13,319 research outputs found
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 . 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 , 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 . 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 of the SWN in the presence of
iSTDP.Comment: arXiv admin note: text overlap with arXiv:1704.0315
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 and processes. The
process corresponds to a directed version of the Barab\'{a}si-Albert
SFN model with growth and preferential attachment, while for the
process only preferential attachments between pre-existing nodes are
made without addition of new nodes. We first consider the "pure"
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 and the noise intensity 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 and 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 process, and (3) the occurrence probability
of the 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 , and
the betweenness centralization . It is thus found that not only and
(affecting global communication between nodes) but also the in-degree
distribution (affecting individual dynamics) are important network factors for
effective population synchronization in SFNs.Comment: arXiv admin note: text overlap with arXiv:1504.0306
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 Barab\'{a}si-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 and the
asymmetry parameter in the SFN.Comment: arXiv admin note: substantial text overlap with arXiv:1708.04543,
arXiv:1801.0138
Fast Sparsely Synchronized Brain Rhythms in A Scale-Free Neural Network
We consider a directed Barab\'{a}si-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 (synaptic inhibition
strength) at a sufficiently large value, and investigate the population states
by increasing (noise intensity). For small , full synchronization with
the same population-rhythm frequency and mean firing rate (MFR) of
individual neurons occurs, while for sufficiently large partial
synchronization with (:
ensemble-averaged MFR) appears due to intermittent discharge of individual
neurons; particularly, the case of 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.Comment: 54 pages, 13 figures. arXiv admin note: text overlap with
arXiv:1403.103
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 Erd\"{o}s-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 and the noise intensity .
Thus, fast sparsely synchronized states of relatively high degree are found to
appear for large values of and . Second, for fixed values of and
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 from
short-range to long-range connection. When passing a small critical value
, fast sparsely synchronized population rhythms are
found to emerge in small-world networks with predominantly local connections
and rare long-range connections
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 , 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 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 . 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 . In addition to
the statistical-mechanical analysis using and , 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
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 for static synaptic
strengths. By varying , 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 , 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 , the degree of good
synchronization (with higher spiking measure) becomes decreased, while in a
region of large , 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 . 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
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) , 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
, was introduced in our recent work to characterize the spike
synchronization transition. Unlike the case of spiking neurons, the IPFR
of bursting neurons exhibits population behaviors with both the slow bursting
and the fast spiking timescales. For our aim, we decompose the IPFR into
the instantaneous population bursting rate (describing the bursting
behavior) and the instantaneous population spike rate (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" and of the
bursting and spiking peaks in the power spectral densities of and
(i.e., "signal to noise" ratio of the spectral peak height and its relative
width). Through calculation of and , 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.Comment: arXiv admin note: substantial text overlap with arXiv:1403.399
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 in the Barab\'asi-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
, 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 . 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).Comment: arXiv admin note: substantial text overlap with arXiv:1704.0315
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 , 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 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
, 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.Comment: arXiv admin note: text overlap with arXiv:1504.0306
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