arXiv subjects

Woochang Lim

Publications and source records attributed to Woochang Lim.

32 records · Page 2Linked to original sources

arXiv2015

Effect of Network Architecture on Burst and Spike Synchronization in A Scale-Free Network of Bursting Neurons

We investigate the effect of network architecture on burst and spike synchronization in a directed scale-free network (SFN) of bursting neurons, evolved via two independent $α-$ and $β-$processes. The $α-$process corresponds to a directed version of the Barabási-Albert SFN model with growth and preferential attachment, while for the $β-$process only preferential attachments between pre-existing nodes are made without addition of new nodes. We first consider the "pure" $α-$process of symmetric preferential attachment (with the same in- and out-degrees), and study emergence of burst and spike synchronization by varying the coupling strength $J$ and the noise intensity $D$ for a fixed attachment degree. Characterizations of burst and spike synchronization are also made by employing realistic order parameters and statistical-mechanical measures. Next, we choose appropriate values of $J$ and $D$ where only the burst synchronization occurs, and investigate the effect of the scale-free connectivity on the burst synchronization by varying (1) the symmetric attachment degree and (2) the asymmetry parameter (representing deviation from the symmetric case) in the $α-$process, and (3) the occurrence probability of the $β-$process. In all these three cases, changes in the type and the degree of population synchronization are studied in connection with the network topology such as the degree distribution, the average path length $L_p$, and the betweenness centralization $B_c$. It is thus found that not only $L_p$ and $B_c$ (affecting global communication between nodes) but also the in-degree distribution (affecting individual dynamics) are important network factors for effective population synchronization in SFNs.

q-bio.NC↗

arXiv2015

Effect of Inter-Modular Connection on Fast Sparse Synchronization in Clustered Small-World Neural Networks

We consider a clustered network with small-world sub-networks of inhibitory fast spiking interneurons, and investigate the effect of inter-modular connection on emergence of fast sparsely synchronized rhythms by varying both the inter-modular coupling strength $J_{inter}$ and the average number of inter-modular links per interneuron $M_{syn}^{(inter)}$. In contrast to the case of non-clustered networks, two kinds of sparsely synchronized states such as modular and global synchronization are found. For the case of modular sparse synchronization, the population behavior reveals the modular structure, because the intra-modular dynamics of sub-networks make some mismatching. On the other hand, in the case of global sparse synchronization, the population behavior is globally identical, independently of the cluster structure, because the intra-modular dynamics of sub-networks make perfect matching. We introduce a realistic cross-correlation modularity measure, representing the matching-degree between the instantaneous sub-population spike rates of the sub-networks, and examine whether the sparse synchronization is global or modular. Furthermore, we characterize the modular and global sparse synchronization by employing the realistic sub- and whole-population order parameters and statistical-mechanical measures. The roles of $J_{inter}$ and $M_{syn}^{(inter)}$ are thus found as follows. For large $J_{inter}$, due to strong inhibition it plays a destructive role to "spoil" the pacing between spikes, while for small $J_{inter}$ it plays a constructive role to "favor" the pacing between spikes. In contrast, $M_{syn}^{(inter)}$ seems to play a role just to favor the pacing between spikes. With increasing $M_{syn}^{(inter)}$, the pacing degree between spikes increases monotonically thanks to the increase in the degree of effectiveness of global communication between spikes.

