personality is disintegrated. Prominent atrophy of predominantly frontal and temporal cor-
tex is observed in neuroimaging studies and large amounts of senile plaques and neurofibril-
liary tangles are found in the brain.
Although new discoveries related to possible AD causes are reported every month real
causes and pathogenesis is still unknown and definitive diagnosis is made only after au-
topsy. The disease is always progressive, without remissions, and with great variability: life
expectancy ranges between 1 and 25 years. Only a few drugs are available for Alzheimer
treatment (for example Cognex and Aricept). They do not slow the progress of AD but are
aimed at improving and stabilizing memory and cognitive state of the patient by helping to
retain and utilize the neurotransmitter acetylcholine.
3. Synaptic deletion and compensation model
Two models of pathogenesis of AD have been proposed, both focusing on synaptic
processes and their role in memory maintenance. The “synaptic deletion and compensation”
model of Horn et al. [12] has been developed further by Ruppin and Reggia [25]. It is based
on experimental observation that in the brains of AD patients the density of synaptic con-
nections per unit of cortical volume decreases with progress of the disease, while the re-
maining synapses increase in size, perhaps trying to compensate for synaptic deletion. In
feedforward neural models pruning is frequently used to delete weak synaptic connections
at the expense of growing values of the remaining connections, necessary for realization of
strongly non-linear behavior. How do these two processes - synaptic deletion and compen-
sation - influence memory deterioration? What are the best compensation strategies that
may slow down this process?
The simplest associative memory models are based on Hopfield networks. Assuming
that the synaptic matrix Wij determines the strength of connections between neurons i and j,
each of the N neurons has threshold Θi for firing and is in one of the two states Vi = ±1, the
external inputs are Ei, the simplest network dynamics is defined by
Ґ 'ɪ
V(t +1) = sgn(Ii(t +1)) = sgn ∑WjVj(t)-Θi+ Ei I (1)
V j=1 √
Memory patterns are point-attractor stationary states of this dynamics corresponding to
the minima of the energy function:
1N
E (V )=- 2 ∑ WjVy1 (2)
2 i≠j