Search

Bernstein Conference 2021 abstract. http://bernstein-conference.de

Bernstein Conference 2021 abstract. http://bernstein-conference.de

Bernstein Conference 2021 abstract. http://bernstein-conference.de

Bernstein Conference 2021 abstract. http://bernstein-conference.de

Bernstein Conference 2021 abstract. http://bernstein-conference.de

Bernstein Conference 2021 abstract. http://bernstein-conference.de

Bernstein Conference 2021 abstract. http://bernstein-conference.de

Bernstein Conference 2021 abstract. http://bernstein-conference.de

Bernstein Conference 2021 abstract. http://bernstein-conference.de

Bernstein Conference 2021 abstract. http://bernstein-conference.de

Bernstein Conference 2021 abstract. http://bernstein-conference.de

Bernstein Conference 2021 abstract. http://bernstein-conference.de

Bernstein Conference 2021 abstract. http://bernstein-conference.de

Bernstein Conference 2021 abstract. http://bernstein-conference.de

Bernstein Conference 2021 abstract. http://bernstein-conference.de

Bernstein Conference 2021 abstract. http://bernstein-conference.de

Bernstein Conference 2021 abstract. http://bernstein-conference.de

Bernstein Conference 2021 abstract. http://bernstein-conference.de

Bernstein Conference 2021 abstract. http://bernstein-conference.de

Bernstein Conference 2021 abstract. http://bernstein-conference.de

Bernstein Conference 2021 abstract. http://bernstein-conference.de

Bernstein Conference 2021 abstract. http://bernstein-conference.de

Bernstein Conference 2021 abstract. http://bernstein-conference.de

Bernstein Conference 2021 abstract. http://bernstein-conference.de

Bernstein Conference 2021 abstract. http://bernstein-conference.de

Bernstein Conference 2021 abstract. http://bernstein-conference.de

Recurrent network models are instrumental in investigating how behaviorally-relevant computations emerge from collective neural dynamics. A recently developed class of models based on low-rank connectivity provides an analytically tractable framework for understanding of how connectivity structure determines the geometry of low-dimensional dynamics and the ensuing computations. Such models however lack some fundamental biological constraints, and in particular represent individual neurons in terms of abstract units that communicate through continuous firing rates rather than discrete action potentials. Here we examine how far the theoretical insights obtained from low-rank rate networks transfer to more biologically plausible networks of spiking neurons. Adding a low-rank structure on top of random excitatory-inhibitory connectivity, we systematically compare the geometry of activity in networks of integrate-and-fire neurons to rate networks with statistically equivalent low-rank connectivity. We show that the mean-field predictions of rate networks allow us to identify low-dimensional dynamics at constant population-average activity in spiking networks, as well as novel non-linear regimes of activity such as out-of-phase oscillations and slow manifolds. We finally exploit these results to directly build spiking networks that perform nonlinear computations.Author summaryBehaviorally relevant information processing is believed to emerge from interactions among neurons forming networks in the brain, and computational modeling is an important approach for understanding this process. Models of neuronal networks have been developed at different levels of detail, with typically a trade off between analytic tractability and biological realism. The relation between network connectivity, dynamics and computations is best understood in abstract models where individual neurons are represented as simplified units with continuous firing activity. Here we examine how far the results obtained in a specific, analytically-tractable class of rate models extend to more biologically realistic spiking networks where neurons interact through discrete action potentials. Our results show that abstract rate models provide accurate predictions for the collective dynamics and the resulting computations in more biologically faithful spiking networks.

