Webservice User Guide

Author: Zhiyuan
20.Oct.24

Tutorials for user usage and Q&A sessions about web services.

webservice overview

Author: Zhiyuan
Date: 20.Oct.24

If you have any advice or problems, feel free to leave comments under here or directly contact us.

Services

Our Service Portal :

https://hub.mai.informatik.tu-darmstadt.de/

Currently, we offer the following services to support our collaborative and organizational needs:

New user registeration

  1. Firstly you need to ask administrator to create a user for you, the following informations are needded:
    • username (note, not able to be changed anymore)
    • Email
    • Lab Postion
  2. Once your account is created, you will receive the validation link in the corresponding Email.
    You should update your password as well as profiles like last name, first name.
  3. Once account is verified, you could go to keycloak management link Link, there you could update your profile.

Mattermost user migration

We have migraed mattermost data from AIML to If you are already the user in AIML, you need to check if there is lost dialogs.

  1. check your dialog and profile, your profile like nickname, profile photo are lost,

  2. Known issues: reactions in reply is lost by migrating.

  3. You need to manually migrate your focal board, just follow the following page, export archive(left page), import archive(right page). (unfortunately some info like creation time, createdBy Assignee are lost)

Description Description

Wiki of web services

Author: Zhiyuan Date: 20.Oct.24

Nextcloud:

Bookstack

Mattermost

Our mattermost will be deployed as soon as possible.

Gitlab

Keycloak

Math macro command for latex support in markdown

Number and Arrays

command visualization comment
a $a$ A scalar
\va $\va$ A vector, additionally $\vzero, \vone, \vmu, \vnu, \vtheta$ for \vzero, \vone, \vmu, \vnu, \vtheta
\mA $\mA$ A matrix
\tA $\tA$ A tensor
\mI_n $\mI_n$ Identity matrix with $n$ rows and $n$ columns
\mI $\mI$ Identity matrix with dimensionality implied by context
\ve^{(i)} $\ve^{(i)}$ Standard basis vector $[0,\dots,0,1,0,\dots,0]$ with a 1 at position $i$
\text{diag}(\va) $\text{diag}(\va)$ A square, diagonal matrix with diagonal entries given by $\va$
\ra $\ra$ A scalar-valued random variable
\rva $\rva$ A vector-valued random variables
\rmA $\rmA$ A matrix-valued random varialbes

Sets and Graphs

Command Visualization Comment
\sA $\sA$ A set
Note: the command covers sA to sZ but don't no sE since it's expectation
\R $\R$ The set of real numbers
{0, 1} ${0, 1}$ The set containing 0 and 1
{0, 1, \dots, n} ${0, 1, \dots, n}$ The set of all integers between $0$ and $n$
[a, b] $[a, b]$ The real interval including $a$ and $b$
(a, b] $(a, b]$ The real interval excluding $a$ but including $b$
\sA \backslash \sB $\sA \backslash \sB$ Set subtraction, i.e., the set containing the elements of $\sA$ not in $\sB$
\gG $\gG$ A graph

Indexing

Command Visualization Comment
\eva_i $\eva_i$ Element $i$ of vector $\va$, with indexing starting at 1
\eva_{-i} $\eva_{-i}$ All elements of vector $\va$ except for element $i$
\emA_{i,j} $\emA_{i,j}$ Element $i, j$ of matrix $\mA$
\mA_{i, :} $\mA_{i, :}$ Row $i$ of matrix $\mA$
\mA_{:, i} $\mA_{:, i}$ Column $i$ of matrix $\mA$
\etA_{i, j, k} $\etA_{i, j, k}$ Element $(i, j, k)$ of a 3-D tensor $\tA$
\tA_{:, :, i} $\tA_{:, :, i}$ 2-D slice of a 3-D tensor
\erva_i $\erva_i$ Element $i$ of the random vector $\rva$

Linear Algebra Operators

Command Visualization Comment
\mA^\top $\mA^\top$ Transpose of matrix $\mA$
\mA^+ $\mA^+$ Moore-Penrose pseudoinverse of $\mA$
\mA \odot \mB $\mA \odot \mB$ Element-wise (Hadamard) product of $\mA$ and $\mB$
\mathrm{det}(\mA) $\mathrm{det}(\mA)$ Determinant of $\mA$
\sign(x) $\sign(x)$ Sign of a variable $x$
\Tr \mA $\Tr(\mA)$ Trace of a matrix A

Calculus

Command Visualization Comment
\diff y / \diff x $\diff y / \diff x$ Derivative of $y$ with respect to $x$
\frac{\partial y}{\partial x} $\frac{\partial y}{\partial x}$ Partial derivative of $y$ with respect to $x$
\nabla_\vx y $\nabla_\vx y$ Gradient of $y$ with respect to $\vx$
\nabla_\mX y $\nabla_\mX y$ Matrix derivatives of $y$ with respect to $\mX$
\nabla_\tX y $\nabla_\tX y$ Tensor containing derivatives of $y$ with respect to $\tX$
\frac{\partial f}{\partial \vx} $\frac{\partial f}{\partial \vx}$ Jacobian matrix $\mJ \in \R^{m\times n}$ of $f: \R^n \rightarrow \R^m$
\nabla_\vx^2 f(\vx)\text{ or }\mH(f)(\vx) $\nabla_\vx^2 f(\vx)\text{ or }\mH(f)(\vx)$ The Hessian matrix of $f$ at input point $\vx$
\int f(\vx) d\vx $\int f(\vx) d\vx$ Definite integral over the entire domain of $\vx$
\int_\sS f(\vx) d\vx $\int_\sS f(\vx) d\vx$ Definite integral with respect to $\vx$ over the set $\sS$

