Some of Dailey’s current research interests

1. 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 below.
    

2. 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 it here:
   http://srufaculty.sru.edu/david.dailey/javascript/StringDistances.html
   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.
    

3. fast exponentiation of integers using Dailey numeric notation
   see http://srufaculty.sru.edu/david.dailey/fibos/outline.htm
    

4. condensations of numeric fields of irrationals http://srufaculty.sru.edu/david.dailey/javascript/exponents.html and http://srufaculty.sru.edu/david.dailey/math.htm
    

5. psychophysical studies of equidistant objects http://srufaculty.sru.edu/david.dailey/EquidistantStimuli.html
    

6. Various issues related to accessibility for the hearing impaired:
   building a gestural language for mobile devices that is more efficient than typing

   http://www.mail-archive.com/svg-developers@yahoogroups.com/msg13321.html
    

7. 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.monmouth.edu/tour_new/map.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
   http://www.openstreetmap.org/?lat=41.0620772838593&lon=-80.0453782081604&zoom=15
   http://granite.sru.edu/~ged7935/CampusMap/AVGCAMPUSMAP.htm
    

8. Finding gravitational flavorings of graphs that motivate simplified navigation of those graphs. Humans use cues to navigate in our physical world. We use landmarks, compasses, and even our sense of gravity. Consider abstract metric spaces (like graphs). May we impose "field effects" like magnetism and gravity into graphs so that navigation is simplified? In particular might a single dimension of "flavoring" (gravity) of a graph , by assigning ordinal ranks to the nodes, allow a greedy algorithm to find a shortest path between any pair of nodes p and q in exactly d(p, q) steps? It turns out that the N-lattice is flavorable with a single dimension of gravity. See more at http://srufaculty.sru.edu/david.dailey/gravity.html
   

9.  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 Science.
    

10. In a n-dimensional Euclidean space, construct a graph as follows: give each node a locus within that space, then connect any two nodes (i.e., draw a line between them) whose distance in that space is less than some threshold d.  Now what is the minimum dimensionality of the space in which a given graph can be realized subject to this constraint? Clearly Kn can be drawn in one dimension (just let d be large enough). Cn is two dimensional Wn the wheel on n nodes (a cycle of n-1 nodes each connected to a central spoke) becomes the problem of packing unit spheres. Frank Morgan of Williams College showed that any graph on n nodes is n-Euclidean. What else might we be able to say?
    

11.  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. See also here for some allied issues.
     

12. Extensions of the <replicate> proposal to SVG WG. http://svgopen.org/2010/papers/46-A_proposal_for_adding_declarative_drawing_to_SVG/index.html
    See here for current progress)
    

13.  Client-side vectorization (using SVG filters). Maybe use <canvas> in conjunction with SVG?
     

14. Picturing an Open World (sort of like Open Street Maps but with photos)
    

15.  Organizing all the 1000 or so pages under the umbrella of http://srufaculty.sru.edu/david.dailey/svg/
    
    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.
     

16. moving ahead and into new directions with public domain imagery possibly involving Dr. Livingston in Geography and Phil Tramdack in library. Look at http://www.google.com/search?q=sru.edu
    At http://granite.sru.edu/~ddailey/plantdominos.html
    At http://granite.sru.edu/~ddailey/Geography/second.php

    And think of using the textual cues in the plant data for example to hypertextually extrapolate inter-image distances such as is done in the “relatives” rectangle of  http://marble.sru.edu/~ddailey/cgi/hyphens?wild  Involvement could be anything from javascript, to algorithms development (rectangular tessellation), to server side code to simple scanning of lots of images. Knowledge of Japanese might be a plus.