Asynchronous Firing Research Articles

Transition and bifurcation mechanism of firing activities in memristor synapse-coupled Hindmarsh–Rose bi-neuron model

Memristor, especially the locally active one, is widely used in emulating the synapse-inspired activities in neural networks, in which the connection between memristor properties and neuronal electrical activities requires further investigation. In this paper, a bi-neuron model is constructed by bi-directionally connecting a locally active memristor between the membrane potentials of two deterministic 3D HR neuron models. Complex spiking/bursting firing activities and their transitions are disclosed under different memristor control parameters. The bifurcation mechanisms of the revealed synchronous and asynchronous firing activities are explored inside each individual neuron by taking the externally input state variables as modulation parameters. These results demonstrate the crucial effect of the locally active memristor synapse on firing activities of its coupled network. FPGA-based digital circuit experiment is finally performed to verify the numerical results. This research is beneficial to understanding, control and application of firing activities in neural networks.

The Interplay of Common Noise and Finite Pulses on Biological Neurons

The response of neurons is highly sensitive to the stimulus. The stimulus can be associated with a direct injection in vitro experimentation (e.g., time dependent and independent inputs); or post-synaptic potentials resulting from the interaction of many neurons. A typical incoming stimulus resembles a noise which in principle can be described as a random variable. In computational neuroscience, the noise has been extensively studied for different setups. In this study, we investigate the effect of noisy inputs in a minimal network of two identical leaky integrate-and-fire (LIF) neurons interacting with finite pulses. In particular, we consider a Gaussian white noise as a standard function for stochastic modelling of neurons, while taking into account the pulse width as an elementary component for the signal transmission. By exploring the role of noise and finite pulses, the two neurons show a synchronous spiking behaviour characterized by fluctuations in the interspike intervals. Above some critical values the synchronous regime collapses onto asynchronous dynamics. The abrupt change in such dynamics is accompanied by a hysteresis, i.e., the coexistence of synchronous and asynchronous firing behaviour.

Analysis of muzzle flow field of asynchronous firing of multi barrel aircraft gun under strong convection

Based on the N - S equation and the k-ε model, this article uses the dynamic grid technology to finish the numerical simulation of projectile-barrel coupling for muzzle flow field of the double-barreled aircraft gun during asynchronous firing under different incoming Mach numbers and different firing intervals. The influence law of muzzle flow field on projectile motion is studied. The results show that when there is supersonic incoming flow, the radial force on the projectile will increase with the increase of incoming Mach number. At the same time, the larger the Mach number, the earlier the radial force of the projectile will be affected. Under the same inflow Mach number, the radial force on the projectile when the double-barreled aircraft gun is fired asynchronously is significantly lower than that when fired synchronously. The larger the firing interval, the smaller the radial force on the projectile.

Asynchronous axonal firing patterns evoked via continuous subthreshold kilohertz stimulation

Objective. Transcutaneous electrical stimulation of peripheral nerves is a common technique to assist or rehabilitate impaired muscle activation. However, conventional stimulation paradigms activate nerve fibers synchronously with action potentials time-locked with stimulation pulses. Such synchronous activation limits fine control of muscle force due to synchronized force twitches. Accordingly, we developed a subthreshold high-frequency stimulation waveform with the goal of activating axons asynchronously. Approach. We evaluated our waveform experimentally and through model simulations. During the experiment, we delivered continuous subthreshold pulses at frequencies of 16.67, 12.5, or 10 kHz transcutaneously to the median and ulnar nerves. We obtained high-density electromyographic (EMG) signals and fingertip forces to quantify the axonal activation patterns. We used a conventional 30 Hz stimulation waveform and the associated voluntary muscle activation for comparison. We modeled stimulation of biophysically realistic myelinated mammalian axons using a simplified volume conductor model to solve for extracellular electric potentials. We compared the firing properties under kHz and conventional 30 Hz stimulation. Main results. EMG activity evoked by kHz stimulation showed high entropy values similar to voluntary EMG activity, indicating asynchronous axon firing activity. In contrast, we observed low entropy values in EMG evoked by conventional 30 Hz stimulation. The muscle forces evoked by kHz stimulation also showed more stable force profiles across repeated trials compared with 30 Hz stimulation. Our simulation results provide direct evidence of asynchronous firing patterns across a population of axons in response to kHz frequency stimulation, while 30 Hz stimulation elicited synchronized time-locked responses across the population. Significance. We demonstrate that the continuous subthreshold high-frequency stimulation waveform can elicit asynchronous axon firing patterns, which can lead to finer control of muscle forces.

