Michael F. Dacey
ABSTRACT
The purpose of this paper is to describe a method for analysis of one type of pictorial information that is abstracted from maps. The picture is a line diagram or graph that, in the language of graph theory, is a planted plane tree in which each vertex has a valency 1 or 3. In hydrology and geomorphology this type of graph is interpreted as a channel network that encompasses the topological properties of the network of rivers and streams comprising a drainage system. A recent survey paper by Dacey identifies a large number of properties of channel networks. Considering that many of these properties are clearly displayed by sketches of channel networks, the mathematical derivations seem unnecessarily complicated. This disparity in level of difficulty may reflect that the pictorial representation of a graph has a structure that is more amenable to analysis than does the conventional linguistic (i.e., mathematical) representation.
- Cavalli-Sforza, L. L., Edwards, A. W. F., "Phylogenetic analysis," Amer. Jour. Human Genetics, 19, pp. 233--257, 1967.Google Scholar
- Dacey, M. F., Summary of Magnitude Properties of Topologically Distinct Channel Networks and Network Patterns, Paper delivered at International Geological Congress meetings, Montreal, August, 1972. To be published in Proceedings.Google Scholar
- Etherington, I. M. H., "On Non-Associative Combinations," Proc. Roy. Soc. Edinburgh, 59, pp. 153--162, 1939.Google ScholarCross Ref
- Harding, E. F., "The Probabilities of Rooted Tree-Shapes Generated by Random Bifurcation," Advances in Appl. Prob., 3, pp. 44--77, 1971.Google ScholarCross Ref
- Shreve, R. L., "Statistical Law of Stream Numbers," Jour. of Geology, 74, pp. 17--37, 1966.Google ScholarCross Ref
- Shreve, R. L., Infinite Topologically Random Channel Networks," Jour. of Geology, 75, pp. 178--186, 1967.Google ScholarCross Ref
- Smart, J. S., "Topological Properties of Channel Networks," Geol. Soc. of America Bull., 80, pp. 1757--1774, 1969.Google ScholarCross Ref
Recommendations
Channel graphs of bit permutation networks
Channel graphs have been widely used in the study of blocking networks. In this paper, we show that a bit permutation network has a unique channel graph if and only if it is connected, and two connected bit permutation networks are isomorphic if and ...
Downlink co-channel interference cancellation in multihop relay networks
In this paper, we study the use of iterative multi-user detectors for co-channel interference suppression in wireless cellular systems. We investigate the benefits of using iterative interference cancellation in the mobile receiver in the downlink ...
Outage-efficient strategies for multiuser MIMO networks with channel distribution information
In this paper, we examine single user and multiuser multiple-input multiple-output (MIMO) beamforming networks with channel distribution information (CDI). Since CDI changes infrequently compared to channel state information (CSI), algorithms based on ...
Comments