• attractor
• memory
• neural nteworks
• short-term plasticity
• synaptic dinamics

Neuronal recordings from animals performing memory tasks have revealed
a phenomenon known as selective persistent activity: the presentation of
stimuli to be remembered increase the level of activity of selective (i.e., depending
on the specific stimulus) neuronal populations which then persist
long after stimulus offset. Such persistent activity is considered to be a major
neuronal correlate of short-term memory.
A time-honored theoretical account of persistent activity is the attrac-
tor hypothesis, originated from the first studies of spin-glass inspired neural
network models [1]. According to this hypothesis, the neurons within the
selective populations have strong recurrent excitatory couplings. The resulting
positive feedback, together with the the nonlinearity of the single-cell
response function, allows such populations to have two stable states of activity:
one corresponding to the spontaneous activity, the other (at higher
rate) corresponding to the mnemonic retention of the stimulus.
Since the neuron response function is typically S-shaped, and the recurrent
input is a linear function of the activity, the stable states generically
occur outside the dynamic range of the neuron function, that is near extremely
low or high activity levels. This constitutes a major inconsistency of
the model, as experimental data show that the activity level at which cortical
neurons operate is much lower than saturation.
It is well established that synapses display activity-dependent modulations
of their efficacy, like short-term depression(STD): whenever a neuron
stays active, the intensity of the signals transmitted through its synapses is
gradually reduced[2]. In the thesis we examined the possibility to obtain
bistability far from saturation by making the recurrent excitatory inputs a
non-linear function of the activity through STD.
The study have been carried out within the framework of balanced networks
[3] as it captures essential features of cortical networks activity while remaining
analytically tractable.
The first chapter, after a short summary of the relevant neurophysiological
background, is dedicated to review the standard balanced network model
of binary neurons and its general properties.
In the second chapter, it is illustrated a possible extension of balanced
networks to the attractor framework: reinforcing suitably the excitatory couplings
between the neurons of certain populations, the system can have multiple
stable attractors corresponding to memory states. This allows us to
illustrate the issue of unrealistically high level of activity in memory states.
The remaining chapters contain the original part of the work.
In the third chapter, the phenomenological model which mimics STD is
introduced. As a first step, it is considered a balanced network endowed
with STD in absence of memory-supporting reinforcement of the couplings.
A mean-field description have been derived to characterize the stationary
states of the network; this has been done by neglecting the time delayed
autocorrelations of the neuron’s activities, which have been approximated as
Markov process to obtain a system of equations in closed form. Numerical
simulations of the network show that, despite the approximation, the meanfield
theory gives an excellent quantitative prediction for the system’s order
parameters.
The content of the fourth chapter is the implementation of the STD
synaptic dynamics into the memory model introduced in chapter two and
the extension of the mean-field theory to the scenario with multiple memory
states. The theoretical analysis of the model shows that it’s indeed possible
to produce stable states with biologically plausible levels of activity, far from
saturation, and network simulations confirm the result. Moreover, the network
operates in a regime such that temporal fluctuations and spatial inhomogeneities
of the neuron’s activity are generated by the dynamics (without
the addition of any source of external noise), reproducing the experimentally
observed statistics of neural activity.