How single neuron properties shape chaotic dynamics and signal transmission in random neural networks

While most models of randomly connected networks assume nodes with simple dynamics, nodes in realistic highly connected networks, such as neurons in the brain, exhibit intrinsic dynamics over multiple timescales. We analyze how the dynamical properties of nodes (such as single neurons) and recurrent connections interact to shape the effective dynamics in large randomly connected networks. A novel dynamical mean-field theory for strongly connected networks of multi-dimensional rate units shows that the power spectrum of the network activity in the chaotic phase emerges from a nonlinear sharpening of the frequency response function of single units. For the case of two-dimensional rate units with strong adaptation, we find that the network exhibits a state of "resonant chaos", characterized by robust, narrow-band stochastic oscillations. The coherence of stochastic oscillations is maximal at the onset of chaos and their correlation time scales with the adaptation timescale of single units. Surprisingly, the resonance frequency can be predicted from the properties of isolated units, even in the presence of heterogeneity in the adaptation parameters. In the presence of these internally-generated chaotic fluctuations, the transmission of weak, low-frequency signals is strongly enhanced by adaptation, whereas signal transmission is not influenced by adaptation in the non-chaotic regime. Our theoretical framework can be applied to other mechanisms at the level of single nodes, such as synaptic filtering, refractoriness or spike synchronization. These results advance our understanding of the interaction between the dynamics of single units and recurrent connectivity, which is a fundamental step toward the description of biologically realistic network models in the brain, or, more generally, networks of other physical or man-made complex dynamical units

Optimal stimulation protocol in a bistable synaptic consolidation model

Consolidation of synaptic changes in response to neural activity is thought to be fundamental for memory maintenance over a timescale of hours. In experiments, synaptic consolidation can be induced by repeatedly stimulating presynaptic neurons. However, the effectiveness of such protocols depends crucially on the repetition frequency of the stimulations and the mechanisms that cause this complex dependence are unknown. Here we propose a simple mathematical model that allows us to systematically study the interaction between the stimulation protocol and synaptic consolidation. We show the existence of optimal stimulation protocols for our model and, similarly to LTP experiments, the repetition frequency of the stimulation plays a crucial role in achieving consolidation. Our results show that the complex dependence of LTP on the stimulation frequency emerges naturally from a model which satisfies only minimal bistability requirements.Comment: 23 pages, 6 figure

Analysis of data systems requirements for global crop production forecasting in the 1985 time frame

Data systems concepts that would be needed to implement the objective of the global crop production forecasting in an orderly transition from experimental to operational status in the 1985 time frame were examined. Information needs of users were converted into data system requirements, and the influence of these requirements on the formulation of a conceptual data system was analyzed. Any potential problem areas in meeting these data system requirements were identified in an iterative process

Nonnormal amplification in random balanced neuronal networks

In dynamical models of cortical networks, the recurrent connectivity can amplify the input given to the network in two distinct ways. One is induced by the presence of near-critical eigenvalues in the connectivity matrix W, producing large but slow activity fluctuations along the corresponding eigenvectors (dynamical slowing). The other relies on W being nonnormal, which allows the network activity to make large but fast excursions along specific directions. Here we investigate the tradeoff between nonnormal amplification and dynamical slowing in the spontaneous activity of large random neuronal networks composed of excitatory and inhibitory neurons. We use a Schur decomposition of W to separate the two amplification mechanisms. Assuming linear stochastic dynamics, we derive an exact expression for the expected amount of purely nonnormal amplification. We find that amplification is very limited if dynamical slowing must be kept weak. We conclude that, to achieve strong transient amplification with little slowing, the connectivity must be structured. We show that unidirectional connections between neurons of the same type together with reciprocal connections between neurons of different types, allow for amplification already in the fast dynamical regime. Finally, our results also shed light on the differences between balanced networks in which inhibition exactly cancels excitation, and those where inhibition dominates.Comment: 13 pages, 7 figure

Event-driven simulations of a plastic, spiking neural network

We consider a fully-connected network of leaky integrate-and-fire neurons with spike-timing-dependent plasticity. The plasticity is controlled by a parameter representing the expected weight of a synapse between neurons that are firing randomly with the same mean frequency. For low values of the plasticity parameter, the activities of the system are dominated by noise, while large values of the plasticity parameter lead to self-sustaining activity in the network. We perform event-driven simulations on finite-size networks with up to 128 neurons to find the stationary synaptic weight conformations for different values of the plasticity parameter. In both the low and high activity regimes, the synaptic weights are narrowly distributed around the plasticity parameter value consistent with the predictions of mean-field theory. However, the distribution broadens in the transition region between the two regimes, representing emergent network structures. Using a pseudophysical approach for visualization, we show that the emergent structures are of "path" or "hub" type, observed at different values of the plasticity parameter in the transition region.Comment: 9 pages, 6 figure

Triplets of Spikes in a Model of Spike Timing-Dependent Plasticity

Classical experiments on spike timing-dependent plasticity (STDP) use a protocol based on pairs of presynaptic and postsynaptic spikes repeated at a given frequency to induce synaptic potentiation or depression. Therefore, standard STDP models have expressed the weight change as a function of pairs of presynaptic and postsynaptic spike. Unfortunately, those paired-based STDP models cannot account for the dependence on the repetition frequency of the pairs of spike. Moreover, those STDP models cannot reproduce recent triplet and quadruplet experiments. Here, we examine a triplet rule (i.e., a rule which considers sets of three spikes, i.e., two pre and one post or one pre and two post) and compare it to classical pair-based STDP learning rules. With such a triplet rule, it is possible to fit experimental data from visual cortical slices as well as from hippocampal cultures. Moreover, when assuming stochastic spike trains, the triplet learning rule can be mapped to a Bienenstock–Cooper–Munro learning rule

Competing synapses with two timescales: a basis for learning and forgetting

Competitive dynamics are thought to occur in many processes of learning involving synaptic plasticity. Here we show, in a game theory-inspired model of synaptic interactions, that the competition between synapses in their weak and strong states gives rise to a natural framework of learning, with the prediction of memory inherent in a timescale for `forgetting' a learned signal. Among our main results is the prediction that memory is optimized if the weak synapses are really weak, and the strong synapses are really strong. Our work admits of many extensions and possible experiments to test its validity, and in particular might complement an existing model of reaching, which has strong experimental support.Comment: 7 pages, 3 figures, to appear in Europhysics Letter

Adherent carbon film deposition by cathodic arc with implantation

A method of improving the adhesion of carbon thin films deposited using a cathodic vacuum arc by the use of implantation at energies up to 20 keV is described. A detailed analysis of carbon films deposited onto silicon in this way is carried out using complementary techniques of transmission electron microscopy and x-ray photoelectron spectroscopy (XPS) is presented. This analysis shows that an amorphous mixing layer consisting of carbon and silicon is formed between the grown pure carbon film and the crystalline silicon substrate. In the mixing layer, it is shown that some chemical bonding occurs between carbon and silicon. Damage to the underlying crystalline silicon substrate is observed and believed to be caused by interstitial implanted carbon atoms which XPS shows are not bonded to the silicon. The effectiveness of this technique is confirmed by scratch testing and by analysis with scanning electron microscopy which shows failure of the silicon substrate occurs before delamination of the carbon film