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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

TLDR

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

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

TLDR

Finding the optimal lengths for three branches at a junction.

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

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Hydraulic geometry and minimum rate of energy dissipation

- C. Yang, Charles C. S. 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

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

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

TLDR

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

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

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

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Relation of branching angles to optimality for four cost principles.

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

TLDR

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

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

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