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Diffusion tensor imaging (DTI) is a magnetic resonance imaging technique that enables the measurement of the restricted diffusion of water in tissue in order to produce neural tract images instead of using this data solely for the purpose of assigning contrast or colors to pixels in a cross-sectional image.
De facto standard for matrix/tensor operations in Python. Pandas , a library for data manipulation and analysis. SageMath is a large mathematical software application which integrates the work of nearly 100 free software projects and supports linear algebra, combinatorics, numerical mathematics, calculus, and more.
Using diffusion tensor MRI, one can measure the apparent diffusion coefficient at each voxel in the image, and after multilinear regression across multiple images, the whole diffusion tensor can be reconstructed. [1] Suppose there is a fiber tract of interest in the sample.
In machine learning, the term tensor informally refers to two different concepts (i) a way of organizing data and (ii) a multilinear (tensor) transformation. Data may be organized in a multidimensional array (M-way array), informally referred to as a "data tensor"; however, in the strict mathematical sense, a tensor is a multilinear mapping over a set of domain vector spaces to a range vector ...
The electromagnetic tensor is the combination of the electric and magnetic fields into a covariant antisymmetric tensor whose entries are B-field quantities. [1] = (/ / / / / /) and the result of raising its indices is = = (/ / / / / /), where E is the electric field, B the magnetic field, and c the speed of light.
The tensor product of two vector spaces is a vector space that is defined up to an isomorphism.There are several equivalent ways to define it. Most consist of defining explicitly a vector space that is called a tensor product, and, generally, the equivalence proof results almost immediately from the basic properties of the vector spaces that are so defined.
Diffusion tensor imaging, a structural medical imaging technique; Direct thrombin inhibitor; Diesel turbo injection, a brand name for common rail; Direct tension indicator; Deep tissue injury, see suspected deep tissue injury in List of medical abbreviations: S; Dye transfer inhibitor
A (0,1) tensor is a covector. A (0,2) tensor is a bilinear form. An example is the metric tensor . A (1,1) tensor is a linear map. An example is the delta, , which is the identity map, or a Lorentz transformation .