arXiv subjects

Woochang Lim

Publications and source records attributed to Woochang Lim.

At least 19 recordsLinked to original sources

arXiv2024

Functions of Direct and Indirect Pathways for Action Selection Are Quantitatively Analyzed in A Spiking Neural Network of The Basal Ganglia

We are concerned about action selection in the basal ganglia (BG). We quantitatively analyze functions of direct pathway (DP) and indirect pathway (IP) for action selection in a spiking neural network with 3 competing channels. For such quantitative analysis, in each channel, we obtain the competition degree ${\cal C}_d$, given by the ratio of strength of DP (${\cal S}_{DP}$) to strength of IP (${\cal S}_{IP}$) (i.e., ${\cal C}_d = {\cal S}_{DP} / {\cal S}_{IP}$). Then, a desired action is selected in the channel with the largest ${\cal C}_d$. Desired action selection is made mainly due to strong focused inhibitory projection to the output nucleus, SNr (substantia nigra pars reticulata) via the DP in the corresponding channel. Unlike the case of DP, there are two types of IPs; intra-channel IP and inter-channel IP, due to widespread diffusive excitation from the STN (subthalamic nucleus). The intra-channel IP serves a function of brake to suppress the desired action selection. In contrast, the inter-channel IP to the SNr in the neighboring channels suppresses competing actions, leading to highlight the desired action selection. In this way, function of the inter-channel IP is opposite to that of the intra-channel IP. However, to the best of our knowledge, no quantitative analysis for such functions of the DP and the two IPs was made. Here, through direct calculations of the DP and the intra- and the inter-channel IP presynaptic currents into the SNr in each channel, we obtain the competition degree of each channel to determine a desired action, and then functions of the DP and the intra- and inter-channel IPs are quantitatively made clear.

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arXiv2023

Break-up and Recovery of Harmony between Direct and Indirect Pathways in The Basal Ganglia; Huntington's Disease and Treatment

The basal ganglia (BG) in the brain exhibit diverse functions for motor, cognition, and emotion. Such BG functions could be made via competitive harmony between the two competing pathways, direct pathway (DP) (facilitating movement) and indirect pathway (IP) (suppressing movement). As a result of break-up of harmony between DP and IP, there appear pathological states with disorder for movement, cognition, and psychiatry. In this paper, we are concerned about the Huntington's disease (HD), which is a genetic neurodegenerative disorder causing involuntary movement and severe cognitive and psychiatric symptoms. For the HD, the number of D2 SPNs ($N_{\rm D2}$) is decreased due to degenerative loss, and hence, by decreasing $x_{\rm D2}$ (fraction of $N_{\rm D2}$), we investigate break-up of harmony between DP and IP in terms of their competition degree ${\cal C}_d$, given by the ratio of strength of DP (${\cal S}_{DP}$) to strength of IP (${\cal S}_{IP}$) (i.e., ${\cal C}_d = {\cal S}_{DP} / {\cal S}_{IP}$). In the case of HD, the IP is under-active, in contrast to the case of Parkinson's disease with over-active IP, which results in increase in ${\cal C}_d$ (from the normal value). Thus, hyperkinetic dyskinesia such as chorea (involuntary jerky movement) occurs. We also investigate treatment of HD, based on optogenetics and GP ablation, by increasing strength of IP, resulting in recovery of harmony between DP and IP. Finally, we study effect of loss of healthy synapses of all the BG cells on HD. Due to loss of healthy synapses, disharmony between DP and IP increases, leading to worsen symptoms of the HD.

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arXiv2023

Quantifying Harmony between Direct and Indirect Pathways in The Basal Ganglia; Healthy and Parkinsonian States

