Won Sup Kim

SYNCHRONIZATION AND DECODING INTERSPIKE INTERVALS

Decoding of a sequence of interspike intervals (ISIs) of a neuron model driven by a chaotic stimulus is performed based on the attractor reconstruction method. As stimulus strength increases, both the stimulus estimation error and the prediction error in predicting stimulus crosswise by exploiting ISIs information tend to decrease with transitional drops at certain parameter values. It is analyzed that such behaviors are well explained in the context of synchronization between two chaotic patterns of stimulus and ISI sequence. The result implies that a new scheme of temporal coding at low firing rate regime can be achieved which exploits the preservation of nonlinear deterministic structures in stimulus.

Estimating network link weights from inverse phase synchronization indices

We investigated the possibility of estimating network link weights from the multivariate time series of phase oscillators on a complex network. The inverse phase synchronization index of the coupled oscillator network is found to grow in proportion to the corresponding link weight, as network synchronization occurs for a strong coupling strength. This implies that the network link weights can be estimated from the measurement of the inverse phase synchronization indices. By adopting this estimation method, we successfully reconstructed the minimal spanning tree of the original network from the inverse phase synchronization indices. Even for the weak coupling case, the estimation of the network link weights could be improved significantly by taking the average of a sufficiently large number of configurations.

Estimation of inter-modular connectivity from the local field potentials in a hierarchical modular network

We propose a method of estimating inter-modular connectivity in a hierarchical modular network. The method is based on an analysis of inverse phase synchronization applied to the local field potentials on a hierarchical modular network of phase oscillators. For a strong-coupling strength, the inverse phase synchronization index of the local field potentials for two modules depends linearly on the corresponding inter-modular connectivity defined as the number of links connecting the modules. The method might enable us to estimate the inter-modular connectivity in various complex systems from the inverse phase synchronization index of the mesoscopic modular activities.

Phase analysis of single-trial EEGs: Phase resetting of alpha and theta rhythms

We perform phase analysis of the @a (8-13Hz) and @q (4-7Hz) rhythmic components of the single-trial electroencephalograms (EEGs), which comprise the most dominant contributions to the event-related potentials (ERPs). The oscillatory ERP patterns of two components are well described by the phase resetting and the inter-trial phase coherency. A method for the estimation of the nonlinear dynamic dependency between two components is proposed. According to the method, the coupling is asymmetric with the coupling from the @q to the @a rhythms stronger than the reversed one.

Is it right to estimate inter-modular connectivity from local field potentials?

Human brains with hundreds of billions of neurons are organized in a hierarchical modular network. There have been many attempts to estimate inter-modular connectivity utilizing coherent neuronal activities of a huge number of neurons, such as the electro-encephalogram, the magneto-encephalogram, and the functional magnetic resonance imaging. Here we ask a question: Is the inter-modular connectivity estimated from the modular activities consistent with the inter-modular connectivity that could be extracted from the network connectivity of individual nodes? To answer this question, we introduce a method of estimating the inter-modular connectivity based on the analysis of inverse phase synchronization [1,2]. For coupled phase oscillators on a hierarchical modular network shown in the Figure 1(A), the local field potential corresponding to a module is defined as the mean phase of oscillators belonging to a subset of the module. Figure 1 (A) A hierarchical modular network model 256-p-q-r, where p denotes the number of links of one node with nodes of its lower-level module, q links with nodes of the rest modules in its upper-level module, and r links with nodes of any modules from the ... For strong coupling strength, it is shown in Figure 1(B) that the inverse phase synchronization index grows linearly with the number of links connecting two modules. This result enables us to estimate the inter-modular connectivity in various complex systems from the inverse phase synchronization index of the mesoscopic modular activities.