Bernstein Conference 2021 abstract. http://bernstein-conference.de

Bernstein Conference 2021 abstract. http://bernstein-conference.de

Bernstein Conference 2021 abstract. http://bernstein-conference.de

Bernstein Conference 2021 abstract. http://bernstein-conference.de

Bernstein Conference 2021 abstract. http://bernstein-conference.de

Bernstein Conference 2021 abstract. http://bernstein-conference.de

Bernstein Conference 2021 abstract. http://bernstein-conference.de

Bernstein Conference 2021 abstract. http://bernstein-conference.de

Bernstein Conference 2021 abstract. http://bernstein-conference.de

Bernstein Conference 2021 abstract. http://bernstein-conference.de

We present a Spiking Neural Network (SNN) based Sparse Distributed Memory (SDM) implemented on the Nengo framework. We have based our work on previous work by Furber et al, 2004, implementing SDM using N-of-M codes. As an integral part of the SDM design, we have implemented Correlation Matrix Memory (CMM) using SNN on Nengo. Our SNN implementation uses Leaky Integrate and Fire (LIF) spiking neuron models on Nengo. Our objective is to understand how well SNN-based SDMs perform in comparison to conventional SDMs. Towards this, we have simulated both conventional and SNN-based SDM and CMM on Nengo. We observe that SNN-based models perform similarly as the conventional ones. In order to evaluate the performance of different SNNs, we repeated the experiment using Adaptive-LIF, Spiking Rectified Linear Unit, and Izhikevich models and obtained similar results. We conclude that it is indeed feasible to develop some types of associative memories using spiking neurons whose memory capacity and other features are similar to the performance without SNNs. Finally we have implemented an application where MNIST images, encoded with N-of-M codes, are associated with their labels and stored in the SNN-based SDM., 8 pages, 11 figures, accepted as poster in Bernstein Conference 2021

We analyze the influence of an external sound source in a network of FitzHugh-Nagumo oscillators with empirical structural connectivity measured in healthy human subjects. We report synchronization patterns, induced by the frequency of the sound source. We show that the level of synchrony can be enhanced by choosing the frequency of the sound source and its amplitude as control parameters for synchronization patterns. We discuss a minimum model elucidating the modalities of the influence of music on the human brain., 6 Figures

Neural population dynamics are often highly coordinated, allowing task-related computations to be understood as neural trajectories through low-dimensional subspaces. How the network connectivity and input structure give rise to such activity can be investigated with the aid of low-rank recurrent neural networks, a recently-developed class of computational models which offer a rich theoretical framework linking the underlying connectivity structure to emergent low-dimensional dynamics. This framework has so far relied on the assumption of all-to-all connectivity, yet cortical networks are known to be highly sparse. Here we investigate the dynamics of low-rank recurrent networks in which the connections are randomly sparsified, which makes the network connectivity formally full-rank. We first analyse the impact of sparsity on the eigenvalue spectrum of low-rank connectivity matrices, and use this to examine the implications for the dynamics. We find that in the presence of sparsity, the eigenspectra in the complex plane consist of a continuous bulk and isolated outliers, a form analogous to the eigenspectra of connectivity matrices composed of a low-rank and a full-rank random component. This analogy allows us to characterise distinct dynamical regimes of the sparsified low-rank network as a function of key network parameters. Altogether, we find that the low-dimensional dynamics induced by low-rank connectivity structure are preserved even at high levels of sparsity, and can therefore support rich and robust computations even in networks sparsified to a biologically-realistic extent.Author summaryIn large networks of neurons, the activity displayed by the population depends on the strength of the connections between each neuron. In cortical regions engaged in cognitive tasks, this population activity is often seen to be highly coordinated and low-dimensional. A recent line of theoretical work explores how such coordinated activity can arise in a network of neurons in which the matrix defining the connections is constrained to be mathematically low-rank. Until now, this connectivity structure has only been explored in fully-connected networks, in which every neuron is connected to every other. However, in the brain, network connections are often highly sparse, in the sense that most neurons do not share direct connections. Here, we test the robustness of the theoretical framework of low-rank networks to the reality of sparsity present in biological networks. By mathematically analysing the impact of removing connections, we find that the low-dimensional dynamics previously found in dense low-rank networks can in fact persist even at very high levels of sparsity. This has promising implications for the proposal that complex cortical computations which appear to rely on low-dimensional dynamics may be underpinned by a network which has a fundamentally low-rank structure, albeit with only a small fraction of possible connections present.

Bernstein Conference 2021 abstract. http://bernstein-conference.de

A theoretical framework describing the set of interactions between neurons in the brain, or functional connectivity, should include dynamical functions representing the propagation of signal from one neuron to another. Green's functions and response functions are natural candidates for this but, while they are conceptually very useful, they are usually defined only for linear time-translationally invariant systems. The brain, instead, behaves nonlinearly and in a time-dependent way. Here, we use nonequilibrium Green's functions to describe the time-dependent functional connectivity of a continuous-variable network of neurons. We show how the connectivity is related to the measurable response functions, and provide two illustrative examples via numerical calculations, inspired from $\textit{C. elegans}$., 6 pages (incl. bibliography), 2 figures + supplement (6 pages)