Probabilities

Command Visualization Comment
\ra \bot \rb $\ra \bot \rb$ The random variables $\ra$ and $\rb$ are independent
\ra \bot \rb \mid \rc $\ra \bot \rb \mid \rc$ They are conditionally independent given $\rc$
P(\ra) $P(\ra)$ A probability distribution over a discrete variable
p(\ra) $p(\ra)$ A probability distribution over a continuous variable, or a variable of unspecified type
\ra \sim P $\ra \sim P$ Random variable $\ra$ has distribution $P$
\E_{\rx \sim P} [ f(x) ] \text{ or } \E f(x) $\E_{\rx \sim P} [ f(x) ] \text{ or } \E f(x)$ Expectation of $f(x)$ with respect to $P(\rx)$
\Var(f(x)) $\Var(f(x))$ Variance of $f(x)$ under $P(\rx)$
\Cov(f(x), g(x)) $\Cov(f(x), g(x))$ Covariance of $f(x)$ and $g(x)$ under $P(\rx)$
H(\rx) $H(\rx)$ Shannon entropy of the random variable $\rx$
\KL(P \Vert Q) $\KL(P \Vert Q)$ Kullback-Leibler divergence of $P$ and $Q$
\mathcal{N}(\vx ; \vmu , \mSigma) $\mathcal{N}(\vx ; \vmu , \mSigma)$ Gaussian distribution over $\vx$ with mean $\vmu$ and covariance $\mSigma$

Functions

Command Visualization Comment
f: \sA \rightarrow \sB $f: \sA \rightarrow \sB$ The function $f$ with domain $\sA$ and range $\sB$
f \circ g $f \circ g$ Composition of the functions $f$ and $g$
f(\vx ; \vtheta) $f(\vx ; \vtheta)$ A function of $\vx$ parametrized by $\vtheta$. Sometimes written as $f(\vx)$ to simplify notation
\log x $\log x$ Natural logarithm of $x$
\sigma(x) $\sigma(x)$ Logistic sigmoid, $\displaystyle \frac{1}{1 + \exp(-x)}$
\zeta(x) $\zeta(x)$ Softplus, $\log(1 + \exp(x))$
\Vert \vx \Vert_p $\Vert \vx \Vert_p$ $L^p$ norm of $\vx$
\Vert \vx \Vert $\Vert \vx \Vert$ $L^2$ norm of $\vx$
x^+ $x^+$ Positive part of $x$, i.e., $\max(0,x)$
\bm{1}_\mathrm{condition} $\bm{1}_\mathrm{condition}$ Is 1 if the condition is true, 0 otherwise

Custom Commands special

Command Visualization Comment
\bm{#1} $\bm{x}$ Bold symbol, e.g., $\boldsymbol{x}$
\sign $\sign$ operator, Sign , $\operatorname{sign}$
\Tr $\Tr$ operator Trace, $\operatorname{Tr}$
\E $\E$ Expectation, $\mathbb{E}$
\KL $\KL$ Kullback-Leibler divergence, $D_\mathrm{KL}$
\NormalDist $\NormalDist$ Gaussian distribution, $\mathcal{N}$
\diag $\diag$ Diagonal matrix, $\mathrm{diag}$
\Ls $\Ls$ Loss function, $\mathcal{L}$
\R $\R$ Real number set, $\mathbb{R}$
\emp $\emp$ Empirical distribution, $\tilde{p}$
\lr $\lr$ Learning rate, $\alpha$
\reg $\reg$ Regularization coefficient, $\lambda$
\rect $\rect$ Rectifier activation, $\mathrm{rectifier}$
\softmax $\softmax$ Softmax function, $\mathrm{softmax}$
\sigmoid $\sigmoid$ Sigmoid function, $\sigma$
\softplus $\softplus$ Softplus function, $\zeta$
\Var $\Var$ Variance, $\mathrm{Var}$
\standarderror $\standarderror$ Standard error, $\mathrm{SE}$
\Cov $\Cov$ Covariance, $\mathrm{Cov}$
\tran $\tran$ Transpose operator, $^\top$
\inv $\inv$ Inverse operator, $^{-1}$
\diff $\diff$ Differential operator, $\mathrm{d}$

Reference

Markdown Math Macro definition

The latex command source

Click to unfold latex macro definition

Latex command definition source

\newcommand{\bm}[1]{\boldsymbol{#1}}

\newcommand{\sign}{\operatorname{sign}} % \DeclareMathOperator{\sign}{sign}
\newcommand{\Tr}{\operatorname{Tr}} % \DeclareMathOperator{\Tr}{Tr}


\newcommand{\E}{\mathbb{E}}
\newcommand{\KL}{D_\mathrm{KL}}
\newcommand{\NormalDist}{\mathcal{N}}
\newcommand{\diag}{\mathrm{diag}}

\newcommand{\Ls}{\mathcal{L}}
\newcommand{\R}{\mathbb{R}}
\newcommand{\emp}{\tilde{p}}
\newcommand{\lr}{\alpha}
\newcommand{\reg}{\lambda}
\newcommand{\rect}{\mathrm{rectifier}}
\newcommand{\softmax}{\mathrm{softmax}}
\newcommand{\sigmoid}{\sigma}
\newcommand{\softplus}{\zeta}
\newcommand{\Var}{\mathrm{Var}}
\newcommand{\standarderror}{\mathrm{SE}}
\newcommand{\Cov}{\mathrm{Cov}}
\newcommand{\tran}{^\top}
\newcommand{\inv}{^{-1}}
\newcommand{\diff}{ \mathrm{d}}

