A Mathematical Analysis of Memory Lifetime in a Simple Network Model of Memory.

We study the learning of an external signal by a neural network and the time to forget it when this network is submitted to noise. The presentation of an external stimulus to the recurrent network of binary neurons may change the state of the synapses. Multiple presentations of a unique signal lead to its learning. Then, during the forgetting time, the presentation of other signals (noise) may also modify the synaptic weights. We construct an estimator of the initial signal using the synaptic currents and in this way define a probability of error. In our model, these synaptic currents evolve as Markov chains. We study the dynamics of these Markov chains and obtain a lower bound on the number of external stimuli that the network can receive before the initial signal is considered forgotten (probability of error above a given threshold). Our results are based on a finite-time analysis rather than large-time asymptotic. We finally present numerical illustrations of our results.

Structural constraints on the emergence of oscillations in multi-population neural networks.

Oscillations arise in many real-world systems and are associated with both functional and dysfunctional states. Whether a network can oscillate can be estimated if we know the strength of interaction between nodes. But in real-world networks (in particular in biological networks) it is usually not possible to know the exact connection weights. Therefore, it is important to determine the structural properties of a network necessary to generate oscillations. Here, we provide a proof that uses dynamical system theory to prove that an odd number of inhibitory nodes and strong enough connections are necessary to generate oscillations in a single cycle threshold-linear network. We illustrate these analytical results in a biologically plausible network with either firing-rate based or spiking neurons. Our work provides structural properties necessary to generate oscillations in a network. We use this knowledge to reconcile recent experimental findings about oscillations in basal ganglia with classical findings.

Cortex-wide topography of 1/f-exponent in Parkinson's disease.

Parkinson's disease (PD) is a progressive and debilitating brain disorder. Besides the characteristic movement-related symptoms, the disease also causes decline in sensory and cognitive processing. The extent of symptoms and brain-wide projections of neuromodulators such as dopamine suggest that many brain regions are simultaneously affected in PD. To characterise brain-wide disease-related changes in neuronal function, we analysed resting state magnetoencephalogram (MEG) from two groups: PD patients and healthy controls. Besides standard spectral analysis, we quantified the aperiodic components (κ, λ) of the neural activity by fitting a power law κ/fλ - f is the frequency, κ and λ are the fitting parameters-to the MEG power spectrum and studied its relationship with age and Unified Parkinson's Disease Rating Scale (UPDRS). Consistent with previous results, the most significant spectral changes were observed in the high theta/low-alpha band (7-10 Hz) in all brain regions. Furthermore, analysis of the aperiodic part of the spectrum showed that in all but frontal regions λ was significantly larger in PD patients than in control subjects. Our results indicate that PD is associated with significant changes in aperiodic activity across the whole neocortex. Surprisingly, even early sensory areas showed a significantly larger λ in patients than in healthy controls. Moreover, λ was not affected by the Levodopa medication. Finally, λ was positively correlated with patient age but not with UPDRS-III. Because λ is closely associated with excitation-inhibition balance, our results propose new hypotheses about neural correlates of PD in cortical networks.