The stability of synchronous states is analysed in the context of two populations of inhibitory and excitatory neurons, characterized by different pulse-widths. The problem is reduced to that of determining the eigenvalues of a suitable class of sparse random matrices, randomness being a consequence of the network structure. A detailed analysis, which includes also the study of finite-amplitude perturbations, is performed in the limit of narrow pulses, finding that the stability depends crucially on the relative pulse-width. This has implications for the overall property of the asynchronous (balanced) regime.
Understanding the role of astrocytes in brain computation is a nascent challenge, promising immense rewards, in terms of new neurobiological knowledge that can be translated into artificial intelligence. In our ongoing effort to identify principles endow-ing the astrocyte with unique functions in brain computation, and translate them into neural-astrocytic networks (NANs), we propose a biophysically realistic model of an astrocyte that preserves the experimentally observed spatial allocation of its distinct subcellular compartments. We show how our model may encode, and modu-late, the extent o…
This paper investigates the dependence of synchronization transitions of bursting oscillations on the information transmission delay over scale-free neuronal networks with attractive and repulsive coupling. It is shown that for both types of coupling, the delay always plays a subtle role in either promoting or impairing synchronization. In particular, depending on the inherent oscillation period of individual neurons, regions of irregular and regular propagating excitatory fronts appear intermittently as the delay increases. These delay-induced synchronization transitions are manifested as wel…
Although recent neurophysiological experiments suggest that synchronous neural activity is involved in some perceptual and cognitive processes, the functional role of such coherent neuronal behavior is not well understood. As a first step in clarifying this role, we investigate how the temporal coherence of certain neuronal activity affects the activity pattern in a neural network. Using a simple network of leaky integrate-and-fire neurons, we study the effects of synchronized incoming spikes on the functioning of two mechanisms typically used in model neural systems, winner-take-all competiti…
Chimera states are spatiotemporal patterns in which coherence and incoherence coexist. We observe the coexistence of synchronous (coherent) and desynchronous (incoherent) domains in a neuronal network. The network is composed of coupled adaptive exponential integrate-and-fire neurons that are connected by means of chemical synapses. In our neuronal network, the chimera states exhibit spatial structures both with spikes and bursts activities. Furthermore, those desynchronised domains not only have either spike or burst activity, but we show that the structures switch between spikes and bursts a…
We study synaptically coupled neuronal networks to identify the role of coupling delays in network's synchronized behaviors. We consider a network of excitable, relaxation oscillator neurons where two distinct populations, one excitatory and one inhibitory, are coupled and interact with each other. The excitatory population is uncoupled, while the inhibitory population is tightly coupled. A geometric singular perturbation analysis yields existence and stability conditions for synchronization states under different firing patterns between the two populations, along with formulas for the periods…
We study the time delay in the synaptic conductance for suppression of spike synchronisation in a random network of Hodgkin Huxley neurons coupled by means of chemical synapses. In the first part, we examine in detail how the time delay acts over the network during the synchronised and desynchronised neuronal activities. We observe a relation between the neuronal dynamics and the syaptic conductance distributions. We find parameter values in which the time delay has high effectiveness in promoting the suppression of spike synchronisation. In the second part, we analyse how the delayed neuronal…
Cell ensembles, originally proposed by Donald Hebb in 1949, are subsets of synchronously firing neurons and proposed to explain basic firing behavior in the brain. Despite having been studied for many years no conclusive evidence has been presented yet for their existence and involvement in information processing such that their identification is still a topic of modern research, especially since simultaneous recordings of large neuronal population have become possible in the past three decades. These large recordings pose a challenge for methods allowing to identify individual neurons forming…
Despite our extensive knowledge of biophysical properties of neurons, there is no commonly accepted algorithmic theory of neuronal function. Here we explore the hypothesis that single-layer neuronal networks perform online symmetric nonnegative matrix factorization (SNMF) of the similarity matrix of the streamed data. By starting with the SNMF cost function we derive an online algorithm, which can be implemented by a biologically plausible network with local learning rules. We demonstrate that such network performs soft clustering of the data as well as sparse feature discovery. The derived al…