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Chaos 30, 123130 (2020) and may be found at https://doi.org/10.1063/5.0021420, We study patterns of partial synchronization in a network of FitzHugh���Nagumo oscillators with empirical structural connectivity measured in human subjects. We report the spontaneous occurrence of synchronization phenomena that closely resemble the ones seen during epileptic seizures in humans. In order to obtain deeper insights into the interplay between dynamics and network topology, we perform long-term simulations of oscillatory dynamics on different paradigmatic network structures: random networks, regular nonlocally coupled ring networks, ring networks with fractal connectivities, and small-world networks with various rewiring probability. Among these networks, a small-world network with intermediate rewiring probability best mimics the findings achieved with the simulations using the empirical structural connectivity. For the other network topologies, either no spontaneously occurring epileptic-seizure-related synchronization phenomena can be observed in the simulated dynamics, or the overall degree of synchronization remains high throughout the simulation. This indicates that a topology with some balance between regularity and randomness favors the self-initiation and self-termination of episodes of seizure-like strong synchronization.

Neuroscience is home to concepts and theories with roots in a variety of domains including information theory, dynamical systems theory, and cognitive psychology. Not all of those can be coherently linked, some concepts are incommensurable, and domain-specific language poses an obstacle to integration. Still, conceptual integration is a form of understanding that provides intuition and consolidation, without which progress remains unguided. This paper is concerned with the integration of deterministic and stochastic processes within an information theoretic framework, linking information entropy and free energy to mechanisms of emergent dynamics and self-organization in brain networks. We identify basic properties of neuronal populations leading to an equivariant matrix in a network, in which complex behaviors can naturally be represented through structured flows on manifolds establishing the internal model relevant to theories of brain function. We propose a neural mechanism for the generation of internal models from symmetry breaking in the connectivity of brain networks. The emergent perspective illustrates how free energy can be linked to internal models and how they arise from the neural substrate.

The synchronization of different γ-rhythms arising in different brain areas has been implicated in various cognitive functions. Here, we focus on the effect of the ubiquitous neuronal heterogeneity on the synchronization of ING (interneuronal network gamma) and PING (pyramidal-interneuronal network gamma) rhythms. The synchronization properties of rhythms depends on the response of their collective phase to external input. We therefore determine the macroscopic phase-response curve for finite-amplitude perturbations (fmPRC) of ING- and PING-rhythms in all-to-all coupled networks comprised of linear (IF) or quadratic (QIF) integrate-and-fire neurons. For the QIF networks we complement the direct simulations with the adjoint method to determine the infinitesimal macroscopic PRC (imPRC) within the exact mean-field theory. We show that the intrinsic neuronal heterogeneity can qualitatively modify the fmPRC and the imPRC. Both PRCs can be biphasic and change sign (type II), even though the phase-response curve for the individual neurons is strictly non-negative (type I). Thus, for ING rhythms, say, external inhibition to the inhibitory cells can, in fact, advance the collective oscillation of the network, even though the same inhibition would lead to a delay when applied to uncoupled neurons. This paradoxical advance arises when the external inhibition modifies the internal dynamics of the network by reducing the number of spikes of inhibitory neurons; the advance resulting from this disinhibition outweighs the immediate delay caused by the external inhibition. These results explain how intrinsic heterogeneity allows ING- and PING-rhythms to become synchronized with a periodic forcing or another rhythm for a wider range in the mismatch of their frequencies. Our results identify a potential function of neuronal heterogeneity in the synchronization of coupled γ-rhythms, which may play a role in neural information transfer via communication through coherence., Author summary The interaction of a large number of oscillating units can lead to the emergence of a collective, macroscopic oscillation in which many units oscillate in near-unison or near-synchrony. This has been exploited technologically, e.g., to combine many coherently interacting, individual lasers to form a single powerful laser. Collective oscillations are also important in biology. For instance, the circadian rhythm of animals is controlled by the near-synchronous dynamics of a large number of individually oscillating cells. In animals and humans brain rhythms reflect the coherent dynamics of a large number of neurons and are surmised to play an important role in the communication between different brain areas. To be functionally relevant, these rhythms have to respond to external inputs and have to be able to synchronize with each other. We show that the ubiquitous heterogeneity in the properties of the individual neurons in a network can contribute to that ability. It can allow the external inputs to modify the internal network dynamics such that the network can follow these inputs over a wider range of frequencies. Paradoxically, while an external perturbation may delay individual neurons, their ensuing within-network interaction can overcompensate this delay, leading to an overall advance of the rhythm.

Bernstein Conference 2021 abstract. http://bernstein-conference.de

Bernstein Conference 2022 abstract. http://bernstein-conference.de