When incorporating more realistic synaptic dynamics, the computational efficiency of population density methods (PDMs) declines sharply due to the increase in the dimension of master equations. To avoid such a decline, we develop an efficient PDM, termed colored-synapse PDM (csPDM), in which the dimension of the master equations does not depend on the number of synapse-associated state variables in the underlying network model. Our goal is to allow the PDM to incorporate realistic synaptic dynamics that possesses not only finite relaxation time but also short-term plasticity (STP). The model equations of csPDM are derived based on the diffusion approximation on synaptic dynamics and probability density function methods for Langevin equations with colored noise. Numerical examples, given by simulations of the population dynamics of uncoupled exponential integrate-and-fire (EIF) neurons, show good agreement between the results of csPDM and Monte Carlo simulations (MCSs). Compared to the original full-dimensional PDM (fdPDM), the csPDM reveals more excellent computational efficiency because of the lower dimension of the master equations. In addition, it permits network dynamics to possess the short-term plastic characteristics inherited from plastic synapses. The novel csPDM has potential applicability to any spiking neuron models because of no assumptions on neuronal dynamics, and, more importantly, this is the first report of PDM to successfully encompass short-term facilitation/depression properties.
IntroductionThe main purpose of this study was to investigate the cerebral areas responsible for winking by observing the activation pattern and learning effects on cerebral cortices by comparing differences in activation pattern during winking before and after learning.MethodsSixty‐three subjects were recruited, including 22 (11 males; 11 females) who could wink bilaterally and 41 (14 males; 27 females) who could wink unilaterally. Event‐related functional magnetic resonance was performed. The subjects were asked to blink and wink according to projected instructions as the events for image analysis. The activation pattern was obtained by contrasting with the baseline images without eyelid movements. Those who could only wink unilaterally were asked to train themselves to wink the other eye. For those who succeeded (n = 24), another imaging study was performed and the results were compared with those before training.Results and conclusionLeft winking resulted in activation in the left frontal lobe, while right winking resulted in activation in bilateral frontal lobes with predominance on the right side. For the subjects capable of only winking unilaterally, learning to wink on the other side activated similar cortical areas to those in the subjects capable of bilateral winking without training.
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