Читать книгу Diatom Morphogenesis - Группа авторов - Страница 34

The number of rotations to use per image was established using least-squares regression analysis for images without regularly spaced valve features. For each masked image, symmetry state was calculated from and plotted against tilt-corrected final entropy. Average taxon symmetry was measured for all images. Average taxon external valve symmetry was also measured. Comparison was made between symmetric Arachnoidiscus and Aulacodiscus valves and asymmetric Asteromphalus valves. Cyclotella meneghiniana was used in comparisons between normal and abnormal valves as well as comparison of initial to vegetative valves. For symmetric/asymmetric and normal/abnormal comparisons, least-squares regression analysis was accomplished. For initial and vegetative valves, a bar graph was used to depict symmetry differences.

Tests were conducted on symmetry changes with respect to valve formation. To model vertical change in morphology and symmetry, external and forming valves were compared. Entropy was measured for external and forming valves of Arachnoidiscus ehrenbergii, Asterolampra marylandica, Asteromphalus heptactis, Asteromphalus imbricatus, Asteromphalus vanheurckii, Cyclotella meneghiniana, Glyphodiscus stellatus, and Triceratium favus. Comparison among taxa was accomplished with a bar graph of external and forming valve symmetries.

For horizontal change in morphology and symmetry, 24 equally spaced concentric circles divided the valve face in a manner presumed to be similar to the time course of the first stage of valve growth [2.126]. Entropy was measured at each accumulative radius, and the resultant values were analyzed for symmetry of eight different circular-shaped taxon images: Actinoptychus senarius, Actinoptychus splendens, Arachnoidiscus ehrenbergii, Arachnoidiscus ornatus, Asteroplampra marylandica, Aulacodiscus oregonus, Coscinodiscus sp., and Cyclotella meneghiniana.

Entropy and symmetry were calculated for an elongated centric diatom as well. The image is masked then flipped along a bisecting horizontal axis, and then flipped along a bisecting vertical axis, illustrating the procedure for measurement of dihedral symmetry. The method of rotation and flipping along a bisecting axis enables entropy measurement of any organism with reflective, glide, or dihedral symmetry including pennate diatoms which develop via a sternum or sternum-raphe system [2.119]. Biddulphia sp. [2.145] was used for illustration (Figure 2.5).

Measurement error of entropy values for masked image matching after rotation and overlaying was calculated to determine accuracy and validity as From this, variation bias due to measurement error expressed as a percentage is based on the root mean square error, RMSE to image matching variance ratio.

For analysis of all images and valve formation simulation, entropy values were characterized by their statistical distributions. A histogram of final entropies was plotted, and a probability density function (PDF) and a cumulative density function (CDF) were determined. Maximum entropy is determined from the PDF [2.65]. For a uniform PDF, maximum entropy indicates that every symmetry state has an equal chance of occurring. For a Gaussian PDF, the least amount of information available means having the lowest probability and is maximum entropy; the highest amount of information available means the lowest entropy and the highest probability of occurring. Maximum entropy is also determined via standardization of the PDF so that a prior probability distribution results [2.65, 2.67].