After reviewing the behavioral studies of working memory and of the cellular substrate of the latter, we argue that metastable states constitute candidates for the type of transient information storage required by working memory. We then present a simple neural network model made of stochastic units whose synapses exhibit short-term facilitation. The Markov process dynamics of this model was specifically designed to be analytically tractable, simple to simulate numerically and to exhibit a quasi-stationary distribution (QSD). Since the state space is finite this QSD is also a Yaglom limit, which allows us to bridge the gap between quasi-stationarity and metastability by considering the relative orders of magnitude of the relaxation and absorption times. We present first analytical results: characterization of the absorbing region of the Markov process, irreducibility outside this absorbing region and consequently existence and uniqueness of a QSD. We then apply Perron-Frobenius spectral analysis to obtain any specific QSD, and design an approximate method for the first moments of this QSD when the exact method is intractable. Finally we use these methods to study the relaxation time toward the QSD and establish numerically the memorylessness of the time of extinction.
Topographic maps are a brain structure connecting pre-synpatic and post-synaptic brain regions. Topographic development is dependent on Hebbian-based plasticity mechanisms working in conjunction with spontaneous patterns of neural activity generated in the pre-synaptic regions. Studies performed in mouse have shown that these spontaneous patterns can exhibit complex spatial-temporal structures which existing models cannot incorporate. Neural field theories are appropriate modelling paradigms for topographic systems due to the dense nature of the connections between regions and can be augmented with a plasticity rule general enough to capture complex time-varying structures. We propose a theoretical framework for studying the development of topography in the context of complex spatial-temporal activity fed-forward from the pre-synaptic to post-synaptic regions. Analysis of the model leads to an analytic solution corroborating the conclusion that activity can drive the refinement of topographic projections. The analysis also suggests that biological noise is used in the development of topography to stabilise the dynamics. MCMC simulations are used to analyse and understand the differences in topographic refinement between wild-type and the $\beta2$ knock-out mutant in mice. The time scale of the synaptic plasticity window is estimated as $0.56$ seconds in this context with a model fit of $R^2 = 0.81$.
Our sensory systems transform external signals into neural activity, thereby producing percepts. We are endowed with an intuitive notion of similarity between percepts, that need not reflect the proximity of the physical properties of the corresponding external stimuli. The quantitative characterization of the geometry of percepts is therefore an endeavour that must be accomplished behaviorally. Here we characterized the geometry of color space using discrimination and matching experiments. We proposed an individually tailored metric defined in terms of the minimal chromatic difference required for each observer to differentiate a stimulus from its surround. Next, we showed that this perceptual metric was particularly adequate to describe two additional experiments, since it revealed the natural symmetry of perceptual computations. In one of the experiments, observers were required to discriminate two stimuli surrounded by a chromaticity that differed from that of the tested stimuli. In the perceptual coordinates, the change in discrimination thresholds induced by the surround followed a simple law that only depended on the perceptual distance between the surround and each of the two compared stimuli. In the other experiment, subjects were asked to match the color of two stimuli surrounded by two different chromaticities. Again, in the perceptual coordinates the induction effect produced by surrounds followed a simple, symmetric law. We conclude that the individually-tailored […]