q-bio.NC↗

arXiv2015

Fast Sparsely Synchronized Brain Rhythms in A Scale-Free Neural Network

We consider a directed Barabási-Albert scale-free network model with symmetric preferential attachment with the same in- and out-degrees, and study emergence of sparsely synchronized rhythms for a fixed attachment degree in an inhibitory population of fast spiking Izhikevich interneurons. For a study on the fast sparsely synchronized rhythms, we fix $J$ (synaptic inhibition strength) at a sufficiently large value, and investigate the population states by increasing $D$ (noise intensity). For small $D$, full synchronization with the same population-rhythm frequency $f_p$ and mean firing rate (MFR) $f_i$ of individual neurons occurs, while for sufficiently large $D$ partial synchronization with $f_p > {\langle f_i \rangle}$ ($\langle f_i \rangle$: ensemble-averaged MFR) appears due to intermittent discharge of individual neurons; particularly, the case of $f_p > 4 {\langle f_i \rangle}$ is referred to as sparse synchronization. Only for the partial and sparse synchronization, MFRs and contributions of individual neuronal dynamics to population synchronization change depending on their degrees, unlike the case of full synchronization. Consequently, dynamics of individual neurons reveal the inhomogeneous network structure for the case of partial and sparse synchronization, which is in contrast to the case of statistically homogeneous random graphs and small-world networks. Finally, we investigate the effect of network architecture on sparse synchronization in the following three cases: (1) variation in the degree of symmetric attachment (2) asymmetric preferential attachment of new nodes with different in- and out-degrees (3) preferential attachment between pre-existing nodes (without addition of new nodes). In these three cases, both relation between network topology and sparse synchronization and contributions of individual dynamics to the sparse synchronization are discussed.

q-bio.NC↗

arXiv2014

Frequency-Domain Order Parameters for the Burst And Spike Synchronization Transitions of Bursting Neurons

We are interested in characterization of synchronization transitions of bursting neurons in the frequency domain. Instantaneous population firing rate (IPFR) $R(t)$, which is directly obtained from the raster plot of neural spikes, is often used as a realistic collective quantity describing population activities in both the computational and the experimental neuroscience. For the case of spiking neurons, a realistic time-domain order parameter, based on $R(t)$, was introduced in our recent work to characterize the spike synchronization transition. Unlike the case of spiking neurons, the IPFR $R(t)$ of bursting neurons exhibits population behaviors with both the slow bursting and the fast spiking timescales. For our aim, we decompose the IPFR $R(t)$ into the instantaneous population bursting rate $R_b(t)$ (describing the bursting behavior) and the instantaneous population spike rate $R_s(t)$ (describing the spiking behavior) via frequency filtering, and extend the realistic order parameter to the case of bursting neurons. Thus, we develop the frequency-domain bursting and spiking order parameters which are just the bursting and spiking "coherence factors" $β_b$ and $β_s$ of the bursting and spiking peaks in the power spectral densities of $R_b$ and $R_s$ (i.e., "signal to noise" ratio of the spectral peak height and its relative width). Through calculation of $β_b$ and $β_s$, we obtain the bursting and spiking thresholds beyond which the burst and spike synchronizations break up, respectively. Consequently, it is shown in explicit examples that the frequency-domain bursting and spiking order parameters may be usefully used for characterization of the bursting and the spiking transitions, respectively.

q-bio.NC↗

arXiv2014

Thermodynamic Order Parameters and Statistical-Mechanical Measures for Characterization of the Burst and Spike Synchronizations of Bursting Neurons

We are interested in characterization of population synchronization of bursting neurons which exhibit both the slow bursting and the fast spiking timescales, in contrast to spiking neurons. Population synchronization may be well visualized in the raster plot of neural spikes which can be obtained in experiments. The instantaneous population firing rate (IPFR) $R(t)$, which may be directly obtained from the raster plot of spikes, is often used as a realistic collective quantity describing population behaviors in both the computational and the experimental neuroscience. For the case of spiking neurons, realistic thermodynamic order parameter and statistical-mechanical spiking measure, based on $R(t)$, were introduced in our recent work to make practical characterization of spike synchronization. Here, we separate the slow bursting and the fast spiking timescales via frequency filtering, and extend the thermodynamic order parameter and the statistical-mechanical measure to the case of bursting neurons. Consequently, it is shown in explicit examples that both the order parameters and the statistical-mechanical measures may be effectively used to characterize the burst and spike synchronizations of bursting neurons.

q-bio.NC↗

arXiv2014

Effect of Small-World Connectivity on Fast Sparsely Synchronized Cortical Rhythms

