_`Math symbols and abbreviations`
=================================

_`Math symbols`
---------------

* :math:`\boldsymbol{x}`: bold lowercase for vector

* :math:`\boldsymbol{X}`: bold italic uppercase for matrix

* :math:`\textbf{X}`: bold orthographic uppercase for tensor

* :math:`\mathrm{r}(\boldsymbol{A})`: the rank of matrix :math:`\boldsymbol{A}`

* :math:`\mathrm{Tr}(\boldsymbol{A})`: the trace of matrix :math:`\boldsymbol{A}`

* :math:`\mathrm{det}(\boldsymbol{A})`: the determinant of matrix :math:`\boldsymbol{A}`

* :math:`\boldsymbol{A}^{-1}`: the inverse of matrix :math:`\boldsymbol{A}`

* :math:`\boldsymbol{A}^\top`: the transpose of matrix :math:`\boldsymbol{A}`

* :math:`\boldsymbol{A}^\ast`: the conjugate of matrix :math:`\boldsymbol{A}`

* :math:`\boldsymbol{A}^\mathrm{H}`: the Hermitian of matrix :math:`\boldsymbol{A}`

* :math:`\varnothing`: empty set

* :math:`\in`: in

* :math:`\mathbb{Z}`: integer numerical domain

* :math:`\mathbb{N}`: natural numerical domain

* :math:`\mathbb{R}`: real numerical domain

* :math:`\mathbb{C}`: complex numerical domain

* :math:`\mathbb{Z}^+`: numerical domain for positive integer

* :math:`\mathbb{R}^+`: numerical domain for positive real number

* :math:`\forall`: for all

* :math:`\cap`: intersection of sets

* :math:`\cup`: union of sets

* :math:`\subset`: subset; e.g. :math:`A\ \subset\ B` for :math:`A` is a subset of :math:`B`

* :math:`\subseteq`: subset or equal; e.g. :math:`A\ \subseteq\ B` for :math:`A\ \subset\ B` or :math:`A = B`

* :math:`\sum`: sum; e.g. :math:`\sum_{i=1}^n a_i = a_1 + a_2 + \dots + a_{n-1} + a_n`

* :math:`\prod`: product; e.g. :math:`\prod_{i=1}^n a_i = a_1 \times a_2 \times \dots \times a_{n-1} \times a_n`

* :math:`p(X)`: the probability of :math:`X`

* :math:`x_i`: the :math:`i`-th element in series :math:`\boldsymbol{x}`

* :math:`x_{(i)}`: the :math:`i`-th smallest in series :math:`\boldsymbol{x}`

* :math:`\bar{x}`: the sample mean of a series :math:`\boldsymbol{x}`

* :math:`\Vert\cdot\Vert_2`: the Euclidean norm of something

* :math:`\mathrm{sgn}(\cdot)`: sign function of something; e.g. :math:`\mathrm{sgn}(x) = 1` if :math:`x \geq 0`
  otherwise -1

* :math:`I_A(\cdot)`: indicator function of something; e.g. :math:`I_A(x) = 1` if :math:`x \in A` otherwise 0

* :math:`\mathrm{sup}(\cdot)`: supremum of something

* :math:`\left[ \cdot \right]_{+}`: the rectified linear function of something; e.g. :math:`\left[ x \right]_{+} = x`
  if :math:`x > 0` otherwise :math:`\left[ x \right]_{+} = 0`

* :math:`\delta ( \cdot )`: Dirac's delta function; 1 if and only if the expression inside established, otherwise 0;
  also called unit impulse function

_`Acronyms`
-----------

* _`AI`: Artificial Intelligence

* _`LoG`: Laplacian of Gaussian

* _`DoG`: Difference of Gaussian

* _`FCA`: Formal Concept Analysis

* _`DOE`: Design of Experiments

* _`MC`: Monte Carlo methods

* _`ANOVA`: Analysis of Variance

* _`ROI`: Region of Interest

* _`DVH`: Dose Volume Histogram

* _`IO`: Input and Output

* _`GPU`: Graphic Processing Unit

* _`DICOM`: Digital Imaging and Communications in Medicine

* _`NIfTI`: Neuroimaging Informatics Technology Initiative

* _`I.I.D.`: Independent and Identically Distributed

* _`DoF`: Degree of Freedom

* _`CT`: Computed Tomography

* _`MR`: Magnetic Resonance

* _`SNR`: Signal to Noise Ratio

* _`ANN`: Artificial Neural Network

* _`IoT`: Internet of Things

* _`WHO`: World Health Organization

----

:Authors: Chen Zhang
:Version: 0.0.5
:|create|: Jul 19, 2023