depending on end-users feedback, which makes the manual evaluation of mobile user interfaces human-centric, time-consuming, and error-prone. Therefore, recent studies have dedicated their effort to focus on the definition of mathematical formulas that each targets a specific structural quality of the interface. As the UX is tightly dependent on the user profile, the combi-nation and calibration of quality attributes, formulas, and users characteristics, when defining a defect, is not straightforward. In this context, we propose a fully automated framework which combines literature quality attributes with the users profile to identify aesthetic defects of MUI. More precisely, we consider the mobile user interface evaluation as a multi-objective optimization problem where the goal is to maximize the number of detected violations while minimizing the detection complexity of detection rules and enhancing the interfaces overall quality in means

Isabelle/PIDE as Platform for Educational Tools

The Isabelle/PIDE platform addresses the question whether proof assistants of the LCF family are suitable as technological basis for educational tools. The traditionally strong logical foundations of systems like HOL, Coq, or Isabelle have so far been counter-balanced by somewhat inaccessible interaction via the TTY (or minor variations like the well-known Proof General / Emacs interface). Thus the fundamental question of math education tools with fully-formal background theories has often been answered negatively due to accidental weaknesses of existing proof engines. The idea of "PIDE" (which means "Prover IDE") is to integrate existing provers like Isabelle into a larger environment, that facilitates access by end-users and other tools. We use Scala to expose the proof engine in ML to the JVM world, where many user-interfaces, editor frameworks, and educational tools already exist. This shall ultimately lead to combined mathematical assistants, where the logical engine is in the background, without obstructing the view on applications of formal methods, formalized mathematics, and math education in particular.Comment: In Proceedings THedu'11, arXiv:1202.453