4.1.1. Math symbols and abbreviations

4.1.1.1. Math symbols

  • \(\boldsymbol{x}\): bold lowercase for vector

  • \(\boldsymbol{X}\): bold italic uppercase for matrix

  • \(\textbf{X}\): bold orthographic uppercase for tensor

  • \(\mathrm{r}(\boldsymbol{A})\): the rank of matrix \(\boldsymbol{A}\)

  • \(\mathrm{Tr}(\boldsymbol{A})\): the trace of matrix \(\boldsymbol{A}\)

  • \(\mathrm{det}(\boldsymbol{A})\): the determinant of matrix \(\boldsymbol{A}\)

  • \(\boldsymbol{A}^{-1}\): the inverse of matrix \(\boldsymbol{A}\)

  • \(\boldsymbol{A}^\top\): the transpose of matrix \(\boldsymbol{A}\)

  • \(\boldsymbol{A}^\ast\): the conjugate of matrix \(\boldsymbol{A}\)

  • \(\boldsymbol{A}^\mathrm{H}\): the Hermitian of matrix \(\boldsymbol{A}\)

  • \(\varnothing\): empty set

  • \(\in\): in

  • \(\mathbb{Z}\): integer numerical domain

  • \(\mathbb{N}\): natural numerical domain

  • \(\mathbb{R}\): real numerical domain

  • \(\mathbb{C}\): complex numerical domain

  • \(\mathbb{Z}^+\): numerical domain for positive integer

  • \(\mathbb{R}^+\): numerical domain for positive real number

  • \(\forall\): for all

  • \(\cap\): intersection of sets

  • \(\cup\): union of sets

  • \(\subset\): subset; e.g. \(A\ \subset\ B\) for \(A\) is a subset of \(B\)

  • \(\subseteq\): subset or equal; e.g. \(A\ \subseteq\ B\) for \(A\ \subset\ B\) or \(A = B\)

  • \(\sum\): sum; e.g. \(\sum_{i=1}^n a_i = a_1 + a_2 + \dots + a_{n-1} + a_n\)

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

  • \(p(X)\): the probability of \(X\)

  • \(x_i\): the \(i\)-th element in series \(\boldsymbol{x}\)

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

  • \(\bar{x}\): the sample mean of a series \(\boldsymbol{x}\)

  • \(\Vert\cdot\Vert_2\): the Euclidean norm of something

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

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

  • \(\mathrm{sup}(\cdot)\): supremum of something

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

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

4.1.1.2. 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

Created on:

Jul 19, 2023