Effects of short-term plasticity in UP-DOWN cortical dynamics

Neuronal dynamics are strongly influenced by short-term plasticity (STP), that is, changes in synaptic efficacy that occur on a short (from milliseconds to seconds) time scale. Depending on the brain areas considered, STP can be dominated by short-term depression (STD), short-term facilitation (STF), or both mechanisms can coexist simultaneously. These two plasticity mechanisms modulate particular patterns of electrophysiological activity characterized by alternating UP and DOWN states. In this work, we develop a network model made up of excitatory and inhibitory multi-compartment neurons endowed with both mechanisms (STD and STF), spatially arranged to emulate the connectivity circuitry observed experimentally in the visual cortex. Our results reveal that both depression and facilitation can be involved in the switching process between different activity patterns, from an alternation of UP and DOWN states (for relatively low levels of depression and high levels of facilitation) to an asynchronous firing regime (for relatively high levels of depression and low levels of facilitation). For STD and STF, we identify the critical levels of depression and facilitation that push the network into the different regimes. Furthermore, we also find that these critical levels separate different growth rates of the mean synaptic conductances of the whole network with respect to the depression levels. This latter data is paramount to understanding how excitation and inhibition are organized to generate different brain activity regimes. Finally, after observing the changes in the trajectories of excitatory and inhibitory instantaneous firing rates near these critical boundaries, we identify dynamic patterns that shed light on the type of bifurcations that should arise in a rate model for this complex network.

Synthesis of optimal covert sensor–actuator attackers for discrete-event systems

This work introduces an approach for the synthesis of optimal covert sensor–actuator attackers in the context of discrete-event systems (DES). Building upon existing works on optimal supervisor synthesis, on one hand, and the base model construction in the transformation of covert sensor–actuator attacker synthesis to supervisor synthesis, on the other hand, we show how the optimal covert sensor–actuator attacker synthesis problem could be transformed to the optimal supervisor synthesis problem, thus generalizing its logic counterpart. We consider several different types of optimization objectives, such as (1) minimization of attack energy cost, and (2) minimization of time cost to cause damage infliction; for the latter one, asynchronous event firings and concurrent event firings at the plant are both considered. We provide the necessary and sufficient conditions for the existence of an optimal attacker for both the energy minimization case and damage infliction time minimization case. Thus, this work may potentially provide a unified approach for the optimal synthesis of covert sensor–actuator attackers in different setups.

Holistic View on the Structure of Immune Response: Petri Net Model.

The simulation of immune response is a challenging task because quantitative data are scarce. Quantitative theoretical models either focus on specific cell-cell interactions or have to make assumptions about parameters. The broad variation of, e.g., the dimensions and abundance between lymph nodes as well as between individual patients hampers conclusive quantitative modeling. No theoretical model has been established representing a consensus on the set of major cellular processes involved in the immune response. In this paper, we apply the Petri net formalism to construct a semi-quantitative mathematical model of the lymph nodes. The model covers the major cellular processes of immune response and fulfills the formal requirements of Petri net models. The intention is to develop a model taking into account the viewpoints of experienced pathologists and computer scientists in the field of systems biology. In order to verify formal requirements, we discuss invariant properties and apply the asynchronous firing rule of a place/transition net. Twenty-five transition invariants cover the model, and each is assigned to a functional mode of the immune response. In simulations, the Petri net model describes the dynamic modes of the immune response, its adaption to antigens, and its loss of memory.

Drosophila SUMM4 complex couples insulator function and DNA replication control.