Fast cortical rhythms with stochastic and intermittent neural discharges have been observed in electric recordings of brain activity. Recently, Brunel et al. developed a framework to describe this kind of fast sparse synchronization in both random and globally-coupled networks of suprathreshold spiking neurons. However, in a real cortical circuit, synaptic connections are known to have complex topology which is neither regular nor random. Hence, in order to extend the works of Brunel et al. to realistic neural networks, we study the effect of network architecture on these fast sparsely synchronized rhythms in an inhibitory population of suprathreshold fast spiking (FS) Izhikevich interneurons. We first employ the conventional Erdös-Renyi random graph of suprathreshold FS Izhikevich interneurons for modeling the complex connectivity in neural systems, and study emergence of the population synchronized states by varying both the synaptic inhibition strength $J$ and the noise intensity $D$. Thus, fast sparsely synchronized states of relatively high degree are found to appear for large values of $J$ and $D$. Second, for fixed values of $J$ and $D$ where fast sparse synchronization occurs in the random network, we consider the Watts-Strogatz small-world network of suprathreshold FS Izhikevich interneurons which interpolates between regular lattice and random graph via rewiring, and investigate the effect of small-world synaptic connectivity on emergence of fast sparsely synchronized rhythms by varying the rewiring probability $p$ from short-range to long-range connection. When passing a small critical value $p^*_c$ $(\simeq 0.12)$, fast sparsely synchronized population rhythms are found to emerge in small-world networks with predominantly local connections and rare long-range connections.

q-bio.NC↗

arXiv2014

Noise-Induced Burst and Spike Synchronizations in An Inhibitory Small-World Network of Subthreshold Bursting Neurons

For modeling complex synaptic connectivity, we consider the Watts-Strogatz small-world network which interpolates between regular lattice and random network via rewiring, and investigate the effect of small-world connectivity on emergence of noise-induced population synchronization in an inhibitory population of subthreshold bursting Hindmarsh-Rose neurons. Thus, noise-induced slow burst synchronization and fasg spike synchronization are found to appear in a synchronized region of the $J-D$ plane. As the rewiring probability $p$ is decreased from 1 (random network) to 0 (regular lattice), the region of spike synchronization shrinks rapidly in the $J-D$ plane, while the region of the burst synchronization decreases slowly. Population synchronization may be well visualized in the raster plot of neural spikes which can be obtained in experiments. Instantaneous population firing rate, $R(t)$, which is directly obtained from the raster plot of spikes, is a realistic population quantity exhibiting collective behaviors with both the slow bursting and the fast spiking timescales. Through frequency filtering, we separate $R(t)$ into $R_b(t)$ (describing the slow bursting behavior) and $R_s(t)$ (describing the fast intraburst spiking behavior). Then, we develop thermodynamic order parameters and statistical-mechanical measures, based on $R_b (t)$ and $R_s (t)$, for characterization of the burst and spike synchronizations of the bursting neurons and show their usefulness in explicit examples. With increase in $p$, both the degrees of the burst and spike synchronizations are found to increase because more long-range connections appear. However, they become saturated for some maximal values of $p$ because long-range short-cuts which appear up to the maximal values of $p$ play sufficient role to get maximal degrees of the burst and spike synchronizations.

q-bio.NC↗

arXiv2014

Coupling-Induced Population Synchronization in An Excitatory Population of Subthreshold Izhikevich Neurons

We consider an excitatory population of subthreshold Izhikevich neurons which exhibit noise-induced firings. By varying the coupling strength $J$, we investigate population synchronization between the noise-induced firings which may be used for efficient cognitive processing such as sensory perception, multisensory binding, selective attention, and memory formation. As $J$ is increased, rich types of population synchronization (e.g., spike, burst, and fast spike synchronization) are found to occur. Transitions between population synchronization and incoherence are well described in terms of an order parameter $\cal{O}$. As a final step, the coupling induces oscillator death (quenching of noise-induced spikings) because each neuron is attracted to a noisy equilibrium state. The oscillator death leads to a transition from firing to non-firing states at the population level, which may be well described in terms of the time-averaged population spike rate $\overline{R}$. In addition to the statistical-mechanical analysis using $\cal{O}$ and $\overline{R}$, each population and individual state are also characterized by using the techniques of nonlinear dynamics such as the raster plot of neural spikes, the time series of the membrane potential, and the phase portrait. We note that population synchronization of noise-induced firings may lead to emergence of synchronous brain rhythms in a noisy environment, associated with diverse cognitive functions.