European Laboratory for Non-Linear Spectroscopy (LENS), University of Florence（佛罗伦萨大学欧洲非线性光谱实验室）；Bioretics SrL（Bioretics SrL公司）；National Institute of Optics, National Research Council (INO-CNR)（国家研究委员会国家光学研究所）；Department of Physics（物理系）
Semantic segmentation of neuronal structures in 3D high-resolution fluorescence microscopy imaging of the human brain cortex can take advantage of bidimensional CNNs, which yield good results in neuron localization but lead to inaccurate surface reconstruction. 3D CNNs, on the other hand, would require manually annotated volumetric data on a large scale and hence considerable human effort. Semi-supervised alternative strategies which make use only of sparse annotations suffer from longer training times and achieved models tend to have increased capacity compared to 2D CNNs, needing more ground…
Neuronal dynamics are fundamentally constrained by the underlying structural network architecture, yet much of the details of this synaptic connectivity are still unknown even in neuronal cultures in vitro. Here we extend a previous approach based on information theory, the Generalized Transfer Entropy, to the reconstruction of connectivity of simulated neuronal networks of both excitatory and inhibitory neurons. We show that, due to the model-free nature of the developed measure, both kinds of connections can be reliably inferred if the average firing rate between synchronous burst events exc…
We show that in model neuronal cultures, where the probability of interneuronal connection formation decreases exponentially with increasing distance between the neurons, there exists a small number of spatial nucleation centers of a network spike, from where the synchronous spiking activity starts propagating in the network typically in the form of circular traveling waves. The number of nucleation centers and their spatial locations are unique and unchanged for a given realization of neuronal network but are different for different networks. In contrast, if the probability of interneuronal c…
Brain plasticity, also known as neuroplasticity, is a fundamental mechanism of neuronal adaptation in response to changes in the environment or due to brain injury. In this review, we show our results about the effects of synaptic plasticity on neuronal networks composed by Hodgkin-Huxley neurons. We show that the final topology of the evolved network depends crucially on the ratio between the strengths of the inhibitory and excitatory synapses. Excitation of the same order of inhibition revels an evolved network that presents the rich-club phenomenon, well known to exist in the brain. For ini…
Neuronal activity in the brain generates synchronous oscillations of the Local Field Potential (LFP). The traditional analyses of the LFPs are based on decomposing the signal into simpler components, such as sinusoidal harmonics. However, a common drawback of such methods is that the decomposition primitives are usually presumed from the onset, which may bias our understanding of the signal's structure. Here, we introduce an alternative approach that allows an impartial, high resolution, hands-off decomposition of the brain waves into a small number of discrete, frequency-modulated oscillatory…
We consider an inhomogeneous small-world network (SWN) composed of inhibitory short-range (SR) and long-range (LR) interneurons. By varying the fraction of LR interneurons $p_{long}$, we investigate the effect of network architecture on emergence of sparsely synchronized rhythms, and make comparison with that in the Watts-Strogatz SWN. Although SR and LR interneurons have the same average in- and out-degrees, their betweenness centralities (characterizing the potentiality in controlling communication between other interneurons) are distinctly different. Hence, in view of the betweenness, SWNs …
One of the central problems in neuroscience is reconstructing synaptic connectivity in neural circuits. Synapses onto a neuron can be probed by sequentially stimulating potentially pre-synaptic neurons while monitoring the membrane voltage of the post-synaptic neuron. Reconstructing a large neural circuit using such a "brute force" approach is rather time-consuming and inefficient because the connectivity in neural circuits is sparse. Instead, we propose to measure a post-synaptic neuron's voltage while stimulating sequentially random subsets of multiple potentially pre-synaptic neurons. To re…
Information transmission is a key element for information processing in the brain. A number of mechanisms have been proposed for transferring volleys of spikes between layers of a feedforward neural circuit. Many of these mechanisms use synchronous activity to provide windows in time when spikes may be transferred more easily from layer to layer. Recently, we have demonstrated that a pulse-gating mechanism can transfer graded information between layers in a feedforward neuronal network. Our transfer mechanism resulted in a time-translationally invariant firing rate and synaptic current wavefor…
We consider the Watts-Strogatz small-world network (SWN) consisting of inhibitory fast spiking Izhikevich interneurons. This inhibitory neuronal population has adaptive dynamic synaptic strengths governed by the inhibitory spike-timing-dependent plasticity (iSTDP). In previous works without iSTDP, fast sparsely synchronized rhythms, associated with diverse cognitive functions, were found to appear in a range of large noise intensities for fixed strong synaptic inhibition strengths. Here, we investigate the effect of iSTDP on fast sparse synchronization (FSS) by varying the noise intensity $D$.…
