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Recurrent neural networks (RNNs) with random, but sufficiently strong and balanced coupling display a well known high-dimensional chaotic dynamics. Here, we investigate if externally applied inputs to these RNNs can stabilize globally synchronous, input-dependent solutions, in spite of the strong chaos-inducing coupling. We find that when the balance between excitation and inhibition is exact, that is when the row-sum of the weights is constant and 0, a globally applied input can readily synchronize all neurons onto a synchronous solution. The stability of the synchronous solution is analytically explored in this work with a master stability function. For any synchronous solution to the network dynamics, the conditional Lyapunov spectrum can be readily determined, with the stability of the synchronous solution critically dependent on the largest real eigenvalue component of the RNN weight matrix. We find that the smaller the maximum real component of the weight matrix eigenvalues, the more readily the network synchronizes. Further, the conditional Lyapunov exponents are easily computed numerically for any synchronization signal without simulating the RNN. Finally, for certain oscillatory synchronization signals, the conditional Lyapunov exponents can be determined analytically., Comment: 3 Figures, 12 pages

Real neurons connect to each other non-randomly. How the connectivity of networks of conductance-based neuron models like the classical Hodgkin-Huxley model, or the Morris-Lecar model, impacts synchronizability remains unknown. One powerful tool to resolve the synchronizability of these networks is the Master Stability Function (MSF). Here, we apply and extend the MSF approach to networks of Morris-Lecar neurons with conductance-based coupling to determine under which parameters and graphs synchronous solutions are stable. We consider connectivity graphs with a constant row-sum, where the MSF approach can be readily extended to conductance-based synapses rather than the more well-studied diffusive connectivity case, which primarily applies to gap junction connectivity. In this formulation, the synchronous solution is a single, self-coupled or 'autaptic' neuron. We find that the primary determining parameter for the stability of the synchronous solution is, unsurprisingly, the reversal potential, as it largely dictates the excitatory/inhibitory potential of a synaptic connection. However, the change between "excitatory" and "inhibitory'' synapses is rapid, with only a few millivolts separating stability and instability of the synchronous state for most graphs. We also find that for specific coupling strengths (as measured by the global synaptic conductance), islands of synchronizability in the MSF can emerge for inhibitory connectivity. We verified the stability of these islands by direct simulation of pairs of neurons coupled with eigenvalues in the matching spectrum. These results were robust for different transitions to spiking (Hodgkin Class I vs Class II), which displayed very similar synchronizability characteristics.

Despite great advances in explaining synaptic plasticity and neuron function, a complete understanding of the brain's learning algorithms is still missing. Artificial neural networks provide a powerful learning paradigm through the backpropagation algorithm which modifies synaptic weights by using feedback connections. Backpropagation requires extensive communication of information back through the layers of a network. This has been argued to be biologically implausible and it is not clear whether backpropagation can be realized in the brain. Here we suggest that biophotons guided by axons provide a potential channel for backward transmission of information in the brain. Biophotons have been experimentally shown to be produced in the brain, yet their purpose is not understood. We propose that biophotons can propagate from each post-synaptic neuron to its pre-synaptic one to carry the required information backward. To reflect the stochastic character of biophoton emissions, our model includes the stochastic backward transmission of teaching signals. We demonstrate that a three-layered network of neurons can learn the MNIST handwritten digit classification task using our proposed backpropagation-like algorithm with stochastic photonic feedback. We model realistic restrictions and show that our system still learns the task for low rates of biophoton emission, information-limited (one bit per photon) backward transmission, and in the presence of noise photons. Our results suggest a new functionality for biophotons and provide an alternate mechanism for backward transmission in the brain., Comment: 14 pages, 4 figures

