Automated recognition of handwritten mathematics

Most software programs that deal with mathematical objects require input expressions to be linearized using somewhat awkward and unfamiliar string-based syntax. It is natural to desire a method for inputting mathematics using the same two-dimensional syntax employed with pen and paper, and the increasing prevalence of pen- and touch-based interfaces causes this topic to be of practical as well as theoretical interest. Accurately recognizing two-dimensional mathematical notation is a difficult problem that requires not only theoretical advancement over the traditional theories of string-based languages, but also careful consideration of runtime efficiency, data organization, and other practical concerns that arise during system construction. This thesis describes the math recognizer used in the MathBrush pen-math system. At a high level, the two-dimensional syntax of mathematical writing is formalized using a relational grammar. Rather than reporting a single recognition result, all recognizable interpretations of the input are simultaneously represented in a data structure called a parse forest. Individual interpretations may be extracted from the forest and reported one by one as the user requests them. These parsing techniques necessitate robust tree scoring functions, which themselves rely on several lower-level recognition processes for stroke grouping, symbol recognition, and spatial relation classification. The thesis covers the recognition, parsing, and scoring aspects of the MathBrush recognizer, as well as the algorithms and assumptions necessary to combine those systems and formalisms together into a useful and efficient software system. The effectiveness of the resulting system is measured through two accuracy evaluations. One evaluation uses a novel metric based on user effort, while the other replicates the evaluation process of an international accuracy competition. The evaluations show that not only is the performance of the MathBrush recognizer improving over time, but it is also significantly more accurate than other academic recognition systems

A hand gesture recognition technique for human-computer interaction

We propose an approach to recognize trajectory-based dynamic hand gestures in real time for human-computer interaction (HCI). We also introduce a fast learning mechanism that does not require extensive training data to teach gestures to the system. We use a six-degrees-of-freedom position tracker to collect trajectory data and represent gestures as an ordered sequence of directional movements in 2D. In the learning phase, sample gesture data is filtered and processed to create gesture recognizers, which are basically finite-state machine sequence recognizers. We achieve online gesture recognition by these recognizers without needing to specify gesture start and end positions. The results of the conducted user study show that the proposed method is very promising in terms of gesture detection and recognition performance (73% accuracy) in a stream of motion. Additionally, the assessment of the user attitude survey denotes that the gestural interface is very useful and satisfactory. One of the novel parts of the proposed approach is that it gives users the freedom to create gesture commands according to their preferences for selected tasks. Thus, the presented gesture recognition approach makes the HCI process more intuitive and user specific. © 2015 Elsevier Inc. All rights reserved

On Intuitionistic Fuzzy Context-Free Languages

Taking intuitionistic fuzzy sets as the structures of truth values, we propose the notions of intuitionistic fuzzy context-free grammars (IFCFGs, for short) and pushdown automata with final states (IFPDAs). Then we investigate algebraic characterization of intuitionistic fuzzy recognizable languages including decomposition form and representation theorem. By introducing the generalized subset construction method, we show that IFPDAs are equivalent to their simple form, called intuitionistic fuzzy simple pushdown automata (IF-SPDAs), and then prove that intuitionistic fuzzy recognizable step functions are the same as those accepted by IFPDAs. It follows that intuitionistic fuzzy pushdown automata with empty stack and IFPDAs are equivalent by classical automata theory. Additionally, we introduce the concepts of Chomsky normal form grammar (IFCNF) and Greibach normal form grammar (IFGNF) based on intuitionistic fuzzy sets. The results of our study indicate that intuitionistic fuzzy context-free languages generated by IFCFGs are equivalent to those generated by IFGNFs and IFCNFs, respectively, and they are also equivalent to intuitionistic fuzzy recognizable step functions. Then some operations on the family of intuitionistic fuzzy context-free languages are discussed. Finally, pumping lemma for intuitionistic fuzzy context-free languages is investigated

Past, present and future mathematical models for buildings (ii)

This article is the second part of a review of the historical evolution of mathematical models applied in the development of building technology. The first part described the current state of the art and contrasted various models with regard to the applications to conventional buildings and intelligent buildings. It concluded that mathematical techniques adopted in neural networks, expert systems, fuzzy logic and genetic models, that can be used to address model uncertainty, are well suited for modelling intelligent buildings. Despite the progress, the possible future development of intelligent buildings based on the current trends implies some potential limitations of these models. This paper attempts to uncover the fundamental limitations inherent in these models and provides some insights into future modelling directions, with special focus on the techniques of semiotics and chaos. Finally, by demonstrating an example of an intelligent building system with the mathematical models that have been developed for such a system, this review addresses the influences of mathematical models as a potential aid in developing intelligent buildings and perhaps even more advanced buildings for the future

Parsing for agile modeling

Agile modeling refers to a set of methods that allow for a quick initial development of an importer and its further refinement. These requirements are not met simultaneously by the current parsing technology. Problems with parsing became a bottleneck in our research of agile modeling. In this thesis we introduce a novel approach to specify and build parsers. Our approach allows for expressive, tolerant and composable parsers without sacrificing performance. The approach is based on a context-sensitive extension of parsing expression grammars that allows a grammar engineer to specify complex language restrictions. To insure high parsing performance we automatically analyze a grammar definition and choose different parsing strategies for different parts of the grammar. We show that context-sensitive parsing expression grammars allow for highly composable, tolerant and variable-grained parsers that can be easily refined. Different parsing strategies significantly insure high-performance of parsers without sacrificing expressiveness of the underlying grammars