The balance between excitation and inhibition is crucial for neuronal computation. It is observed that the balanced state of neuronal networks exists in many experiments, yet its underlying mechanism remains to be fully clarified. Theoretical studies of the balanced state mainly focus on the analysis of the homogeneous Erd$\ddot{\text{o}}$s-Rényi network. However, neuronal networks have been found to be inhomogeneous in many cortical areas. In particular, the connectivity of neuronal networks can be of the type of scale-free, small-world, or even with specific motifs. In this work, we examine …
Neurons in the brain are wired into adaptive networks that exhibit a range of collective dynamics. Oscillations, for example, are paradigmatic synchronous patterns of neural activity with a defined temporal scale. Neuronal avalanches, in contrast, are scale-free cascades of neural activity, often considered as evidence of brain tuning to criticality. While models have been developed to account for oscillations or avalanches separately, they typically do not explain both phenomena, are too complex to analyze analytically, or intractable to infer from data rigorously. Here we propose a non-equil…
A synfire chain is a simple neural network model which can propagate stable synchronous spikes called a pulse packet and widely researched. However how synfire chains coexist in one network remains to be elucidated. We have studied the activity of a layered associative network of Leaky Integrate-and-Fire neurons in which connection we embed memory patterns by the Hebbian Learning. We analyzed their activity by the Fokker-Planck method. In our previous report, when a half of neurons belongs to each memory pattern (memory pattern rate $F=0.5$), the temporal profiles of the network activity is sp…
We have studied neuronal synchronisation in a random network of adaptive exponential integrate-and-fire neurons. We study how spiking or bursting synchronous behaviour appears as a function of the coupling strength and the probability of connections, by constructing parameter spaces that identify these synchronous behaviours from measurements of the inter-spike interval and the calculation of the order parameter. Moreover, we verify the robustness of synchronisaton by applying an external perturbation to each neuron. The simulations show that bursting synchronisation is more robust than spike …
We consider clustered small-world networks with both inhibitory (I) and excitatory (E) populations. This I-E neuronal network has adaptive dynamic I to E and E to I interpopulation synaptic strengths, governed by interpopulation spike-timing-dependent plasticity (STDP). In previous works without STDPs, fast sparsely synchronized rhythms, related to diverse cognitive functions, were found to appear in a range of noise intensity $D$ for static synaptic strengths. By varying $D$, we investigate the effect of interpopulation STDPs on diverse population and individual properties of fast sparsely sy…
We explore the dynamics of the preBötzinger complex, the mammalian central pattern generator with $N \sim 10^3$ neurons, which produces a collective metronomic signal that times the inspiration. Our analysis is based on a simple firing-rate model of excitatory neurons with dendritic adaptation (the Feldman Del Negro model [Nat. Rev. Neurosci. 7, 232 (2006), Phys. Rev. E 2010 :051911]) interacting on a fixed, directed Erdős-Rényi network. In the all-to-all coupled variant of the model, there is spontaneous symmetry breaking in which some fraction of the neurons become stuck in a high firing-rat…
Random matrix theory of sparse neuronal networks with heterogeneous timescales
Complex Systems, Department of Physics, Faculty of Science, Chulalongkorn University, Bangkok, Thailand；High Energy Physics Research Unit, Faculty of Science, Chulalongkorn University, Bangkok, Thailand；International Solvay Institutes, Brussels, Belgium；Mark Kac Center for Complex Systems Research, Jagiellonian University, Krak\'ow, Poland；Department of Mathematics, King's College London, London, UK
During development, the mammalian brain differentiates into specialized regions with distinct functional abilities. While many factors contribute to functional specialization, we explore the effect of neuronal density on the development of neuronal interactions in vitro. Two types of cortical networks, dense and sparse, with 50,000 and 12,000 total cells respectively, are studied. Activation graphs that represent pairwise neuronal interactions are constructed using a competitive first response model. These graphs reveal that, during development in vitro, dense networks form activation connecti…
Many experiments have evidenced that electrical and chemical synapses -- hybrid synapses -- coexist in most organisms and brain structures. The role of electrical and chemical synapse connection in diversity of neural activity generation has been investigated separately in networks of varying complexities. Nevertheless, theoretical understanding of hybrid synapses in diverse dynamical states of neural networks for self-organization and robustness still has not been fully studied. Here, we present a model of neural network built with hybrid synapses to investigate the emergence of global and co…
A Synchronous EEG-fNIRS BCI: A Proof-of-Concept for Multimodal Avalanche Analysis of Motor Cognition in Older Adults
