On the number of sides necessary for polygonal approximation of black-and-white figures in a plane

A bound on the number of extreme points or sides necessary to approximate a convex planar figure by an enclosing polygon is described. This number is found to be proportional to the fourth root of the figure's area divided by the square of a maximum Euclidean distance approximation parameter.An extension of this bound, preserving its fourth root quality, is made to general planar figures. This is done by decomposing the general figure into nearly convex sets defined by inflection points, cusps, and multiple windings.A procedure for performing actual encoding of this type is described. Comparisons of parsimony are made with contemporary figure encoding schemes

Cognitive Information Processing

Contains reports on one research project.National Science Foundation (Grant GK-3373X1)Joint Services Electronics Program (Contract DAAB07-71-C-0300)National Institutes of Health (Grant 5 P01 GM14940-07

Cognitive Information Processing

Contains research objectives and reports on two research objectives.National Science Foundation (Grant GP-2495)National Institutes of Health (Grant MH-04737-04)National Aeronautics and Space Administration (Grant NsG-496)Joint Services Electronics Program by the U. S. Army Research Office, Durha

Speech Communication

Contains reports on four research projects.National Science FoundationUnited States Air Force, Air Force Cambridge Research Center, Air Research and Development Command (Contract AF19(604)-2061

Cognitive Information Processing

Contains reports on three research projects.Joint Services Electronics Program (Contract DAAB07-74-C-0630)National Science Foundation (Grant GK-33736X2

Communications Biophysics

Contains research objectives and reports on four research projects.National Science Foundation (Grant G-16526)National Science Foundation (Grant G-7364)National Institutes of Health (Grant MP-4737)U.S. Air Force (Electronic Systems Division) under Contract AF19(604)-411

Cognitive Information Processing

Contains reports on four research projects.National Aeronautics and Space Administration (Grant NsG-496)National Institutes of Health (Grant MH-04737-04)National Science Foundation (Grant GP-2495

Communications Biophysics

Contains reports on five research projects.United States Air Force (Contract AF19(604)-4112)National Institute of Neurological Diseases and Blindness (B369 Physiology

Cognitive Information Processing

Contains reports on five research projects.National Institutes of Health (Grant 5 PO1 GM-14940-02)National Institutes of Health (Grant 5 P01 GM-15006-02)Joint Services Electronics Programs (U. S. Army, U. S. Navy, and U. S. Air Force) under Contract DA 28-043-AMC-02536(E

Mechanically driven growth of quasi-two dimensional microbial colonies

We study colonies of non-motile, rod-shaped bacteria growing on solid substrates. In our model, bacteria interact purely mechanically, by pushing each other away as they grow, and consume a diffusing nutrient. We show that mechanical interactions control the velocity and shape of the advancing front, which leads to features that cannot be captured by established Fisher-Kolmogorov models. In particular, we find that the velocity depends on the elastic modulus of bacteria or their stickiness to the surface. Interestingly, we predict that the radius of an incompressible, strictly two-dimensional colony cannot grow linearly in time. Importantly, mechanical interactions can also account for the nonequilibrium transition between circular and branching colonies, often observed in the lab.Comment: 5 pages, 4 colour figure