Connectome Gigandet, Xavier, et al. "Estimating the confidence level of white matter connections obtained with MRI tractography." PLoS One 3.12 (2008): e4006. Hagmann, Patric, et al. "Mapping the structural core of human cerebral cortex." PLoS biology 6.7 (2008): e159. 1000 1
脳における同期の遷移 Betzel, Richard F., et al. "Synchronization dynamics and evidence for a repertoire of network states in resting EEG." Frontiers in computational neuroscience 6 (2012). ニューラルネットワークの 活動状態は目まぐるしく変化 脳は動的
(Computational Neuro Science)
( ) M.I. Rabinovich, P. Varona, A.I. Selverston, H.D. I. Abarbanel Dynamical principles in neuroscience (2006)
(Rat ) (E.M. Izhikevich 2003)
Rabinovich, M. I., Varona, P., Selverston, A. I. & Abarbanel, H. D. Dynamical principles in neuroscience. Reviews of modern physics 78, 1213 1265 (2006).
Hodgkin-Huxley : : / : Integrated-and-fired FitzHugh-Nagumo Hindmarsh-Rose Review: M.I. Rabinovich, P. Varona, A.I. Selverston, H.D. I. Abarbanel Dynamical principles in neuroscience (2006) (# of features) (# of FLOPS) (E.M. Izhikevich 2004)
2 Morris-Lecar
v-nullcline/u-nullcline (I = 0) 1 2 1 ( #1) ( =0.5) ( #2) ( =0.3) : :
v-nullcline/u-nullcline #1( =0.5,I =0.004) #2 ( =0.3,I =0.02)
#1 ( =0.5) #2 ( =0.3) sadle-node (type I neuron) Hopf (type II neuron)
Type I/II neuron Type I neuron Type II neuron Spiking Freq Spiking Freq I I
(# of features) (# of FLOPS) (E.M. Izhikevich 2004)
Izhikevich /
#1(type I) #2(type II) 0.1 v r =0.15 v r =0.33 v r =0.395 without reset 0.08 0.07 v r =0.12 v r =0.14 v r =0.20 without reset 0.06 0.05 0.05 u i+1 u i+1 0.04 0.03 0 0.02 0 0.05 0.1 u i 0.01 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 u i * : S. Nobukawa et al., Routes to Chaos Induced by a Discontinuous Resetting Process in a Hybrid Spiking Neuron Model." Scientific Reports 8 (2018):379.
Izhikevich (a) (b)
/ M.A. Arbib 2003 (Takahashi et al. 2006) (Weiss, Béla, et al. 2009) (Nobukawa et al. 2017)
(Chaotic Resonance: CR) (Stochastic Resonance: SR) (1)!! ( / ) /!! ( / ) /
(Chaotic Resonance: CR) (Stochastic Resonance: SR) (2)! SR " " ( / ) /! CR " " " / " / " " S. Nobukawa, et al. "Chaotic Dynamical States in Izhikevich Neuron Model." Emerging Trends in Computational Biology, Bioinformatics, and Systems Biology-Algorithms and Software Tools (chapter19), Elsevier/MK (2015).
(M.D. McDonnell and L.M. Ward, 2011) ( stochastic frascilitation theory ) EEG/MEG (T.Takahashi et al. 2009; C.J. Stam 2005; A.R.McIntosh et al. 2008, T. Takahashi 2013; A.C. Yang and S.J. Tsai 2013; A.Zalesky et al. 2014) fmri (R.F.Betzel et al. 2016; J.Zhang et al 2016; E.A. Allen et al. 2014)
( ) ( )
( Hz) S. Nobukawa, and H. Nishimura. "Chaotic resonance in coupled inferior olive neurons with the Llinás approach neuron model." Neural computation (2016).
CR SR S. Nobukawa, and H. Nishimura. "Chaotic resonance in coupled inferior olive neurons with the Llinás approach neuron model." Neural computation (2016).
(a) (b) 1 1 0.8 0.8 C( ) max τ C(τ) max 0.6 0.4 0.2 C( ) max τ C(τ) max 0.6 0.4 0.2 0 0 0.01 0.02 0.03 0.04 0.05 0.06 0 0 0.01 0.02 0.03 0.04 0.05 0.06 λ 1 1 1 S. Nobukawa et al., Chaotic Resonance in Typical Routes to Chaos in the Izhikevich Neuron Model." Scientific Reports 7.1 (2017): 1331. S. Nobukawa, et al. "Analysis of chaotic resonance in Izhikevich neuron model." PloS one 10.9 (2015): e0138919. λ 1
max C( ) > 0.5
(spike timing dependent synaptic plasticity: STDP)
S. Nobukawa,, and H. Nishimura. "Enhancement of spike-timing-dependent plasticity in spiking neural systems with noise." International journal of neural systems 26.05 (2016): 1550040.
Brian2: python. Goodman, Dan FM, and Romain Brette. "Brian: a simulator for spiking neural networks in Python." Frontiers in neuroinformatics2 (2008): 5. (https://brian2.readthedocs.io/en/stable/) NEST: python Jordan, Jakob, et al. "Extremely scalable spiking neural network simulation code: from laptops to exascale computers." Frontiers in Neuroinformatics 12 (2018): 2. (http:// www.nest-simulator.org/) SUNDIALS: Hindmarsh, Alan C., et al. "SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers." ACM Transactions on Mathematical Software (TOMS) 31.3 (2005): 363-396. (https://computation.llnl.gov/projects/sundials)
EEG/MEG
(M. Rubinov & O. Sporns, 2010) : : Watts-Strogatz (D.J. Watts et al. and S.H. Strogatz, 1998)
PLI vs. Beta Gamma t-value Multiscale entropy EEG (T. Takahashi, T. Goto, S. Nobukawa et al., 2018) vs. (T. Takahashi et al., 2010) (T. Takahashi, T.Yamanishi, S. Nobukawa et al., 2017)