The basal ganglia (BG) show a variety of functions for motor and cognition. There are two competitive pathways in the BG; direct pathway (DP) which facilitates movement and indirect pathway (IP) which suppresses movement. It is well known that diverse functions of the BG may be made through "balance" between DP and IP. But, to the best of our knowledge, so far no quantitative analysis for such balance was done. In this paper, as a first time, we introduce the competition degree ${\cal C}_d$ between DP and IP. Then, by employing ${\cal C}_d$, we quantify their competitive harmony (i.e., competition and cooperative interplay), which could lead to improving our understanding of the traditional "balance" so clearly and quantitatively. We first consider the case of normal dopamine (DA) level of $\phi^*=0.3$. In the case of phasic cortical input (10 Hz), a healthy state with ${\cal C}_d^* = 2.82$ (i.e., DP is 2.82 times stronger than IP) appears. In this case, normal movement occurs via harmony between DP and IP. Next, we consider the case of decreased DA level, $\phi = \phi^*(=0.3)~x_{DA}$ ($1 > x_{DA} \geq 0$). With decreasing $x_{DA}$ from 1, the competition degree ${\cal C}_d$ between DP and IP decreases monotonically from ${\cal C}_d^*$, which results in appearance of a pathological Parkinsonian state with reduced ${\cal C}_d$. In this Parkinsonian state, strength of IP is much increased than that in the case of normal healthy state, leading to disharmony between DP and IP. Due to such break-up of harmony between DP and IP, impaired movement occurs. Finally, we also study treatment of the pathological Parkinsonian state via recovery of harmony between DP and IP.

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arXiv2023

Effect of Adult Neurogenesis on Sparsely Synchronized Rhythms of The Granule Cells in The Hippocampal Dentate Gyrus

We are concerned about the main encoding granule cells (GCs) in the hippocampal dentate gyrus (DG). Young immature GCs (imGCs) appear through adult neurogenesis. In comparison to the mature GCs (mGCs) (born during development), the imGCs show high activation due to lower firing threshold. On the other hand, they receive low excitatory drive from the entorhinal cortex via perforant paths and from the hilar mossy cells with lower connection probability $p_c~(=20~x~\%)$ ($x:$ synaptic connectivity fraction; $ 0 \leq x \leq 1$) than the mGCs with the connection probability $p_c~(=20~\%)$. Thus, the effect of low excitatory innervation (reducing activation degree) for the imGCs counteracts the effect of their high excitability. We consider a spiking neural network for the DG, incorporating both the mGCs and the imGCs. With decreasing $x$ from 1 to 0, we investigate the effect of young adult-born imGCs on the sparsely synchronized rhythms (SSRs) of the GCs (mGCs, imGC, and whole GCs). For each $x$, population and individual firing behaviors in the SSRs are characterized in terms of the amplitude measure ${\cal M}_a^{(X)}$ ($X=m,~im,~w$ for the mGCs, the imGCs, and the whole GCs, respectively) (representing the population synchronization degree) and the random phase-locking degree ${\cal L}_d^{(X)}$ (characterizing the regularity of individual single-cell discharges), respectively. We also note that, for $0 \leq x \leq 1,$ the mGCs and the imGCs exhibit pattern separation (i.e., a process of transforming similar input patterns into less similar output patterns) and pattern integration (making association between patterns), respectively. Quantitative relationship between SSRs and pattern separation and integration is also discussed.

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arXiv2023

Effect of Adult-Born Immature Granule Cells on Pattern Separation in The Hippocampal Dentate Gyrus

Young immature granule cells (imGCs) appear via adult neurogenesis in the hippocampal dentate gyrus (DG). In comparison to mature GCs (mGCs) (born during development), the imGCs exhibit two competing distinct properties such as high excitability and low excitatory innervation. We develop a spiking neural network for the DG, incorporating the imGCs, and investigate their effect on pattern separation. We first consider the effect of high excitability. The imGCs become very highly active due to their low firing threshold. Then, strong pattern correlation occurs, which results in pattern integration. On the other hand, the mGCs exhibit very sparse firing activity due to strongly increased feedback inhibition. As a result of high sparsity, the pattern separation efficacy (PSE) of the mGCs becomes very high. Thus, the whole population of GCs becomes a heterogeneous one, composed of a (major) subpopulation of mGCs (i.e., pattern separators) with very low activation degree and a (minor) subpopulation of imGCs (i.e., pattern integrators) with very high activation degree. In the whole heterogeneous population, the overall activation degree of all the GCs is a little reduced in comparison to the activation degree in the presence of only mGCs without imGCs. However, no pattern separation occurs, due to heterogeneous sparsity, in contrast to the usual intuitive thought that sparsity could improve PSE. Next, we consider the effect of low excitatory innervation for the imGCs. In this case, the imGCs perform pattern integration. The PSE of the mGCs decreases from a high value to a limit value. In the whole population of all the GCs, when passing through a threshold, pattern separation starts, the overall PSE increases and approaches that of the mGCs. However, due to heterogeneity caused by the imGCs, the overall PSE becomes deteriorated, in comparison with that in the presence of only mGCs.