Asynchronous replication of chromosome domains during S phase is essential for eukaryotic genome function, but the mechanisms establishing which domains replicate early versus late in different cell types remain incompletely understood. Intercalary heterochromatin domains replicate very late in both diploid chromosomes of dividing cells and in endoreplicating polytene chromosomes where they are also underreplicated. Drosophila SNF2-related factor SUUR imparts locus-specific underreplication of polytene chromosomes. SUUR negatively regulates DNA replication fork progression; however, its mechanism of action remains obscure. Here, we developed a novel method termed MS-Enabled Rapid protein Complex Identification (MERCI) to isolate a stable stoichiometric native complex SUMM4 that comprises SUUR and a chromatin boundary protein Mod(Mdg4)-67.2. Mod(Mdg4) stimulates SUUR ATPase activity and is required for a normal spatiotemporal distribution of SUUR in vivo. SUUR and Mod(Mdg4)-67.2 together mediate the activities of gypsy insulator that prevent certain enhancer-promoter interactions and establish euchromatin-heterochromatin barriers in the genome. Furthermore, SuUR or mod(mdg4) mutations reverse underreplication of intercalary heterochromatin. Thus, SUMM4 can impart late replication of intercalary heterochromatin by attenuating the progression of replication forks through euchromatin/heterochromatin boundaries. Our findings implicate a SNF2 family ATP-dependent motor protein SUUR in the insulator function, reveal that DNA replication can be delayed by a chromatin barrier, and uncover a critical role for architectural proteins in replication control. They suggest a mechanism for the establishment of late replication that does not depend on an asynchronous firing of late replication origins.

Exact mean-field models for spiking neural networks with adaptation.

Networks of spiking neurons with adaption have been shown to be able to reproduce a wide range of neural activities, including the emergent population bursting and spike synchrony that underpin brain disorders and normal function. Exact mean-field models derived from spiking neural networks are extremely valuable, as such models can be used to determine how individual neurons and the network they reside within interact to produce macroscopic network behaviours. In the paper, we derive and analyze a set of exact mean-field equations for the neural network with spike frequency adaptation. Specifically, our model is a network of Izhikevich neurons, where each neuron is modeled by a two dimensional system consisting of a quadratic integrate and fire equation plus an equation which implements spike frequency adaptation. Previous work deriving a mean-field model for this type of network, relied on the assumption of sufficiently slow dynamics of the adaptation variable. However, this approximation did not succeed in establishing an exact correspondence between the macroscopic description and the realistic neural network, especially when the adaptation time constant was not large. The challenge lies in how to achieve a closed set of mean-field equations with the inclusion of the mean-field dynamics of the adaptation variable. We address this problem by using a Lorentzian ansatz combined with the moment closure approach to arrive at a mean-field system in the thermodynamic limit. The resulting macroscopic description is capable of qualitatively and quantitatively describing the collective dynamics of the neural network, including transition between states where the individual neurons exhibit asynchronous tonic firing and synchronous bursting. We extend the approach to a network of two populations of neurons and discuss the accuracy and efficacy of our mean-field approximations by examining all assumptions that are imposed during the derivation. Numerical bifurcation analysis of our mean-field models reveals bifurcations not previously observed in the models, including a novel mechanism for emergence of bursting in the network. We anticipate our results will provide a tractable and reliable tool to investigate the underlying mechanism of brain function and dysfunction from the perspective of computational neuroscience.

Action potential amplitude and baroreflex resetting of action potential clusters mediate hypoxia‐induced sympathetic long‐term facilitation

Baroreflex resetting permits sympathetic long-term facilitation (sLTF) following hypoxia; however, baroreflex control of action potential (AP) clusters and AP recruitment patterns facilitating sLTF is unknown. We hypothesized that baroreflex resetting of arterial pressure operating points (OPs) of AP clusters and recruitment of large-amplitude APs would mediate sLTF following hypoxia. Eight men (age: 24 (3) years; body mass index: 24 (3) kg/m2 ) underwent 20min isocapnic hypoxia ( : 47 (2) mmHg) and 30min recovery. Multi-unit microneurography (muscle sympathetic nerve activity; MSNA) and a continuous wavelet transform with matched mother wavelet was used to detect sympathetic APs during baseline, hypoxia, early (first 5min), and late recovery (last 5min). AP amplitude (normalized to largest baseline AP amplitude), percentage APs occurring outside a MSNA burst (percentage asynchronous APs), and proportion of APs firing in small (1-3), medium (4-6) and large (7-10) normalized cluster sizes was calculated. Normalized clusters were used to assess baroreflex OPs and sensitivity. Hypoxia increased total MSNA activity, which remained elevated during recovery (P<0.0001). Baroreflex OPs were shifted rightward for all clusters in recovery, with no effect on slope. Compared to baseline, AP amplitude was elevated by 3 (2)% and 4 (2)% while asynchronous APs were reduced by 9 (5)% and 7 (6)% in early and late recovery, respectively. In early recovery, the proportion of APs firing in large clusters was increased compared to baseline. Hypoxia-induced sLTF is mediated by baroreflex resetting of AP clusters to higher OPs, reduced asynchronous AP firing, and increased contribution from large-amplitude APs. KEY POINTS: Acute isocapnic hypoxia resets the arterial baroreflex and permits long-lasting sympathoexcitation, termed sympathetic long-term facilitation. Our understanding of sympathetic long-term facilitation following hypoxia in humans is based on multiunit muscle sympathetic nerve activity and does not fully characterize the underlying baroreflex control of sympathetic neuronal subpopulations or their discharge/recruitment strategies. We show that sympathetic long-term facilitation is mediated by baroreflex resetting of sympathetic action potential clusters to higher arterial pressure operating points, a reduction in the percentage of action potentials firing asynchronously, and a shift toward larger amplitude action potential activity. The results advance our fundamental understanding of how the sympathetic nervous system mediates sympathetic long-term facilitation following exposure to acute isocapnic hypoxia in humans.