Shanghai Jiao Tong University（上海交通大学）；CenBRAIN Neurotech, School of Engineering, Westlake University（西湖大学工学院 CenBRAIN 神经技术）；Department of Neurology, Affiliated Hangzhou First People’s Hospital, Westlake University, School of Medicine（西湖大学医学院附属杭州市第一人民医院神经内科）
Columbia University（哥伦比亚大学）；Kavli Institute of Brain Science（卡弗里脑科学研究所）；Göttingen Campus Institute for Dynamics of Biological Networks（哥廷根校区生物网络动力学研究所）；Max Planck Institute for Dynamics and Self-Organization（马克斯·普朗克动力学与自组织研究所）；Georg-August-Universität Göttingen（哥廷根大学）；Bernstein Center for Computational Neuroscience（伯恩斯坦计算神经科学中心）
The brain forms and stores distributed representations from sparse external input that compete for neuronal resources with already stored memory traces. It is unclear what dynamical properties of neural systems allow formation and subsequent consolidation of new, distributed memory representations under these conditions. Here we use analytical, computational, and experimental approaches to show that a dynamical regime near a phase-transition in neuronal network activity (i.e. criticality) may play an important role in this process. Our results reveal that near-critical dynamics are necessary t…
Janelia Farm Research Campus, Howard Hughes Medical Institute（霍华德·休斯医学研究所珍妮利亚研究园区）
A central problem in neuroscience is reconstructing neuronal circuits on the synapse level. Due to a wide range of scales in brain architecture such reconstruction requires imaging that is both high-resolution and high-throughput. Existing electron microscopy (EM) techniques possess required resolution in the lateral plane and either high-throughput or high depth resolution but not both. Here, we exploit recent advances in unsupervised learning and signal processing to obtain high depth-resolution EM images computationally without sacrificing throughput. First, we show that the brain tissue ca…
Cortical neural circuits display highly irregular spiking in individual neurons but variably sized collective firing, oscillations and critical avalanches at the population level, all of which have functional importance for information processing. Theoretically, the balance of excitation and inhibition inputs is thought to account for spiking irregularity and critical avalanches may originate from an underlying phase transition. However, the theoretical reconciliation of these multilevel dynamic aspects in neural circuits remains an open question. Herein, we study excitation-inhibition (E-I) b…
A model of the columnar functional organization of neocortical association areas is studied. The neuronal network is composed of many Hebbian autoassociators, or modules, each of which interacts with a relatively small number of the others. Every module encodes and stores a number of elementary percepts, or features. Memory items, or patterns, are peculiar combinations of features sparsely distributed over the multi-modular network. Any feature stored in any module can be involved in several of the stored patterns; feature-sharing is in fact source of local ambiguities and, consequently, a pot…
Topology-Dependent Emergence of Polychronous Neuronal Groups: A Recurrence-Plot Characterization
Complex Systems Modelling Graduate Program, School of Arts, Sciences and Humanities (EACH), University of São Paulo（圣保罗大学艺术与人文科学学院复杂系统建模研究生项目）；Department of Physics, Faculty of Philosophy, Sciences and Letters of Ribeirão Preto (FFCLRP), University of São Paulo（圣保罗大学里贝朗普雷图哲学、科学与文学院物理系）
The mathematical theory of pattern formation in electrically coupled networks of excitable neurons forced by small noise is presented in this work. Using the Freidlin-Wentzell large deviation theory for randomly perturbed dynamical systems and the elements of the algebraic graph theory, we identify and analyze the main regimes in the network dynamics in terms of the key control parameters: excitability, coupling strength, and network topology. The analysis reveals the geometry of spontaneous dynamics in electrically coupled network. Specifically, we show that the location of the minima of a ce…
A major goal of neuroscience, statistical physics and nonlinear dynamics is to understand how brain function arises from the collective dynamics of networks of spiking neurons. This challenge has been chiefly addressed through large-scale numerical simulations. Alternatively, researchers have formulated mean-field theories to gain insight into macroscopic states of large neuronal networks in terms of the collective firing activity of the neurons, or the firing rate. However, these theories have not succeeded in establishing an exact correspondence between the firing rate of the network and the…
In this work, we propose to catch the complexity of the membrane potential's dynamic of a motoneuron between its spikes, taking into account the spikes from other neurons around. Our approach relies on two types of data: extracellular recordings of multiple spikes trains and intracellular recordings of the membrane potential of a central neuron. Our main contribution is to provide a unified framework and a complete pipeline to analyze neuronal activity from data extraction to statistical inference. The first step of the procedure is to select a subnetwork of neurons impacting the central neuro…