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arXiv2021

Disynaptic Effect of Hilar Cells on Pattern Separation in A Spiking Neural Network of Hippocampal Dentate Gyrus

We investigate disynaptic effect of the hilar cells on pattern separation in a spiking neural network of the hippocampal dentate gyrus (DG). The principal granule cells (GCs) in the DG perform pattern separation, transforming similar input patterns into less-similar output patterns. The hilus consists of excitatory mossy cells (MCs) and inhibitory HIPP (hilar perforant path-associated) cells. Here, we consider the disynaptic effects of the MCs and the HIPP cells on the GCs, mediated by the inhibitory basket cells (BCs); MC $\rightarrow$ BC $\rightarrow$ GC and HIPP $\rightarrow$ BC $\rightarrow$ GC. By changing synaptic strength $K^{\rm (BC, X)}$ ( X = MC or HIPP) from the default value ${K^{\rm (BC, X)}}^*$, we study the change in the pattern separation degree ${\cal S}_d$. When decreasing $K^{\rm (BC, MC)}$ or independently increasing $K^{\rm (BC, HIPP)}$ from their default values, ${\cal S}_d$ is found to decrease (i.e., pattern separation is reduced). On the other hand, as $K^{\rm (BC, MC)}$ is increased or independently $K^{\rm (BC, HIPP)}$ is decreased from their default values, pattern separation becomes enhanced (i.e., ${\cal S}_d$ increases). In this way, the disynaptic effects of the MCs and the HIPP cells on the pattern separation are opposite ones. Thus, when simultaneously varying both $K^{\rm (BC, MC)}$ and $K^{\rm (BC, HIPP)}$, as a result of balance between the two competing disynaptic effects of the MCs and the HIPP cells, ${\cal S}_d$ forms a bell-shaped curve with an optimal maximum at their default values. Moreover, the population and individual behaviors of the sparsely synchronized rhythm of the GCs are found to be strongly correlated with the pattern separation degree ${\cal S}_d$. Consequently, the larger the synchronization and the random phase-locking degrees of the sparsely synchronized rhythm is, the more the pattern separation becomes enhanced.

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arXiv2021

Population and Individual Firing Behaviors in Sparsely Synchronized Rhythms in The Hippocampal Dentate Gyrus

We investigate population and individual firing behaviors in sparsely synchronized rhythms (SSRs) in a spiking neural network of the hippocampal dentate gyrus (DG). The main encoding granule cells (GCs) are grouped into lamellar clusters. In each GC cluster, there is one inhibitory (I) basket cell (BC) along with excitatory (E) GCs, and they form the E-I loop. Winner-take-all competition, leading to sparse activation of the GCs, occurs in each GC cluster. Such sparsity has been thought to enhance pattern separation performed in the DG. During the winner-take-all competition, SSRs are found to appear in each population of the GCs and the BCs through interaction of excitation of the GCs with inhibition of the BCs. Sparsely synchronized spiking stripes appear successively with the population frequency $f_p~ (= 13$ Hz) in the raster plots of spikes. We also note that excitatory hilar mossy cells (MCs) control the firing activity of the GC-BC loop by providing excitation to both the GCs and the BCs. SSR also appears in the population of MCs via interaction with the GCs (i.e., GC-MC loop). Population behaviors in the SSRs are quantitatively characterized in terms of the synchronization measures. In addition, we investigate individual firing activity of GCs, BCs, and MCs in the SSRs. Individual GCs exhibit random spike skipping, leading to a multi-peaked inter-spike-interval histogram, which is well characterized in terms of the random phase-locking degree. On the other hand, both BCs and MCs show "intrastripe" burstings within stripes, together with "interstripe" random spike skipping. MC loss may occur during epileptogenesis. With decreasing the fraction of the MCs, changes in the population and individual firings in the SSRs are also studied. Finally, quantitative association between the population/individual firing behaviors in the SSRs and the winner-take-all competition is discussed.

