M. Woldenberg

Publications37
h-index15
Citations942
Highly Influential Citations51
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Tree asymmetry--a sensitive and practical measure for binary topological trees.
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
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Diameters and cross‐sectional areas of branches in the human pulmonary arterial tree
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
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Hydraulic geometry and minimum rate of energy dissipation
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
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Finding the optimal lengths for three branches at a junction.
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
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Branching and Self‐Organization in Marine Modular Colonial Organisms: A Model
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
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A generalization of the optimal models of arterial branching
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
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Models for growth, decline and regrowth of the dendrites of rat Purkinje cells induced from magnitude and link-length analysis.
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
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Relation of branching angles to optimality for four cost principles.
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
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HORTON'S LAWS JUSTIFIED IN TERMS OF ALLOMETRIC GROWTH AND STEADY STATE IN OPEN SYSTEMS
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
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Energy Flow and Spatial Order Mixed Hexagonal Hierarchies of Central Places
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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