On the Diverse Functions of Electrical Synapses.

Electrical synapses are the neurophysiological product of gap junctional pores between neurons that allow bidirectional flow of current between neurons. They are expressed throughout the mammalian nervous system, including cortex, hippocampus, thalamus, retina, cerebellum, and inferior olive. Classically, the function of electrical synapses has been associated with synchrony, logically following that continuous conductance provided by gap junctions facilitates the reduction of voltage differences between coupled neurons. Indeed, electrical synapses promote synchrony at many anatomical and frequency ranges across the brain. However, a growing body of literature shows there is greater complexity to the computational function of electrical synapses. The paired membranes that embed electrical synapses act as low-pass filters, and as such, electrical synapses can preferentially transfer spike after hyperpolarizations, effectively providing spike-dependent inhibition. Other functions include driving asynchronous firing, improving signal to noise ratio, aiding in discrimination of dissimilar inputs, or dampening signals by shunting current. The diverse ways by which electrical synapses contribute to neuronal integration merits furthers study. Here we review how functions of electrical synapses vary across circuits and brain regions and depend critically on the context of the neurons and brain circuits involved. Computational modeling of electrical synapses embedded in multi-cellular models and experiments utilizing optical control and measurement of cellular activity will be essential in determining the specific roles performed by electrical synapses in varying contexts.

Hypoxia‐induced sympathetic long‐term facilitation is mediated by a rightward shift in sympathetic action potential amplitude distribution and baroreflex resetting of action potential clusters

