Table 2.

List of variables and mathematical notation used in this article

Xj Discrete random variable representing primary input j(j = 1,2,3)
Xj Specific activity level of primary input
nx Number of primary inputs (= 3)
X Discrete random vector representing primary input [X1X2X3]
Yk Discrete random variable representing modulatory input k(k = 1,2,3)
yk Specific activity level of modulatory input
ny Number of modulatory inputs (= 3)
Y Discrete random vector representing modulatory input [Y1Y2Y3]
Zi Random variable specifying activity of DSC unit i (i = 1,2,..., 100)
zi Specific activity level of DSC unit i
nz Number of DSC units (= 100)
T Random variable representing the target
t Target state (t = 0,1,...., 7)
ps Modality-specific target probability
pc Cross-modal target probability (pc = ½ − ps)
px0, px1 Spontaneous and driven activation probabilities for primary input Xj
py0, py1 Spontaneous and driven activation probabilities for modulatory input Yk
p Probability that a binary random variable takes value 1
n Total number of binary random variables for binomial process
b(n, p) Binomial distribution with parameters n and p
r Number of binary variables taking state 1 for binomial process
uij Unmodulated weight of primary input j onto DSC unit i
Wij Modulated weight of primary input j onto DSC unit i
Vijk Weight of the modulatory input k onto the primary input connection uij
dijk Dummy variable for accumulating Vijk
α Learning rate for stage-one training
β Learning rate for stage-two training
θu Primary weight threshold for stage-one training
θx Primary input threshold for stage-two training
θy Modulatory input threshold for stage-two training
θz DSC unit threshold for stage-two training
ψ Sum of active DSC units with activity zi exceeding threshold θz
θl DSC unit threshold for information gain computation
h Index for DSC units in a neighborhood
P Probability
Dx Kullback-Leibler divergence measure for primary input
Dy Kullback-Leibler divergence measure for modulatory input
I Information in bits
H Entropy in bits
ϕ Tonic, bias input (= 10)
γ Squashing function sensitivity (= ⅕)
← Update symbol
exp Exponential
Σ Summation
! Factorial