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parameters. As is shown in the figure, there is a monotonic, nearly linear,
increase in the rate of SBE. As the network matures, it eventually reaches a
steady state of a constant average rate. In addition, there is a gradual increase in
the intensity of SBEs, as reflected by all three measures of SBE intensity: number
of neurons in SBE, duration of activation time τ
act
and spike-train duration τ
st
,
which increase monotonically with the culture age.
Fig. 12.4. Increase of SBE intensity in an immature developing network. The plots show the SBE
firing rate and three measures of SBE intensity for a developing network. This network began to
show activity at around 3-4 DIV, and the first synchronized events (within a window of 100 msec)
of at least 3 neurons at 5 DIV. The plot on the far left is of the firing rate of SBE following 3 days
from the first appearing SBE. The rest of the plots show the measures of SBE intensity for the same
time period. The measures are (from left to right): number of neurons in SBE, duration of activation
time (τ
act
) and spike-train duration (τ
st
).
After few more days the network reaches a mature state, in which the activity
shows complex patterns of SBE firing. In Segev
et al
. (2002) it was shown that a
mature network, monitored over long periods of time (days and weeks), will
show non trivial statistics of SBE rate (measured by inter-burst-interval,
IBI
) and
its derivatives. In their article, Segev
et al
. (2002) show that the derivative of the
IBI
s follow a Lévy distribution (Bertoin, 1996) which is characterized by the
distribution's tail that decreases on many time scales, and the
IBI
s power
spectrum covers a wide range of frequencies. This latter result hints to a complex
dynamics of the network and the ability of the culture to serve as a template for
long and short term memory. In Wagenaar
et al
. (2006) it was also shown that a
network never really reaches a steady state behavior with stationary statistics.
The above experimental observations of scale-free collective activity can be
explained within the framework of generative network modeling, as detailed in
Volman
et al.
(2004). Bursting events in these model networks emerge as some
spikes are spontaneously generated by background noise current, and spread to
other neurons through synapses that adjust their strength in an activity-related
way. As soon as inhibitory neurons are recruited, the collective activity is
terminated. It was shown that the Levy distribution in individual neuronal intra-