% % Vectors
\newcommand{\vzero}{\bm{0}}
\newcommand{\vone}{\bm{1}}
\newcommand{\vmu}{\bm{\mu}}
\newcommand{\vnu}{\bm{\nu}}
\newcommand{\vtheta}{\bm{\theta}}

\renewcommand{\va}{\bm{a}}
\renewcommand{\vb}{\bm{b}}
% \newcommand{\va}{\bm{a}}
% \newcommand{\vb}{\bm{b}}
\newcommand{\vc}{\bm{c}}
\newcommand{\vd}{\bm{d}}
\newcommand{\ve}{\bm{e}}
\newcommand{\vf}{\bm{f}}
\newcommand{\vg}{\bm{g}}
\newcommand{\vh}{\bm{h}}
\newcommand{\vi}{\bm{i}}
\newcommand{\vj}{\bm{j}}
\newcommand{\vk}{\bm{k}}
\newcommand{\vl}{\bm{l}}
\newcommand{\vm}{\bm{m}}
\newcommand{\vn}{\bm{n}}
\newcommand{\vo}{\bm{o}}
\newcommand{\vp}{\bm{p}}
\newcommand{\vq}{\bm{q}}
\newcommand{\vr}{\bm{r}}
\newcommand{\vs}{\bm{s}}
\newcommand{\vt}{\bm{t}}
\newcommand{\vu}{\bm{u}}
\newcommand{\vv}{\bm{v}}
\newcommand{\vw}{\bm{w}}
\newcommand{\vx}{\bm{x}}
\newcommand{\vy}{\bm{y}}
\newcommand{\vz}{\bm{z}}


% % Random variables
% % old latex command \rm is overwritten, now should use `\textrm` or `\mathrm`
% \newcommand{\reta}{{\textnormal{$\eta$}}}
\newcommand{\ra}{{\textnormal{a}}}
\newcommand{\rb}{{\textnormal{b}}}
\newcommand{\rc}{{\textnormal{c}}}
\newcommand{\rd}{{\textnormal{d}}}
\newcommand{\re}{{\textnormal{e}}}
\newcommand{\rf}{{\textnormal{f}}}
\newcommand{\rg}{{\textnormal{g}}}
\newcommand{\rh}{{\textnormal{h}}}
\newcommand{\ri}{{\textnormal{i}}}
\newcommand{\rj}{{\textnormal{j}}}
\newcommand{\rk}{{\textnormal{k}}}
\newcommand{\rl}{{\textnormal{l}}}
\renewcommand{\rm}{{\textnormal{m}}}  % note \rm is old command
\newcommand{\rn}{{\textnormal{n}}}
\newcommand{\ro}{{\textnormal{o}}}
\newcommand{\rp}{{\textnormal{p}}}
\newcommand{\rq}{{\textnormal{q}}}
\newcommand{\rr}{{\textnormal{r}}}
\newcommand{\rs}{{\textnormal{s}}}
\newcommand{\rt}{{\textnormal{t}}}
\newcommand{\ru}{{\textnormal{u}}}
\newcommand{\rv}{{\textnormal{v}}}
\newcommand{\rw}{{\textnormal{w}}}
\newcommand{\rx}{{\textnormal{x}}}
\newcommand{\ry}{{\textnormal{y}}}
\newcommand{\rz}{{\textnormal{z}}}

% % Random vectors  % TODO, greek vector valued random variables and vectors are same
\newcommand{\rvepsilon}{\bm{\epsilon}}
\newcommand{\rvtheta}{\bm{\theta}}
\newcommand{\rva}{\mathbf{a}}
\newcommand{\rvb}{\mathbf{b}}
\newcommand{\rvc}{\mathbf{c}}
\newcommand{\rvd}{\mathbf{d}}
\newcommand{\rve}{\mathbf{e}}
\newcommand{\rvf}{\mathbf{f}}
\newcommand{\rvg}{\mathbf{g}}
\newcommand{\rvh}{\mathbf{h}}
\newcommand{\rvi}{\mathbf{i}}
\newcommand{\rvj}{\mathbf{j}}
\newcommand{\rvk}{\mathbf{k}}
\newcommand{\rvl}{\mathbf{l}}
\newcommand{\rvm}{\mathbf{m}}
\newcommand{\rvn}{\mathbf{n}}
\newcommand{\rvo}{\mathbf{o}}
\newcommand{\rvp}{\mathbf{p}}
\newcommand{\rvq}{\mathbf{q}}
\newcommand{\rvr}{\mathbf{r}}
\newcommand{\rvs}{\mathbf{s}}
\newcommand{\rvt}{\mathbf{t}}
\newcommand{\rvu}{\mathbf{u}}
\newcommand{\rvv}{\mathbf{v}}
\newcommand{\rvw}{\mathbf{w}}
\newcommand{\rvx}{\mathbf{x}}
\newcommand{\rvy}{\mathbf{y}}
\newcommand{\rvz}{\mathbf{z}}