IntroductionBaroreflex resetting permits sympathetic long‐term facilitation (sLTF) following hypoxia. Muscle sympathetic nerve activity (MSNA) bursts are generated by synchronous discharge of varying‐amplitude action potentials (APs), with medium APs under strong baroreflex control. AP discharge strategies and baroreflex control of AP clusters facilitating sLTF is unknown. We hypothesized that recruitment of previously latent, large‐amplitude APs and baroreflex resetting of AP cluster operating points (OPs) would mediate sLTF following acute hypoxia.MethodsEight men (age = 24±3 yrs; BMI = 24±3 kg/m2) were exposed to 20 min isocapnic hypoxia (PETO2: 47±2 mmHg) and 30 min recovery. Blood pressure (BP; photoplethysmography) and MSNA (fibular microneurography) were acquired during baseline, hypoxia, early (first 5‐min) and late recovery (last 5‐min). Multi‐unit MSNA burst frequency (BF) and total activity (TA) were quantified. A continuous wavelet transform with matched mother wavelet was used to extract sympathetic APs. AP frequency, AP amplitude (normalized % of largest baseline AP amplitude), percent APs occurring outside a MSNA burst (% asynchronous APs) and total AP clusters was calculated. The proportion of APs firing in small (1‐3), medium (4‐6) and large (7‐10) normalized cluster sizes was assessed. Baroreflex OP was measured by plotting the intersection point of mean cluster incidence and mean diastolic BP (DBP). Friedman repeated‐measures analysis of variance on ranks was used to determine the effect of condition (baseline, hypoxia, early, late). Data are means ± standard deviation or 95% confidence intervals.ResultsHypoxia increased BF (P&lt;0.01), TA (P&lt;0.01), AP frequency (Δ124{‐30, 279} AP/min, P&lt;0.05), AP amplitude (Δ3{1, 5} %, P&lt;0.05) and decreased asynchronous APs (Δ‐10{‐17, ‐4} %, P&lt;0.03). Compared to baseline, BF (P&lt;0.03), TA (P&lt;0.02) and AP amplitude (early: Δ3{0, 5} %, P&lt;0.05; late: Δ4{1, 6} %, P&lt;0.05) was elevated during recovery while asynchronous APs (early: Δ‐9{‐16, ‐3} %, P&lt;0.03; late: Δ‐7{‐14, ‐1} %, P&lt;0.03) were reduced. The total number of AP clusters was increased (P&lt;0.05) with no one condition different compared to baseline (hypoxia: Δ3{‐1, 7} clusters; early and late: Δ3{‐1, 6} clusters, P&gt;0.10). Proportion of APs in small clusters was reduced in hypoxia (hypoxia: 44±18 %, P&lt;0.05), early (46±21 %, P&lt;0.05) and late recovery (44±17 %, P&lt;0.05) compared with baseline (53±20 %) while the proportion of APs in large clusters was increased in early recovery (7±6 %, P&lt;0.05) compared with baseline (5±5 %). Baroreflex OPs were shifted rightward for all AP clusters in recovery (baseline DBP: 63±5; early DBP: 64±5; late DBP: 65±4, mmHg; P&lt;0.05) with no effect on slope (P&gt;0.20).ConclusionsHypoxia‐induced sLTF is mediated by reduced asynchronous AP firing, a proportional shift toward large‐amplitude AP activity, and baroreflex resetting of AP clusters to higher OPs.

Neural Suppression Elicited During Motor Imagery Following the Observation of Biological Motion From Point-Light Walker Stimuli.

Introduction: Advantageous effects of biological motion (BM) detection, a low-perceptual mechanism that allows the rapid recognition and understanding of spatiotemporal characteristics of movement via salient kinematics information, can be amplified when combined with motor imagery (MI), i.e., the mental simulation of motor acts. According to Jeannerod’s neurostimulation theory, asynchronous firing and reduction of mu and beta rhythm oscillations, referred to as suppression over the sensorimotor area, are sensitive to both MI and action observation (AO) of BM. Yet, not many studies investigated the use of BM stimuli using combined AO-MI tasks. In this study, we assessed the neural response in the form of event-related synchronization and desynchronization (ERD/S) patterns following the observation of point-light-walkers and concordant MI, as compared to MI alone.Methods: Twenty right-handed healthy participants accomplished the experimental task by observing BM stimuli and subsequently performing the same movement using kinesthetic MI (walking, cycling, and jumping conditions). We recorded an electroencephalogram (EEG) with 32 channels and performed time-frequency analysis on alpha (8–13 Hz) and beta (18–24 Hz) frequency bands during the MI task. A two-way repeated-measures ANOVA was performed to test statistical significance among conditions and electrodes of interest.Results: The results revealed significant ERD/S patterns in the alpha frequency band between conditions and electrode positions. Post hoc comparisons showed significant differences between condition 1 (walking) and condition 3 (jumping) over the left primary motor cortex. For the beta band, a significantly less difference in ERD patterns (p < 0.01) was detected only between condition 3 (jumping) and condition 4 (reference).Discussion: Our results confirmed that the observation of BM combined with MI elicits a neural suppression, although just in the case of jumping. This is in line with previous findings of AO and MI (AOMI) eliciting a neural suppression for simulated whole-body movements. In the last years, increasing evidence started to support the integration of AOMI training as an adjuvant neurorehabilitation tool in Parkinson’s disease (PD).Conclusion: We concluded that using BM stimuli in AOMI training could be promising, as it promotes attention to kinematic features and imitative motor learning.