q-bio.NC↗

arXiv2014

Realistic Thermodynamic and Statistical-Mechanical Measures for Neural Synchronization

Synchronized brain rhythms, associated with diverse cognitive functions, have been observed in electrical recordings of brain activity. Neural synchronization may be well described by using the population-averaged global potential $V_G$ in computational neuroscience. The time-averaged fluctuation of $V_G$ plays the role of a "thermodynamic" order parameter $\cal {O}$ used for describing the synchrony-asynchrony transition in neural systems. Population spike synchronization may be well visualized in the raster plot of neural spikes. The degree of neural synchronization seen in the raster plot is well measured in terms of a "statistical-mechanical" spike-based measure $M_s$ introduced by considering the occupation and the pacing patterns of spikes. The global potential $V_G$ is also used to give a reference global cycle for the calculation of $M_s$. Hence, $V_G$ becomes an important collective quantity because it is associated with calculation of both $\cal {O}$ and $M_s$. However, it is practically difficult to directly get $V_G$ in real experiments. To overcome this difficulty, instead of $V_G$, we employ the instantaneous population spike rate (IPSR) which can be obtained in experiments, and develop realistic thermodynamic and statistical-mechanical measures, based on IPSR, to make practical characterization of the neural synchronization in both computational and experimental neuroscience. Particularly, more accurate characterization of weak sparse spike synchronization can be achieved in terms of realistic statistical-mechanical IPSR-based measure, in comparison with the conventional measure based on $V_G$.

q-bio.NC↗

arXiv2011

Strange Nonchaotic Oscillations in The Quasiperiodically Forced Hodgkin-Huxley Neuron

We numerically study dynamical behaviors of the quasiperiodically forced Hodgkin-Huxley neuron and compare the dynamical responses with those for the case of periodic stimulus. In the periodically forced case, a transition from a periodic to a chaotic oscillation was found to occur via period doublings in previous numerical and experimental works. We investigate the effect of the quasiperiodic forcing on this period-doubling route to chaotic oscillation. In contrast to the case of periodic forcing, new type of strange nonchaotic (SN) oscillating states (that are geometrically strange but have no positive Lyapunov exponents) are found to exist between the regular and chaotic oscillating states as intermediate ones. Their strange fractal geometry leads to aperiodic "complex" spikings. Various dynamical routes to SN oscillations are identified, as in the quasiperiodically forced logistic map. These SN spikings are expected to be observed in experiments of the quasiperiodically forced squid giant axon.

physics.bio-ph↗

arXiv2011

Statistical-Mechanical Measure of Stochastic Spiking Coherence in A Population of Inhibitory Subthreshold Neurons

By varying the noise intensity, we study stochastic spiking coherence (i.e., collective coherence between noise-induced neural spikings) in an inhibitory population of subthreshold neurons (which cannot fire spontaneously without noise). This stochastic spiking coherence may be well visualized in the raster plot of neural spikes. For a coherent case, partially-occupied "stripes" (composed of spikes and indicating collective coherence) are formed in the raster plot. This partial occupation occurs due to "stochastic spike skipping" which is well shown in the multi-peaked interspike interval histogram. The main purpose of our work is to quantitatively measure the degree of stochastic spiking coherence seen in the raster plot. We introduce a new spike-based coherence measure $M_s$ by considering the occupation pattern and the pacing pattern of spikes in the stripes. In particular, the pacing degree between spikes is determined in a statistical-mechanical way by quantifying the average contribution of (microscopic) individual spikes to the (macroscopic) ensemble-averaged global potential. This "statistical-mechanical" measure $M_s$ is in contrast to the conventional measures such as the "thermodynamic" order parameter (which concerns the time-averaged fluctuations of the macroscopic global potential), the "microscopic" correlation-based measure (based on the cross-correlation between the microscopic individual potentials), and the measures of precise spike timing (based on the peri-stimulus time histogram). In terms of $M_s$, we quantitatively characterize the stochastic spiking coherence, and find that $M_s$ reflects the degree of collective spiking coherence seen in the raster plot very well. Hence, the "statistical-mechanical" spike-based measure $M_s$ may be used usefully to quantify the degree of stochastic spiking coherence in a statistical-mechanical way.