The synchronization of different brain regions is widely observed under both normal and pathological conditions such as epilepsy. However, the relationship between the dynamics of these brain regions, the connectivity between them, and the ability to synchronize remains an open question. We investigated the problem of inter-region synchronization in networks of Wilson-Cowan/Neural field equations with homeostatic plasticity, each of which acts as a model for an isolated brain region. We considered arbitrary connection profiles with only one constraint: the rows of the connection matrices are all identically normalized. We found that these systems often synchronize to the solution obtained from a single, self-coupled neural region. We analyze the stability of this solution through a straightforward modification of the Master Stability Function (MSF) approach and found that synchronized solutions lose stability for connectivity matrices when the second largest positive eigenvalue is sufficiently large, for values of the global coupling parameter that are not too large. This result was numerically confirmed for ring systems and lattices and was also robust to small amounts of heterogeneity in the homeostatic set points in each node. Finally, we tested this result on connectomes obtained from 196 subjects over a broad age range (4-85 years) from the Human Connectome Project. We found that the second largest eigenvalue tended to decrease with age, indicating an increase in synchronizability that may be related to the increased prevalence of epilepsy with old age., Comment: 24 pages, 5 figures

Nowadays a diverse range of physiological data can be captured continuously for various applications in particular wellbeing and healthcare. Such data require efficient methods for classification and analysis. Deep learning algorithms have shown remarkable potential regarding such analyses, however, the use of these algorithms on low-power wearable devices is challenged by resource constraints such as area and power consumption. Most of the available on-chip deep learning processors contain complex and dense hardware architectures in order to achieve the highest possible throughput. Such a trend in hardware design may not be efficient in applications where on-node computation is required and the focus is more on the area and power efficiency as in the case of portable and embedded biomedical devices. This paper presents an efficient time-series classifier capable of automatically detecting effective features and classifying the input signals in real-time. In the proposed classifier, throughput is traded off with hardware complexity and cost using resource sharing techniques. A Convolutional Neural Network (CNN) is employed to extract input features and then a Long-Short-Term-Memory (LSTM) architecture with ternary weight precision classifies the input signals according to the extracted features. Hardware implementation on a Xilinx FPGA confirm that the proposed hardware can accurately classify multiple complex biomedical time series data with low area and power consumption and outperform all previously presented state-of-the-art records. Most notably, our classifier reaches 1.3$\times$ higher GOPs/Slice than similar state of the art FPGA-based accelerators.

Low-dimensional yet rich dynamics often emerge in the brain. Examples include oscillations and chaotic dynamics during sleep, epilepsy, and voluntary movement. However, a general mechanism for the emergence of low dimensional dynamics remains elusive. Here, we consider Wilson-Cowan networks and demonstrate through numerical and analytical work that a type of homeostatic regulation of the network firing rates can paradoxically lead to a rich dynamical repertoire. The dynamics include mixed-mode oscillations, mixed-mode chaos, and chaotic synchronization. This is true for single recurrently coupled node, pairs of reciprocally coupled nodes without self-coupling, and networks coupled through experimentally determined weights derived from functional magnetic resonance imaging data. In all cases, the stability of the homeostatic set point is analytically determined or approximated. The dynamics at the network level are directly determined by the behavior of a single node system through synchronization in both oscillatory and non-oscillatory states. Our results demonstrate that rich dynamics can be preserved under homeostatic regulation or even be caused by homeostatic regulation., Comment: 25 pages, 5 figures

Patterns of waxing and waning oscillations, called spindles, are observed in multiple brain regions during sleep. Spindle are thought to be involved in memory consolidation. The origin of spindle oscillations is ongoing work but experimental results point towards the thalamic reticular nucleus (TRN) as a likely candidate. The TRN is rich in electrical synapses, also called gap junctions, which promote synchrony in neural activity. Moreover, gap junctions undergo activity-dependent long-term plasticity. We hypothesized that gap junction plasticity can modulate spindle oscillations. We developed a computational model of gap junction plasticity in recurrent networks of TRN and thalamocortical neurons (TC). We showed that gap junction coupling can modulate the TRN-TC network synchrony and that gap junction plasticity is a plausible mechanism for the generation of sleep-spindles. Finally, our results are robust to the simulation of pharmacological manipulation of spindles, such as the administration of propofol, an anesthetics known to generate spindles in humans., Comment: arXiv admin note: text overlap with arXiv:1707.02324

Cortical oscillations are thought to be involved in many cognitive functions and processes. Several mechanisms have been proposed to regulate oscillations. One prominent but understudied mechanism is gap-junctional coupling. Gap junctions are ubiquitous in cortex between GABAergic interneurons. Moreover, recent experiments indicate their strength can be modified in an activity-dependent manner, similar to chemical synapses. We hypothesized that activity-dependent gap junction plasticity acts as a mechanism to regulate oscillations in the cortex. We developed a computational model of gap junction plasticity in a recurrent cortical network. We showed that gap junction plasticity can serve as a homeostatic mechanism for oscillations by maintaining a tight balance between two network states: asynchronous irregular activity and synchronized oscillations. This homeostatic mechanism allows for robust communication between neuronal assemblies through two different mechanisms: transient oscillations and frequency modulation. This implies a direct functional role for gap junction plasticity in information transmission in cortex.

