Yasuhiko Igarashi

Mean Field Analysis of Stochastic Neural Network Models with Synaptic Depression

We investigated the effects of synaptic depression on the macroscopic behavior of stochastic neural networks. Dynamical mean field equations were derived for such networks by taking the average of two stochastic variables: a firing state variable and a synaptic variable. In these equations, their average product is decoupled as the product of averaged them because the two stochastic variables are independent. We proved the independence of these two stochastic variables assuming that the synaptic weight is of the order of 1/N with respect to the number of neurons N. Using these equations, we derived macroscopic steady state equations for a network with uniform connections and a ring attractor network with Mexican hat type connectivity and investigated the stability of the steady state solutions. An oscillatory uniform state was observed in the network with uniform connections due to a Hopf instability. With the ring network, high-frequency perturbations were shown not to affect system stability. Two mechanisms destabilize the inhomogeneous steady state, leading two oscillatory states. A Turing instability leads to a rotating bump state, while a Hopf instability leads to an oscillatory bump state, which was previous unreported. Various oscillatory states take place in a network with synaptic depression depending on the strength of the interneuron connections.

Stability Analysis of Stochastic Neural Network with Depression and Facilitation Synapses

We investigate dynamical properties of a stochastic neural network model in which neurons are connected by dynamic synapses that undergo short-term depression and facilitation. In this model, the state of the neuron is described by a binary variable that represents the active or resting state of the neuron and changes stochastically. Synaptic transmission efficacy is described by variables that represent the releasable neurotransmitters and the calcium concentration of the synaptic terminal. Here, we focus on a neural network with uniform connections, and we elucidate its neural dynamics, which is influenced by dynamic synapses. We derive a macroscopic mean field model that approximates the overall behavior of the stochastic neural network. We apply stability and bifurcation analyses to the macroscopic mean field model, and we find that the network exhibits a variety of dynamical structures, including ferromagnetic and paramagnetic states, as well as an oscillatory uniform state according to the parameter...

Estimation of the reaction times in tasks of varying difficulty from the phase coherence of the auditory steady-state response using the least absolute shrinkage and selection operator analysis

Quantitative estimation of the workload in the brain is an important factor for helping to predict the behavior of humans. The reaction time when performing a difficult task is longer than that when performing an easy task. Thus, the reaction time reflects the workload in the brain. In this study, we employed an N-back task in order to regulate the degree of difficulty of the tasks, and then estimated the reaction times from the brain activity. The brain activity that we used to estimate the reaction time was the auditory steady-state response (ASSR) evoked by a 40-Hz click sound. Fifteen healthy participants participated in the present study and magnetoencephalogram (MEG) responses were recorded using a 148-channel magnetometer system. The least absolute shrinkage and selection operator (LASSO), which is a type of sparse modeling, was employed to estimate the reaction times from the ASSR recorded by MEG. The LASSO showed higher estimation accuracy than the least squares method. This result indicates that LASSO overcame the over-fitting to the learning data. Furthermore, the LASSO selected channels in not only the parietal region, but also in the frontal and occipital regions. Since the ASSR is evoked by auditory stimuli, it is usually large in the parietal region. However, since LASSO also selected channels in regions outside the parietal region, this suggests that workload-related neural activity occurs in many brain regions. In the real world, it is more practical to use a wearable electroencephalography device with a limited number of channels than to use MEG. Therefore, determining which brain areas should be measured is essential. The channels selected by the sparse modeling method are informative for determining which brain areas to measure.

Recurrent network for multisensory integration-identification of common sources of audiovisual stimuli

We perceive our surrounding environment by using different sense organs. However, it is not clear how the brain estimates information from our surroundings from the multisensory stimuli it receives. While Bayesian inference provides a normative account of the computational principle at work in the brain, it does not provide information on how the nervous system actually implements the computation. To provide an insight into how the neural dynamics are related to multisensory integration, we constructed a recurrent network model that can implement computations related to multisensory integration. Our model not only extracts information from noisy neural activity patterns, it also estimates a causal structure; i.e., it can infer whether the different stimuli came from the same source or different sources. We show that our model can reproduce the results of psychophysical experiments on spatial unity and localization bias which indicate that a shift occurs in the perceived position of a stimulus through the effect of another simultaneous stimulus. The experimental data have been reproduced in previous studies using Bayesian models. By comparing the Bayesian model and our neural network model, we investigated how the Bayesian prior is represented in neural circuits.

Statistical mechanics of attractor neural network models with synaptic depression

Synaptic depression is known to control gain for presynaptic inputs. Since cortical neurons receive thousands of presynaptic inputs, and their outputs are fed into thousands of other neurons, the synaptic depression should influence macroscopic properties of neural networks. We employ simple neural network models to explore the macroscopic effects of synaptic depression. Systems with the synaptic depression cannot be analyzed due to asymmetry of connections with the conventional equilibrium statistical-mechanical approach. Thus, we first propose a microscopic dynamical mean field theory. Next, we derive macroscopic steady state equations and discuss the stabilities of steady states for various types of neural network models.

Inter-Layer Correlation in a Feed-Forward Network with Intra-Layer Common Noise

Neural networks generate correlated neural activities. In a multi-layer network, experimental studies have shown that spike correlations appear within a layer and between different layers. It is input common among neurons in each layer that realizes such correlated activities. Theoretical studies have demonstrated that common input given to neurons within a layer, which we call “intra-layer common noise”, generates spike correlation within the layer, which is “intra-layer correlation”, in a feed-forward network. However, it has not been studied whether the common noise can generate spike correlation between different layers, which is “inter-layer correlation”. In this study, we constructed a theory of inter-layer correlation and calculated the theoretical values of the inter-layer correlation in a multi-layer feed-forward network with intra-layer common noise. Our theory revealed that the common noise generates the inter-layer correlation, which coincided with results of simulation.

Robust One-dimensional Phase Unwrapping using a Markov Random Field Model

In natural sciences and engineering, observed data are often measured as a wrapped phase. Phase unwrapping is the problem of restoring such discontinuous wrapped phases to the continuous original phase. This is one of the most challenging problems in signal processing because phase unwrapping is an inverse problem and ill-posed, which means the solution contains the arbitrariness of 2πk (\(k = 0, \pm 1, \pm 2, \ldots \)). One of the challenges in phase unwrapping research is how to distinguish whether the wrapping is genuine or fake. To address this, we denote the one-dimensional phase unwrapping problem from a Bayesian perspective using a Markov random field (MRF) model. We clarify that a previous MRF-based work was not robust against fake wrapping and demonstrate through experiments how our proposed method solves this problem.