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arXiv2021

Dynamical Origin for Winner-Take-All Competition in A Biological Network of The Hippocampal Dentate Gyrus

We consider a biological network of the hippocampal dentate gyrus (DG). The DG is a pre-processor for pattern separation which facilitates pattern storage and retrieval in the CA3 area of the hippocampus. The main encoding cells in the DG are the granule cells (GCs) which receive the input from the entorhinal cortex (EC) and send their output to the CA3. The activation degree of GCs is so low (~ 5%). This sparsity has been thought to enhance the pattern separation. We investigate the dynamical origin for winner-take-all (WTA) competition which leads to sparse activation of the GCs. The whole GCs are grouped into lamellar clusters. In each GC cluster, there is one inhibitory (I) basket cell (BC) along with excitatory (E) GCs. There are three kinds of external inputs into the GCs; the direct excitatory EC input, the indirect inhibitory EC input, mediated by the HIPP (hilar perforant path-associated) cells, and the excitatory input from the hilar mossy cells (MCs). The firing activities of the GCs are determined via competition between the external E and I inputs. The E-I conductance ratio ${\cal{R}}_{\rm E-I}^{\rm (con)*}$ (given by the time average of the external E to I conductances) may represents well the degree of such external E-I input competition. GCs become active when their $\cal{R}_{\rm E-I}^{\rm (con)*}$ is larger than a threshold ${\cal{R}}_{th}^*$, and then the mean firing rates of the active GCs are strongly correlated with $\cal{R}_{\rm E-I}^{\rm (con)*}$. In each GC cluster, the feedback inhibition of the BC may select the winner GCs. GCs with larger $\cal{R}_{\rm E-I}^{\rm (con)*}$ than the threshold ${\cal{R}}_{th}^*$ survive, and they become winners; all the other GCs with smaller $\cal{R}_{\rm E-I}^{\rm (con)*}$ become silent. The WTA competition occurs via competition between the firing activity of the GCs and the feedback inhibition from the BC in each GC cluster.

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arXiv2020

Effect of Diverse Recoding of Granule Cells on Optokinetic Response in A Cerebellar Ring Network with Synaptic Plasticity

We consider a cerebellar ring network for the optokinetic response (OKR), and investigate the effect of diverse recoding of granule (GR) cells on OKR by varying the connection probability $p_c$ from Golgi to GR cells. For an optimal value of $p_c^*~(=0.06)$, individual GR cells exhibit diverse spiking patterns which are in-phase, anti-phase, or complex out-of-phase with respect to their population-averaged firing activity. Then, these diversely-recoded signals via parallel fibers (PFs) from GR cells are effectively depressed by the error-teaching signals via climbing fibers from the inferior olive which are also in-phase ones. Synaptic weights at in-phase PF-Purkinje cell (PC) synapses of active GR cells are strongly depressed via strong long-term depression (LTD), while those at anti-phase and complex out-of-phase PF-PC synapses are weakly depressed through weak LTD. This kind of "effective" depression (i.e., strong/weak LTD) at the PF-PC synapses causes a big modulation in firings of PCs, which then exert effective inhibitory coordination on the vestibular nucleus (VN) neuron (which evokes OKR). For the firing of the VN neuron, the learning gain degree ${\cal{L}}_g$, corresponding to the modulation gain ratio, increases with increasing the learning cycle, and it saturates at about the 300th cycle. By varying $p_c$ from $p_c^*$, we find that a plot of saturated learning gain degree ${\cal L}_g^*$ versus $p_c$ forms a bell-shaped curve with a peak at $p_c^*$ (where the diversity degree in spiking patterns of GR cells is also maximum). Consequently, the more diverse in recoding of GR cells, the more effective in motor learning for the OKR adaptation.

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arXiv2020

Influence of Various Temporal Recoding on Pavlovian Eyeblink Conditioning in The Cerebellum

