This paper describes some of the basic applications of the algebraic theory of canonical decomposition to the analysis of data. The notions of structured data and symmetry studies are discussed and applied to demonstrate their role in well known principles of analysis of variance and their applicability in more general experimental settings.

OBJECTIVE The main object of this study was to use a geometric morphometric approach to quantify the left-right symmetry of talus bones. METHODS Analysis was carried out using CT scan images of 11 pairs of intact tali. Two important geometric parameters, volume and surface area, were quantified for left and right talus bones. The geometric shape variations between the right and left talus bon...

This paper discusses a new method of detecting symmetry in two-and three-dimensional objects. A multi-dimensional approach is used to interrogate a set-theoretic representation of an object. A method for detecting planes of true symmetry is described, as well as more advanced methods for partial symmetry, ro-tational symmetry and partial rotational symmetry. The examples given in the paper are ...

‎In this work‎, ‎a regular polygon with $n$ sides is described by a periodic (circular) sequence with period $n$‎. ‎Each element of the sequence represents a vertex of the polygon‎. ‎Each symmetry of the polygon is the rotation of the polygon around the center-point and/or flipping around a symmetry axis‎. ‎Here each symmetry is considered as a system that takes an input circular sequence and g...

In recent years, some investigations have been carried out to examine the assumptions like stationarity, symmetry and separability of spatio-temporal covariance function which would considerably simplify fitting a valid covariance model to the data by parametric and nonparametric methods. In this article, assuming a Gaussian random field, we consider the likelihood ratio separability test, a va...

Fullerene chemistry is nowadays a well-established field of both theoretical and experimental investigations‎. This study considers the symmetry of small fullerenes cage C24 and C28‎. ‎Using PM3 program for C24 and C28 fullerenes, Oh and Td symmetry were confirmed, respectively‎. ‎ The mentioned algorithm to compute the automorphism group of these fullerenes with connectivity and geometry of th...

Finite strain and vorticity analyses were carried out in the deformed conglomerate and micro-conglomerate of Goushti shear zone in the Sanandaj-Sirjan metamorphic belt (Zagros Mountains Iran). These deformed rocks are bounded between two NE and SW major thrust faults. Finite strain measurements on three principal planes of strain ellipsoid show the higher amounts of strain ratios near the major...