Biomedical subjects

Kim Marriott

Publications and source records attributed to Kim Marriott.

4 recordsLinked to original sources

PubMed2003

Comprehension of algebraic expressions by experienced users of mathematics.

Little is known about how people comprehend mathematical expressions. In the present study we investigate the internal representations used by experienced users of mathematics to encode algebraic expressions. Initially, a memory recognition task was conducted that examined the role of mathematical syntax in the encoding of algebraic expressions. The results indicate that participants could more readily identify those parts of a previously seen expression that were syntactically well formed than those that were not well formed, suggesting that syntax plays an important role. To determine the level of syntactic structure involved, a second recognition task was conducted. The results indicate that algebraic expressions are encoded into components that represent the phrasal constituents of the expression. However, the results of these experiments did not rule out the possibility that the visual processes of perceptual organization were used to encode the expressions, or that the data were a consequence of a mathematical "lexicon" of common mathematical "phrases". Three further experiments were conducted to examine this, the results of which indicate that the encoding of algebraic expressions is based primarily on processes that occur beyond the level of visual or "lexical" processing. This is consistent with our finding that syntactic structure plays a key role.

Adolescent↗

PubMed2003

A tool for tracking visual attention: the Restricted Focus Viewer.

Eye-tracking equipment has proven useful in examining the cognitive processes people use when understanding and reasoning with visual stimuli. However, eye-tracking has several drawbacks: accurate eye-tracking equipment is expensive, it is often awkward for participants, it requires frequent recalibration, and the data can be difficult to interpret. We introduce an alternative tool: the Restricted Focus Viewer (RFV). This is a computer program that takes an image, blurs it, and displays it on a computer monitor, allowing the participant to see only a small region of the image in focus at any time. The region in focus can be moved using the computer mouse. The RFV records what the participant is focusing on at any point in time. It is cheap, nonintrusive, does not require calibration, and provides accurate data about which region is being focused on. We describe this tool and also provide experimental comparisons with eye-tracking. The RFV (Version 2.1) is freely available at http://www.csse.monash.edu. au/projects/RFV/.

Algorithms↗

PubMedDate not supplied

IPSEP-COLA: an incremental procedure for separation constraint layout of graphs.

We extend the popular force-directed approach to network (or graph) layout to allow separation constraints, which enforce a minimum horizontal or vertical separation between selected pairs of nodes. This simple class of linear constraints is expressive enough to satisfy a wide variety of application-specific layout requirements, including: layout of directed graphs to better show flow; layout with non-overlapping node labels; and layout of graphs with grouped nodes (called clusters). In the stress majorization force-directed layout process, separation constraints can be treated as a quadratic programming problem. We give an incremental algorithm based on gradient projection for efficiently solving this problem. The algorithm is considerably faster than using generic constraint optimization techniques and is comparable in speed to unconstrained stress majorization. We demonstrate the utility of our technique with sample data from a number of practical applications including gene-activation networks, terrorist networks and visualization of high-dimensional data.

Journal Article↗

PubMedDate not supplied

Drawing directed graphs using quadratic programming.

We describe a new method for visualization of directed graphs. The method combines constraint programming techniques with a high performance force-directed placement (FDP) algorithm. The resulting placements highlight hierarchy in directed graphs while retaining useful properties of FDP; such as emphasis of symmetries and preservation of proximity relations. Our algorithm automatically identifies those parts of the digraph that contain hierarchical information and draws them accordingly. Additionally, those parts that do not contain hierarchy are drawn at the same quality expected from a nonhierarchical, undirected layout algorithm. Our experiments show that this new approach is better able to convey the structure of large digraphs than the most widely used hierarchical graph-drawing method. An interesting application of our algorithm is directional multidimensional scaling (DMDS). DMDS deals with low-dimensional embedding of multivariate data where we want to emphasize the overall flow in the data (e.g., chronological progress) along one of the axes.

Computer Graphics↗