% % Elements of random vectors
\newcommand{\erva}{{\textnormal{a}}}
\newcommand{\ervb}{{\textnormal{b}}}
\newcommand{\ervc}{{\textnormal{c}}}
\newcommand{\ervd}{{\textnormal{d}}}
\newcommand{\erve}{{\textnormal{e}}}
\newcommand{\ervf}{{\textnormal{f}}}
\newcommand{\ervg}{{\textnormal{g}}}
\newcommand{\ervh}{{\textnormal{h}}}
\newcommand{\ervi}{{\textnormal{i}}}
\newcommand{\ervj}{{\textnormal{j}}}
\newcommand{\ervk}{{\textnormal{k}}}
\newcommand{\ervl}{{\textnormal{l}}}
\newcommand{\ervm}{{\textnormal{m}}}
\newcommand{\ervn}{{\textnormal{n}}}
\newcommand{\ervo}{{\textnormal{o}}}
\newcommand{\ervp}{{\textnormal{p}}}
\newcommand{\ervq}{{\textnormal{q}}}
\newcommand{\ervr}{{\textnormal{r}}}
\newcommand{\ervs}{{\textnormal{s}}}
\newcommand{\ervt}{{\textnormal{t}}}
\newcommand{\ervu}{{\textnormal{u}}}
\newcommand{\ervv}{{\textnormal{v}}}
\newcommand{\ervw}{{\textnormal{w}}}
\newcommand{\ervx}{{\textnormal{x}}}
\newcommand{\ervy}{{\textnormal{y}}}
\newcommand{\ervz}{{\textnormal{z}}}

% % Random matrices
\newcommand{\rmA}{{\mathbf{A}}}
\newcommand{\rmB}{{\mathbf{B}}}
\newcommand{\rmC}{{\mathbf{C}}}
\newcommand{\rmD}{{\mathbf{D}}}
\newcommand{\rmE}{{\mathbf{E}}}
\newcommand{\rmF}{{\mathbf{F}}}
\newcommand{\rmG}{{\mathbf{G}}}
\newcommand{\rmH}{{\mathbf{H}}}
\newcommand{\rmI}{{\mathbf{I}}}
\newcommand{\rmJ}{{\mathbf{J}}}
\newcommand{\rmK}{{\mathbf{K}}}
\newcommand{\rmL}{{\mathbf{L}}}
\newcommand{\rmM}{{\mathbf{M}}}
\newcommand{\rmN}{{\mathbf{N}}}
\newcommand{\rmO}{{\mathbf{O}}}
\newcommand{\rmP}{{\mathbf{P}}}
\newcommand{\rmQ}{{\mathbf{Q}}}
\newcommand{\rmR}{{\mathbf{R}}}
\newcommand{\rmS}{{\mathbf{S}}}
\newcommand{\rmT}{{\mathbf{T}}}
\newcommand{\rmU}{{\mathbf{U}}}
\newcommand{\rmV}{{\mathbf{V}}}
\newcommand{\rmW}{{\mathbf{W}}}
\newcommand{\rmX}{{\mathbf{X}}}
\newcommand{\rmY}{{\mathbf{Y}}}
\newcommand{\rmZ}{{\mathbf{Z}}}

% % Elements of random matrices
\newcommand{\ermA}{{\textnormal{A}}}
\newcommand{\ermB}{{\textnormal{B}}}
\newcommand{\ermC}{{\textnormal{C}}}
\newcommand{\ermD}{{\textnormal{D}}}
\newcommand{\ermE}{{\textnormal{E}}}
\newcommand{\ermF}{{\textnormal{F}}}
\newcommand{\ermG}{{\textnormal{G}}}
\newcommand{\ermH}{{\textnormal{H}}}
\newcommand{\ermI}{{\textnormal{I}}}
\newcommand{\ermJ}{{\textnormal{J}}}
\newcommand{\ermK}{{\textnormal{K}}}
\newcommand{\ermL}{{\textnormal{L}}}
\newcommand{\ermM}{{\textnormal{M}}}
\newcommand{\ermN}{{\textnormal{N}}}
\newcommand{\ermO}{{\textnormal{O}}}
\newcommand{\ermP}{{\textnormal{P}}}
\newcommand{\ermQ}{{\textnormal{Q}}}
\newcommand{\ermR}{{\textnormal{R}}}
\newcommand{\ermS}{{\textnormal{S}}}
\newcommand{\ermT}{{\textnormal{T}}}
\newcommand{\ermU}{{\textnormal{U}}}
\newcommand{\ermV}{{\textnormal{V}}}
\newcommand{\ermW}{{\textnormal{W}}}
\newcommand{\ermX}{{\textnormal{X}}}
\newcommand{\ermY}{{\textnormal{Y}}}
\newcommand{\ermZ}{{\textnormal{Z}}}



% % Elements of vectors
\newcommand{\evalpha}{{\alpha}}
\newcommand{\evbeta}{{\beta}}
\newcommand{\evepsilon}{{\epsilon}}
\newcommand{\evlambda}{{\lambda}}
\newcommand{\evomega}{{\omega}}
\newcommand{\evmu}{{\mu}}
\newcommand{\evpsi}{{\psi}}
\newcommand{\evsigma}{{\sigma}}
\newcommand{\evtheta}{{\theta}}