We consider the Pavlovian eyeblink conditioning (EBC) via repeated presentation of paired conditioned stimulus (tone) and unconditioned stimulus (airpuff). The influence of various temporal recoding of granule cells on the EBC is investigated in a cerebellar network where the connection probability $p_c$ from Golgi to granule cells is changed. In an optimal case of $p_c^*~(=0.029)$, individual granule cells show various well- and ill-matched firing patterns relative to the unconditioned stimulus. Then, these variously-recoded signals are fed into the Purkinje cells (PCs) through parallel-fibers (PFs). In the case of well-matched PF-PC synapses, their synaptic weights are strongly depressed through strong long-term depression (LTD). On the other hand, practically no LTD occurs for the ill-matched PF-PC synapses. This type of "effective" depression at the PF-PC synapses coordinates firings of PCs effectively, which then make effective inhibitory coordination on cerebellar nucleus neuron [which elicits conditioned response (CR; eyeblink)]. When the learning trial passes a threshold, acquisition of CR begins. In this case, the timing degree ${\cal T}_d$ of CR becomes good due to presence of the ill-matched firing group which plays a role of protection barrier for the timing. With further increase in the trial, strength $\cal S$ of CR (corresponding to the amplitude of eyelid closure) increases due to strong LTD in the well-matched firing group. Thus, with increasing the learning trial, the (overall) learning efficiency degree ${\cal L}_e$ (taking into consideration both timing and strength of CR) for the CR is increased, and eventually it becomes saturated. By changing $p_c$ from $p_c^*$, we also investigate the influence of various temporal recoding on the EBC. It is thus found that, the more various in temporal recoding, the more effective in learning for the Pavlovian EBC.

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arXiv2020

Effect of Interpopulation Spike-Timing-Dependent Plasticity on Synchronized Rhythms in Neuronal Networks with Inhibitory and Excitatory Populations

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 synchronized rhythms that emerge in both the I- and the E-populations. Depending on values of $D$, long-term potentiation (LTP) and long-term depression (LTD) for population-averaged values of saturated interpopulation synaptic strengths are found to occur, and they make effects on the degree of fast sparse synchronization. In a broad region of intermediate $D$, the degree of good synchronization (with higher spiking measure) becomes decreased, while in a region of large $D$, the degree of bad synchronization (with lower spiking measure) gets increased. Consequently, in each I- or E-population, the synchronization degree becomes nearly the same in a wide range of $D$. This kind of "equalization effect" is found to occur via cooperative interplay between the average occupation and pacing degrees of fast sparsely synchronized rhythms. We note that the equalization effect in interpopulation synaptic plasticity is distinctly in contrast to the Matthew (bipolarization) effect in intrapopulation (I to I and E to E) synaptic plasticity where good (bad) synchronization gets better (worse). Finally, emergences of LTP and LTD of interpopulation synaptic strengths are intensively investigated via a microscopic method based on the distributions of time delays between the pre- and the post-synaptic spike times.

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arXiv2019

Cluster Burst Synchronization in A Scale-Free Network of Inhibitory Bursting Neurons

We consider a scale-free network of inhibitory Hindmarsh-Rose (HR) bursting neurons, and investigate coupling-induced cluster burst synchronization by varying the average coupling strength $J_0$. For sufficiently small $J_0$, non-cluster desynchronized states exist. However, when passing a critical point $J^*_c~(\simeq 0.16)$, the whole population is segregated into 3 clusters via a constructive role of synaptic inhibition to stimulate dynamical clustering between individual burstings, and thus 3-cluster desynchronized states appear. As $J_0$ is further increased and passes a lower threshold $J^*_l~(\simeq 0.78)$, a transition to 3-cluster burst synchronization occurs due to another constructive role of synaptic inhibition to favor population synchronization. In this case, HR neurons in each cluster exhibit burst synchronization. However, as $J_0$ passes an intermediate threshold $J^*_m~(\simeq 5.2)$, HR neurons begin to make intermittent hoppings between the 3 clusters. Due to the intermittent intercluster hoppings, the 3 clusters are integrated into a single one. In spite of break-up of the 3 clusters, (non-cluster) burst synchronization persists in the whole population, which is well visualized in the raster plot of burst onset times where bursting stripes (composed of burst onset times and indicating burst synchronization) appear successively. With further increase in $J_0$, intercluster hoppings are intensified, and bursting stripes also become smeared more and more due to a destructive role of synaptic inhibition to spoil the burst synchronization. Eventually, when passing a higher threshold $J^*_h~(\simeq 17.8)$ a transition to desynchronization occurs via complete overlap between the bursting stripes. Finally, we also investigate the effects of stochastic noise on both 3-cluster burst synchronization and intercluster hoppings.

