VMEXT: A Visualization Tool for Mathematical Expression Trees

Mathematical expressions can be represented as a tree consisting of terminal symbols, such as identifiers or numbers (leaf nodes), and functions or operators (non-leaf nodes). Expression trees are an important mechanism for storing and processing mathematical expressions as well as the most frequently used visualization of the structure of mathematical expressions. Typically, researchers and practitioners manually visualize expression trees using general-purpose tools. This approach is laborious, redundant, and error-prone. Manual visualizations represent a user's notion of what the markup of an expression should be, but not necessarily what the actual markup is. This paper presents VMEXT - a free and open source tool to directly visualize expression trees from parallel MathML. VMEXT simultaneously visualizes the presentation elements and the semantic structure of mathematical expressions to enable users to quickly spot deficiencies in the Content MathML markup that does not affect the presentation of the expression. Identifying such discrepancies previously required reading the verbose and complex MathML markup. VMEXT also allows one to visualize similar and identical elements of two expressions. Visualizing expression similarity can support support developers in designing retrieval approaches and enable improved interaction concepts for users of mathematical information retrieval systems. We demonstrate VMEXT's visualizations in two web-based applications. The first application presents the visualizations alone. The second application shows a possible integration of the visualizations in systems for mathematical knowledge management and mathematical information retrieval. The application converts LaTeX input to parallel MathML, computes basic similarity measures for mathematical expressions, and visualizes the results using VMEXT.Comment: 15 pages, 4 figures, Intelligent Computer Mathematics - 10th International Conference CICM 2017, Edinburgh, UK, July 17-21, 2017, Proceeding

Understanding analogical reasoning : viewpoints from psychology and related disciplines

Analogy and metaphor have a long history of study in linguistics, education, philosophy and psychology. Consensus over what analogy is or how analogy functions in language and thought, however, has been elusive. This paper, the first in a two part series, examines these various research traditions, attempting to bring out major lines of agreement over the role of analogy in individual human experience. As well as being a general literature review which may be helpful for newcomers to the study of analogy, this paper attempts to extract from these literatures existing theories, models and concepts which may be interesting or useful for computational studies of analogical reasoning

A Perceptually Based Comparison of Image Similarity Metrics

The assessment of how well one image matches another forms a critical component both of models of human visual processing and of many image analysis systems. Two of the most commonly used norms for quantifying image similarity are L1 and L2, which are specific instances of the Minkowski metric. However, there is often not a principled reason for selecting one norm over the other. One way to address this problem is by examining whether one metric, better than the other, captures the perceptual notion of image similarity. This can be used to derive inferences regarding similarity criteria the human visual system uses, as well as to evaluate and design metrics for use in image-analysis applications. With this goal, we examined perceptual preferences for images retrieved on the basis of the L1 versus the L2 norm. These images were either small fragments without recognizable content, or larger patterns with recognizable content created by vector quantization. In both conditions the participants showed a small but consistent preference for images matched with the L1 metric. These results suggest that, in the domain of natural images of the kind we have used, the L1 metric may better capture human notions of image similarity

Intensity-based image registration using multiple distributed agents

Image registration is the process of geometrically aligning images taken from different sensors, viewpoints or instances in time. It plays a key role in the detection of defects or anomalies for automated visual inspection. A multiagent distributed blackboard system has been developed for intensity-based image registration. The images are divided into segments and allocated to agents on separate processors, allowing parallel computation of a similarity metric that measures the degree of likeness between reference and sensed images after the application of a transform. The need for a dedicated control module is removed by coordination of agents via the blackboard. Tests show that additional agents increase speed, provided the communication capacity of the blackboard is not saturated. The success of the approach in achieving registration, despite significant misalignment of the original images, is demonstrated in the detection of manufacturing defects on screen-printed plastic bottles and printed circuit boards

Planning ahead: How recent experience with structures and words changes the scope of linguistic planning

The scope of linguistic planning, i.e., the amount of linguistic information that speakers prepare in advance for an utterance they are about to produce, is highly variable. Distinguishing between possible sources of this variability provides a way to discriminate between production accounts that assume structurally incremental and lexically incremental sentence planning. Two picture-naming experiments evaluated changes in speakers’ planning scope as a function of experience with message structure, sentence structure, and lexical items. On target trials participants produced sentences beginning with two semantically related or unrelated objects in the same complex noun phrase. To manipulate familiarity with sentence structure, target displays were preceded by prime displays that elicited the same or different sentence structures. To manipulate ease of lexical retrieval, target sentences began either with the higher-frequency or lower-frequency member of each semantic pair. The results show that repetition of sentence structure can extend speakers’ scope of planning from one to two words in a complex noun phrase, as indexed by the presence of semantic interference in structurally primed sentences beginning with easily retrievable words. Changes in planning scope tied to experience with phrasal structures favor production accounts assuming structural planning in early sentence formulation