\newcommand{\eva}{{a}}
\newcommand{\evb}{{b}}
\newcommand{\evc}{{c}}
\newcommand{\evd}{{d}}
\newcommand{\eve}{{e}}
\newcommand{\evf}{{f}}
\newcommand{\evg}{{g}}
\newcommand{\evh}{{h}}
\newcommand{\evi}{{i}}
\newcommand{\evj}{{j}}
\newcommand{\evk}{{k}}
\newcommand{\evl}{{l}}
\newcommand{\evm}{{m}}
\newcommand{\evn}{{n}}
\newcommand{\evo}{{o}}
\newcommand{\evp}{{p}}
\newcommand{\evq}{{q}}
\newcommand{\evr}{{r}}
\newcommand{\evs}{{s}}
\newcommand{\evt}{{t}}
\newcommand{\evu}{{u}}
\newcommand{\evv}{{v}}
\newcommand{\evw}{{w}}
\newcommand{\evx}{{x}}
\newcommand{\evy}{{y}}
\newcommand{\evz}{{z}}

% %% Matrix
\newcommand{\mBeta}{{\bm{\beta}}}
\newcommand{\mPhi}{{\bm{\Phi}}}
\newcommand{\mLambda}{{\bm{\Lambda}}}
\newcommand{\mSigma}{{\bm{\Sigma}}}

\newcommand{\mA}{{\bm{A}}}
\newcommand{\mB}{{\bm{B}}}
\newcommand{\mC}{{\bm{C}}}
\newcommand{\mD}{{\bm{D}}}
\newcommand{\mE}{{\bm{E}}}
\newcommand{\mF}{{\bm{F}}}
\newcommand{\mG}{{\bm{G}}}
\newcommand{\mH}{{\bm{H}}}
\newcommand{\mI}{{\bm{I}}}
\newcommand{\mJ}{{\bm{J}}}
\newcommand{\mK}{{\bm{K}}}
\newcommand{\mL}{{\bm{L}}}
\newcommand{\mM}{{\bm{M}}}
\newcommand{\mN}{{\bm{N}}}
\newcommand{\mO}{{\bm{O}}}
\newcommand{\mP}{{\bm{P}}}
\newcommand{\mQ}{{\bm{Q}}}
\newcommand{\mR}{{\bm{R}}}
\newcommand{\mS}{{\bm{S}}}
\newcommand{\mT}{{\bm{T}}}
\newcommand{\mU}{{\bm{U}}}
\newcommand{\mV}{{\bm{V}}}
\newcommand{\mW}{{\bm{W}}}
\newcommand{\mX}{{\bm{X}}}
\newcommand{\mY}{{\bm{Y}}}
\newcommand{\mZ}{{\bm{Z}}}


% \DeclareMathAlphabet{\mathsfit}{\encodingdefault}{\sfdefault}{m}{sl}
% \SetMathAlphabet{\mathsfit}{bold}{\encodingdefault}{\sfdefault}{bx}{n}
% \newcommand{\tens}[1]{\bm{\mathsfit{#1}}}
% in mathjax use mathsf insteadly
\newcommand{\tens}[1]{ \bm{\mathit{\mathsf{#1}}} }
% % Tensor
\newcommand{\tA}{{\tens{A}}}
\newcommand{\tB}{{\tens{B}}}
\newcommand{\tC}{{\tens{C}}}
\newcommand{\tD}{{\tens{D}}}
\newcommand{\tE}{{\tens{E}}}
\newcommand{\tF}{{\tens{F}}}
\newcommand{\tG}{{\tens{G}}}
\newcommand{\tH}{{\tens{H}}}
\newcommand{\tI}{{\tens{I}}}
\newcommand{\tJ}{{\tens{J}}}
\newcommand{\tK}{{\tens{K}}}
\newcommand{\tL}{{\tens{L}}}
\newcommand{\tM}{{\tens{M}}}
\newcommand{\tN}{{\tens{N}}}
\newcommand{\tO}{{\tens{O}}}
\newcommand{\tP}{{\tens{P}}}
\newcommand{\tQ}{{\tens{Q}}}
\newcommand{\tR}{{\tens{R}}}
\newcommand{\tS}{{\tens{S}}}
\newcommand{\tT}{{\tens{T}}}
\newcommand{\tU}{{\tens{U}}}
\newcommand{\tV}{{\tens{V}}}
\newcommand{\tW}{{\tens{W}}}
\newcommand{\tX}{{\tens{X}}}
\newcommand{\tY}{{\tens{Y}}}
\newcommand{\tZ}{{\tens{Z}}}


% % Graph
\newcommand{\gA}{{\mathcal{A}}}
\newcommand{\gB}{{\mathcal{B}}}
\newcommand{\gC}{{\mathcal{C}}}
\newcommand{\gD}{{\mathcal{D}}}
\newcommand{\gE}{{\mathcal{E}}}
\newcommand{\gF}{{\mathcal{F}}}
\newcommand{\gG}{{\mathcal{G}}}
\newcommand{\gH}{{\mathcal{H}}}
\newcommand{\gI}{{\mathcal{I}}}
\newcommand{\gJ}{{\mathcal{J}}}
\newcommand{\gK}{{\mathcal{K}}}
\newcommand{\gL}{{\mathcal{L}}}
\newcommand{\gM}{{\mathcal{M}}}
\newcommand{\gN}{{\mathcal{N}}}
\newcommand{\gO}{{\mathcal{O}}}
\newcommand{\gP}{{\mathcal{P}}}
\newcommand{\gQ}{{\mathcal{Q}}}
\newcommand{\gR}{{\mathcal{R}}}
\newcommand{\gS}{{\mathcal{S}}}
\newcommand{\gT}{{\mathcal{T}}}
\newcommand{\gU}{{\mathcal{U}}}
\newcommand{\gV}{{\mathcal{V}}}
\newcommand{\gW}{{\mathcal{W}}}
\newcommand{\gX}{{\mathcal{X}}}
\newcommand{\gY}{{\mathcal{Y}}}
\newcommand{\gZ}{{\mathcal{Z}}}

