Statistical methods for polyhedral shape classification with incomplete data - application to cryo-electron tomographic images

A certain type of bacterial inclusion, known as a bacterial microcompartment, was recently identified and imaged through cryo-electron tomography. A reconstructed 3D object from single-axis limited angle tilt-series cryo-electron tomography contains missing regions and this problem is known as the missing wedge problem. Due to missing regions on the reconstructed images, analyzing their 3D structures is a challenging problem. The existing methods overcome this problem by aligning and averaging several similar shaped objects. These schemes work well if the objects are symmetric and several objects with almost similar shapes and sizes are available. Since the bacterial inclusions studied here are not symmetric, are deformed, and show a wide range of shapes and sizes, the existing approaches are not appropriate. This research develops new statistical methods for analyzing geometric properties, such as volume, symmetry, aspect ratio, polyhedral structures etc., of these bacterial inclusions in presence of missing data. These methods work with deformed and non-symmetric varied shaped objects and do not necessitate multiple objects for handling the missing wedge problem. The developed methods and contributions include: (a) an improved method for manual image segmentation, (b) a new approach to 'complete' the segmented and reconstructed incomplete 3D images, (c) a polyhedral structural distance model to predict the polyhedral shapes of these microstructures, (d) a new shape descriptor for polyhedral shapes, named as polyhedron profile statistic, and (e) the Bayes classifier, linear discriminant analysis and support vector machine based classifiers for supervised incomplete polyhedral shape classification. Finally, the predicted 3D shapes for these bacterial microstructures belong to the Johnson solids family, and these shapes along with their other geometric properties are important for better understanding of their chemical and biological characteristics.

The Hurst exponent as an indicator of the behaviour of a model monopile in an ocean wave testing basin

With the importance of renewable energy well-established worldwide, and targets of such energy quantified in many cases, there exists a considerable interest in the assessment of wind and wave devices. While the individual components of these devices are often relatively well understood and the aspects of energy generation well researched, there seems to be a gap in the understanding of these devices as a whole and especially in the field of their dynamic responses under operational conditions. The mathematical modelling and estimation of their dynamic responses are more evolved but research directed towards testing of these devices still requires significant attention. Model-free indicators of the dynamic responses of these devices are important since it reflects the as-deployed behaviour of the devices when the exposure conditions are scaled reasonably correctly, along with the structural dimensions. This paper demonstrates how the Hurst exponent of the dynamic responses of a monopile exposed to different exposure conditions in an ocean wave basin can be used as a model-free indicator of various responses. The scaled model is exposed to Froude scaled waves and tested under different exposure conditions. The analysis and interpretation is carried out in a model-free and output-only environment, with only some preliminary ideas regarding the input of the system. The analysis indicates how the Hurst exponent can be an interesting descriptor to compare and contrast various scenarios of dynamic response conditions.