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arXiv2018

Burst Synchronization in A Scale-Free Neuronal Network with Inhibitory Spike-Timing-Dependent Plasticity

We are concerned about burst synchronization (BS), related to neural information processes in health and disease, in the Barabási-Albert scale-free network (SFN) composed of inhibitory bursting Hindmarsh-Rose neurons. This inhibitory neuronal population has adaptive dynamic synaptic strengths governed by the inhibitory spike-timing-dependent plasticity (iSTDP). In previous works without considering iSTDP, BS was found to appear in a range of noise intensities for fixed synaptic inhibition strengths. In contrast, in our present work, we take into consideration iSTDP and investigate its effect on BS by varying the noise intensity. Our new main result is to find occurrence of a Matthew effect in inhibitory synaptic plasticity: good BS gets better via LTD, while bad BS get worse via LTP. This kind of Matthew effect in inhibitory synaptic plasticity is in contrast to that in excitatory synaptic plasticity where good (bad) synchronization gets better (worse) via LTP (LTD). We note that, due to inhibition, the roles of LTD and LTP in inhibitory synaptic plasticity are reversed in comparison with those in excitatory synaptic plasticity. Moreover, emergences of LTD and LTP of synaptic inhibition strengths are intensively investigated via a microscopic method based on the distributions of time delays between the pre- and the post-synaptic burst onset times. Finally, in the presence of iSTDP we investigate the effects of network architecture on BS by varying the symmetric attachment degree $l^*$ and the asymmetry parameter $Δl$ in the SFN.

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arXiv2018

Effect of Inhibitory Spike-Timing-Dependent Plasticity on Fast Sparsely Synchronized Rhythms in A Small-World Neuronal Network

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 $D$. We employ an asymmetric anti-Hebbian time window for the iSTDP update rule [which is in contrast to the Hebbian time window for the excitatory STDP (eSTDP)]. Depending on values of $D$, population-averaged values of saturated synaptic inhibition strengths are potentiated [long-term potentiation (LTP)] or depressed [long-term depression (LTD)] in comparison with the initial mean value, and dispersions from the mean values of LTP/LTD are much increased when compared with the initial dispersion, independently of $D$. In most cases of LTD where the effect of mean LTD is dominant in comparison with the effect of dispersion, good FSS (with higher spiking measure) is found to get better via LTD, while bad FSS (with lower spiking measure) is found to get worse via LTP. This kind of Matthew effect in inhibitory synaptic plasticity is in contrast to that in excitatory synaptic plasticity where good (bad) synchronization gets better (worse) via LTP (LTD). Emergences of LTD and LTP of synaptic inhibition strengths are intensively investigated via a microscopic method based on the distributions of time delays between the pre- and the post-synaptic spike times. Furthermore, we also investigate the effects of network architecture on FSS by changing the rewiring probability $p$ of the SWN in the presence of iSTDP.

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arXiv2017

Effect of Spike-Timing-Dependent Plasticity on Stochastic Burst Synchronization in A Scale-Free Neuronal Network

We consider an excitatory population of subthreshold Izhikevich neurons which cannot fire spontaneously without noise. As the coupling strength passes a threshold, individual neurons exhibit noise-induced burstings. This neuronal population has adaptive dynamic synaptic strengths governed by the spike-timing-dependent plasticity (STDP). In the absence of STDP, stochastic burst synchronization (SBS) between noise-induced burstings of subthreshold neurons was previously found to occur over a large range of intermediate noise intensities. Here, we study the effect of additive STDP on the SBS by varying the noise intensity $D$ in the Barabási-Albert scale-free network (SFN) for the case of symmetric preferential attachment. This type of SFN exhibits a power-law degree distribution, and hence it becomes an inhomogeneous one with a few "hubs" (i.e., super-connected nodes). Occurrence of a "Matthew" effect in synaptic plasticity is found to occur due to a positive feedback process. Good burst synchronization gets better via long-term potentiation (LTP) of synaptic strengths, while bad burst synchronization gets worse via long-term depression (LTD). Consequently, a step-like rapid transition to SBS occurs by changing $D$, in contrast to a relatively smooth transition in the absence of STDP. In the presence of additive STDP, we also investigate the effects of network architecture on the SBS for a fixed $D$. Emergences of LTP and LTD of synaptic strengths are investigated in details via microscopic studies based on both the distributions of time delays between the burst onset times of the pre- and the post-synaptic neurons and the pair-correlations between the pre- and the post-synaptic IIBRs (instantaneous individual burst rates). Finally, a multiplicative STDP case (depending on states) is also investigated in comparison with the additive STDP case (independent of states).

