Nomenclature:

PCA: Principal Component Analysis
ICA: Independent Component Analysis
pdf: probability density function
Variables and constants:
i: General-purpose index, also: imaginary unit
m: Dimension of the observed data
n: Dimension of the transformed component vector
t: Time or iteration index
x and y: General-purpose scalar random variables
y_i: Output of the i-th neuron in a neural network
$\alpha$: A scalar constant
$\mu$: Learning rate constant or sequence
All the vectors are printed in boldface lowercase letters, and are column vectors:
${\bf x}$: Observed data, an m-dimensional random vector
Also: the input vector of a neural network
${\bf s}$: n-dimensional random vector of transformed components s_i
${\bf n}$: m-dimensional random noise vector
${\bf w}$: m-dimensional constant vector
${\bf w}_i$: Weight vectors of a neural network indexed by i
${\bf y}$: m-dimensional general-purpose random vector
Also: the output vector of a neural network
All the matrices are printed in boldface capital letters:
${\bf A}$: The constant $m\times n$ mixing matrix in the ICA model
${\bf B}$: A transformed $m\times m$ mixing matrix
${\bf C}$: Covariance matrix of ${\bf x}$, ${\bf C}=E\{{\bf x}{\bf x}^T\}$
${\bf W}$: The weight matrix of an artificial neural network, with rows ${\bf w}_i^T$
Also: A general transformation matrix
Functions:
$E\{.\}$: Mathematical expectation
f(.): A probability density function
f_i(.): Marginal probability density functions
$\hat{f}(.)$: The characteristic function of a random variable
g(.): A scalar non-linear function
H(.): Differential entropy
I(.): Mutual information
J(.): Negentropy
$\delta(.)$: Kullback-Leibler divergence
J_G(.): Generalized contrast function
${\bf f}(.)$: A general transformation from R^m to Rⁿ
h(t): A FIR filter
$\kappa_i(.)$: The i-th order cumulant of a scalar random variable
$\:\mbox{kurt}\:(.)$: Kurtosis, or fourth-order cumulant
$\mbox{cum}\:(...)$: Cumulant (cross-cumulant) of several random variables
Other notation:
$\Delta$: Change in parameter
$\propto$: Proportional to (proportionality constant may change with t)
f': First derivative of function f