Here we introduce multivariate tensor-based surface morphometry using holomorphic one-forms to study brain anatomy. We computed new statistics from the Riemannian metric tensors that retain the full information in the deformation tensor fields. We introduce two different holomorphic one-forms that induce different surface conformal parameterizations. We applied this framework to 3D MRI data to ...

With each C2-domain and material parameter, an infinite number of tensors, called the Generalized Polarization Tensors (GPTs), is associated. The GPTs contain significant information on the shape of the domain and its material parameter. They generalize the concept of Polarization Tensor (PT), which can be seen as the first-order GPT. It is known that given an arbitrary shape, one can find an e...

We present the complete gauged N = 4 (half-maximal) supergravities in four and five spacetime dimensions coupled to an arbitrary number of vector mul-tiplets. The gaugings are parameterized by a set of appropriately constrained constant tensors, which transform covariantly under the global symmetry groups SL(2) × SO(6, n) and SO(1, 1) × SO(5, n), respectively. In terms of these tensors the univ...

We present a new approach for the computation of the deformation field between three dimensional (3D) images. The deformation field locally minimizes the sum of the squared differences between the images to be matched and is constrained by the physical properties of the different objects represented by the image. The objects are modeled as elastic bodies. Compared to optical flow methods, this ...

Tracking tissue deformation is often hampered by material inhomogeneity, so local measurements tend to be insufficient thus lending to the necessity of full-field optical measurements. This study presents a novel approach to factoring heterogeneous deformation of soft and hard tissues in a fracture callus by introducing an anisotropic metric derived from the deformation gradient tensor (F). The...

A two-dimensional continuum model of epithelial tissue mechanics was formulated using cellular-level mechanical ingredients and cell morphogenetic processes, including cellular shape changes and cellular rearrangements. This model incorporates stress and deformation tensors, which can be compared with experimental data. Focusing on the interplay between cell shape changes and cell rearrangement...

Using mode-coupling theory, we derive a constitutive equation for the nonlinear rheology of dense colloidal suspensions under arbitrary time-dependent homogeneous flow. Generalizing previous results for simple shear, this allows the full tensorial structure of the theory to be identified. Macroscopic deformation measures, such as the Cauchy-Green tensors, thereby emerge. So does a direct relati...