Markdown Example

Links

Markdown quick reference

Table (Playing with Kaggle; uses Markdown includes)

--- snip ---

--- snap ---

(1) augmented: one additional variant per image rotated randomly in [-5,5] degree.
(2) bn: batch-norm

Mathematics

Inline Math: $f_{i}(x) = \int_{\tau(\pi)}^\infty e(x,y)dy$

Display Math:

$$\begin{bmatrix} a_{11} & a_{12} & \dots \\ \vdots & \ddots & \\ a_{n1} & & a_{nn} \end{bmatrix}$$

Inline Math: $(\Omega,\mathcal{F},P) \coloneqq (\Omega^+\times\Omega^-,\mathcal{F^+}\otimes\mathcal{F^-},P^+\times P^-)$

Display Math:

The Wiener process in $(\Omega,\mathcal{F},P)$ is defined by

$$\omega(t) \coloneqq \left\{ \begin{array}{cc} (\omega^+(t),0) & t\geq 0 \\ (0,\omega^-(t)) & t<0 \end{array} \right.$$

More math...

$$\tag{3.1a} \begin{aligned} dy_t &= \sum_{i=1}^n \frac{x_t^i}{\|x_t\|^2} \left( \sum_{j=1}^n u_{ij} x_t^i\,dt + \sum_{k=1}^m \sum_{j=1}^n v_{ij}^k x_t^j\circ dW_t^k\right) + \cdots\\ \cdots &+ \frac{1}{2} \sum_{i,j}^n \left( \frac{\delta_{ij}}{\|x_t\|^2} - \frac{2x_t^i x_t^j}{\|x_t\|^4} \right)\; \sum_k^m \sum_{l,p}^n v_{il}^k v_{jp}^k\, x_t^l x_t^p\;dt \end{aligned}$$

With $z_t \coloneqq \frac{x_t}{\|x_t\|}$ we get the following differential equation on the unit sphere:

$$\tag{3.1b} \begin{aligned} y_t &= y_0 + \int_0^t z_t^TUz_t- \|z_t\|^{-2} z_t^T\hat{V}\hat{V}^T z_t + \frac{1}{2}\text{ trace }(\hat{V}\hat{V}^T)\,dt +\cdots\\ \cdots &+ \sum_{k=1}^m \int_0^t z_t^TV^kz_t\circ dW_t^k \end{aligned}$$

Outline as partial TeX file inclusion

Line block - takes only the inner part of a LaTeX display-math environment by specifying row delimiters for the included LaTeX file:

--- snip --- $$\begin{aligned} z &= z(x, y)\\ x &= x(s_1, s_2)\\ y &= y(t_1, t_2)\\ s_i &= s_i(w) \; \forall i \in \{1,2\} \\ t_i &= t_i(w) \; \forall i \in \{1,2\} \end{aligned}$$ --- snap ---

Single line (as inline): start include -> ${\partial z\over\partial w}={\partial z\over\partial x}\cdot\Bigg({\partial x\over\partial s_1}\cdot{\partial s_1\over\partial w} + {\partial x\over\partial s_2}\cdot{\partial s_2\over\partial w}\Bigg) + {\partial z\over\partial y}\cdot\Bigg({\partial y\over\partial t_1}\cdot{\partial t_1\over\partial w} + {\partial y\over\partial t_2}\cdot{\partial t_2\over\partial w}\Bigg)$ <- stop include

Footnotes

Footnotes are possible, like using ¹ and ².

Citations

• Cited text 1: (Touchette, 2012)
• Cited text 2³: Dematteis et al. (2018)

SVG Image

Embedded using Markdown extension (attr_list) and table (for caption):

Neuron image - 80%

Code

Verbatim file inclusion

# include example

from torch.utils.data import TensorDataset
from torch import Tensor, LongTensor, FloatTensor


def loadData(path) -> Tuple[np.ndarray, np.ndarray]:
    '''
    Load data from kaggle mnist set.
    '''
    # Read
    df = pd.read_csv(str(path))  # 40.000 entries
    # tdata = pd.read_csv(data_raw_dir + sep + 'train.csv') # 28.000 entries

    has_labels = True if 'label' in df.columns else False

Normal code block

from torch.utils.data import TensorDataset
from torch import Tensor, LongTensor, FloatTensor


def loadData(path) -> Tuple[np.ndarray, np.ndarray]:
    '''
    Load data from kaggle mnist set.

    path -- input csv

    Return scaled images [0,1] and labels (if available)
    as numpy arrays (dtype: float32, int64)
    '''
    # Read
    df = pd.read_csv(str(path))  # 40.000 entries
    # tdata = pd.read_csv(data_raw_dir + sep + 'train.csv') # 28.000 entries

    has_labels = True if 'label' in df.columns else False

Some inline code.