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arXiv2017

Stochastic Spike Synchronization in A Small-World Neural Network with Spike-Timing-Dependent Plasticity

We consider the Watts-Strogatz small-world network consisting of subthreshold neurons which exhibit noise-induced spikings. This neuronal network has adaptive dynamic synaptic strengths governed by the spike-timing-dependent plasticity (STDP). In previous works without STDP, stochastic spike synchronization (SSS) between noise-induced spikings of subthreshold neurons was found to occur in a range of intermediate noise intensities through competition between the constructive and the destructive roles of noise. Here, we investigate the effect of additive STDP on the SSS by varying the noise intensity. Occurrence of a "Matthew" effect in synaptic plasticity is found due to a positive feedback process. As a result, good synchronization gets better via long-term potentiation (LTP) of synaptic strengths, while bad synchronization gets worse via long-term depression (LTD). Emergence of LTP and LTD of synaptic strengths are intensively investigated via microscopic studies based on the pair-correlations between the pre- and the post-synaptic IISRs (instantaneous individual spike rates) as well as the distributions of time delays between the pre- and the post-synaptic spike times. Furthermore, the effects of multiplicative STDP (which depends on the states) on the SSS are also studied and discussed in comparison with the case of additive STDP.

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arXiv2016

Dynamical Responses to External Stimuli for Both Cases of Excitatory and Inhibitory Synchronization in A Complex Neuronal Network

For studying how dynamical responses to external stimuli depend on the synaptic-coupling type, we consider two types of excitatory and inhibitory synchronization (i.e., synchronization via synaptic excitation and inhibition) in complex small-world networks of excitatory regular spiking (RS) pyramidal neurons and inhibitory fast spiking (FS) interneurons. For both cases of excitatory and inhibitory synchronization, effects of synaptic couplings on dynamical responses to external time-periodic stimuli $S(t)$ (applied to a fraction of neurons) are investigated by varying the driving amplitude $A$ of $S(t)$. Stimulated neurons are phase-locked to external stimuli for both cases of excitatory and inhibitory couplings. On the other hand, the stimulation effect on non-stimulated neurons depends on the type of synaptic coupling. The external stimulus $S(t)$ makes a constructive effect on excitatory non-stimulated RS neurons (i.e., it causes external phase lockings in the non-stimulated sub-population), while $S(t)$ makes a destructive effect on inhibitory non-stimulated FS interneurons (i.e., it breaks up original inhibitory synchronization in the non-stimulated sub-population). As results of these different effects of $S(t)$, the type and degree of dynamical response (e.g., synchronization enhancement or suppression), characterized by the dynamical response factor $D_f$ (given by the ratio of synchronization degree in the presence and absence of stimulus), are found to vary in a distinctly different way, depending on the synaptic-coupling type. Furthermore, we also measure the matching degree between the dynamics of the two sub-populations of stimulated and non-stimulated neurons in terms of a "cross-correlation" measure $M_c$. With increasing $A$, based on $M_c$, we discuss the cross-correlations between the two sub-populations, affecting the dynamical responses to $S(t)$.

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arXiv2016

Emergence of Sparsely Synchronized Rhythms and Their Responses to External Stimuli in An Inhomogeneous Small-World Complex Neuronal Network

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 we consider are inhomogeneous, unlike the "canonical" Watts-Strogatz SWN with nearly same betweenness centralities. As $p_{long}$ is increased, the average path length becomes shorter, and the load of communication traffic is less concentrated on LR interneurons, which leads to better efficiency of global communication between interneurons. Eventually, when passing a critical value $p_{long}^{(c)}$ $(\simeq 0.16)$, sparsely synchronized rhythms are found to emerge. We also consider two cases of external time-periodic stimuli applied to sub-groups of LR and SR interneurons, respectively. Dynamical responses (such as synchronization suppression and enhancement) to these two cases of stimuli are studied and discussed in relation to the betweenness centralities of stimulated interneurons, representing the effectiveness for transfer of stimulation effect in the whole network.

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