% % Sets
\newcommand{\sA}{{\mathbb{A}}}
\newcommand{\sB}{{\mathbb{B}}}
\newcommand{\sC}{{\mathbb{C}}}
\newcommand{\sD}{{\mathbb{D}}}
% % Don't use a set called E, because this would be the same as our symbol
% % for expectation.
\newcommand{\sF}{{\mathbb{F}}}
\newcommand{\sG}{{\mathbb{G}}}
\newcommand{\sH}{{\mathbb{H}}}
\newcommand{\sI}{{\mathbb{I}}}
\newcommand{\sJ}{{\mathbb{J}}}
\newcommand{\sK}{{\mathbb{K}}}
\newcommand{\sL}{{\mathbb{L}}}
\newcommand{\sM}{{\mathbb{M}}}
\newcommand{\sN}{{\mathbb{N}}}
\newcommand{\sO}{{\mathbb{O}}}
\newcommand{\sP}{{\mathbb{P}}}
\newcommand{\sQ}{{\mathbb{Q}}}
\newcommand{\sR}{{\mathbb{R}}}
\newcommand{\sS}{{\mathbb{S}}}
\newcommand{\sT}{{\mathbb{T}}}
\newcommand{\sU}{{\mathbb{U}}}
\newcommand{\sV}{{\mathbb{V}}}
\newcommand{\sW}{{\mathbb{W}}}
\newcommand{\sX}{{\mathbb{X}}}
\newcommand{\sY}{{\mathbb{Y}}}
\newcommand{\sZ}{{\mathbb{Z}}}

% % Entries of a matrix
\newcommand{\emSigma}{{\Sigma}}
\newcommand{\emLambda}{{\Lambda}}
\newcommand{\emA}{{A}}
\newcommand{\emB}{{B}}
\newcommand{\emC}{{C}}
\newcommand{\emD}{{D}}
\newcommand{\emE}{{E}}
\newcommand{\emF}{{F}}
\newcommand{\emG}{{G}}
\newcommand{\emH}{{H}}
\newcommand{\emI}{{I}}
\newcommand{\emJ}{{J}}
\newcommand{\emK}{{K}}
\newcommand{\emL}{{L}}
\newcommand{\emM}{{M}}
\newcommand{\emN}{{N}}
\newcommand{\emO}{{O}}
\newcommand{\emP}{{P}}
\newcommand{\emQ}{{Q}}
\newcommand{\emR}{{R}}
\newcommand{\emS}{{S}}
\newcommand{\emT}{{T}}
\newcommand{\emU}{{U}}
\newcommand{\emV}{{V}}
\newcommand{\emW}{{W}}
\newcommand{\emX}{{X}}
\newcommand{\emY}{{Y}}
\newcommand{\emZ}{{Z}}



% % entries of a tensor
% % Same font as tensor, without \bm wrapper
% \newcommand{\etens}[1]{\mathsfit{#1}}
\newcommand{\etens}[1]{  \mathit{\mathsf{#1}}  }
\newcommand{\etLambda}{{\etens{\Lambda}}}
\newcommand{\etA}{{\etens{A}}}
\newcommand{\etB}{{\etens{B}}}
\newcommand{\etC}{{\etens{C}}}
\newcommand{\etD}{{\etens{D}}}
\newcommand{\etE}{{\etens{E}}}
\newcommand{\etF}{{\etens{F}}}
\newcommand{\etG}{{\etens{G}}}
\newcommand{\etH}{{\etens{H}}}
\newcommand{\etI}{{\etens{I}}}
\newcommand{\etJ}{{\etens{J}}}
\newcommand{\etK}{{\etens{K}}}
\newcommand{\etL}{{\etens{L}}}
\newcommand{\etM}{{\etens{M}}}
\newcommand{\etN}{{\etens{N}}}
\newcommand{\etO}{{\etens{O}}}
\newcommand{\etP}{{\etens{P}}}
\newcommand{\etQ}{{\etens{Q}}}
\newcommand{\etR}{{\etens{R}}}
\newcommand{\etS}{{\etens{S}}}
\newcommand{\etT}{{\etens{T}}}
\newcommand{\etU}{{\etens{U}}}
\newcommand{\etV}{{\etens{V}}}
\newcommand{\etW}{{\etens{W}}}
\newcommand{\etX}{{\etens{X}}}
\newcommand{\etY}{{\etens{Y}}}
\newcommand{\etZ}{{\etens{Z}}}

The command in markdown are defined as follows in mathJax

Click to unfold latex macro definition

<script>
window.MathJax = {
  tex: {
    inlineMath: [['$', '$']],
    displayMath: [['$$', '$$']],
    macros: {
      // General commands
      bm: ["\\boldsymbol{#1}", 1],
      sign: "\\operatorname{sign}",
      Tr: "\\operatorname{Tr}",
      E: "\\mathbb{E}",
      KL: "D_{\\mathrm{KL}}",
      NormalDist: "\\mathcal{N}",
      diag: "\\mathrm{diag}",
      Var: "\\mathrm{Var}",
      Cov: "\\mathrm{Cov}",
      standarderror: "\\mathrm{SE}",
      diff: "\\mathrm{d}",
      tran: "^{\\top}",
      inv: "^{-1}",
      rect: "\\mathrm{rectifier}",
      softmax: "\\mathrm{softmax}",
      sigmoid: "\\sigma",
      softplus: "\\zeta",
      R: "\\mathbb{R}",
      emp: "\\tilde{p}",
      lr: "\\alpha",
      reg: "\\lambda",
      Ls: "\\mathcal{L}",

