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Fortunately, the transport matrix is symmetric and often data-sparse.
Raskar, R. & Davis, J. 5d time-light transport matrix: what can we reason about scene properties?
It is a challenging task to acquire this transport matrix due to its large size.
Besides providing an efficient representation for storage, it enables fast acquisition of the approximated transport matrix and fast rendering of images from the captured matrix.
We introduce the use of hierarchical tensors as the underlying data structure to capture this data-sparseness, specifically through local rank-1 factorizations of the transport matrix.
The technique models the 8D reflectance field as a transport matrix between the 4D incident light field and the 4D exitant light field.
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The mathematical structure of the transport matrices is readily used to build transport algorithms inspired by Ern and Giovangigli [J. Comput. Phys. 120 (1995) 105].
These cubic liquid crystals function as ion transporting matrices whose ionic conductivities are enhanced owing to the presence of a 3D continuous proton conduction pathway along the hydrophilic surface.
The transport factor matrix is the transformation matrix from sources to receptors.
Transport of matrix molecules in the hydrogel contributes both to the development of the pericellular matrix and the extracellular matrix and is dependent on the relative size of matrix molecules and the hydrogel mesh.
Furthermore, limitations in nutrient transport and matrix accumulation in engineered constructs hinders maturation within the central core of large constructs.
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