Some of Dailey’s current research interests
helping take grapher
http://granite.sru.edu/dailey09/grapher.html into the next phase of research
on navigation (gravity in graphs)
http://srufaculty.sru.edu/david.dailey/gravity.html See gravity graphs
working on string (and graph) similarity metrics w Drs. Gocal and
Whitfield and me. See any of us for a description, but you can glimpse some of
talk for PACISE
The basic premise is this. Take a set of discrete structures (graphs, strings, groups, discrete metric spaces). Consider the union of all their substructures. Measure the number of occurrences of each substructure within each structure. (For example, the number of occurances of K1 in a graph is its number of nodes; the occurances of K2 represents its number of lines.) Consider each substructure to be a dimension in a vector space. These measures of structures give to each structure a position in that vector space. The distances between any two structures can then be calculated using, for example, a Minkowski distance (Euclidean when r=2, Manhattan when r=1). If the Manhattan distance is used, then the resulting metric space is discrete, hence modelable by a graph. See embedding metric spaces in graphs, below.
fast exponentiation of integers using Dailey numeric
condensations of numeric fields of irrationals
psychophysical studies of equidistant objects
Various issues related to accessibility for the hearing
building a gestural language for mobile devices that is more efficient than typing
Build an SRU campus map in SVG -- ultimately make it
into an interactive kiosk like this:
World's busiest pedestrian intersection (Shibuya station Tokyo) .
For discussion: mapdiscuss.html
http://www.sru.edu/index/Documents/CampusMap.pdf , http://srufaculty.sru.edu/david.dailey/svg/maker2.svg , http://granite.sru.edu/~mes1735/moarmaps/map_redux.html , http://granite.sru.edu/~txa6139/map/prototype/map_tabbed.html
Each discrete metric space (in which all distances are
integers) can have its metric properties exactly modeled by a graph, in the
sense that graph theoretic distances (shortest paths) can perfectly represent
the distances of the metric space (by introducing new "leprechaun" nodes -- sort
of like inventing imaginary axes to describe certain simpler spaces, like
Euclidean n-space). One question then is "what is the smallest graph that models
a given metric space." In this 1994 paper, encouraged by and collaborated on
with Frank Harary, I proved a few things including the very poetic sounding
theorem: "the tree is the smallest container of the metric space defined on its
leaves." “On the Graphical Containment of Discrete Metric Spaces”
David Dailey,.Discrete Mathematics, 1994, 131, 51-66. Elsevier
Build the Parisian street model of font-design and web
layout. Consider using
Voronoi tessellations, but basically, design a
font-editor which also creates rich geometries for flowed content. Think: nonrectilinear layout models for HTML, CSS, and SVG.
here for some allied issues.
Client-side vectorization (using SVG filters). Maybe
use <canvas> in conjunction with SVG?
Organizing all the 1000 or so pages under the umbrella
The site has been growing for 12 years now (with much content predating that and having been created over 25 years at four institutions). It is all in need of reworking, reorganizing, styling and so forth.