By Wolfgang Alt, Gerhard Hoffmann
" . . . habit isn't really, what an organism does itself, yet to what we element. accordingly, no matter if one of those habit of an organism is sufficient as a definite configuration of pursuits, depends on the surroundings during which we de scribe it. " (Humberto Maturana, Francisco Varela: El arbol del conocimiento, 1984) "A thorough research of habit needs to bring about a scheme, that exhibits all regularities which are to be came upon among the sensorical enter and the motorical output of an animal. This scheme is an summary illustration of the mind. " (Valentin Braitenberg: Gehirngespinste, 1973) throughout the 70ies, while Biomathematics (beyond Biomedical records and Com puting) turned extra well known at universities and examine institutes, the issues handled got here usually from the overall fields of 'Population Biology' and 'Complex structures research' equivalent to epidemics, ecosystems research, morphogenesis, genetics, immunology and neurology (see the 1st sequence of Springer Lecture Notes in Biomathematics). considering then, the image has no longer significantly replaced, and it appears "a thorough research of habit" of unmarried organisms and, additionally, in their mutual interactions, is much from being understood. to the contrary, mathematical modellers and analysts were good prompt to limit their investigations to express elements of 'biological behavior', one in every of that's 'biological motion'. in the past, just a couple of convention complaints or Lecture Notes have paid recognition to this crucial element, many of the past examples being Vol. 24: 'The size of organic form and form adjustments' (1978) or Vol.
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Additional resources for Biological Motion: Proceedings of a Workshop held in Königswinter, Germany, March 16–19, 1989
F. (1987) A unified approach to analysing cell motility. J. Cell Sci. Suppl. 8: 81-102. Hu, M-K. (1962) Visual pattern recognition by moment invariants. IRE Trans. Inf. Theory 8: 179-187. G. & stuart, A. (1977) The Advanced Theory of Statistics. Vol. I Distribution Theory. 4th edition, Griffin, London. A. B. (1984) The Mathematical Description of Shape and Form. , Chichester. M. H. (1988) The shape of cultured epithelial cells does not depend on the integrity of their microtubules. J. Cell Sci.
Area of the normalised equimomental ellipse is The therefore a measure of this dispersion of mass away from the centroid. Dunn and Brown (1986) proposed dispersion as a measure of how much a cell shape differs from an ellipse and it can be shown that this is equivalent to log 2 (~ab). A cell of elliptical shape has the minimum dispersion of zero. A cell shape with a dispersion of 1 has a non-normalised equimomental ellipse of twice the cell's area and a density of 1/2. Figure 2 shows how it is possible to use this theory of equimomental ellipses to construct a simple shape with any given elongation and dispersion.
A definition of a pseudopod, in dynamic terms, is not readily available and so we chose a definition that was a compromise based on the nature of the dynamic data obtainable from the image analysis tempered with the knowledge of pseudopods in general. For our purposes, a pseudopod has elongated shape, concave corners and ceases to exist when it's area is equal to one half the total cell area. Without this latter constraint, a dominant pseudopod would eventually become the whole cell. It is now possible to investigate the dynamic properties of pseudopods as they grow and collapse and to relate these dynamic behaviours, over a period of time, to the trajectory of the cell as a whole.
Biological Motion: Proceedings of a Workshop held in Königswinter, Germany, March 16–19, 1989 by Wolfgang Alt, Gerhard Hoffmann