Reverberating activity in a neural network with distributed signal transmission delays

It is known that an identical delay in all transmission lines can destabilize macroscopic stationarity of a neural network, causing oscillation or chaos. We analyze the collective dynamics of a network whose intra-transmission delays are distributed in time. Here, a neuron is modeled as a discrete-time threshold element that responds in an all-or-nothing manner to a linear sum of signals that arrive after delays assigned to individual transmission lines. Even though transmission delays are distributed in time, a whole network exhibits a single collective oscillation with a period close to the average transmission delay. The collective oscillation can not only be a simple alternation of the consecutive firing and resting, but also nontrivially sequenced series of firing and resting, reverberating in a certain period of time. Moreover, the system dynamics can be made quasiperiodic or chaotic by changing the distribution of delays.Comment: 8pages, 9figure

Bursting activity spreading through asymmetric interactions

People communicate with those who have the same background or share a common interest by using a social networking service (SNS). News or messages propagate through inhomogeneous connections in an SNS by sharing or facilitating additional comments. Such human activity is known to lead to endogenous bursting in the rate of message occurrences. We analyze a multi-dimensional self-exciting process to reveal dependence of the bursting activity on the topology of connections and the distribution of interaction strength on the connections. We determine the critical conditions for the cases where interaction strength is regulated at either the point of input or output for each person. In the input regulation condition, the network may exhibit bursting with infinitesimal interaction strength, if the dispersion of the degrees diverges as in the scale-free networks. In contrast, in the output regulation condition, the critical value of interaction strength, represented by the average number of events added by a single event, is a constant $1-1/\sqrt{2} \approx 0.3$, independent of the degree dispersion. Thus, the stability in human activity crucially depends on not only the topology of connections but also the manner in which interactions are distributed among the connections.Comment: 8 pages, 8 figure

Emergence of event cascades in inhomogeneous networks

There is a commonality among contagious diseases, tweets, urban crimes, nuclear reactions, and neuronal firings that past events facilitate the future occurrence of events. The spread of events has been extensively studied such that the systems exhibit catastrophic chain reactions if the interaction represented by the ratio of reproduction exceeds unity; however, their subthreshold states for the case of the weaker interaction are not fully understood. Here, we report that these systems are possessed by nonstationary cascades of event-occurrences already in the subthreshold regime. Event cascades can be harmful in some contexts, when the peak-demand causes vaccine shortages, heavy traffic on communication lines, frequent crimes, or large fluctuations in nuclear reactions, but may be beneficial in other contexts, such that spontaneous activity in neural networks may be used to generate motion or store memory. Thus it is important to comprehend the mechanism by which such cascades appear, and consider controlling a system to tame or facilitate fluctuations in the event-occurrences. The critical interaction for the emergence of cascades depends greatly on the network structure in which individuals are connected. We demonstrate that we can predict whether cascades may emerge in a network, given information about the interactions between individuals. Furthermore, we develop a method of reallocating connections among individuals so that event cascades may be either impeded or impelled in a network.Comment: 16 pages, 5 figure

Made-to-Order Spiking Neuron Model Equipped with a Multi-Timescale Adaptive Threshold

Information is transmitted in the brain through various kinds of neurons that respond differently to the same signal. Full characteristics including cognitive functions of the brain should ultimately be comprehended by building simulators capable of precisely mirroring spike responses of a variety of neurons. Neuronal modeling that had remained on a qualitative level has recently advanced to a quantitative level, but is still incapable of accurately predicting biological data and requires high computational cost. In this study, we devised a simple, fast computational model that can be tailored to any cortical neuron not only for reproducing but also for predicting a variety of spike responses to greatly fluctuating currents. The key features of this model are a multi-timescale adaptive threshold predictor and a nonresetting leaky integrator. This model is capable of reproducing a rich variety of neuronal spike responses, including regular spiking, intrinsic bursting, fast spiking, and chattering, by adjusting only three adaptive threshold parameters. This model can express a continuous variety of the firing characteristics in a three-dimensional parameter space rather than just those identified in the conventional discrete categorization. Both high flexibility and low computational cost would help to model the real brain function faithfully and examine how network properties may be influenced by the distributed characteristics of component neurons

Elemental Spiking Neuron Model for Reproducing Diverse Firing Patterns and Predicting Precise Firing Times

In simulating realistic neuronal circuitry composed of diverse types of neurons, we need an elemental spiking neuron model that is capable of not only quantitatively reproducing spike times of biological neurons given in vivo-like fluctuating inputs, but also qualitatively representing a variety of firing responses to transient current inputs. Simplistic models based on leaky integrate-and-fire mechanisms have demonstrated the ability to adapt to biological neurons. In particular, the multi-timescale adaptive threshold (MAT) model reproduces and predicts precise spike times of regular-spiking, intrinsic-bursting, and fast-spiking neurons, under any fluctuating current; however, this model is incapable of reproducing such specific firing responses as inhibitory rebound spiking and resonate spiking. In this paper, we augment the MAT model by adding a voltage dependency term to the adaptive threshold so that the model can exhibit the full variety of firing responses to various transient current pulses while maintaining the high adaptability inherent in the original MAT model. Furthermore, with this addition, our model is actually able to better predict spike times. Despite the augmentation, the model has only four free parameters and is implementable in an efficient algorithm for large-scale simulation due to its linearity, serving as an element neuron model in the simulation of realistic neuronal circuitry