physics.bio-ph↗

arXiv2011

Heterogeneity-Induced Inhibitory Coherence in An Ensemble of Subthreshold and Suprathreshold Type-I Neurons

We study inhibitory coherence (i.e., collective coherence by synaptic inhibition) in an ensemble of globally-coupled type-I neurons which can fire at arbitrarily low frequencies. No inhibitory coherence is observed in a homogeneous ensemble composed of only subthreshold neurons (which cannot fire spontaneously without noise). By increasing the fraction of (spontaneously firing) suprathreshold neurons $P_{supra}$, heterogeneity-induced inhibitory coherence is investigated in a heterogeneous ensemble of subthreshold and suprathreshold neurons. As $P_{supra}$ passes a threshold $P_{supra}^*$, suprathreshold neurons begin to synchronize and play the role of coherent inhibitors for the emergence of inhibitory coherence. Thus, regularly-oscillating ensemble-averaged global potential appears for $P_{supra} > P_{supra}^*$. For this coherent case suprathreshold neurons exhibit coherent mixed-mode oscillations with a fast subthreshold (small-amplitude) hopping frequency and a lower spiking frequency. By virtue of their coherent inhibition, sparsely synchronized suprathreshold neurons suppress noisy activities of subthreshold neurons. Thus, only coherent subthreshold hoppings appear in the individual potentials of subthreshold neurons. We also characterize the inhibitory coherence in terms of the "statistical-mechanical" spike-based and correlation-based measures and find that the degree of inhibitory coherence increases with increasing $P_{supra}$ for $P_{supra} > P_{supra}^*$. Finally, effect of sparse randomness of synaptic connectivity on the inhibitory coherence and universality of the heterogeneity-induced inhibitory coherence are briefly discussed.

physics.bio-ph↗

arXiv2011

Strange Nonchaotic Bursting in A Quasiperiodially-Forced Hindmarsh-Rose Neuron

We study the transition from a silent state to a bursting state by varying the dc stimulus in the Hindmarsh-Rose neuron under quasiperiodic stimulation. For this quasiperiodically forced case, a new type of strange nonchaotic (SN) bursting state is found to occur between the silent state and the chaotic bursting state. This is in contrast to the periodically forced case where the silent state transforms directly to a chaotic bursting state. Using a rational approximation to the quasiperiodic forcing, the mechanism for the appearance of such an SN bursting state is investigated. Thus, a smooth torus (corresponding to a silent state) is found to transform to an SN bursting attractor through a phase-dependent subcritical period-doubling bifurcation. These SN bursting states, together with chaotic bursting states, are characterized in terms of the interburst interval, the bursting length, and the number of spikes in each burst. Both bursting states are found to be aperiodic complex ones. Consequently, aperiodic complex burstings may result from two dynamically different states with strange geometry (one is chaotic and the other one is nonchaotic). Thus, in addition to chaotic burstings, SN burstings may become a dynamical origin for complex physiological rhythms which are ubiquitous in organisms.

physics.bio-ph↗

arXiv2002

Mechanism for the Intermittent Route to Strange Nonchaotic Attractors

Intermittent strange nonchaotic attractors (SNAs) appear typically in quasiperiodically forced period-doubling systems. As a representative model, we consider the quasiperiodically forced logistic map and investigate the mechanism for the intermittent route to SNAs using rational approximations to the quasiperiodic forcing. It is thus found that a smooth torus is transformed into an intermittent SNA via a phase-dependent saddle-node bifurcation when it collides with a new type of ``ring-shaped'' unstable set. Besides this intermittent transition, other transitions such as the interior, boundary, and band-merging crises may also occur through collision with the ring-shaped unstable sets. Hence the ring-shaped unstable sets play a central role for such dynamical transitions. Furthermore, these kinds of dynamical transitions seem to be ``universal,'' in the sense that they occur typically in a large class of quasiperiodically forced period-doubling systems.

nlin.CD↗