      // Added missing bold Greek matrices
      mBeta: "\\bm{\\beta}",
      mPhi: "\\bm{\\Phi}",
      mLambda: "\\bm{\\Lambda}",
      mSigma: "\\bm{\\Sigma}",

      // Random Greek vector
      rvepsilon: "\\bm{\\epsilon}",

      // Greek Vectors
      vzero: "\\bm{0}",
      vone: "\\bm{1}",
      vmu: "\\bm{\\mu}",
      vnu: "\\bm{\\nu}",
      vtheta: "\\bm{\\theta}",

      va: "\\bm{a}", vb: "\\bm{b}", vc: "\\bm{c}", vd: "\\bm{d}", ve: "\\bm{e}",
      vf: "\\bm{f}", vg: "\\bm{g}", vh: "\\bm{h}", vi: "\\bm{i}", vj: "\\bm{j}",
      vk: "\\bm{k}", vl: "\\bm{l}", vm: "\\bm{m}", vn: "\\bm{n}", vo: "\\bm{o}",
      vp: "\\bm{p}", vq: "\\bm{q}", vr: "\\bm{r}", vs: "\\bm{s}", vt: "\\bm{t}",
      vu: "\\bm{u}", vv: "\\bm{v}", vw: "\\bm{w}", vx: "\\bm{x}", vy: "\\bm{y}", vz: "\\bm{z}",

      // Random vectors
      rva: "\\mathbf{a}", rvb: "\\mathbf{b}", rvc: "\\mathbf{c}", rvd: "\\mathbf{d}", rve: "\\mathbf{e}",
      rvf: "\\mathbf{f}", rvg: "\\mathbf{g}", rvh: "\\mathbf{h}", rvi: "\\mathbf{i}", rvj: "\\mathbf{j}",
      rvk: "\\mathbf{k}", rvl: "\\mathbf{l}", rvm: "\\mathbf{m}", rvn: "\\mathbf{n}", rvo: "\\mathbf{o}",
      rvp: "\\mathbf{p}", rvq: "\\mathbf{q}", rvr: "\\mathbf{r}", rvs: "\\mathbf{s}", rvt: "\\mathbf{t}",
      rvu: "\\mathbf{u}", rvv: "\\mathbf{v}", rvw: "\\mathbf{w}", rvx: "\\mathbf{x}", rvy: "\\mathbf{y}", rvz: "\\mathbf{z}",

      // Random variables (single letters)
      ra: "{\\textnormal{a}}", rb: "{\\textnormal{b}}", rc: "{\\textnormal{c}}", rd: "{\\textnormal{d}}", re: "{\\textnormal{e}}",
      rf: "{\\textnormal{f}}", rg: "{\\textnormal{g}}", rh: "{\\textnormal{h}}", ri: "{\\textnormal{i}}", rj: "{\\textnormal{j}}",
      rk: "{\\textnormal{k}}", rl: "{\\textnormal{l}}", rm: "{\\textnormal{m}}", rn: "{\\textnormal{n}}", ro: "{\\textnormal{o}}",
      rp: "{\\textnormal{p}}", rq: "{\\textnormal{q}}", rr: "{\\textnormal{r}}", rs: "{\\textnormal{s}}", rt: "{\\textnormal{t}}",
      ru: "{\\textnormal{u}}", rv: "{\\textnormal{v}}", rw: "{\\textnormal{w}}", rx: "{\\textnormal{x}}", ry: "{\\textnormal{y}}", rz: "{\\textnormal{z}}",

      // Matrices (bold)
      mA: "\\bm{A}", mB: "\\bm{B}", mC: "\\bm{C}", mD: "\\bm{D}", mE: "\\bm{E}",
      mF: "\\bm{F}", mG: "\\bm{G}", mH: "\\bm{H}", mI: "\\bm{I}", mJ: "\\bm{J}",
      mK: "\\bm{K}", mL: "\\bm{L}", mM: "\\bm{M}", mN: "\\bm{N}", mO: "\\bm{O}",
      mP: "\\bm{P}", mQ: "\\bm{Q}", mR: "\\bm{R}", mS: "\\bm{S}", mT: "\\bm{T}",
      mU: "\\bm{U}", mV: "\\bm{V}", mW: "\\bm{W}", mX: "\\bm{X}", mY: "\\bm{Y}", mZ: "\\bm{Z}",

      // Random Matrices
      rmA: "\\mathbf{A}", rmB: "\\mathbf{B}", rmC: "\\mathbf{C}", rmD: "\\mathbf{D}", rmE: "\\mathbf{E}",
      rmF: "\\mathbf{F}", rmG: "\\mathbf{G}", rmH: "\\mathbf{H}", rmI: "\\mathbf{I}", rmJ: "\\mathbf{J}",
      rmK: "\\mathbf{K}", rmL: "\\mathbf{L}", rmM: "\\mathbf{M}", rmN: "\\mathbf{N}", rmO: "\\mathbf{O}",
      rmP: "\\mathbf{P}", rmQ: "\\mathbf{Q}", rmR: "\\mathbf{R}", rmS: "\\mathbf{S}", rmT: "\\mathbf{T}",
      rmU: "\\mathbf{U}", rmV: "\\mathbf{V}", rmW: "\\mathbf{W}", rmX: "\\mathbf{X}", rmY: "\\mathbf{Y}", rmZ: "\\mathbf{Z}",