Dynamic analysis of recurrent phase patterns in spontaneous human EEG

Spontaneous human EEG during the resting state is modulating with long lasting high amplitude synchronization and very brief low amplitude de-synchronization states [1]. For the dynamic characterization of modulating alpha rhythm in the resting state EEG, we introduce a method of spontaneous-event related potential (SERP) analysis. Our method consists of three steps: At first, ensemble phase patterns of alpha rhythm at the moment of alpha de-synchronization state are classified using the K-mean clustering algorithm; Secondly, short time evolution of the phase pattern around each de-synchronization event is analyzed using the symbolic sequence dynamics; Finally, a global map of dynamic organization is constructed by integrating the temporal motifs representing the recurrent phase patterns around de-synchronization state. Using the EEG data from seven subjects, very large number of de-synchronization event is collected from spike-like events in the time plot of inverse of alpha amplitude. The classification of the phase patterns of the de-synchronization state produces four different kinds of traveling waves, two propagating from posterior to anterior (PAL and PAR) and two in reverse directions (APL and APR) for C = 8 classification. The presence of two spiral waves, one rotating in clockwise (CS) and the other in count clockwise (CCS), are also observed in addition to two standing waves (STA and STP). For the symbolic sequence analysis, we construct a triad symbol for each de-synchronization event. It is composed of a present pattern and its previous and next patterns, as a sequence of pre-present-post patterns. Then the occurrence rates of all possible triad symbols are compared with those of surrogate data where the sequence of all phase patterns is completely randomized. The triad symbols with very large normalized Z-score could be identified as dominant temporal motifs [2], which include the triad symbols, STP-CCS-STA, STP-CS-STA, CCS-STA-APL, and so on. We could also identify temporal anti-motifs as the triad symbols with very large negative Z-score. The anti-motifs include the triad symbols where strongly inhibited transitions like the transitions between CS and CCS, between STP and two PA patterns, and between SPA and two AP patterns are included. Integrating the information on the temporal motifs and anti-motifs, we could construct a global map of recurrent transition dynamic during the resting state. The global map contains the information on how the transitions among four traveling waves PAL, PAR, APL and APR occur. It is very interesting to notice the role played by the two spiral waves CS and CCS. As the motion of a spiral wave is recorded by tracing the phase singular point of a spiral wave, we observed that a traveling wave could switch its propagation as the spiral wave crosses the traveling wave in a transverse direction. This result indicates that the role of two spiral waves is to switch the propagation of traveling waves systematically. In conclusion, using the SERP analysis of the spontaneous human EEG, we identified the recurrent phase patterns that involve the switching of traveling waves. Very interestingly, it is shown that the propagation of a traveling wave is systematically controlled by a spiral wave which drifts across the traveling wave. It is to be investigated on the function roles of the traveling waves and spiral waves, and also on the neural mechanisms of switching the propagation of the traveling waves [3] and the formation of spiral waves [4].

Inferring neural connectivity from multiple spike trains

Recently the temporal coding based on spike timing is one of the hot issues in neuroscience. In the neural network, spike timing depends on the external stimulus and also on the internal network structure. In this study, we propose a method of inferring network connectivity from multiple spike trains. It is based on the phase model description of the spike trains. A continuous phase variable is introduced for each of the spike trains by assigning 2 pi phase for each of the spike intervals and by the linear interpolation. The relative strength of the mutual dependence allows us to estimate the relative strength of the coupling as well as the type of coupling. We report the results of our test on the coupled neural network model and also on the electronic circuit experiment. When compared with the conventional method based on the cross-correlogram, the proposed method is much more effective in estimating the network connectivity. At the same time, the measurement of the effective coupling allows us to estimate the type of coupling.

Temporal segmentation and selective attention in the stochastic oscillator neural network

A stochastic oscillator neural network (STONN) model of the Hopfield-type memory is proposed for the pattern segmentation tasks, that exploits temporal dynamics of the stochastic nonlinear oscillators. For an input pattern which is an overlapped superposition of several stored patterns the proposed model network is shown to be capable of segmenting out each pattern one after another as the network evolves its temporal dynamics. The temporal segmentation attains its optimal performance at an intermediate noise intensity and the performance becomes improved as the coupling strength between oscillators increases. A mechanism for the selective attention is also introduced in the STONN by controlling the level of noise applied to the most salient pattern and by adopting the inhibition-of-return into the patterns that have been segmented before.