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Diffusion tensor imaging (DTI) is important when a tissue—such as the neural axons of white matter in the brain or muscle fibers in the heart—has an internal fibrous structure analogous to the anisotropy of some crystals. Water will then diffuse more rapidly in the direction aligned with the internal structure (axial diffusion), and more ...
Tensorial [8] "Tensorial 4.0" is a general purpose tensor calculus package for Mathematica. xAct: [9] Efficient Tensor Computer Algebra for Mathematica. xAct is a collection of packages for fast manipulation of tensor expressions. GREAT [10] is a free package for Mathematica that computes the Christoffel connection and the basic tensors of ...
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.
Download QR code; Print/export Download as PDF; Printable version; In other projects ... move to sidebar hide. DTI may refer to: Science and technology . Deep trench ...
String diagrams (with generators from ) are arrows in the free monoidal category . [8] The interpretation in a monoidal category D {\displaystyle D} is a defined by a monoidal functor F : C Σ → D {\displaystyle F:C_{\Sigma }\to D} , which by freeness is uniquely determined by a morphism of monoidal signatures F : Σ → U ( D ...
For a 3rd-order tensor , where is either or , Tucker Decomposition can be denoted as follows, = () where is the core tensor, a 3rd-order tensor that contains the 1-mode, 2-mode and 3-mode singular values of , which are defined as the Frobenius norm of the 1-mode, 2-mode and 3-mode slices of tensor respectively.
MATLAB + Deep Learning Toolbox (formally Neural Network Toolbox) MathWorks: 1992 Proprietary: No Linux, macOS, Windows: C, C++, Java, MATLAB: MATLAB: No No Train with Parallel Computing Toolbox and generate CUDA code with GPU Coder [23] No Yes [24] Yes [25] [26] Yes [25] Yes [25] Yes With Parallel Computing Toolbox [27] Yes Microsoft Cognitive ...
Thus, the TVP of a tensor to a P-dimensional vector consists of P projections from the tensor to a scalar. The projection from a tensor to a scalar is an elementary multilinear projection (EMP). In EMP, a tensor is projected to a point through N unit projection vectors. It is the projection of a tensor on a single line (resulting a scalar ...