      // Elements of random matrices
      ermA: "{\\textnormal{A}}", ermB: "{\\textnormal{B}}", ermC: "{\\textnormal{C}}", ermD: "{\\textnormal{D}}",
      ermE: "{\\textnormal{E}}", ermF: "{\\textnormal{F}}", ermG: "{\\textnormal{G}}", ermH: "{\\textnormal{H}}",
      ermI: "{\\textnormal{I}}", ermJ: "{\\textnormal{J}}", ermK: "{\\textnormal{K}}", ermL: "{\\textnormal{L}}",
      ermM: "{\\textnormal{M}}", ermN: "{\\textnormal{N}}", ermO: "{\\textnormal{O}}", ermP: "{\\textnormal{P}}",
      ermQ: "{\\textnormal{Q}}", ermR: "{\\textnormal{R}}", ermS: "{\\textnormal{S}}", ermT: "{\\textnormal{T}}",
      ermU: "{\\textnormal{U}}", ermV: "{\\textnormal{V}}", ermW: "{\\textnormal{W}}", ermX: "{\\textnormal{X}}",
      ermY: "{\\textnormal{Y}}", ermZ: "{\\textnormal{Z}}",

      // Elements of vectors (Greek)
      evalpha: "\\alpha",
      evbeta: "\\beta",
      evepsilon: "\\epsilon",
      evlambda: "\\lambda",
      evomega: "\\omega",
      evmu: "\\mu",
      evpsi: "\\psi",
      evsigma: "\\sigma",
      evtheta: "\\theta",

      // Elements of vectors (Latin)
      eva: "a", evb: "b", evc: "c", evd: "d", eve: "e",
      evf: "f", evg: "g", evh: "h", evi: "i", evj: "j",
      evk: "k", evl: "l", evm: "m", evn: "n", evo: "o",
      evp: "p", evq: "q", evr: "r", evs: "s", evt: "t",
      evu: "u", evv: "v", evw: "w", evx: "x", evy: "y", evz: "z",

      // Matrix elements
      emSigma: "\\Sigma",
      emLambda: "\\Lambda",
      emA: "A", emB: "B", emC: "C", emD: "D", emE: "E",
      emF: "F", emG: "G", emH: "H", emI: "I", emJ: "J",
      emK: "K", emL: "L", emM: "M", emN: "N", emO: "O",
      emP: "P", emQ: "Q", emR: "R", emS: "S", emT: "T",
      emU: "U", emV: "V", emW: "W", emX: "X", emY: "Y", emZ: "Z",

      // Tensors
      tens: ["\\bm{\\mathsf{#1}}",1],
      tA: "\\tens{A}", tB: "\\tens{B}", tC: "\\tens{C}", tD: "\\tens{D}", tE: "\\tens{E}",
      tF: "\\tens{F}", tG: "\\tens{G}", tH: "\\tens{H}", tI: "\\tens{I}", tJ: "\\tens{J}",
      tK: "\\tens{K}", tL: "\\tens{L}", tM: "\\tens{M}", tN: "\\tens{N}", tO: "\\tens{O}",
      tP: "\\tens{P}", tQ: "\\tens{Q}", tR: "\\tens{R}", tS: "\\tens{S}", tT: "\\tens{T}",
      tU: "\\tens{U}", tV: "\\tens{V}", tW: "\\tens{W}", tX: "\\tens{X}", tY: "\\tens{Y}", tZ: "\\tens{Z}",

      // Graph (calligraphic)
      gA: "\\mathcal{A}", gB: "\\mathcal{B}", gC: "\\mathcal{C}", gD: "\\mathcal{D}", gE: "\\mathcal{E}",
      gF: "\\mathcal{F}", gG: "\\mathcal{G}", gH: "\\mathcal{H}", gI: "\\mathcal{I}", gJ: "\\mathcal{J}",
      gK: "\\mathcal{K}", gL: "\\mathcal{L}", gM: "\\mathcal{M}", gN: "\\mathcal{N}", gO: "\\mathcal{O}",
      gP: "\\mathcal{P}", gQ: "\\mathcal{Q}", gR: "\\mathcal{R}", gS: "\\mathcal{S}", gT: "\\mathcal{T}",
      gU: "\\mathcal{U}", gV: "\\mathcal{V}", gW: "\\mathcal{W}", gX: "\\mathcal{X}", gY: "\\mathcal{Y}", gZ: "\\mathcal{Z}",

      // Sets
      sA: "\\mathbb{A}", sB: "\\mathbb{B}", sC: "\\mathbb{C}", sD: "\\mathbb{D}",
      sF: "\\mathbb{F}", sG: "\\mathbb{G}", sH: "\\mathbb{H}", sI: "\\mathbb{I}", sJ: "\\mathbb{J}",
      sK: "\\mathbb{K}", sL: "\\mathbb{L}", sM: "\\mathbb{M}", sN: "\\mathbb{N}", sO: "\\mathbb{O}",
      sP: "\\mathbb{P}", sQ: "\\mathbb{Q}", sR: "\\mathbb{R}", sS: "\\mathbb{S}", sT: "\\mathbb{T}",
      sU: "\\mathbb{U}", sV: "\\mathbb{V}", sW: "\\mathbb{W}", sX: "\\mathbb{X}", sY: "\\mathbb{Y}", sZ: "\\mathbb{Z}"
    }
  }
};
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