Populations of neurons display an extraordinary diversity in the behaviors they affect and display. Machine learning techniques have recently emerged that allow us to create networks of model neurons that display behaviours of similar complexity. Here, we demonstrate the direct applicability of one such technique, the FORCE method, to spiking neural networks. We train these networks to mimic dynamical systems, classify inputs, and store discrete sequences that correspond to the notes of a song. Finally, we use FORCE training to create two biologically motivated model circuits. One is inspired by the zebra-finch and successfully reproduces songbird singing. The second network is motivated by the hippocampus and is trained to store and replay a movie scene. FORCE trained networks reproduce behaviors comparable in complexity to their inspired circuits and yield information not easily obtainable with other techniques such as behavioral responses to pharmacological manipulations and spike timing statistics.

Mean-field systems have been previously derived for networks of coupled, two-dimensional, integrate-and-fire neurons such as the Izhikevich, adapting exponential (AdEx) and quartic integrate and fire (QIF), among others. Unfortunately, the mean-field systems have a degree of frequency error and the networks analyzed often do not include noise when there is adaptation. Here, we derive a one-dimensional partial differential equation (PDE) approximation for the marginal voltage density under a first order moment closure for coupled networks of integrate-and-fire neurons with white noise inputs. The PDE has substantially less frequency error than the mean-field system, and provides a great deal more information, at the cost of analytical tractability. The convergence properties of the mean-field system in the low noise limit are elucidated. A novel method for the analysis of the stability of the asynchronous tonic firing solution is also presented and implemented. Unlike previous attempts at stability analysis with these network types, information about the marginal densities of the adaptation variables is used. This method can in principle be applied to other systems with nonlinear partial differential equations., Comment: 26 Pages, 6 Figures

Mean-field systems have been recently derived that adequately predict the behaviors of large networks of coupled integrate-and-fire neurons [14]. The mean-field system for a network of neurons with spike frequency adaptation is typically a pair of differential equations for the mean adaptation and mean synaptic gating variable of the network. These differential equations are non-smooth, and in particular are piecewise smooth continuous (PWSC). Here, we analyze the smooth and non-smooth bifurcation structure of these equations and show that the system is organized around a pair of co-dimension two bifurcations that involve, respectively, the collision between a Hopf equilibrium point and a switching manifold, and a saddle-node equilibrium point and a switching manifold. These two co-dimension 2 bifurcations can coalesce into a co-dimension 3 non-smooth bifurcation. As the mean-field system we study is a non-generic piecewise smooth continuous system, we discuss possible regularizations of this system and how the bifurcations which occur are related to non-smooth bifurcations displayed by generic PWSC systems., Comment: 35 Pages , 12 figures, 1 table

We analytically derive mean-field models for all-to-all coupled networks of heterogeneous, adapting, two-dimensional integrate and fire neurons. The class of models we consider includes the Izhikevich, adaptive exponential, and quartic integrate and fire models. The heterogeneity in the parameters leads to different moment closure assumptions that can be made in the derivation of the mean-field model from the population density equation for the large network. Three different moment closure assumptions lead to three different mean-field systems. These systems can be used for distinct purposes such as bifurcation analysis of the large networks, prediction of steady state firing rate distributions, parameter estimation for actual neurons, and faster exploration of the parameter space. We use the mean-field systems to analyze adaptation induced bursting under realistic sources of heterogeneity in multiple parameters. Our analysis demonstrates that the presence of heterogeneity causes the Hopf bifurcation associated with the emergence of bursting to change from sub-critical to super-critical. This is confirmed with numerical simulations of the full network for biologically reasonable parameter values. This change decreases the plausibility of adaptation being the cause of bursting in hippocampal area CA3, an area with a sizable population of heavily coupled, strongly adapting neurons., Comment: 39 pages, 12 figures