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Publications Influence

Tree asymmetry--a sensitive and practical measure for binary topological trees.

- J. van Pelt, H. Uylings, R. Verwer, R. Pentney, M. Woldenberg
- Mathematics, Medicine
- Bulletin of mathematical biology
- 1 September 1992

The topological structure of a binary tree is characterized by a measure called tree asymmetry, defined as the mean value of the asymmetry of its partitions. The statistical properties of this… Expand

116 11

Diameters and cross‐sectional areas of branches in the human pulmonary arterial tree

- K. Horsfield, M. Woldenberg
- Biology, Medicine
- The Anatomical record
- 1 March 1989

Measurements were made of the diameters of the three branches meeting at each of 1,937 difurcations in the pulmonary arterial tree, using resin casts from two fully inflated human lungs.… Expand

60 8

Hydraulic geometry and minimum rate of energy dissipation

- C. Yang, C. Song, M. Woldenberg
- Geology
- 1 August 1981

The theory of minimum rate of energy dissipation states that a system is in an equilibrium condition when its rate of energy dissipation is at its minimum value. This minimum value depends on the… Expand

118 6

Finding the optimal lengths for three branches at a junction.

- M. Woldenberg, K. Horsfield
- Mathematics, Medicine
- Journal of theoretical biology
- 21 September 1983

This paper presents an exact analytical solution to the problem of locating the junction point between three branches so that the sum of the total costs of the branches is minimized. When the cost… Expand

50 5

Branching and Self‐Organization in Marine Modular Colonial Organisms: A Model

- J. A. Sánchez, H. Lasker, E. G. Nepomuceno, J. D. Sánchez, M. Woldenberg
- Biology, Medicine
- The American Naturalist
- 17 February 2004

Despite the universality of branching patterns in marine modular colonial organisms, there is neither a clear explanation about the growth of their branching forms nor an understanding of how these… Expand

42 5

A generalization of the optimal models of arterial branching

- A. Roy, M. Woldenberg
- 1982

Optimal models of arterial branching angles are usually based on the assumption that the equation relating flow and radius is given byf=kr3, as proposed by Murray in 1926. An exception is the model… Expand

14 4

Models for growth, decline and regrowth of the dendrites of rat Purkinje cells induced from magnitude and link-length analysis.

- M. Woldenberg, M. P. O'Neill, L. Quackenbush, R. Pentney
- Mathematics, Medicine
- Journal of theoretical biology
- 21 June 1993

This study examines Purkinje neurons of rats aged 1, 10, 18 and 28 months to investigate growth and decline in the magnitude of the dendritic tree, i.e. the number of exterior links (terminal… Expand

21 3

Relation of branching angles to optimality for four cost principles.

- M. Woldenberg, K. Horsfield
- Mathematics, Medicine
- Journal of theoretical biology
- 21 September 1986

The literature has suggested that branching angles depend on some principle of optimality. Most often cited are the minimization of lumen surface, volume, power and drag. The predicted angles depend… Expand

51 2

HORTON'S LAWS JUSTIFIED IN TERMS OF ALLOMETRIC GROWTH AND STEADY STATE IN OPEN SYSTEMS

- M. Woldenberg
- Geology
- 1 April 1966

Rivers are open systems and achieve a steady state or grow allometrically, according to the general equation y = ax b . This equation yields a straight line on double logarithmic paper and reflects a… Expand

68 2

Energy Flow and Spatial Order Mixed Hexagonal Hierarchies of Central Places

- M. Woldenberg
- History
- 1 October 1968

r T HE existence and nature of the central-place hierarchy have been hotly debated, and one criticism has been that methods used to detect the hierarchy are subjective and probably biased. In answer… Expand

31 1