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United States Department of Agriculture

Agricultural Research Service

Title: Calculation of Fractal Dimension from Cattle Thermoregulatory Responses

Authors
item Korthals, Rodney
item Chen, Yud
item Hahn, George
item Eigenberg, Roger

Submitted to: Journal of Thermal Biology
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: July 1, 1997
Publication Date: N/A

Interpretive Summary: Body temperature measures have been successfully used to objectively classify levels of stress responses for animals in thermoneutral and hot environments. The classification of stress levels is based on measuring the "roughness" (fractal dimension) of the body temperature measured at short intervals of 3 to 15 minutes. This report develops and evaluates procedures for calculating fractal dimension values to obtain acceptable accuracy for classifying stress levels.

Technical Abstract: A procedure is defined for calculating fractal dimensions of tympanic temperatures of cattle. Analysis of the procedure used to compute fractal dimensions was performed to determine recommended sampling resolutions, sampling rates, duration of sample datasets, and the effects of noise on the calculation of fractal dimension. A minimum recommended measurement resolution is 0.16 deg C. A sampling interval of one sample every 600-750 seconds (10 to 12.5 minutes) is suggested, but any sampling rate between 180-900 seconds (3 to 15 minutes) can be used to calculate fractal dimensions. Although integer multiples of a full day's data can be used to compute a composite fractal dimension, comparisons among the morning's, afternoon's, and a full day's data indicate that tympanic temperatures are not fully fractal in that the resulting fractal dimension is not constant irrespective of scale. Gaussian noise in tympanic temperature data was shown to drive fractal dimension to two at an exponential rate of 6.64 times the standard deviation of the noise. The number of errors in the dataset multiplied by the magnitude of that error linearly decreases the accuracy of the fractal dimension. To limit the impact of missing or questionable data on fractal dimension to 5% or less, the number of errors times the magnitude of the errors should be limited to less than 0.64 (points * deg C). Other evaluations of fractal dimensions suggest that fractal dimensions can be used as a stress indicator for evaluating individual animal's ability to cope with stressors, or for monitoring stress to aid in management decision-making.

Last Modified: 12/19/2014
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