We demonstrate that waves in distinct layers of a neuronal network can become phase-locked by common spatiotemporal noise. This phenomenon is studied for stationary bumps, traveling waves, and breathers. A weak noise expansion is used to derive an effective equation for the position of the wave in each layer, yielding a stochastic differential equation with multiplicative noise. Stability of the synchronous state is characterized by a Lyapunov exponent, which we can compute analytically from the reduced system. Our results extend previous work on limit-cycle oscillators, showing common noise c…
Finding actions that satisfy the constraints imposed by both external inputs and internal representations is central to decision making. We demonstrate that some important classes of constraint satisfaction problems (CSPs) can be solved by networks composed of homogeneous cooperative-competitive modules that have connectivity similar to motifs observed in the superficial layers of neocortex. The winner-take-all modules are sparsely coupled by programming neurons that embed the constraints onto the otherwise homogeneous modular computational substrate. We show rules that embed any instance of t…
The result of computational operations performed at the single cell level are coded into sequences of action potentials (APs). In the cerebral cortex, due to its columnar organization, large number of neurons are involved in any individual processing task. It is therefore important to understand how the properties of coding at the level of neuronal populations are determined by the dynamics of single neuron AP generation. Here we analyze how the AP generating mechanism determines the speed with which an ensemble of neurons can represent transient stochastic input signals. We analyze a generali…
We propose a population model for $δ$-pulse-coupled oscillators with sparse connectivity. The model is given as an evolution equation for the phase density which take the form of a partial differential equation with a non-local term. We discuss the existence and stability of stationary solutions and exemplify our approach for integrate-and-fire-like oscillators. While for strong couplings, the firing rate of stationary solutions diverges and solutions disappear, small couplings allow for partially synchronous states which emerge at a supercritical Andronov-Hopf bifurcation.
Deducing the structure of neural circuits is one of the central problems of modern neuroscience. Recently-introduced calcium fluorescent imaging methods permit experimentalists to observe network activity in large populations of neurons, but these techniques provide only indirect observations of neural spike trains, with limited time resolution and signal quality. In this work we present a Bayesian approach for inferring neural circuitry given this type of imaging data. We model the network activity in terms of a collection of coupled hidden Markov chains, with each chain corresponding to a si…
Lobachevsky State University of Nizhny Novgorod（罗巴切夫斯基国立下诺夫哥罗德大学）；Institute of Applied Physics of the Russian Academy of Sciences（俄罗斯科学院应用物理研究所）；Immanuel Kant Baltic Federal University（伊曼努尔·康德波罗的海联邦大学）；Sechenov First Moscow State Medical University (Sechenov University)（谢切诺夫第一莫斯科国立医科大学（谢切诺夫大学））；University College London（伦敦大学学院）；Innopolis University（因诺波利斯大学）
Modeling the neuronal processes underlying short-term working memory remains the focus of many theoretical studies in neuroscience. Here we propose a mathematical model of spiking neuron network (SNN) demonstrating how a piece of information can be maintained as a robust activity pattern for several seconds then completely disappear if no other stimuli come. Such short-term memory traces are preserved due to the activation of astrocytes accompanying the SNN. The astrocytes exhibit calcium transients at a time scale of seconds. These transients further modulate the efficiency of synaptic transm…
Synchronous neural activity can improve neural processing and is believed to mediate neuronal interaction by providing temporal windows during which information is more easily transferred. We demonstrate a pulse gating mechanism in a feedforward network that can exactly propagate graded information through a multilayer circuit. Based on this mechanism, we present a unified framework wherein neural information coding and processing can be considered as a product of linear maps under the active control of a pulse generator. Distinct control and processing components combine to form the basis for…
Local patterns of excitation and inhibition that can generate neural waves are studied as a computational mechanism underlying the organization of neuronal tunings. Sparse coding algorithms based on networks of excitatory and inhibitory neurons are proposed that exhibit topographic maps as the receptive fields are adapted to input stimuli. Motivated by a leaky integrate-and-fire model of neural waves, we propose an activation model that is more typical of artificial neural networks. Computational experiments with the activation model using both natural images and natural language text are pres…
Zebrafish pretectal neurons exhibit specificities for large-field optic flow patterns associated with rotatory or translatory body motion. We investigate the hypothesis that these specificities reflect the input statistics of natural optic flow. Realistic motion sequences were generated using computer graphics simulating self-motion in an underwater scene. Local retinal motion was estimated with a motion detector and encoded in four populations of directionally tuned retinal ganglion cells, represented as two signed input variables. This activity was then used as input into one of two learning…