Asynchrony Increases Efficiency: Time Encoding of Videos and Low-Rank Signals

In event-based sensing, many sensors independently and asynchronously emit events when there is a change in their input. Event-based sensing can present significant improvements in power efficiency when compared to traditional sampling, because (1) the output is a stream of events where the important information lies in the timing of the events, and (2) the sensor can easily be controlled to output information only when interesting activity occurs at the input. Moreover, event-based sampling can often provide better resolution than standard uniform sampling. Not only does this occur because individual event-based sensors have higher temporal resolution, it also occurs because the asynchrony of events allows for less redundant and more informative encoding. We would like to explain how such curious results come about. To do so, we use ideal time encoding machines as a proxy for event-based sensors. We explore time encoding of signals with low rank structure, and apply the resulting theory to video. We then see how the asynchronous firing times of the time encoding machines allow for better reconstruction than in the standard sampling case, if we have a high spatial density of time encoding machines that fire less frequently.

Integration, coincidence detection and resonance in networks of spiking neurons expressing Gamma oscillations and asynchronous states.

Gamma oscillations are widely seen in the awake and sleeping cerebral cortex, but the exact role of these oscillations is still debated. Here, we used biophysical models to examine how Gamma oscillations may participate to the processing of afferent stimuli. We constructed conductance-based network models of Gamma oscillations, based on different cell types found in cerebral cortex. The models were adjusted to extracellular unit recordings in humans, where Gamma oscillations always coexist with the asynchronous firing mode. We considered three different mechanisms to generate Gamma, first a mechanism based on the interaction between pyramidal neurons and interneurons (PING), second a mechanism in which Gamma is generated by interneuron networks (ING) and third, a mechanism which relies on Gamma oscillations generated by pacemaker chattering neurons (CHING). We find that all three mechanisms generate features consistent with human recordings, but that the ING mechanism is most consistent with the firing rate change inside Gamma bursts seen in the human data. We next evaluated the responsiveness and resonant properties of these networks, contrasting Gamma oscillations with the asynchronous mode. We find that for both slowly-varying stimuli and precisely-timed stimuli, the responsiveness is generally lower during Gamma compared to asynchronous states, while resonant properties are similar around the Gamma band. We could not find conditions where Gamma oscillations were more responsive. We therefore predict that asynchronous states provide the highest responsiveness to external stimuli, while Gamma oscillations tend to overall diminish responsiveness.

Network Asynchrony Underlying Increased Broadband Gamma Power.

Synchronous activity of cortical inhibitory interneurons expressing parvalbumin (PV) underlies expression of cortical γ rhythms. Paradoxically, deficient PV inhibition is associated with increased broadband γ power in the local field potential. Increased baseline broadband γ is also a prominent characteristic in schizophrenia and a hallmark of network alterations induced by NMDAR antagonists, such as ketamine. Whether enhanced broadband γ is a true rhythm, and if so, whether rhythmic PV inhibition is involved or not, is debated. Asynchronous and increased firing activities are thought to contribute to broadband power increases spanning the γ band. Using male and female mice lacking NMDAR activity specifically in PV neurons to model deficient PV inhibition, we here show that neuronal activity with decreased synchronicity is associated with increased prefrontal broadband γ power. Specifically, reduced spike time precision and spectral leakage of spiking activity because of higher firing rates (spike "contamination") affect the broadband γ band. Desynchronization was evident at multiple time scales, with reduced spike entrainment to the local field potential, reduced cross-frequency coupling, and fragmentation of brain states. Local application of S(+)-ketamine in (control) mice with intact NMDAR activity in PV neurons triggered network desynchronization and enhanced broadband γ power. However, our investigations suggest that disparate mechanisms underlie increased broadband γ power caused by genetic alteration of PV interneurons and ketamine-induced power increases in broadband γ. Our study confirms that enhanced broadband γ power can arise from asynchronous activities and demonstrates that long-term deficiency of PV inhibition can be a contributor.SIGNIFICANCE STATEMENT Brain oscillations are fundamental to the coordination of neuronal activity across neurons and structures. γ oscillations (30-80 Hz) have received particular attention through their association with perceptual and cognitive processes. Synchronous activity of inhibitory parvalbumin (PV) interneurons generates cortical γ oscillation, but, paradoxically, PV neuron deficiency is associated with increases in γ oscillations. We here reconcile this conundrum and show how deficient PV inhibition can lead to increased and asynchronous excitatory firing, contaminating the local field potential and manifesting as increased γ power. Thus, increased γ power does not always reflect a genuine rhythm. Further, we show that ketamine-induced γ increases are caused by separate network mechanisms.

Network mechanism for insect olfaction.

Early olfactory pathway responses to the presentation of an odor exhibit remarkably similar dynamical behavior across phyla from insects to mammals, and frequently involve transitions among quiescence, collective network oscillations, and asynchronous firing. We hypothesize that the time scales of fast excitation and fast and slow inhibition present in these networks may be the essential element underlying this similar behavior, and design an idealized, conductance-based integrate-and-fire model to verify this hypothesis via numerical simulations. To better understand the mathematical structure underlying the common dynamical behavior across species, we derive a firing-rate model and use it to extract a slow passage through a saddle-node-on-an-invariant-circle bifurcation structure. We expect this bifurcation structure to provide new insights into the understanding of the dynamical behavior of neuronal assemblies and that a similar structure can be found in other sensory systems.

Asynchronous Chaos and Bifurcations in a Model of Two Coupled Identical Hindmarsh – Rose Neurons

We study a minimal network of two coupled neurons described by the Hindmarsh – Rose model with a linear coupling. We suppose that individual neurons are identical and study whether the dynamical regimes of a single neuron would be stable synchronous regimes in the model of two coupled neurons. We find that among synchronous regimes only regular periodic spiking and quiescence are stable in a certain range of parameters, while no bursting synchronous regimes are stable. Moreover, we show that there are no stable synchronous chaotic regimes in the parameter range considered. On the other hand, we find a wide range of parameters in which a stable asynchronous chaotic regime exists. Furthermore, we identify narrow regions of bistability, when synchronous and asynchronous regimes coexist. However, the asynchronous attractor is monostable in a wide range of parameters. We demonstrate that the onset of the asynchronous chaotic attractor occurs according to the Afraimovich – Shilnikov scenario. We have observed various asynchronous firing patterns: irregular quasi-periodic and chaotic spiking, both regular and chaotic bursting regimes, in which the number of spikes per burst varied greatly depending on the control parameter.

The information propagation model of Weibo network based on spiking neural P systems

Information propagation models in the Weibo network play a primary role in analyzing user behaviors, obtaining the propagation paths, determining the opinion leaders, and discovering the hot spots of public opinion. Existing research recognizes the critical role played by information propagation models from different aspects. However, few studies have investigated the specific details of information propagation in any systematic way. Spiking neural P (SNP, for short) systems are one of the most potential research carriers of information propagation by applying their concurrent structures and asynchronous firing rules. This paper proposes a simple and intuitive SNP variant, namely DWIP-SNP, for user behavior analysis in Weibo. The fundamental objects of information propagation in Weibo are represented by a similar SNP formalization. The forward, comment, delete, and other users’ behaviors in the Weibo network can be observed and proceeded more intuitively. Then, the DWIP-SNP systems are combined with time delays to indicate the dynamic information diffusion from the perspective of the Bio-computing systems. Finally, a real-world example of information propagation with Weibo data set is utilized to verify the effectiveness and feasibility of the model. The insights of the DWIP-SNP based propagation model gained from this study may be of assistance to user behavior understanding and information propagation in other complex networks.

Dynamic Transitions in Neuronal Network Firing Sustained by Abnormal Astrocyte Feedback.

Astrocytes play a crucial role in neuronal firing activity. Their abnormal state may lead to the pathological transition of neuronal firing patterns and even induce seizures. However, there is still little evidence explaining how the astrocyte network modulates seizures caused by structural abnormalities, such as gliosis. To explore the role of gliosis of the astrocyte network in epileptic seizures, we first established a direct astrocyte feedback neuronal network model on the basis of the hippocampal CA3 neuron-astrocyte model to simulate the condition of gliosis when astrocyte processes swell and the feedback to neurons increases in an abnormal state. We analyzed the firing pattern transitions of the neuronal network when astrocyte feedback starts to change via increases in both astrocyte feedback intensity and the connection probability of astrocytes to neurons in the network. The results show that as the connection probability and astrocyte feedback intensity increase, neuronal firing transforms from a nonepileptic synchronous firing state to an asynchronous firing state, and when astrocyte feedback starts to become abnormal, seizure-like firing becomes more severe and synchronized; meanwhile, the synchronization area continues to expand and eventually transforms into long-term seizure-like synchronous firing. Therefore, our results prove that astrocyte feedback can regulate the firing of the neuronal network, and when the astrocyte network develops gliosis, there will be an increase in the induction rate of epileptic seizures.